application of accelerometers in the sport of rowing€¦ · interaction and the sliding seat)....

APPLICATION OF ACCELEROMETERS

IN THE SPORT OF ROWING

by

Alan Lai

A thesis submitted for the degree of

Doctor of Philosophy

at the

Industrial Research Institute Swinburne

Faculty of Engineering and Industrial Sciences

Swinburne University of Technology

Australia

2011

ii

ABSTRACT

Rowing biomechanics is traditionally difficult to measure because of the nature of

the sport. Rowing takes place in an aquatic environment, covers a relatively large

distance (standard world championship race distance of 2,000 metres) and the

mechanics of the rowing is complex (because of boat rigging, hydrodynamic

interaction and the sliding seat). Traditionally, instrumented boats have been the

standard for monitoring and analysing rowing technique, but they are expensive

and complex to setup. Inertial sensors showed great potential as an alternative and

were selected as focus of investigation. This thesis examines the use of Micro-

Electro-Mechanical Systems (MEMS) accelerometers that are small, unobtrusive

and relatively easy to set up, yet with the appropriate methodology can yield

analogous information for rowing technique analysis.

In undertaking the investigation of using a triaxial accelerometer as a rowing

technique assessment tool, a thorough understanding of rowing biomechanics is

required to help solve the inverse problem. One must understand how the shell

acceleration trace is generated and how it relates to all the rowing mechanics

variables in order to interpret it. Thus, the two aims of this thesis were a

comprehensive rowing biomechanics model and solving the inverse problem to

determine rower biomechanics using Micro-Electro-Mechanical Systems (MEMS)

accelerometers. These aims were achieved and they were contributions to

knowledge in the field of rowing biomechanics.

The first contribution of this thesis was that it revealed the relationship between the

combination of propulsion, resistance and rower motion against the resultant shell

acceleration. This was achieved with the development of a rowing model to

represent a single scull. The forces acting on the single scull and the resultant

motion of the rowing shell was represented with a differential equation. A detailed

multi-segment rower model was created to represent the rower motion. Also, a

hydrodynamic model was developed to calculate the force at the oar blade, which

iii

is the propulsive force on the rowing system. On-water rowing data was collected

and used as inputs to the rowing model to ‘simulate’ the rowing shell motion. The

rowing model revealed how the rowing shell acceleration trace was generated from

all the variables and parameters of the rowing system.

The second contribution to knowledge of this research was the development of a

methodology to use accelerometers with shell velocity and seat position

measurements to monitor all the forces acting on a single scull and the resultant

shell acceleration. The proposed methodology is based on a differential equation

describing the motion of a single scull, which basically states that the force acting

on the single scull is the sum of the force due to rower motion and the propulsive

and resistive forces on the rowing system. The resultant force on the single scull

was measured using a triaxial accelerometer, that is, product of the mass of the

rowing system and the shell acceleration. The resistive force on the single scull

was estimated from the shell velocity measurement and a coefficient representing

the drag characteristics on the rowing system, that is, product of the drag

coefficient and square of the shell velocity. The force due to the motion of the

rower’s centre of mass relative to the rowing shell was estimated using seat

position measurement and a compensation difference curve to account for the

motion of the upper body, including the arms. The resultant force and resistive

force on the single scull and the force due to the motion of the rower’s centre of

mass were then used to calculate the propulsive force on the rowing system. The

proposed methodology of calculating the propulsive force provides great insight to

a rower's technique, as all the forces acting on the rowing system and the resultant

shell motion are collectively monitored

iv

Acknowledgements

I would like to express my gratitude to my supervisors, Professor Erol Harvey, Dr.

Jason Hayes and Dr. Daniel James for their guidance, encouragement and

patience.

I would like to sincerely thank Emeritus Professor Marinus van Holst of the Delft

University of Technology, Dr Leo Lazauskas and William C. Atkinson for their help

and discussions on the development of the rowing model.

I would like to show my utmost appreciation to Dr. Anthony Rice of the Australian

Institute of Sport for his assistance on the collection of data.

I would also like to thank the aforementioned people and all my other friends at

IRIS and MiniFab, who have made the years of my PhD candidature a part of my

life that I will always cherish.

Finally, I would like to thank my family for their unconditional love and support.

v

Declaration of Originality

This thesis contains no material which has been accepted for the award of any

other degree or diploma in any university, and to the best of my knowledge

contains no material previously published or written by another person, except

where due reference is made in the text of the thesis. Work based on joint research

or publications in this thesis fully acknowledges the relative contributions of the

respective authors or workers.

Signed…………………………………………

Alan Lai

Date………………………………….

vi

TABLE OF CONTENTS

1 INTRODUCTION ..............................................................................................1

1.1 BACKGROUND AND MOTIVATIONS FOR THE RESEARCH .................1

1.2 SUMMARY OF FINDINGS ........................................................................3

1.3 AIMS AND HYPOTHESIS .........................................................................6

1.4 CONTRIBUTIONS TO KNOWLEDGE.......................................................7

1.5 OVERVIEW OF THE THESIS ...................................................................7

1.5.1 LITERATURE REVIEW......................................................................7

1.5.2 ACCELEROMETERS FOR ROWING TECHNIQUE ANALYSIS........8

1.5.3 A SINGLE SCULL ROWING MODEL ................................................9

1.5.4 ROWING MODEL SENSITIVITY ANALYSIS ...................................10

1.5.5 MOTION OF THE ROWER’S CENTRE OF MASS ..........................10

1.5.6 ANALYSIS OF THE MECHANICS OF ROWING .............................12

1.6 REFERENCES........................................................................................13

2 LITERATURE REVIEW ..................................................................................16

2.1 OVERVIEW .............................................................................................16

2.2 THE MECHANICS OF ROWING.............................................................17

2.2.1 PROPULSION..................................................................................17

2.2.2 RELATIVE MOVEMENT OF THE CENTRE OF MASSES...............19

2.2.3 RESISTANCE ..................................................................................22

2.2.4 SPEED VARIATION.........................................................................25

2.2.5 FORCES ON THE ROWING SYSTEM AND THE RESULTANT

SHELL MOTION.............................................................................................28

2.3 CURRENT METHODOLOGIES FOR ROWING PERFORMANCE

ASSESSMENT...................................................................................................32

2.3.1 CURRENT APPLICATIONS OF ACCELEROMETERS IN ROWING

32

2.3.2 COMMON METHODOLOGIES FOR ROWING TECHNIQUE AND

PERFORMANCE ANALYSIS .........................................................................34

2.4 EXISTING ROWING MODELS................................................................46

vii

2.5 CONCLUSION.........................................................................................53

2.6 REFERENCES ........................................................................................53

3. ACCELEROMETERS FOR ROWING TECHNIQUE ANALYSIS ....................58

3.1 OVERVIEW .............................................................................................58

3.2 MOTIVATION FOR USING MEMS ACCELEROMETERS FOR ROWING

TECHNIQUE ASSESSMENT.............................................................................58

3.3 CALIBRATION TECHNIQUE...................................................................61

3.4 ERRORS IN THE CALIBRATION TECHNIQUE......................................66

3.4.1 ERRORS FROM THE ACCELEROMETER .....................................66

3.4.2 VARIATIONS IN THE GRAVITY FIELD VECTOR ...........................67

3.4.3 NON-ORTHOGONALITY BETWEEN THE THREE SENSING AXES

69

3.5 CALIBRATION TECHNIQUE ASSESSMENT .........................................72

3.6 CALIBRATION TECHNIQUE RESULTS .................................................73

3.6.1 RATE OF CONVERGENCE.............................................................74

3.6.2 VARIANCE IN THE OFFSETS AND SCALE FACTORS..................75

3.6.3 PRECISION OF THE CALIBRATION TECHNIQUE.........................77

3.7 ACCURACY OF THE TRIAXIAL ACCELEROMETER WHEN USED FOR

STATIC MEASUREMENTS ...............................................................................79

3.8 CONCLUSION.........................................................................................83

3.9 REFERENCES ........................................................................................84

4 A SINGLE SCULL ROWING MODEL.............................................................87

4.1 INTRODUCTION .....................................................................................87

4.2 DEVELOPMENT OF THE ROWING MODEL..........................................88

4.2.1 ASSUMPTIONS ...............................................................................88

4.2.2 EQUATION OF MOTION FOR THE SINGLE-SCULL ROWING

MODEL 90

4.2.3 ROWER MODEL..............................................................................97

4.3 MODEL VERIFICATION WITH ON-WATER DATA...............................102

4.3.1 ON WATER DATA COLLECTION..................................................102

4.3.2 MODEL VERIFICATION METHOD ................................................105

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4.3.3 RELIABILITY ANALYSIS OF THE ROWER BODY ANGLES

MEASURED FROM VIDEO FRAMES..........................................................111

4.4 RESULTS AND DISCUSSION ..............................................................114

4.4.1 PROPULSIVE FORCE CALCULATED FROM THE

HYDRODYNAMICS OAR BLADE MODEL VERSUS THE FORCE

CALCULATED FROM THE OAR HANDLE FORCE, OAR LEVER RATIO AND

COSINE OF THE OAR ANGLE....................................................................114

4.4.2 COMPARISON BETWEEN THE SIMULATED SHELL

ACCELERATION AND THE MEASURED SHELL ACCELERATION...........123

4.4.3 SOURCES OF ERROR THAT CONTRIBUTED TO THE

SIMULATION ERROR DURING THE DRIVE PHASE..................................128

4.5 CONCLUSION.......................................................................................139

4.6 REFERENCES......................................................................................140

5. ROWING MODEL SENSITIVITY ANALYSIS ...............................................143

5.1 INTRODUCTION ...................................................................................143

5.2 METHOD...............................................................................................143


5.3.1 ROWING MODEL SIMULATION ERROR......................................153

5.3.2 THE EFFECT OF VARIATIONS IN THE MODEL CONSTANTS ON

THE SIMULATION OUTPUT........................................................................157

5.3.3 THE EFFECT OF RANDOM ERRORS IN THE MODEL INPUTS ON

THE SIMULATION OUTPUT........................................................................175

5.3.4 COMBINED UNCERTAINTY..........................................................180

5.3.5 SYNCHRONISATION ERRORS ....................................................181

5.4 CONCLUSION.......................................................................................185

5.5 REFERENCES......................................................................................186

6. MOTION OF THE ROWER’S centre of mass...............................................187

6.1 OVERVIEW ...........................................................................................187

6.2 INTRODUCTION ...................................................................................188

6.3 METHOD...............................................................................................189


ix

6.5 CONCLUSION.......................................................................................214

6.6 REFERENCES ......................................................................................216

7. ANALYSIS OF THE MECHANICS OF ROWING..........................................218

7.1 INTRODUCTION ...................................................................................218

7.2 BACKGROUND.....................................................................................219

7.3 ANALYSIS OF THE ROWING MODEL SIMULATION FOR SUBJECT

TWO 222

7.3.1 VECTOR ANALYSIS OF THE HYDRODYNAMICS MODELLING .222

7.3.2 DATA ANALYSIS OF THE HYDRODYNAMICS VARIABLES........231

7.3.3 ANALYSIS OF ROWER MOTION..................................................258

7.3.4 PROPULSIVE FORCE, ROWER MOTION AND SHELL DRAG –

THEIR CONTRIBUTIONS TO THE RESULTANT SHELL ACCELERATION

263

7.4 COMPARING THE ROWING MODEL SIMULATION RESULTS

BETWEEN TWO SINGLE SCULLERS ROWING AT DIFFERENT STROKE

RATES .............................................................................................................266

7.5 CALCULATING THE PROPULSIVE FORCE AT THE OAR BLADE WITH

THE DIFFERENTIAL EQUATION DESCRIBING THE MOTION OF THE

ROWING SYSTEM ..........................................................................................280

7.6 CONCLUSION.......................................................................................287

7.7 REFERENCES ......................................................................................289

8 CONCLUSIONS AND RECOMMENDATIONS.............................................291

8.1 CONTRIBUTIONS TO KNOWLEDGE...................................................291

8.2 RESEARCH FINDINGS.........................................................................293

8.3 RECOMMENDATIONS FOR FURTHER RESEARCH..........................297

8.3.1 ACCELEROMETERS FOR ROWING TECHNIQUE ANALYSIS....297

8.3.2 A SINGLE SCULL ROWING MODEL.............................................298

8.3.3 ROWING MODEL SENSITIVITY ANALYSIS .................................299

8.3.4 MOTION OF THE ROWER’S CENTRE OF MASS ........................300

8.3.5 ANALYSIS OF THE MECHANICS OF ROWING ...........................300

8.4 REFERENCE ........................................................................................301

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LIST OF FIGURES

Figure 2.1: The law of conservation of momentum governs the propulsion of the

rowing shell ( sm = rowing system mass (kg), w

m = water mass (kg), sv =

shell velocity (ms-1) and wv =water velocity (ms-1)). .......................................17

Figure 2.2: The change in momentum from the sliding motion of the sculler and its

effect on the motion of the rowing shell (shell

x (square) = absolute coordinate of

the rowing shell, shellrower

x_

(circle) = relative coordinate of the rower with

respect to the rowing shell, and combined

x (diamond) = absolute coordinate of the

joint centre of mass of the rower and the rowing shell)...................................20

Figure 2.3: (a) Rower at the end of the drive phase and is stationary relative to the

shell. (b) Rower is recovery and is moving at 0.5 ms-1 away from the heading.

The shell velocity increases to conserve momentum......................................22

Figure 2.4: The forces acting on a single scull. (The double-headed arrows indicate

lengths. The solid single headed arrows are the applied forces and the dashed

arrows indicate the reactive forces. The shell velocity arrow is heavier

weighted to make a distinction that it is a velocity vector.)..............................28

Figure 3.1: Conventional calibration technique for accelerometers. The z-axis is

being calibrated in the figure. This process is repeated for the other two axes.

........................................................................................................................61

Figure 3.2: Calibration of the triaxial accelerometer using the principle that the

vector sum of the three axes’ inputs equals to the gravity vector. The

calibration technique requires six measurements to resolve the six unknowns:

scale factors and offsets in all three axes. ......................................................63

Figure 3.3: Errors due to the non-orthogonality between the sensing axes (x’, y’, z’)

and the reference axes (x, y, z). .....................................................................70

Figure 3.4: Offset calibration of the triaxial accelerometer. ....................................74

Figure 3.5: Scale factor calibration of the triaxial accelerometer............................74

Figure 3.6: Offsets throughout the calibration sessions. ........................................75

Figure 3.7: Scale factors throughout the calibration sessions................................76

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Figure 3.8: Self-verification of the calibrations. The precision of each calibration

was assessed by using its evaluated scale factors and offsets to check how

close they re-calculated their respective 6 gravity measurements in analogue-

to-digital units to the gravity magnitude of 9.80 ms-2. The 6 measurements

(numbered 1 to 6 with different markers) were plotted against its own

calibration number. The vertical axis is the difference from the gravity

magnitude of 9.80 ms-2 in units of 10-6 ms-2. ...................................................78

Figure 3.9: Verification of the calibration accuracy. The accuracy of the 48

calibrations was assessed by using their scale factors and offsets to calculate

the gravity vector magnitude with all 288 gravity measurements (from the

calibration data). .............................................................................................79

Figure 3.10: Verification of the evaluated scale factors and offsets from calibration

number 22.......................................................................................................81


number 37.......................................................................................................81

Figure 4.1: Vector diagram of the oar blade slip velocity and the resultant

propulsive force. .............................................................................................93

Figure 4.2: Drag coefficient as a function of the angle of attack from the literature

(Atkinson 2001; Cabrera, Ruina & Kleshnev 2006; Caplan & Gardner 2005;

van Holst 1996)...............................................................................................96

Figure 4.3: Lift coefficient as a function of the angle of attack from the literature

(Atkinson 2001; Cabrera, Ruina & Kleshnev 2006; Caplan & Gardner 2005;

van Holst 1996)...............................................................................................97

Figure 4.4: Diagram of the body segment lengths expressed as a fraction of the

body height, H, (Winter 2004). ........................................................................98

Figure 4.5: Rower model in the catch position. The x-axis is the longitudinal axis of

the rowing shell, y-axis is the vertical axis and z-axis is the transverse axis.

The graph is in units of metres and the coordinate (0,0) on the graph is the

rower’s ankle and assumed to be stationary relative to the rower shell (i.e., a

non-inertial reference frame).........................................................................101

Figure 4.6: Model verification method. .................................................................106

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Figure 4.7: Image analysis of the video data to determine body segment rotation.

......................................................................................................................107

Figure 4.8: Rower motion raw data (3 strokes of measured data). (a) Seat position.

(b) Trunk orientation. (c) Shoulder angle. (d) Elbow angle. ..........................108

Figure 4.9: Comparing the total forward blade force derived from the measured

handle force using the oar lever ratio against the forward blade force

calculated from oar blade hydrodynamics model. Results for subject 1. ......116

Figure 4.10: Comparing the total forward blade force derived from the measured

handle force using the oar lever ratio against the forward blade force

calculated from oar blade hydrodynamics model. Results for subject 2. ......117

Figure 4.11: Comparing two sets of simulated shell acceleration against the

measured shell acceleration for subject 1. ‘Simulated’ was the shell

acceleration calculated using the hydrodynamics model, while ‘oar leverage’

was the shell acceleration calculated using the measured oar handle force, oar

lever ratio and cosine of the oar angle..........................................................121

Figure 4.12: Comparing two sets of simulated shell acceleration against the

measured shell acceleration for subject 2. ‘Simulated’ was the shell

acceleration calculated using the hydrodynamics model, while ‘oar leverage’

was the shell acceleration calculated using the measured oar handle force, oar

lever ratio and cosine of the oar angle..........................................................122

Figure 4.13: Comparison of simulated shell acceleration with measured shell

acceleration. (a) Subject 1, (b) Subject 2, (c) Subject 3, (d) Subject 4. Three

consecutive strokes are shown. Subject 1 rowed at a higher nominal stroke

rate of 32 strokes per minute. Subjects 2, 3 and 4 rowed at a nominal stroke

rate of 20 strokes per minute. .......................................................................124

Figure 4.14: Three consecutive video frames showing blade exit........................131

Figure 4.15: Blade velocity vector at the catch and release.................................132

Figure 4.16: Comparison of simulated shell velocity with measured shell velocity. (a)

Subject 1, (b) Subject 2, (c) Subject 3, (d) Subject 4. ...................................137

Figure 5.1: Rowing model flow chart. The rowing model numerically solves for the

shell velocity and acceleration with measured rower motion and oar angles as

xiii

the inputs. The colour coding is as follows: red boxes are the measurement

systems, purple boxes are the force components on the rowing system, green

boxes are constants, the blue boxes are the measured variables and the filled

yellow boxes are the measured and simulated shell velocity and acceleration.

......................................................................................................................146

Figure 5.2: (a) plot of the simulated shell acceleration and the two sets of

independently measured shell acceleration data for subject 2. (b) plot of the

simulation error (simulated data minus the “Biomech” measured data). .......155

Figure 5.3: Plot of the simulated and measured shell velocity data. ....................157

Figure 5.4: Propulsive force variation with a change in a selected model parameter:

(a) oar blade area (water density, and blade drag and lift coefficients had the

exact same effect); (b) oar length; (c) rower mass; (d) shell mass; and (e) shell

drag coefficient. ............................................................................................159

Figure 5.5: Rower (centre of mass) velocity variation with a change in a selected

model parameter: (a) oar blade area had no effect on rower velocity (water

density, and blade drag and lift coefficients had no effect either); (b) rower

mass had an imperceptible effect on rower velocity graph. The graphs for oar

length, shell mass and shell drag coefficient were omitted because they had

no effect on the rower velocity in the rowing model. .....................................162

Figure 5.6: Shell acceleration variation with a change in a selected model

parameter: (a) oar blade area (water density, and blade drag and lift

coefficients had the exact same effect); (b) oar length. The graphs for rower

mass, shell mass and shell drag coefficient were omitted because the change

in the shell acceleration graph were too small to see, like the oar blade area

graph. ...........................................................................................................163

Figure 5.7: Shell velocity variation with a change in a selected model parameter: (a)

oar blade area (water density, and blade drag and lift coefficients had the

exact same effect); (b) oar length; (c) rower mass; and (d) shell drag

coefficient. The graph for shell mass was omitted because the change in the

shell velocity graph was too small to see. .....................................................164

xiv

Figure 5.8: Plot of the mean error in the shell acceleration output against

uncertainty in the model parameters.............................................................171

Figure 5.9: Plot of the mean error in the shell velocity output against error in the

model parameters.........................................................................................172

Figure 5.10: Plot of the mean error in the shell acceleration output against error in

the model inputs. ..........................................................................................175

Figure 5.11: Plot of the simulated shell acceleration data with increasing amount of

error added to the seat position data. Note that only 1 of the 20 sets of random

errors, but with all the scaled levels of error percentages, is shown. ............176

Figure 5.12: Plot of the simulated shell acceleration data with increasing amount of

error added to the oar angle data. Note that only 1 of the 20 sets of random


Figure 5.13: Plot of the mean error in the shell velocity output against error in the

model inputs. ................................................................................................178

Figure 5.14: Plot of the simulated shell velocity data with increasing amount of

error added to the oar angle data. Note that only 1 of the 20 sets of random

errors, but with all the scaled levels of error percentages, is shown.............178

Figure 5.15: Plot of the simulated shell velocity data with increasing amount of

error added to the seat position data. Note that only 1 of the 20 sets of random


Figure 5.16: Plot of the simulated shell acceleration for the original aligned data

and with synchronisation error (out by 1 data point). ....................................182

Figure 5.17 Plot of the simulated shell velocity for the original aligned data and with

synchronisation error (out by 1 data point). ..................................................183

Figure 6.1: Plot of the seat position and the rower c.o.m. position for subject 2 of

the four subjects. ..........................................................................................190

Figure 6.2: Plot of the rower c.o.m. position data against the seat position data .192

Figure 6.3: Plot of all the normalised and interpolated seat position and rower c.o.m.

position data. ................................................................................................193

Figure 6.4: Plot of the mean seat position curves, mean rower c.o.m. position

curves and the difference curves. .................................................................194

xv

Figure 6.5: Plots for the video-derived and estimated rower c.o.m. position. Video

was calculated from seat position data and video analysis (i.e. using the rower

model). Individual was the estimated data using each subject’s individual

difference curve. Combined was the estimated data using the combined

difference curve. (a) Subject 1. (b) Subject 2. (c) Subject 3. (d) Subject 4. ..197

Figure 6.6: Subject 1’s shell acceleration (a) and velocity (b) plots. Video is the

simulation result that used the rower c.o.m. motion calculated from the video

data and seat position data. Estimated is the simulation result that used the

rower c.o.m. motion estimated from the seat position data and individual

difference curve. Rover is the measured data using the Rover

accelerometer/GPS measurement system. Biomech is the measured shell

acceleration using the biomechanics measurement system. ........................205

Figure 6.7: Subject 2’s shell acceleration (a) and velocity (b) plots. The figure

legend is the same as Figure 6.6..................................................................206





Figure 7.1: Flow diagram illustrating the interaction of the hydrodynamic variables.

The x-component is in the heading direction, while the y-component is

orthogonal to the heading in the plane of the water. .....................................221

Figure 7.2: Oar blade vector diagram during the catch of the rowing cycle. Oar (on

the right hand side) is the blue line connected to the rowing shell, which is the

long and narrow oval. Vshell is the shell velocity vector, Oar ang v is the oar

angular velocity vector, Vslip is the slip velocity (or blade velocity), FD is the

drag force at the oar blade, FL is the lift force at the blade, Fblade is the resultant

force (from the drag and lift forces) at the blade and Fblade-f is the forward

component (in the heading direction) of the resultant force at the blade. .....223

Figure 7.3: Oar blade vector diagram during the early phase of the drive when the

drag force was relatively small......................................................................224

xvi

Figure 7.4: Oar blade vector diagram before the oar was orthogonal to the shell’s

heading and when the lift force was almost parallel to the shell’s heading. ..226

Figure 7.5: Oar blade vector diagram when the oar was orthogonal to the shell’s

heading.........................................................................................................227

Figure 7.6: Oar blade vector diagram half way between when the oar was

orthogonal to the shell’s heading and the release of the rowing cycle. .........228

Figure 7.7: Oar blade vector diagram at the release phase of the rowing cycle. .230

Figure 7.8: Diagram illustrating how to interpret the vector direction of the

hydrodynamics variables at the oar blades...................................................232

Figure 7.9: Derivation of the oar angular velocity vector from the measured oar

angle. (a) Oar angle. (b) Oar angular velocity. (c) x-component of the oar

angular velocity. (d) y-component of the oar angular velocity.......................234

Figure 7.10: The x component of the slip velocity is the sum of the shell velocity

vector and the x component of the oar angular velocity. (a) Shell velocity. (b)

x-component of the oar angular velocity. (c) x-component of the slip velocity.

......................................................................................................................235

Figure 7.11: Transformation of the slip velocity from Cartesian form to polar form.

(a) x-component of the slip velocity. (b) y-component of the slip velocity. (c)

Slip velocity magnitude. (d) Slip velocity direction. .......................................237

Figure 7.12: The angle of attack is the angle between the slip velocity vector and

the oar’s longitudinal axis. (a) Slip velocity direction. (b) Oar direction. (c)

Angle of attack (plotted from 0° to 360°). (d) Angle of attack (plotted from -180°

to 180°). ........................................................................................................238

Figure 7.13: The coefficient of drag and lift are functions of the angle of attack. (a)

Angle of attack. (b) Coefficient of drag. (c) Coefficient of lift. ........................241

Figure 7.14: The blade drag force is proportional to the coefficient of drag and the

square of the slip velocity. (a) Coefficient of drag. (b) Slip velocity magnitude.

(c) Immersed blade area fraction. (d) Blade drag force. ...............................242

Figure 7.15: The blade lift force is proportional to the coefficient of lift and the

square of the slip velocity. (a) Coefficient of lift. (b) Slip velocity magnitude. (c)

Immersed blade area fraction. (d) Blade lift force. ........................................244

xvii

Figure 7.16: The blade drag force is opposite in direction to the slip velocity. (a)

Slip velocity direction. (b) Blade drag force direction. ...................................245

Figure 7.17: The blade lift force is orthogonal to the blade drag force. The

coefficient of lift determines whether it is 90° clockwise or anti-clockwise. (a)

Blade drag force direction. (b) Coefficient of lift. (c) Blade lift force direction.

......................................................................................................................247

Figure 7.18: Transformation of the blade drag force from polar form to Cartesian

form. (a) Blade drag force magnitude. (b) Blade drag force direction. (c) x-

component of the blade drag force. (d) y-component of the blade drag force.

......................................................................................................................248

Figure 7.19: Transformation of the blade lift force from polar form to Cartesian form.

(a) Blade lift force magnitude. (b) Blade lift force direction. (c) x-component of

the blade lift force. (d) y-component of the blade lift force. ...........................250

Figure 7.20: The forward propulsive force is the sum of the forward components of

the blade drag and lift forces. (a) x-component of the blade drag force. (b) x-

component of the blade lift force. (c) x-component of the blade force (i.e.

forward propulsive force). .............................................................................251

Figure 7.21: The lateral blade force is the sum of the lateral components of the

drag and lift forces. (a) y-component of the drag force. (b) y-component of the

lift force. (c) y-component of the blade force (i.e. lateral blade force). ..........253

Figure 7.22: Transformation of the blade force from Cartesian form to polar form. (a)

x-component of the blade force. (b) y-component of the blade force. (c) Blade

force magnitude. (d) Blade force direction. ...................................................254

Figure 7.23: Verifying that the direction of the blade force vector was consistently

orthogonal to the oar direction. (a) Blade force direction. (b) Oar direction. (c)

Angle between the blade force vector and the oar........................................256

Figure 7.24: The total forward and lateral forces on the rowing shell. (a) Forward

force on the rowing shell. (b) Lateral force on the rowing shell. ....................257

Figure 7.25: Graphs for the rower motion. (a) Rower body angles. (b) Seat position

and rower centre of mass position. ...............................................................259

xviii

Figure 7.26: Graphs for the rower’s centre of mass motion. (a) Position. (b) Velocity.

(c) Acceleration.............................................................................................260

Figure 7.27: Comparing the rower centre of mass position and the seat position

against the oar angle and oar angular velocity. (a) Rower centre of mass

position and seat position. (b) Oar angle. (c) Oar angular velocity. ..............261

Figure 7.28: The shell acceleration curve compared with each of the components

in the system equation. (a) Acceleration due to propulsive force. (b)

Acceleration due to rower motion. (c) Acceleration due to shell drag. (d) Shell

acceleration. .................................................................................................264

Figure 7.29: Inter-subject comparison for rower angles (elbow, shoulder and trunk),

seat position and position of the rower’s centre of mass. (a) Subject 2’s rower

angles. (b) Subject 1’s rower angles. (c) Subject 2’s seat position and position

of the rower’s centre of mass. (d) Subject 1’s seat position and position of the

rower’s centre of mass..................................................................................267

Figure 7.30: Inter-subject comparison for rower centre of mass position, velocity

and acceleration. (a) Subject 2’s position. (b) Subject 1’s position. (c) Subject

2’s velocity. (d) Subject 1’s velocity. (e) Subject 2’s acceleration. (f) Subject 1’s

acceleration. .................................................................................................267

Figure 7.31: Inter-subject comparison for oar angle and oar angular velocity. (a)

Subject 2’s oar angle. (b) Subject 1’s oar angle. (c) Subject 2’s oar angular

velocity. (d) Subject 1’s oar angular velocity. ................................................269

Figure 7.32: Inter-subject comparison for slip velocity magnitude and direction. (a)

Subject 2’s slip velocity magnitude. (b) Subject 1’s slip velocity magnitude. (c)

Subject 2’s slip velocity direction. (d) Subject 1’s slip velocity direction........269

Figure 7.33: Inter-subject comparison for the angle of attack. (a) Subject 2’s angle

of attack. (b) Subject 1’s angle of attack. ......................................................271

Figure 7.34: Inter-subject comparison for the blade drag and lift coefficients. (a)

Subject 2’s coefficient of drag. (b) Subject 1’s coefficient of drag. (c) Subject

2’s coefficient of lift. (d) Subject 1’s coefficient of lift. ....................................272

Figure 7.35: Inter-subject comparison for the blade drag force magnitude and

direction. (a) Subject 2’s blade drag force magnitude. (b) Subject 1’s blade

xix

drag force magnitude. (c) Subject 2’s blade drag force direction. (d) Subject

1’s blade drag force direction........................................................................273

Figure 7.36: Inter-subject comparison for the blade lift force magnitude and

direction. (a) Subject 2’s blade lift force magnitude. (b) Subject 1’s blade lift

force magnitude. (c) Subject 2’s blade lift force direction. (d) Subject 1’s blade

lift force direction...........................................................................................274

Figure 7.37: Inter-subject comparison for the blade force’s x and y component. (a)

Subject 2’s x-component of the blade force. (b) Subject 1’s x-component of the

blade force. (c) Subject 2’s y-component of the blade force. (d) Subject 1’s y-

component of the blade force. ......................................................................275

Figure 7.38: Inter-subject comparison for the shell velocity. (a) Subject 2’s shell

velocity. (b) Subject 1’s shell velocity............................................................277

Figure 7.39: Inter-subject comparison for the acceleration contributions from each

component of the rowing system. (a) Subject 2’s propulsive component. (b)

Subject 1’s propulsive component. (c) Subject 2’s rower motion. (d) Subject

1’s rower motion. (e) Subject 2’s shell drag. (f) Subject 1’s shell drag. (f)

Subject 2’s shell acceleration. (g) Subject 1’s shell acceleration. .................279

Figure 7.40: The acceleration contributions from each component of the rowing

system. The propulsive component was determined from the other three

components as described above using Equation 7.2. (a) Subject 1’s propulsive

component. (b) Subject 1’s rower motion. (c) Subject 1’s shell drag. (d)

Subject 1’s shell acceleration........................................................................282

Figure 7.41: The acceleration contributions from each component of the rowing

system. The propulsive component was determined from the other three

components as described above using Equation 7.2. (a) Subject 2’s propulsive

component. (b) Subject 2’s rower motion. (c) Subject 2’s shell drag. (d)

Subject 2’s shell acceleration........................................................................282

Figure 7.42: Comparing the propulsive force at the oar blade (calculated from

measurements and using the equation describing the motion of the rowing

system) against the applied force measured at the oar handle. (a) Results for

xx

subject 1. (b) Results for subject 2. (c) Results for subject 3. (d) Results for

subject 4. ......................................................................................................285

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LIST OF TABLES

Table 2.1: Rowing measurement systems found in the literature...........................36

Table 2.2: Rowing models found in the literature. ..................................................51

Table 3.1: Summary of the order of magnitudes for some of the sources of

variations that affect the Earth’s gravity field...................................................68

Table 3.2: Summary of the difference in measurement between an orthogonal and

a non-orthogonal triaxial accelerometer..........................................................71

Table 3.3: Calibration log. ......................................................................................72

Table 3.4: Mean and standard deviation for the offsets and scale factors. Symbols

are as defined in Equation 3.2 ........................................................................76

Table 3.5: Mean and standard deviation for the offsets and scale factors omitting

the defective calibrations. ...............................................................................76

Table 4.1: Rowing model assumptions. .................................................................88

Table 4.2: Mass and inertial properties of female body segments (de Leva 1996).

........................................................................................................................99

Table 4.3: Measured anthropometric properties of the rowing subjects...............100

Table 4.4: Methods for obtaining the time dependent variables for the rowing model

simulation......................................................................................................103

Table 4.5: Makeshift standard deviation for the rower body angle measurements.

......................................................................................................................114

Table 4.6: Error in the simulated shell acceleration using hydrodynamics modelling

versus oar leverage calculation. ...................................................................119

Table 4.7: Cross correlation coefficients for the comparison of the measured and

simulated rowing shell acceleration data. .....................................................127

Table 4.8: Error in the simulated shell acceleration during the drive phase versus

recovery phase. ............................................................................................128

Table 4.9: The maximum deviations between the simulated and the measured

acceleration data. Over-estimation is positive and under-estimation is negative.

The actual measured acceleration value is shown in the bracket. The

percentage of error was not calculated because some of the actual measured

xxii

values were very close to zero, which produced excessively large error

percentages. .................................................................................................134


simulated velocity data. ................................................................................135


velocity data. Over-estimation is positive and under-estimation is negative.

The actual measured velocity value is shown in the bracket. The percentage of

error was calculated and shown in the last column.......................................136

Table 5.1: Rowing model input variables. ............................................................147

Table 5.2: Constant parameters of the rowing model. .........................................148

Table 5.3: Model parameters and their uncertainty (used for sensitivity analysis).

The expected uncertainties are shown in red bold italic. ..............................149

Table 5.4: Measurement data and the added random error used for sensitivity

analysis. The values calculated from the percentage change were used as the

standard deviation of the normally distributed random error with mean values

of zero. The expected error magnitudes are shown in red bold italic. Note that

the seat position was limited to a maximum of ± 7 % random error, because of

the physical limit of the rower’s leg length. ...................................................152

Table 5.5: Mean error between the simulated and the two measured acceleration

data...............................................................................................................156

Table 5.6: Mean error between the simulated and measured velocity data. ........156

Table 5.7: A summary for the effect of each of the model parameters against the

four rowing system variables. .......................................................................166

Table 5.8: Ranking table for the model parameters based on their influence on the

simulated shell motion (based on a ±10% error in the model parameters). ..172

Table 5.9: Expected uncertainties of the model parameters and the corresponding

error propagation in the simulated shell acceleration and simulated shell

velocity..........................................................................................................174

Table 5.10: Ranking table for the measurements based on the effect of their errors

on the rowing model output error. .................................................................179

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Table 5.11: Combined uncertainty of the rowing model simulation compared

against the mean error between the simulated and measured data (the latter is

shown in brackets). .......................................................................................181

Table 5.12: Mean error between the simulated acceleration data and the out of

synchronisation acceleration data.................................................................184

Table 5.13: Mean error between the simulated velocity data and the out of

synchronisation velocity data. .......................................................................184

Table 6.1: Comparison of the estimated rower c.o.m. position against the video-

derived rower c.o.m. position. .......................................................................201

Table 6.2: Comparison of the measured and simulated sets of shell acceleration

data for all 4 subjects, along the columns, respectively. The 4 error

quantification statistics (as detailed in section 6.3 – STEP 5) are shown along

the rows, respectively. ..................................................................................209

Table 6.3: Comparison of the 3 sets of rowing shell velocity data for all 4 subjects,

along the columns, respectively. The 4 error quantification statistics are shown

along the rows, respectively, following the format of Table 6.2.....................210

Table 6.4: Shell acceleration comparison table. The correlation coefficient, sum of

squared error and absolute mean error are the mean values for the four

subjects (row 1, 2 and 3, respectively, in each cell block). The largest

maximum deviation value among the four subjects was selected for display in

this table (row 4 in each cell block). ..............................................................212

Table 6.5: Shell velocity comparison table. The correlation coefficient, sum of

squared error and absolute mean error are the mean values for the four

subjects (row 1, 2 and 3, respectively, in each cell block). The largest

maximum deviation value among the four subjects was selected for display in

this table (row 4 in each cell block). ..............................................................213

Table 7.1: Impulse of force effective index for the three rowing strokes of all four

subjects.........................................................................................................286

Table 7.2: Limitations with the experimental setup. .............................................287

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GLOSSARY

Backstop

The stop mechanism on the seat slides which prevents the rower's seat

from falling off the sliding tracks at the back end (towards the boat's bow) of the

slide tracks. Also, the back part of the slide where the rower’s legs are flat and their

hands are pulled into their chest.

Blade

The spoon or hatchet shaped end of the oar or sweep.

Bow

The front section of a shell – that is behind the rower.

Bowside (also called Starboard)

All rowers whose oars are in the water on the right hand side of the boat

when viewed from the stern

Button

Plastic sheath on oar to prevent it from slipping through the rowlock;

adjustable on modern oars

Catch

The part of the stroke at which the oar blade enters the water and the drive

begins. Rowers conceptualize the oar blade as 'catching' or grabbing hold of the

water.

Drive (also called Pull Through)

The portion of the stroke from the time the oar blade enters the water

('catch') until it is removed from the water ('release'). This is the propulsive part of

the stroke.

Ergometer (also called Ergo or Erg)

An indoor rowing machine that most closely simulates rowing in a boat. It is

used for training, testing and competitions. The ergometer can be equipped with a

fixed seat and/or a seat with a support back.

xxv

Feather

Rotating the oar in the oarlock so that the blade is parallel to the surface of

the water at the start of the recovery to reduce wind resistance

FISA

Federation Internationale des Sovietes d'Aviron; the International Rowing

Federation

Foot stretcher (also called Footplate or Footchock)

A frame with straps or shoes to anchor the rower’s feet. An adjustable

footplate which allows the rower to easily adjust his or her physical position relative

to the slide and the oarlock. The footplate can be moved (or "stretched") either

closer to or farther away from the slide frontstops.

Frontstop

The stop mechanism on the seat slides which prevents the rower's seat

from falling off the sliding tracks at the front end (towards the boat's stern) of the

slide tracks. Also, the furthermost point of the slide where the rower’s legs are

compressed and their hands are outstretched ready for the catch or next stroke.

Gate

Bar across the top of rowlock, secured with a nut, which prevents the oar

from coming out of the rowlock.

Handle

The part of the oar that the rowers hold and pull with during the stroke.

Hull

The actual body of the shell.

Inboard

The distance between the far end of the handle of an oar and the face of the

button.

xxvi

Oar

A slender pole which is attached to a boat at the Oarlock. One end of the

pole, called the "handle," is gripped by the rower, the other end has a "blade,"

which is placed in the water during the propulsive phase of the stroke. The blade is

curved into a sort of hydrofoil, which helps provide much of the thrust. The oar is a

lever, approximately 12 feet (360cm) long, by which the rower pulls against the

rowlock to move the boat through the water.

Oarlock (also called Rowlock)

The rectangular lock at the end of the rigger which physically attaches the

oar to the boat. The oarlock also allows the rower to rotate the oar blade between

the "square" and "feather" positions.

Outboard

The length of the oar shaft measured from the button to the tip of the blade.

Pin

The vertical metal rod on which the rowlock rotates.

Port or Portside (also called Strokeside)

The left side of the boat when looking from stern to bow.

Rating (also called Stroke Rate)

The number of strokes executed per minute.

Ratio

The relationship between the time taken during the drive and recovery

phases of a rowing or sculling action.

Recovery

The non-work phase of the stroke where the rower moves up the slide for

the next catch or next stroke and returns the oar from the release to the catch.

Regatta

A competitive event raced in boats

Release (also called Finish)

At the end of the drive portion of the stroke. It is when the oar blade is taken

out of the water.

xxvii

Rigger (also called Outrigger)

A metal framework or a carbon-fibre reinforced arm mounted on the side of

the boat to provide support for the oarlock and carry the oar. The oarlock is

attached to the far end of the rigger away from the boat. The rigger allows the

racing shell to be narrow thereby decreasing drag, while at the same time placing

the oarlock at a point that optimize leverage of the oar. There are several styles of

riggers, but they are most often a triangle frame, with two points attached to the

boat, and the third point being where the oarlock is placed.

Rigging

The settings for the riggers and other adjustable parts of the boat to allow

the rowers to perform their most efficient stroke. (e.g. pitch, height, span, etc.).

Sculler

A rower who rows with two oars, one in each hand.

Sculling

In a sculling boat, each rower has two oars, one on each side of the boat.

Seat

Moulded seat mounted on wheels, single action or double action. Single

action is fixed bearing wheel, double action is wheel on axle that rolls on track and

rolls on horns of seat. A secondary meaning of location in the shell]], the bow seat

is one, and is numbered upward to the stroke seat (8, in an 8 man shell). Thirdly

can mean a competitive advantage in a race, to lead a competitor by a seat is to be

in front of them by the length of a single rower's section of a shell.

Shell

The boat used for rowing.

Slide

To move the seat up the slide-runners (the pair of adjustable rails).

Square

Oar blade perpendicular to the water

Starboard or Starboard side (also called Bowside)

The right side of the boat when looking from stern to bow.

xxviii

Stern

The rear or aft of the boat.

Stroke

The complete cycle of moving the boat through the water using oars

Stroke Rate (also called Stroke Rating)

The number of strokes executed per minute by a crew.

1

1 INTRODUCTION

1.1 BACKGROUND AND MOTIVATIONS FOR THE RESEARCH

This PhD thesis examines the application of triaxial accelerometers to measure

the rowing shell motion as a means to assess rowing technique.

Rowing biomechanics is traditionally difficult to measure because of the nature

of the sport. Rowing takes place in an aquatic environment, covers a relatively

large distance (standard world championship race distance of 2,000 metres)

and the mechanics of the rowing is complex (because of boat rigging,

hydrodynamic interaction and the sliding seat). Traditionally, instrumented boats

(Baudouin & Hawkins 2004; Hill 2002; Kleshnev 1999; McBride 1998; Smith &

Loschner 2002; Soper 2004) have been the standard for monitoring and

analysing rowing technique, but they are expensive and complex to setup.

Inertial sensors showed great potential as an alternative and were selected as

focus of investigation. This thesis examines the use of Micro-Electro-

Mechanical Systems (MEMS) accelerometers that are small, unobtrusive and

relatively easy to set up, yet with the appropriate methodology can yield

analogous information for rowing technique analysis.

Inertial acceleration sensors have been applied to study biomechanics in many

sports (Anderson, Harrison & Lyons 2002), ranging from swimming (Ichikawa et

al. 2002; Ohgi & Ichikawa 2002) to javelin throwing (Maeda & Shamoto 2002).

The measurement of rowing kinematics is very suitable for accelerometers

because they are small, self contained and can be sampled at a high rate (i.e.

hundreds of Hertz), ample to cover the frequency content of rowing kinematics.

The accuracy and reliability of accelerometers for sporting applications have

also been established as satisfactory. Anderson et al. (2002) have compared

MEMS accelerometers (ADXL202) against a motion analysis system

(Panasonic AGDP800 broadcast quality cameras with the Motus 2000 motion

analysis software package) and concluded that the former offered more

accurate acceleration data than the latter. Maeda and Shamoto (2002) have

verified that a semi-conductor strain gauge accelerometer (Kyowa ASP-2000GA)

2

recorded data that were in good agreement with a piezoelectric accelerometer

(Teac 708-type) and a force sensor (PCB 208A05).

Rowing biomechanists and researchers have made rowing shell acceleration

measurements since accelerometers have become commercially accessible.

The earliest article found on rowing acceleration measurement was (Young &

Muirhead 1991), however, there was a lack of publication on how to interpret

the shell acceleration data for rowing technique assessment up until the time of

this thesis. Furthermore, coaches were still mainly focusing on the shell velocity

trace to analyse a rower’s technique. The shell acceleration profile can provide

additional insight into a rower’s technique because it is the rate of change of the

shell velocity trace.

All of the rowers have a shell acceleration trace that follows a general form, but

its exact shape is a signature of the rower’s force application and movement. In

other words, every rower has his/her own shell acceleration trace. Identifying

the differences in the shell acceleration trace between rowers requires an in-

depth comprehension of how the shell acceleration trace is generated and

thorough examination of the traces. The analysis of the shell acceleration trace

can be simplified by breaking it down into its contributing components. The

rowing shell moves as a result of the combined effect of the propulsive and

resistive forces on the rowing system, and the rower motion. Specifically, these

3 components dictate the net resultant force on the rowing system, which is

proportional to shell acceleration. Thus, measuring and analysing these four

variables is the key to rowing technique assessment and a triaxial

accelerometer is the ideal tool for this purpose.

In undertaking the investigation of using a triaxial accelerometer as a rowing

technique assessment tool, a thorough understanding of rowing biomechanics

is required to help solve the inverse problem. One must understand how the

shell acceleration trace is generated and how it relates to all the rowing

mechanics variables in order to interpret it. The relationship between all of the

forces on the rowing system and their effect on the rowing shell motion can be

represented by a single differential equation (Baudouin, Hawkins & Seiler 2002;

3

Brearley & de Mestre 1996; Cabrera, Ruina & Kleshnev 2006; Lazauskas 1997;

Millward 1987; van Holst 1996; Zatsiorsky & Yakunin 1991). The differential

equation states that the shell acceleration is the sum of the acceleration

components that originates from the propulsive force at the oar blades, the shell

drag resistance and the rower motion. Many rowing models (Atkinson 2001;

Brearley & de Mestre 1996; Cabrera, Ruina & Kleshnev 2006; Lazauskas 1997,

2004; Millward 1987; van Holst 1996) were found in the literature and they all

used the same differential equation, with minor variations, to represent the

motion of a rowing system. These models were developed to examine the

relationship between rowing parameters and their effect on performance. Some

of these models assumed force and/or kinematic profiles that differed in many

respects from real rowing data (Atkinson 2001; Brearley & de Mestre 1996;

Lazauskas 1997; Millward 1987; van Holst 1996). Moreover, with the exception

of the model developed by Cabrera et al. (2006) none of these models were

objectively verified against real on-water data to assess their accuracy. One

particular aspect that was not studied with any of these models was that they

did not look at the cause and effect relationship between the combination of

propulsion, resistance and rower motion against shell acceleration. This

particular aspect was identified as a subject that should be researched. Thus, in

order to understand the rowing shell acceleration measurement, a single-scull

rowing model was created to understand on how the shell acceleration trace is

generated. This understanding is essential in order to use the shell acceleration

data to give feedback to the rowers about their rowing technique. It is believed

that examining the use of accelerometers as a tool for rowing technique

assessment is a contribution to knowledge in rowing biomechanics.

1.2 SUMMARY OF FINDINGS

Through the development of the rowing model, it was discovered that the

forward propulsive force on the rowing system had to be calculated using a

hydrodynamic model of the force at the oar blades. The established method of

calculating the oar blade force from the oar handle force, oar lever ratio and

cosine of the oar angle produced a different result. The inadequacy of the

established method of blade force calculation is ascribed to inadequacy of the

assumptions underlying the calculation. Specifically, the established method

4

reconstructs the net blade force, the net force exerted by the water on the

blades, on the basis of:

1. measurement of the oar handle force, where only the component normal

to the oar is measured;

2. knowledge of the inboard-outboard oar length ratio, which requires an

assumption regarding the point of application of the handle force and the

point of application of the net blade force;

3. the assumption that the oar is infinitely stiff;

4. the assumption that oar inertia is negligible;

5. the assumption that the blade force has no component in the direction of

the oar.

The finding that the forward propulsive force was not equivalent to the oar blade

force calculated using the established method prompted the idea of using the

Rover kinematic measurement system (Grenfell 2007; James, Davey & Rice

2004) to estimate the forward propulsive force on the rowing system on a stroke

to stroke basis. This would be a valuable piece of information to provide to the

biomechanists, coaches and rowers. The rowing model study indicated that the

motion of the rowing system could be represented by a single differential

equation and that a drag coefficient was adequate in representing the

resistance characteristics of the rowing shell. The Rover system measures the

rowing shell acceleration, the resultant acceleration data on the rowing system,

and shell velocity, which is needed to estimate the resistance. All that is left is

the motion of the rower’s centre of mass to complete the differential equation

and solve for the forward propulsive force.

A detailed multi-segment rower model was created in Matlab SimMechanics.

The length, mass and inertial properties of the body segments were modelled

specifically for each of the four rower subjects. Rower motion was measured by

video recording the rower from the side during the on-water rowing sessions

and then manually evaluated the trunk orientation, shoulder angle and elbow

angle. Seat position was also measured to provide the data for the sliding

motion. This was an immense amount of work to estimate the motion of the

5

rower’s centre of mass. A simpler methodology was desired. Thus, it was set

out to see whether it was possible to calculate the position of the rower’s centre

of mass from the seat position data by using an average difference

compensation curve. Due to a very limited amount of good quality video data to

estimate the motion of the rower’s upper body, the analysis was very limited

and no significant conclusion could be drawn. For future work, the rower motion

analysis should be conducted by using a motion capture system (including

motion capture software, reflective markers and a video camera mounted on the

outrigger). This will ensure that the video will have a fixed field of view and the

data of good quality. Most importantly, a validation of the predictive value of the

compensation curves on data that are not part of the fitting procedure should be

conducted. The absence of a validation on out-of-sample data implied that no

significant conclusion could be drawn in this thesis. As it stands, it could only be

concluded that it was possible to come up with a difference curve that

adequately described the data of an individual rower at a specific stroke rate

during a specific rowing session. Nevertheless, the data analysis showed that

elite rowers have very consistent rowing motion, which implies that constructing

an empirical curve to represent the motion of the rower’s upper body relative to

the sliding seat is a reasonable approach.

The satisfactory results with the rowing model and the rower motion study

indicated that the forward propulsive force can be estimated on a stroke-to-

stroke basis using the Rover system along with seat position measurement.

This proposed methodology of evaluating the propulsive force provides great

insight to a rower’s technique, as all the forces acting on the rowing system and

the resultant shell acceleration are collectively monitored.

The ratio of the impulse of force at the oar blade to the impulse of force at the

oar handle was calculated, as the force applied at the oar handle was measured

in the experiments. This ‘impulse of force effective index’ is related to the

‘effectiveness of oar propulsion’, as defined in (Zatsiorsky & Yakunin 1991), and

shows how much of the rower’s effort is effectively used to propel the rowing

system forward. The results showed that it warrants further research to assess

the use of this parameter for gauging the effectiveness of a single sculler.

6

1.3 AIMS AND HYPOTHESIS

The aims of the PhD research were to:

1. Investigate the use of accelerometers as a tool for rowing technique

assessment

2. Understand how the rowing shell moves as a result of all the forces

on the rowing system. In particular, how the shell acceleration trace

was generated

It was hypothesised that;

1. The biomechanics of a single sculler could be examined by using a

rowing model.

a. The relationship between the rowing shell acceleration and the

forces on the rowing system could be represented by a single

differential equation.

b. The resistance on the rowing shell could be represented by a drag

coefficient.

c. The propulsive force could be calculated using a static

hydrodynamic model of the oar blades (using experimental drag

and lift coefficients found in the literature).

d. The motion of the rower’s centre of mass could be calculated

using a multi-segment rower model, with video analysed data for

the rower angles (trunk orientation, shoulder angle and elbow

angle) and seat position data for the sliding motion.

2. The effectiveness of a single sculler could be assessed and quantified by

employing accelerometers to monitor the rowing shell motion.

a. All the forces acting on the rowing system and the resultant shell

motion could be analysed using accelerometers and additional

measurements (shell velocity, and rower motion estimated from

seat position, as described in hypothesis 2b) based on a

differential equation describing the motion of the rowing system.

7

b. The motion of the rower’s centre of mass could be estimated

using a simplified methodology as a simplification to the method

described in hypothesis 1d. This simplified methodology estimates

the motion of the rower’s centre of mass from seat position data

and a rower and stroke rate specific compensation curve.

c. A parameter can be deduced to gauge the effectiveness of a

single sculler. The propulsive force on the rowing system (i.e.,

blade force) could be estimated using the methodology as

described in hypothesis 2a. With oar handle force measurement,

the ratio of the impulse of force at the blade to the impulse of force

at the oar handle could be calculated. This ‘impulse of force

effective index’ can be used to show how much of the rower’s

effort is effectively used to propel the rowing system forward.

1.4 CONTRIBUTIONS TO KNOWLEDGE

The contributions to knowledge of this thesis in the field of rowing biomechanics

included two aspects. First, this thesis revealed the relationship between the

combination of propulsion, resistance and rower motion against the resultant

shell acceleration. In particular, the rowing model showed how the rowing shell

acceleration trace was generated from all the variables and parameters of the

rowing system. Second, this thesis detailed a methodology to employ

accelerometers as a tool to assess rowing technique. This contribution is

important because at the time of this thesis there is no publication on how to

interpret the shell acceleration data for rowing technique assessment.

1.5 OVERVIEW OF THE THESIS

1.5.1 LITERATURE REVIEW

Chapter 2 examines the mechanics of rowing. In particular, it presents the

derivation of the differential equation that relates all the forces on the rowing

system and their effect on the rowing shell motion. It also covers the common

methods used to assess rowing performance and technique. This

understanding of the physics of rowing and the existing methods of

8

performance/technique assessment is essential in order to appreciate the use

of a triaxial accelerometer unit as a tool for rowing technique assessment.

A single scull rowing model was created to simulate the rowing shell motion and

learn how the shell acceleration trace is generated. Many rowing models in the

literature were reviewed. The advantages, assumptions and simplifications of

these models will be discussed in chapter 2. Two aspects have been identified

as extensions to the existing models. First, only one model had been objectively

compared against on-water rowing data. Second, none of these models looked

at how changes in the propulsion, resistance and rower motion affected the

shell acceleration, which is proportional to the resultant force on the rowing

system.

1.5.2 ACCELEROMETERS FOR ROWING TECHNIQUE ANALYSIS

The first task before using a measurement system is calibration. The

accelerometers must be calibrated in order to relate the arbitrary output from

the sensors to a meaningful parameter, which was the rowing shell acceleration

in the case of the research project. A triaxial accelerometer calibration

technique that evades the problems of the conventional calibration method of

aligning with gravity is presented in chapter 3. The technique is based on the

principle that when the triaxial accelerometer is stationary the vector sum of

acceleration from the three orthogonal sensing axes is equal to the gravity

vector; the technique had also been used by (Lötters et al. 1998). It will be

explained how this technique eliminated the systematic errors that are inherent

with the conventional calibration method of aligning with gravity (Analog

Devices Inc. 2000). The precision of the calibration method and the accuracy of

the triaxial accelerometer when used for static measurements are the main

focus of chapter 3.

To evaluate the total combined error in using the triaxial accelerometers for

static measurements, all of the calibration measurements were used as

individual gravity measurements. This is valid because the Earth’s gravity

magnitude is essentially constant at a fixed location. The total combined error

included A/D quantisation error, alignment error, noise, non-linearity, non-

9

orthogonality, and calibration error. Gravity was measured a total of 288 times

with the triaxial accelerometer, and the error in measuring this constant was

determined.

1.5.3 A SINGLE SCULL ROWING MODEL

Chapter 4 describes the development of the single-scull rowing model (Lai,

Hayes et al. 2005; Lai, James et al. 2005). It was developed in Matlab®, in

which the motion of the rowing system was represented by a differential

equation. The rower model was developed in Matlab SimMechanics in which

the rower body segments were modelled in great detail, including length, weight

and inertial properties.

During the development of the rowing model, it was realised that the oar blade

force calculated using the measured oar handle force, oar leverage and cosine

of the oar angle is not equivalent to the blade force that propels the rowing

system. The inadequacy of the oar handle force based method of blade force

calculation is ascribed to inadequacy of the assumptions underlying the

calculation as detailed in section 1.2. Thus, a hydrodynamic blade force model

was developed to determine the propulsive force at the blade. The

hydrodynamics oar blade model took into account the effort applied by the

rower using the measured oar angle and the derived oar angular velocity. It

accounted for the hydrodynamics effects at the oar blade with the immersed oar

blade area, coefficients of drag and lift, and the oar blade’s slip velocity. Most

importantly, it accounted for the constant change in the kinematics of the rowing

system with the shell velocity vector, which affects the oar blade’s slip velocity

vector, and consequently, blade force. The hydrodynamic blade force model

intrinsically accounts for the hydrodynamic phenomenon of slip. To explain the

concept of slip, if the oar blades are leveraging off a solid medium, then there is

no slip, however, as water is fluid and does yield (i.e., accelerate aft), slip must

be taken into account. The hydrodynamics blade force model reconstructs the

net blade force on the basis of:

1. measurement of the oar angle in the plane parallel to the water surface

and shell velocity;

10

2. knowledge of the outboard oar length, which requires an assumption

regarding the point of application of the net blade force;



On-water data was collected to verify the model and the model verification steps

are outlined in chapter 4. Results are presented to show how well the model

represented a real single sculler. More in-depth analysis of the model will be

discussed in subsequent chapters.

1.5.4 ROWING MODEL SENSITIVITY ANALYSIS

Chapter 5 documents the findings from the rowing model sensitivity analysis.

The main purpose for doing the sensitivity analysis was to determine whether

the difference between the measured and simulated rowing shell motion (i.e.,

the simulation error) could be accounted for by the uncertainty in the rowing

model output. Specifically, if the simulation error is within the uncertainty of the

rowing model output, then the simulation error can be accounted for by the

uncertainties in the rowing model constants and model inputs, and confirms that

the rowing model is an adequate representation of the rowing system.

The sensitivity analysis was performed by introducing error into the model

inputs (i.e. error added to the measured data) and model constants one at a

time and then quantifying the variation in the model outputs (the simulated shell

acceleration and velocity). The resulting contributions, from each of the model

constants and variables, to the uncertainty in the rowing model output are

summed in quadrature to estimate the combined uncertainty. It will be shown

that the simulation error was within the uncertainty of the rowing model output

established from the sensitivity analysis.

1.5.5 MOTION OF THE ROWER’S CENTRE OF MASS

It would be valuable to provide the biomechanists, coaches and rowers with the

propulsive force at the oar blade. The Rover kinematic measurement system

(Grenfell 2007; James, Davey & Rice 2004) measures the shell velocity and

acceleration, and the simulation results indicated that the shell resistance could

11

be estimated using shell velocity and a coefficient of drag. Therefore, if the

motion of the rower’s centre of mass (c.o.m.) could be monitored, then the

propulsive force could be calculated by using the Rover system to determine

the other variables in the differential equation describing the motion of the

rowing system.

The rower motion affects the rowing shell motion as a single point mass, which

is dependent on the movement of all the body segments, so it required many

variables and parameters to be measured, rower model set up and data

processing to determine this to a reasonable accuracy. A simpler methodology

was desired. Chapter 6 documents the investigation of estimating the “position

of the rower’s c.o.m.” (it will now be referred to as “rower c.o.m. position” from

here on) from the seat position measurement and using average difference

compensation. This method basically calculated the average difference

between the rower c.o.m. position data and the seat position data, and was

subsequently used to compensate the seat position data to estimate the rower

c.o.m. position data. Specifically, this method assumes that the difference

between the rower c.o.m. position data and the seat position data is always

highly consistent, so that a single average difference curve could be used to

accurately estimate the rower c.o.m. motion from the seat position data for

every rowing stroke. Further, for the application in practice, it assumes that the

rower technique does not change and consistency is maintained, so that the

difference curve could be used with all future seat position data.

The results showed that the “estimated rower c.o.m. motion” (using the average

difference compensation curve and the seat position data) was very close to the

“video-derived rower c.o.m. motion” (calculated using the rower model that

required video analysis for the rower’s upper body movement combined with the

seat position data). Further, the “estimated rower c.o.m. motion” was used to re-

simulate the rowing shell motion. It will be shown that the simulated rowing shell

motion using the “estimated rower c.o.m. motion” was also very close to that

using the “video-derived rower c.o.m. motion”. It was observed that the

difference curve was specific to the rower as well as the stroke rate, as both of

these aspects change the shape of the rower c.o.m. position curve. As

12

discussed earlier, due to the limited amount of good quality video data, a

validation of the predictive value of the compensation method on out of sample

data was not carried out. As it stands, it could only be stated that it was possible

to come up with a compensation curve that accurately described the data of an

individual rower at a specific stroke rate during a specific rowing session.

Nevertheless, the low amount of error in the “estimated rower c.o.m. motion”

indicated that elite rowers have very consistent rowing motion and that using

the average difference compensation method is a reasonable approach to

estimating the rower c.o.m. motion. This simplified method to estimating the

rower c.o.m. motion would be very convenient in practice in order to calculate

the propulsive force at the blade using the differential equation describing the

motion of the rowing system. This topic will be discussed in the chapter 7.

1.5.6 ANALYSIS OF THE MECHANICS OF ROWING

Chapter 7 looks at the rowing model variables in further detail. First, it will be

shown that the oar blade force estimated using the hydrodynamics model was

consistent with oar blade theory (Sykes-Racing 2009). Further, the graphs of all

the variables will be plotted together to show how the rowing model (the

differential equation describing the motion of the rowing system, the rower

model and the hydrodynamic blade force model) was able to relate all of the

rowing variables to the shell acceleration. The data of subject 2, who sculled at

the nominal rate of 20 strokes per minute, will be examined in detail. This set of

data will then be compared to that of subject 1, who sculled at the nominal rate

of 32 strokes per minute. The comparison was by no means an analysis of the

‘optimal technique’, but just to highlight the similarities and differences between

two different rowers who sculled at different stroke ratings. A more conclusive

comparison would warrant a significant improvement in the experimental set up

in terms of equipment and resource.

From the findings in chapters 4 to 6,

• Chapter 4 – Identified that the oar blade force calculated using the

measure oar handle force, oar leverage and cosine of the oar angle is

not equivalent to the blade force that propels the rowing system, as it is

13

ascribed to the inadequacy of the assumptions underlying the calculation

as detailed in section 1.2.

• Chapter 5 – Determined that the differential equation describing the

motion of the rowing system is an adequate representation of a single

sculler.

• Chapter 6 – Shown that using seat position measurement and a

compensating difference curve to represent the motion of the rower’s

upper body relative to the sliding seat is a reasonable approach to

estimating the rower motion relative to the shell.

It was recognised that the differential equation describing the motion of the

rowing system could be used to calculate the propulsive force at the blade using

the Rover system to measure the shell motion and estimating the rower motion

from the seat position measurement. This proposed methodology of evaluating

the propulsive force provides great insight to a rower’s technique, as all the

forces acting on the rowing system and the resultant motions are collectively

monitored.


oar handle was calculated to quantify the rower’s effectiveness. This ‘impulse of

force effective index’ is related to the ‘effectiveness of oar propulsion’, as

defined in (Zatsiorsky & Yakunin 1991), and shows how much of the rower’s

effort is effectively used to propel the rowing system forward. The preliminary

results using the proposed methodology to gauge the effectiveness of a single

sculler showed that it warrants further research.

1.6 REFERENCES

Analog Devices Inc. 2000, 'ADXL202E datasheet', <http://www.analog.com/static/imported-files/data_sheets/ADXL202E.pdf>. Anderson, R, Harrison, AJ & Lyons, GM 2002, 'Accelerometer based kinematic biofeedback to improve athletic performance', in SJH S. Ujihashi (ed.), The 4th International Conference on the Engineering of Sport, Kyoto, Japan, pp. 803-9. Atkinson, WC 2001, Modeling the dynamics of rowing - A comprehensive description of the computer model ROWING 9.00, viewed 1 May 2004, <http://www.atkinsopht.com/row/rowabstr.htm>.

14

Baudouin, A & Hawkins, D 2004, 'Investigation of biomechanical factors affecting rowing performance', Journal of Biomechanics, vol. 37, no. 7, pp. 969-76. Baudouin, A, Hawkins, D & Seiler, S 2002, 'A biomechanical review of factors affecting rowing performance', Br J Sports Med, vol. 36, no. 6, pp. 396-402. Brearley, M & de Mestre, NJ 1996, 'Modelling the rowing stroke and increasing its efficiency', in 3rd Conference on Mathematics and Computers in Sport, Bond University, Queensland, Australia, pp. 35-46. Cabrera, D, Ruina, A & Kleshnev, V 2006, 'A simple 1+ dimensional model of rowing mimics observed forces and motions', Human Movement Science, vol. 25, no. 2, pp. 192-220. Grenfell, RM, AU), Zhang, Kefei (Melbourne, AU), Mackintosh, Colin (Bruce, AU), James, Daniel (Nathan, AU), Davey, Neil (Nathan, AU) 2007, Monitoring water sports performance, Sportzco Pty Ltd (Victoria, AU), patent, United States, <http://www.freepatentsonline.com/7272499.html>. Hill, H 2002, 'Dynamics of coordination within elite rowing crews: evidence from force pattern analysis', Journal of Sports Sciences, vol. 20, no. 2, pp. 101-17. Ichikawa, H, Ohgi, Y, Miyaji, C & Nomura, T 2002, 'Application of a mathematical model of arm motion in front crawl swimming to kinematical analysis using an accelerometer', in SJH S. Ujihashi (ed.), The 4th International Conference on the Engineering of Sport, Kyoto, Japan, pp. 645-51. James, DA, Davey, N & Rice, T 2004, 'An accelerometer based sensor platform for insitu elite athlete performance analysis', in Sensors, 2004. Proceedings of IEEE, pp. 1373-6 vol.3. Kleshnev, V 1999, 'Propulsive efficiency of rowing', in RH Sanders & BJ Gibson (eds), 17th International Symposium on Biomechanics in Sports, Edith Cowan University, Perth, Western Australia, Australia, pp. 224-8. Lai, A, Hayes, JP, Harvey, EC & James, DA 2005, 'A single-scull rowing model', in A Subic & S Ujihashi (eds), The Impact of Technology on Sport, Australasian Sports Technology Alliance Pty. Ltd., Tokyo, Japan, pp. 466-72. Lai, A, James, DA, Hayes, JP & Harvey, EC 2005, 'Validation Of A Theoretical Rowing Model Using Experimental Data ', in Proceedings of the International Society of Biomechanics XXth Congress and American Society of Biomechanics 29th Annual Meeting, Cleveland, Ohio, U.S.A., p. 778. Lazauskas, L 1997, A performance prediction model for rowing races, viewed 2004/05/01, <http://www.cyberiad.net/library/rowing/stroke/stroke.htm>.

15

—— 2004, Michlet rowing 8.08, viewed 2004/12/01 2004, <http://www.cyberiad.net/library/rowing/rrp/rrp1.htm>. Lötters, JC, Schipper, J, Veltink, PH, Olthuis, W & Bergveld, P 1998, 'Procedure for in-use calibration of triaxial accelerometers in medical applications', Sensors and Actuators A: Physical, vol. 68, no. 1-3, pp. 221-8. Maeda, M & Shamoto, E 2002, 'Measurement of acceleration applied to javelin during throwing', in SJH S. Ujihashi (ed.), The 4th International Conference on the Engineering of Sport, Kyoto, Japan, pp. 553-9. McBride, ME 1998, 'The role of individual and crew technique in the enhancement of boat velocity in rowing', PhD thesis, University of Western Australia. Millward, A 1987, 'A study of the forces exerted by an oarsman and the effect on boat speed', Journal of Sports Sciences, vol. 5, no. 2, pp. 93 - 103. Ohgi, Y & Ichikawa, H 2002, 'Microcomputer-based data logging device for accelerometry in swimming', in SJH S. Ujihashi (ed.), The 4th International Conference on the Engineering of Sport, Kyoto, Japan, pp. 638-44. Smith, RM & Loschner, C 2002, 'Biomechanics feedback for rowing', Journal of Sports Sciences, vol. 20, no. 10, pp. 783 - 91. Soper, C 2004, 'Foot-stretcher angle and rowing performance', PhD thesis, Auckland University of Technology, <http://repositoryaut.lconz.ac.nz/theses/3>. Sykes-Racing 2009, Oar Theory (Presented by Pete and Dick Dreissigacker at the XXIX FISA Coaches Conference, Sevilla, Spain 2000), viewed 2009/02/01, <http://www.sykes.com.au/content/view/51/46/>. van Holst, M 1996, Simulation of rowing, viewed 2010/2/22 2010, <http://home.hccnet.nl/m.holst/report.html>. Young, K & Muirhead, R 1991, 'On-board-shell measurement of acceleration', RowSci, vol. 91-5. Zatsiorsky, VM & Yakunin, N 1991, 'Mechanics and biomechanics of rowing: A review', International Journal of Sport Biomechanics, vol. 7, pp. 229-81.

16

2 LITERATURE REVIEW

2.1 OVERVIEW

This review is specifically focused on the topic of rowing technique and

performance assessment. Section 2.2 provides the background on the mechanics

of rowing, regarding propulsion, rower motion relative to the shell and shell velocity

variation. It also explains all of the forces that act on the rowing system and the

resultant shell motion that is generated. In particular, the relationship between all of

these forces can be simplified and represented by a single differential equation.

The understanding of the mechanics of rowing is essential in order to appreciate

how the triaxial accelerometer unit was employed as a tool for rowing technique

assessment.

Next, a review of the existing work on rowing technique and performance

monitoring and analysis is presented in section 2.3, which covers a range of

common measurement techniques adopted by biomechanists to quantity rowing

performance. Although accelerometers have been commercially available for more

than a decade (since the start of this PhD project in 2002), there was a very limited

amount of publications on the use of accelerometers for rowing motion sensing and

virtually none on the methodology of using acceleration data for rowing technique

assessment. Thus, assessing the feasibility of using rowing shell acceleration

measurement for technique assessment would be a contribution to knowledge in

rowing biomechanics. As there was a lack of understanding of the rowing shell

acceleration, the author decided that a rowing model should be developed to

understand how the rowing shell acceleration is generated. Thus, section 2.4 looks

at existing work on rowing modelling and how they were used to study rowing

technique and performance. The advantages and limitations of these models are

highlighted.

17

2.2 THE MECHANICS OF ROWING

The following section is the background material on the mechanics of rowing. A

large proportion of it is based on selected material written by Dudhia (2001); a

physicist and rowing coach who created a web page on the physics of rowing. This

section will describe the mechanics of propulsion, relative motion of the rower with

respect to the shell, resistance, speed variation in rowing and most importantly, the

forces on the rowing system and the resultant effect on motion.

2.2.1 PROPULSION

In order to generate the propulsive force to accelerate the rowing shell, the rower

moves the water in one direction with the oar blades and the shell moves in the

opposite direction. The law of conservation of momentum governs this effect. Thus,

the momentum that the rower puts into the water will be equal and opposite to the

momentum acquired by the shell. Before the drive, the total momentum is zero,

since everything is at rest. At the end of the drive phase, the total momentum is

conserved, as illustrated by Figure 2.1 and is represented by Equation 2.1.

Figure 2.1: The law of conservation of momentum governs the propulsion of the rowing shell

( sm = rowing system mass (kg), w

m = water mass (kg), sv = shell velocity (ms

-1) and w

v

=water velocity (ms-1

)).

0=+=∆

wwssvmvmp ( 2.1 )

where p∆ is the change in momentum (kg ms-1)

sm , w

m , sv and w

v are as described in Figure 2.1

Rowing shell at rest

m = ms

m = mw

v = 0

v = 0

Rowing shell after the first drive phase

m = ms v = vs

v = vw m = mw Water

18

Example 1

In order to accelerate a rowing shell, with a total mass of 100 kg including the mass

of the rower, to a velocity of 1 ms-1, it can be achieved by using the oars to make

20 kg of water move at a velocity of 5 ms-1 according to Equation 2.1. Note that

resistance is ignored.

Example 2

The same effect to the rowing system can be achieved by accelerating 10 kg of

water to a velocity of 10 ms-1. In fact, any other combination of w

m and w

v that

gives the product of 100 kg ms-1 will make the rowing system travel at a velocity of

1 ms-1 according to Equation 2.1.

From an energy expenditure perspective, it is actually more efficient for the rower

to achieve a certain shell velocity by displacing a large mass of water slowly than

by a small mass of water quickly. The explanation for this concept is now

presented.

The translational kinetic energy of a mass is defined by:

2

2

1 mvEKinetic

= ( 2.2 )

Thus, the total kinetic energy left in the system at the end of the drive phase is:

2

2

1

2

2

1

wwssKineticTotalvmvmE +=

⋅ ( 2.3 )

where KineticTotalE

⋅ is the total kinetic energy in the system (J)

sm , w

m , sv and w

v are as described in Figure 2.1

19

Using the previous examples on propelling the rowing shell, the kinetic energy for

the two examples, that is, the energy expended by the rower would be:

Example 1

sm = 100 kg, s

v = 1 ms-1, wm = 20 kg and w

v = 5 ms-1.

3005201100

2

2

1

2

2

1

=××+××=⋅KineticTotal

E J

Example 2

sm = 100 kg, s

v = 1 ms-1, wm = 10 kg and w

v = 10 ms-1.

55010101100

2

2

1

2

2

1

=××+××=⋅KineticTotal

E J

Thus, less energy is needed to achieve the same shell velocity by moving a large

mass of water slowly compared to moving a small mass of water quickly. This is

the reason, from a mechanics perspective, to why a large surface area for the

blades is desired.

2.2.2 RELATIVE MOVEMENT OF THE CENTRE OF MASSES

Considering only one-dimensional motion in the heading axis, the mass of a rowing

team is composed of three components, which can move relative to each other:

1. Crew, rowerm , amounts to 70-80 % of the total mass;

2. Hull (and cox), shellm , representing 20-30 % of the total mass;

3. Oars, oarm ,make up less than 5 %.

The motion of the rowing shell is primarily characterised by the propulsion during

the drive phase and the continuous resistance from the air and water. The sliding

movement of the crew and the swivelling of the oars both also complicate the

motion of the rowing shell. As the oars make up less than 5 % of the total mass,

their change in momentum and the consequent effect on the motion of the rowing

shell is minimal. The effect that the sliding motion of the rower has on the rowing

20

shell is illustrated in Figure 2.2, which is based on a single scull taking only the

motion in the heading axis into consideration.

Figure 2.2: The change in momentum from the sliding motion of the sculler and its effect on

the motion of the rowing shell (shell

x (square) = absolute coordinate of the rowing shell,

shellrowerx

_

(circle) = relative coordinate of the rower with respect to the rowing shell, and

combinedx (diamond) = absolute coordinate of the joint centre of mass of the rower and the

rowing shell).

The relative movement of the centre of masses is represented by Equation 2.4,

which states that the combined centre of mass of the rowing system is determined

from the centre of mass locations of the rower and the shell.

rowershellrowershellshellshellshellrowercombined

mxxmxmmx ⋅++⋅=+⋅ )()(

_

( 2.4 )

where rowerm is the mass of the rower (kg)

shellm is the mass of the rowing shell (kg)

shellrowerx

_

is the relative position of the rower’s centre of mass relative to

the rowing shell’s centre of mass (m)

shellx is the absolute position (i.e., relative to the start line) of the rowing

shell (m)

combinedx is the combined centre of mass position of the rowing system (m)

shellrowerx

_

shellx

combinedx

Heading

21

Therefore, the combined centre of mass is related to the rower’s centre of mass

and the rowing shell’s centre of mass by:

)(

_

shellrower

rower

shellrowershellcombined

mm

mxxx

+

⋅+= ( 2.5 )

Equation 2.5 can be differentiated to obtain the combined centre of mass velocity

(Equation 2.6) and double differentiated for acceleration (Equation 2.7).

)(

_

shellrower

rowershellrowershellcombined

mm

m

dt

dx

dt

dx

dt

dx

+

⋅+= ( 2.6 )

)(

2

_

2

2

2

2

2

shellrower

rowershellrowershellcombined

mm

m

dt

xd

dt

xd

dt

xd

+

⋅+= ( 2.7 )

The following explains the concept of Equation 2.6. When the rower is sitting still at

backstops (the end of the drive) and the blades have been removed from the water,

the rower is at rest with respect to the rowing shell, so they both move at the same

velocity. When the rower is sliding towards the stern to recover (i.e., away from the

heading), it causes the shell to surge forward with an extra velocity. This is the

result of the conservation of momentum. Losses and resistance are neglected and

they do reduce the system’s total momentum, but in practice, the surging forward

of the rowing shell during recovery is still very obvious to an observer.

To appreciate the extent of the sliding effect, let us consider a rower who weighs

80 kg and a shell that weighs 20kg. Again, we ignore losses and resistance. Figure

2.3a shows the rower right at the end of the drive, who is stationary relative to the

shell and both the shell velocity and the velocity of the combined centre of mass

are 3 ms-1. If the rower moves towards the stern during recovery at 0.5 ms-1 and in

22

order to retain the combined velocity at 3 ms-1, then the rowing shell will increase

its velocity to 3.4 ms-1 according to Equation 2.6 (illustrated in Figure 2.3b).

(a)

(b)

Figure 2.3: (a) Rower at the end of the drive phase and is stationary relative to the shell. (b)

Rower is recovery and is moving at 0.5 ms-1

away from the heading. The shell velocity

increases to conserve momentum.

2.2.3 RESISTANCE

A rowing shell moving in the water slows down mainly due to the water resistance

force or drag. This ‘loss in velocity’ is actually due to the transfer of momentum

from the boat to the water. That is, the surrounding fluid speeds up as the shell

slows down, so that momentum is conserved. Drag forces are comprised of air and

hydrodynamic drag.

Air drag is dependent on several factors and is represented by:

=shellrower

v_

–0.5 ms-1

=shell

v 3.4 ms-1

=combined

v 3 ms-1

Heading

=shellrower

v_

0

=shell

v 3 ms-1

=combined

v 3 ms-1

Heading

23

2

2

1

_ AshellrowerDairairDVACF

+= ρ ( 2.8 )

where airDF

_

is the drag force due to air (N)

airρ is the density of air (kgm-3)

DC is the drag coefficient of air (dimensionless)

shellrowerA

+ is the cross sectional area of the rower and shell (m2)

2

AV is the velocity of the rowing shell relative to the air (ms-1)

The rower’s continuous motion throughout the stroke alters the instantaneous

velocity, cross sectional area and coefficient of drag. Thus, the magnitude of the air

drag force varies during the stroke cycle. Although it is complicated to determine

the air drag, its contribution to the total drag force is only about 10% (Lazauskas

1997; Millward 1987; Sanderson & Martindale 1986). In the presence of strong

winds (significant change in air velocity), the resistance can rise to tens of percent

of water resistance.

Hydrodynamic drag acting on the rowing shell is composed of three types of drag

(Equation 2.9):

1. Skin drag ( skinDF

_

) – due to friction between the hull and the water as

the rowing shell moves;

2. Form drag ( formDF

_

) – due to the turbulence created by the passage of

the hull;

3. Wave drag ( waveDF

_

) – due to the energy lost in creating waves.

waveDformDskinDhydroD

FFFF____

++= ( 2.9 )

24

Wave drag is the dominant resistive force for most watercraft, however, racing

shells are unusual in that skin drag is the major source of resistance (about 80%)

(Dudhia 2001; Millward 1987), while the wave resistance is generally only about

10% of the total resistance (Tuck & Lazauskas 1996). Skin drag is proportional to

the square of the rowing shell velocity, and assuming that the skin drag contributes

80% of the total resistance, the total hydrodynamic drag can be represented by

(Baudouin, Hawkins & Seiler 2002):

2

_

2

_

2

_8.0

1

_

25.1

watershellwatershellwatershellhydroDcvkvkvF === ( 2.10 )

where 2

_ watershellv is the velocity of the rowing shell relative to the water (ms-2)

k is a constant that depends on the wetted surface area and hull shape

(this constant has to be determined experimentally and it remains the

same for a given shell and crew, units of kgm-1)

c the lumped constant (kgm-1)

To maintain a constant shell velocity (over many strokes), the force applied by the

crew must equal the resistance, so that there is no net acceleration (nor

deceleration). From the perspective of increasing the velocity with a greater effort,

Equation 2.10 can be rewritten into a power equation.

3

___ watershellwatershellhydroDcvvFP =⋅= ( 2.11 )

Equation 2.11 indicates that in order to increase the shell velocity by a factor of 2,

the crew needs to supply 8 (i.e., 23) times the power. Similarly, if the crew

increases the power input by a factor of 2, the shell velocity will increase by a

factor of 1.26 (i.e., 3

2 ). This illustrates the importance of efficiency in rowing when

it is so “expensive” to increase shell velocity with “raw power”. Speed variation is

explained in section 2.2.4 below.

25

2.2.4 SPEED VARIATION

The velocity-cubed dependence of power (Equation 2.11) has significant

implications when considering the power or work required to counteract drag forces

and maintaining the rowing shell at a certain velocity. A less variable boat velocity

will reduce the velocity cost, which is defined as the average power required to

maintain the boat velocity divided by that boat velocity. This effect had actually

been measured experimentally by Smith and Loschner (2004b). Their preliminary

study showed that less variable boat velocity with a smoother power production will

result in a lower velocity cost

The following examples demonstrate the difference in the velocity cost between a

varying shell velocity and a constant shell velocity. If a rower rows 1 minute at 3

ms-1 and then 1 minute at 5 ms-1 the total distance covered would be

480560360 =×+× m. If it is assumed that the coefficient of drag, c , is 1 kgm-1 to

keep the arithmetic simple, the average power input required over the two minutes

would be:

Example 1

2731

3

1

=×=P W in the first minute, and

12551

3

2

=×=P W in the second minute.

762)12527( =+=average

P W

Therefore, velocity cost 19476 == W/(ms-1)

However, if the rower was to cover the 480m in 2 minutes rowing at a constant

pace of 4 ms-1 (i.e., 4804120 =× m), then the average power input required over

the two minutes would be:

Example 2

6441

3

=×=P W

26

Therefore, velocity cost 16464 == W/(ms-1)

So, it is more energy efficient for the rower to row at a constant pace than a varying

pace. Furthermore, speed consistency is not just important from stroke to stroke,

but minimising the fluctuation in velocity within each stroke is also vital (Smith, R.M.

& Loschner 2004b). This assertion can be substantiated with a similar argument to

the variation in the rowing pace. Since skin drag resistance depends on the shell

velocity (Equation 2.10), it is more efficient if the shell velocity is maintained at 4

ms-1 throughout each stroke than spending half of each stroke at 3 ms-1 and half at

5 ms-1.

The benefit of the “constant velocity approach” were actually observed in a sliding

rigger boat in which the seats were fixed to the shell, but the stretchers and riggers

were connected and free to slide on bearings (Jones & Miller 2002). As the riggers

of a boat were significantly lighter than the crew (the major mass of the whole

system), the sliding mass was reduced, and therefore, the variation in shell velocity

throughout the stroke was also reduced. Further, research indicated that the pitch

and yaw of the rowing shell was diminished with the sliding rigger, thereby,

decreasing the skin and wave drag (Jones & Miller 2002). These boats were

banned by FISA (the International Rowing Federation) in the early 1980s on the

basis that they were more expensive than the sliding seat fixed rigger boats and

that their inherent speed advantage would immediately disenfranchise the teams

that didn’t have the system. Thus, the theory that reducing the shell velocity

variation could significantly improve efficiency was confirmed.

From the above argument that shell velocity fluctuations increases drag force

losses, one would wonder if rowers should actually follow this “constant pace

racing strategy”. According to Kleshnev (2001a), the answer is no, because there

are two other important factors that have influence on race performance. The first

is the physiological factor. At the start of the race when a crew needs to get the

rowing shell up to pace as quickly as possible, the energy production is

27

predominantly from the anaerobic source. This powerful yet short term source of

energy makes the first 500 m considerably faster than the rest of the (standard)

2000 m race, when the energy production is 70 – 80 % from aerobic source. The

second is the psychological factor. Rowers make modifications to their pace

depending on their competitors performance and if they feel that they are

comparable in physiological work capacity and technique. Kleshnev believed that

rowers could more easily control the race and obtain some psychological

advantage when they lead the race from the start.

Using the Sydney 2000 Olympics data, Kleshnev (2001a) examined the strategy

adopted by the rowing teams for different race types (heats, semi-finals and finals)

and boat types (singles, pairs/doubles, fours/quads, eights). Analysis of racing

strategy was based on the official results: split times for each 500 m pieces and

finish times (i.e., the pace throughout the race). The total race pattern (speed at

each 500m piece relative to average speed during the standard 2000m race)

during the finals was: +2.8 %, –1.2 %, –1.3 % and –0.1 %. That is, most rowing

crews implemented a strong start (because of the anaerobic energy production at

the beginning of the race) and a fast race finish. Although all rowing crews

implemented a strong start, Kleshnev found that the medal winners have a general

pattern of leading the race while conserving their power for the finish – the rowing

medal winners were 0.6 % slower in the first 500 m and 0.6 % faster in the last 500

m relative to their own 2000 m average velocity when compared to crews that did

not win medals. Moreover, it was found that rowing crews were intentionally slower

in heats and it was even more so in bigger boats, thus, highlighting the importance

of psychology in racing. Kleshnev’s studies (2001a, 2001b) indicated that although

rowing is a sport that require the highest degree of consistency in technique, there

are other important factors that contribute to the overall rowing performance.

28

2.2.5 FORCES ON THE ROWING SYSTEM AND THE RESULTANT

SHELL MOTION

This section will examine the forces that act on a single scull, as illustrated in

Figure 2.4.

Figure 2.4: The forces acting on a single scull. (The double-headed arrows indicate lengths.

The solid single headed arrows are the applied forces and the dashed arrows indicate the

reactive forces. The shell velocity arrow is heavier weighted to make a distinction that it is a

velocity vector.)

The forces acting on the shell:

dragfootboardgate

shell

shellFFF

dt

dvm −−=

( 2.12 )

where shellm is the mass of the rowing shell (kg)

shellv is the velocity of the shell with respect to the start line (ms-1)

Fblade

Fgate

Fhandle

Fdrag

Vshell

L

Lout

Lin

Ffootboard

x

y

29

gateF is the force at the oar gate (N)

footboardF is the force applied at the footboard by the rower (N)

dragF is the total resistive force on the rowing system, including

aerodynamic drag on the rowing system’s front cross sectional area and

hydrodynamic drag on the shell (N).

The forces acting on the rower:

handlefootboard

shellshellrower

rowerFF

dt

dv

dt

dvm −=

+

_

( 2.13 )

where rowerm is the mass of the rower (kg)

shellrowerv

_

is the velocity of the rower with respect to the shell (ms-1)

shellv is the velocity of the shell with respect to the start line (ms-1)

footboardF is the reaction force to the force applied at the footboard by the

rower, which is the same in magnitude, but opposite in direction (N)

handleF is the reaction force to the force applied on the oar handle by the

rower (N)

The forces acting on the oar:

handlegateblade

oar

oarFFF

dt

dvm +−=

( 2.14 )

where oarm is the mass of the oar (kg)

oarv is the velocity of the oar with respect to the start line (ms-1)

bladeF is the reaction force at the oar blade’s centre of pressure (N)

30

gateF is the reaction force on the oar at the oar gate (N)

handleF is the rower’s applied force on the oar handle (N)

Ignoring the force due to the oar’s acceleration since it is small relative to the

forces at the oar blade, oar gate and oar handle and its mass is small compared to

the shell and rower, Equation 2.14 becomes:

handlegateblade

FFF −= ( 2.15 )

The equations will now be combined to obtain a differential equation to describe

the motion of the rowing system. Combining Equation 2.12 and Equation 2.13, it

becomes:

( )

dt

dvmFFF

dt

dvmm

shellrower

rowerdraghandlegate

shell

rowershell

_

−−−=+ ( 2.16 )

Substituting Equation 2.15 into Equation 2.16, it becomes:

( )

dt

dvmFF

dt

dvmm

shellrower

rowerdragblade

shell

rowershell

_

−−=+ ( 2.17 )

where all the variables are as declared previously.

Simulating a rowing shell in water to model its drag characteristics is a very

complex problem. While most boats are propelled at a relatively constant rate, a

rowing shell moves under the rhythmic rowing action of the crew. As the shell

accelerates and decelerates through each successive stroke, both the pitch of the

shell and its attitude in the water are dynamically varied, making this a complicated

problem with multiple degrees of freedom. There had been work on simulating

rowing shell motion in water by Filippi Boats (part of Filippi Lido shipyards) and

31

partners, in collaboration with Politecnico di Milano (Ferguson 2004). They used

CD-adapco’s computational fluid dynamics code Comet for their simulation. Thus,

it is certainly possible to model the water/shell interface in detail and greater

accuracy. Nevertheless, a constant drag coefficient can be used as a simple

representation of the complex drag characteristics of the rowing system in fluids

(i.e. air and water), as discussed in section 2.2.3. This approach had been used in

many existing rowing models (Atkinson 2001; Brearley & de Mestre 1996; Cabrera,

Ruina & Kleshnev 2006; Lazauskas 1997; Millward 1987; van Holst 1996). In

contrast, Leroyer et al. (2008) stated that some computational fluid dynamics

studies have been carried out to calculate the coefficient of drag of an oar blade in

a two-dimensional case without a free surface, based on a quasi-static model, but

this simplified configuration is too far from the specific of flow around oar blades to

be helpful. Thus, Leroyer et al. essentially argued that the validity of models based

on steady state hydrodynamics considerations are questionable, which was their

motivation for investigating the flow around an oar blade both experimentally and

numerically.

Combining the aerodynamic (Equation 2.8) and hydrodynamic (Equation 2.10)

drag forces, the total resistive force, dragF , is represented by:

2

shelldragcvF = ( 2.18 )

where c is the coefficient of drag taking into account both the aerodynamic and

hydrodynamic components.

dragF and shell

v are as defined in Equation 2.12.

Substituting Equation 2.18 into Equation 2.17, a differential equation describing the

motion of the rowing system is obtained:

32

( )

dt

dvmcvF

dt

dvmm

shellrower

rowershellblade

shell

rowershell

_2

−−=+ ( 2.19 )

The physical meaning of Equation 2.19 is that the rowing shell motion is the result

of the propulsive force at the oar blade, the drag force on the rowing system and

the rower motion.

2.3 CURRENT METHODOLOGIES FOR ROWING PERFORMANCE

ASSESSMENT

Performance monitoring of rowers is critical to improving performance. These

involve a range of technologies and methodologies.

2.3.1 CURRENT APPLICATIONS OF ACCELEROMETERS IN ROWING

The earliest literature on rowing acceleration measurement found was by (Young &

Muirhead 1991). This article, titled “on board shell measurements of acceleration”,

basically indicated that the shell acceleration trace contained rowing stroke

features corresponding to the catch and release, and was useful for qualitative

analysis. Young pointed out that the use of accelerometers verifies the models of

rowing and the efficacy of rowing styles. There was no further publication by this

late author on the topic of accelerometer application in rowing.

More recent work found in this area was by Lin et al. (2003), a group from

Dartmouth College in the U.S. collaborating with Analog Devices. Accelerometers

were instrumented onto the oar blades to analyse their trajectory throughout each

stroke and on the backs of the rowers to monitor their movements. The data

analysis was limited to a very qualitative approach. It basically showed the timing

and consistency of the rowers and illustrated the differences in their techniques.

Smith and Loschner (2002) published an article on their comprehensive rowing

biomechanics system, which measured the forces at the pin (i.e., oar gate) and

foot stretcher, vertical and horizontal oar angles, boat speed relative to water, seat

33

position, as well as both three-axis acceleration and angular rate. The sum of the

pin and stretcher forces was graphed along with the forward shell acceleration,

which indicated that they were very similar in shape. The acceleration is a

reflection of the net force on the shell, whereas the sum of the pin and stretcher

force does not account for the drag force due to air and water resistance. The

study identified that although rowers and coaches valued the graphical feedback

they obtained from the system, further research was needed to provide a sound

basis for comparing the effectiveness of this type of feedback compared with more

traditional forms, such as verbal feedback of performance from biomechanists. The

article did not discuss how to use the angular rate measurement to assess rowing

technique.

Kleshnev is a biomechanist who has published many newsletters online on rowing

biomechanics (Kleshnev 2005) and has used accelerometers extensively. On the

occasions when he discussed the use of shell acceleration in rowing technique

assessment in his newsletters, one would immediate realise that you must have a

deep and extensive understanding of rowing biomechanics in order to appreciate

the information concealed in the shell acceleration trace. Specifically, Kleshnev

was able to qualitatively analyse the subtle relationship between some of the

biomechanical parameters (such as oar angle, handle force and rower acceleration)

and the shell acceleration (mainly looking at the occurrence and timing of events)

using his profound knowledge and experience in rowing.

The few publications, on the topic of using accelerometers in rowing, indicated that

there was a lack of knowledge in the rowing community on how acceleration

measurement could be used to quantitatively assess rowing technique and

performance. In particular, there was no established methodology to extract

indicators from the acceleration data to quantitatively assess rowing technique at

the time of this thesis.

34

2.3.2 COMMON METHODOLOGIES FOR ROWING TECHNIQUE AND

PERFORMANCE ANALYSIS

This section discusses some of the most common methodologies used to assess

rowing technique and performance.

Elite rowers regularly use the rowing ergometer as part of their routine training.

Thus, a lot of research had been dedicated to the biomechanics of rowing on an

ergometer. Some have developed measurement systems to look at different

biomechanical aspects for ergometer rowing (Hawkins 2000; Soper 2004), while

others have developed rower models to study the biomechanics of ergometer

rowing (Hase et al. 2004; Kuchler & Gföhler 2003). Using a modified rowing

ergometer, Hofmijster, van Soest and de Koning found a positive relationship

between velocity efficiency and 2 km performance, and that velocity efficiency

appeared to be related to movement execution, in particular the timing of handle

and foot stretcher forces (2008), as well as that within the range of stroke rates

applied in competitive rowing, internal power losses are not influenced by stroke

rate (2009). Although ergometers are undeniably important for training, there are

considerable differences to on-water rowing because a lot of the inherent

technique for on-water rowing is not required on an ergometer (Soper (2004)

reviewed a collection of papers that directly compared the similarities and

differences between ergometer and on-water rowing in her PhD thesis). For

instance, some athletes might have the fitness and strength to perform extremely

well on an ergometer, but if they do not have good technique (e.g. clean oar blade

entry and exit to minimise resistance, good balance to minimise rotation, and so

forth) then their physiological advantage will have less effect. For the above

reasons, literature regarding the biomechanics of ergometer rowing will not be

discussed for the rest of this chapter.

Numerous research groups have developed monitoring systems to study rowing

biomechanics. Table 2.1 summarises each of the research groups’ monitoring

systems in terms of the biomechanical parameters measured and the technology

35

employed. As can be seen in Table 2.1, the most commonly measured parameters

for studying rowing biomechanics were oar force, oar angle and shell velocity. The

oar force represents the effort of the rower/crew and was supplemented by the oar

angle, which provides angular information of the oar arc and to allow the

determination of the forward component of the force. The shell velocity was used

as the measure for performance. Seat position was often used to look at each of

the rower’s timing. The details of how these authors’ used the monitoring systems

to study rowing biomechanics are discussed below.

36

Table 2.1: Rowing measurement systems found in the literature.

Published

study

Oar force Foot stretcher

force

Oar angle Seat position Shell velocity Shell

acceleration

Shell

orientation

1. (Smith,

Richard M.

& Loschner

2002)

2. (Smith,

R.M. &

Loschner

2004b)

3. (Smith,

R.M. &

Loschner

2004a)

Oar lock pin force was

measured using 3-

dimensional piezoelectric

transducers. (not used in

study 3)

Foot stretcher

force was

measured with

two shear-beam

load cells. (not

used in study 3)

Study 1 and 2.

Low friction

servo

potentiometers.

Study 3.

Electro-

goniometers

Cable and

drum driven

potentiometer

(not used in

study 2)

A magnetic

turbine, pick-

up coil and

frequency-to-

voltage

converter

(not used in

study 3)

Three

accelerometers

for all three

axes (only used

in study 1)

Three

gyroscope

s for all

three axes

(not used

in study 2)

(Hofmijster,

M, De

Koning &

Van Soest

2010)

Oar lock pin force was

measured using custom-

made strain-gauge force

transducers. Parallel blade

force was measured using

custom-built oar shaft

sensors that each consisted

of two individual strain-

gauge force sensors.

Servo-

potentiometers

(FCP12-AC,

Feteris

Components)

Nielsen-

Kellerman

impeller and

induction coil

unit

Analog Devices

ADXL204

accelerometer

37

Published

study


force


acceleration

Shell

orientation

(McBride

1998)

Oarlock force measured

with quartz force

transducers

Oar angular

displacement –

rubber band

electro-

goniometry

Hall effect

device

(output

proportional

to seat

velocity)

Vaned

impeller

(Soper

2004)

Force applied to the oars

was determined by

measuring the strain

produced in each oar with a

linear proximity transducer.

Normal and

shear forces

applied to the

foot stretcher

were measured

with a custom

built plate

housing two

strain gauges

Oar angle was

measured

using a rotary

potentiometer

Nielsen-

Kellerman

impeller and

induction coil

unit

(Baudouin &

Hawkins

2004)

Oar bending force was

measured using two foil

strain gauges located on

opposite sides of the oar

shaft between the handle

and the sleeve and

perpendicular to the plane

of the oar blade.

A one-turn

linear

potentiometer

was used to

track the angle

of each

oarlock.

Seat

displacement

was

measured

using a linear

position

transducer

Nielsen-

Kellerman

impeller and

induction coil

unit.

38

Published

study


force


acceleration

Shell

orientation

1. (Kleshnev

1999)

2. (Kleshnev

2000)

3. (Cabrera,

Ruina &

Kleshnev

2006)

Study 1. Oar handle force

measured with an inductive

proximity sensor.

Study 2. The perpendicular

and axial forces applied to

the oarlock were measured

using an instrumented gate.

Study 3. The force applied

to the oar handle was

measured using strain

gauges.

Servo

potentiometers

Multi-turn

potentiometer

(not used in

study 1)

Nielsen-

Kellerman

impeller and

induction coil

unit

Piezoresistive

accelerometer

(not used in

study 3)

(Hill 2002) Force patterns were

recorded using four strain

gauges attached on to the

oars inboard near the point

of rotation.

Potentiometers

mounted on the

oar gate

39

The instrumented boat developed by Smith and Loschner was perhaps the most

comprehensive rowing biomechanics measurement system of all the ones

reviewed. The system was tested in a case study (Smith, Richard M. & Loschner

2002) with participants drawn from elite and sub-elite rowers training with the New

South Wales Institute of Sport. Basically, rowers and coaches who used the

system valued the feedback they obtained. However, Smith and Loschner pointed

that further research must be undertaken to compare the effectiveness of the

graphical feedback that the instrumented boat provided compared with more

traditional forms, such as verbal feedback of performance. A very important

question with regards to the graphical feedback was just how much biomechanics

expertise was needed to interpret the results and whether it was possible to

provide simple parameters to indicate good technique.

In another study (Smith, R.M. & Loschner 2004b), Smith and Loschner looked at

the power production pattern for three female international level scullers. It was

found that all three scullers had good work efficiency, which is the ratio of

propulsive work done (the integral of propulsive power over time for one stroke) to

the total work done. One of the rowers, a world champion junior women’s sculler,

showed a significantly lower velocity cost (as discussed in section 2.2.4, which

indicated that velocity cost increases with speed variation. In fact, velocity cost

increases with boat velocity). This was because she produced power more

smoothly resulting in a less variable boat velocity. Some of the characteristics of

her rowing may provide some insight into which technique make for efficient and

effective rowing. Smith stated that a much larger number of rowers in

homogeneous groups were required before firm generalisations to other rowers

could be made.

Smith and Loschner (2004a) also examined the relationship between boat

orientation and seat and hand position. As an indication of hand position,

electrogoniometers were mounted over the gate pin on both sides of the rowing

shell. The testing group consisted of 6 male and 7 female elite level single scullers.

40

The results demonstrated that there was a high variability in the boat orientation

among the rowers even though their timing and amplitude of the leg and arm drive

(calculated from the seat and hand position measurements) were remarkably

similar. This suggested that boat orientation is related to technique, and pitch is

related to the weight of the rowers.

The rowing biomechanics measurement system developed in (Smith, Richard M. &

Loschner 2002) was further used in the study (Hofmijster, MJ et al. 2007) to assess

the effect of stroke rate on the distribution of mechanical power in short-duration

maximum-effort rowing. As the average net mechanical power output generated at

the highest stroke rates investigated is unlikely to be sustainable over a 2000-m

race, Hoftmijster et al. stated that further research should address the possible

changes in power flow during a longer period of exertion. The results of the study

showed that the power equation is an adequate conceptual model to analyse

rowing performance and that stroke rate not only affects the net mechanical power

output of the rower, but also affects the power loss at the blades and the power

loss associated with velocity fluctuations.

(Hofmijster, M, De Koning & Van Soest 2010) custom built oar shaft sensors to

measure the blade force component that is parallel to the longitudinal axis of the

oars. The study evaluated how reconstructed blade kinematics, kinetics and

average power loss were affected by the traditional assumptions that the oar is

infinitely rigid and that there is no axial force in the oar. Hofmijster et al. found that

estimated power losses at the blades were 18% higher when parallel blade force

was incorporated. That is, neglecting parallel blade forces led to a substantial

underestimation of power losses at the blades. Incorporating oar deformation in the

reconstruction of blade kinematics had an effect on instantaneous power loss at

the blades, but, on average, power loss at the blade was not affected. Assumptions

on oar deformation and blade force direction have large implications for the

reconstructed blade kinetics and kinematics.

41

McBride investigated “the role of individual and crew technique in the enhancement

of boat velocity in rowing” for her PhD project (McBride 1998). The oarlock force,

oar angular displacement and seat velocity measurements were the basis for

rowing technique assessment (i.e., to gauge the rower’s effort), and performance

was based on the shell velocity (i.e., to gauge the result of the rower’s effort).

McBride conducted four studies:

1. Investigation on the role of stroke rate in enhancing boat velocity

As expected, it was found that an increase in stroke rate was associated with a

statistically significant increase in average boat velocity1. The rowers modified their

rowing technique with increased cadence so that less time was spent in the drive

phase per stroke, but a greater percentage of the stroke cycle was spent pulling

(i.e. reduced stroke period, but increased drive to recovery ratio). An increase in

stroke rate was also found to produce several changes to technique, which would

not logically be associated with optimal strategies. These changes included

increase in the amplitude of intra-stroke boat velocity fluctuations and reaching the

peak force on the oarlock earlier in the stroke arc than at lower cadence. McBride

stated that optimisation strategies would require specific modification of individual

technique to ensure that each rower maintained maximal oarlock force through the

orthogonal position when performing at race cadence, so that all of it is in the

forward direction and there is no lateral component. However, she recognised that

this may not be possible within the constraints imposed by the design of racing

boats and the physical limitations of the human body. Further, the design of sliding

seat racing shells forces the strong lower limb and trunk extensors to be recruited

early in the stroke when the boat velocity is at a minimum and the perceived load is

1 There is obviously a balance between an effective stroke and a high stroke rate. From the Sydney

2000 Olympics rowing regatta data, Kleshnev (2001b) found that gold medals were won by means

of either higher stroke rate or longer stroke distance depending on the boat type. Sweep crews won

by means of a higher stroke rate and scullers adopted the longer stroke distance approach. Further,

by analysing the stroke rate versus stroke distance, Kleshnev explained that it is more preferable to

use a balanced or longer stroke distance approach than a higher stroke rate approach.

42

greatest, which results in a greater percentage of the total impulse occurring prior

to the oar reaching the orthogonal position.

2. Intra-stroke evaluation of individual and crew technique and the impact on

instantaneous boat velocity

A statistical analysis of the data obtained from multiple crews was performed to

examine the general relationships between selected performance variables and

average boat velocity. The aim was to relate the simultaneous measurements of

instantaneous oarlock force, oar angular displacement, shell velocity and seat

velocity to intra-stroke fluctuations in shell velocity. The limitation in this method of

evaluation was that it did not provide insight into the subtle, dynamic interaction

among individual technique and crew compatibility and the overall impact on the

instantaneous shell velocity. The findings in this study were restricted to a general

relationship between the biomechanical variables and shell velocity, and allowed

comparisons only in a qualitative approach. More importantly, only sub-elite crews

participated in this study, so it would be questionable to make generalised

technique recommendations from the data. Thus, no definite conclusions were

drawn.

3. Investigation on the theory of “seat specific rowing technique”

The aim of the study was to establish whether evidence existed to support a theory

which claimed that effective propulsion of a coxless pair required the force-time

histories of each rower to differ with respect to shape, power and timing (Roth 1991;

Schneider, Angst & Brandt 1977). It was proposed that the most effective boat

propulsion was achieved when the rower in the stern of the boat reached a higher

peak force which occurred earlier in the stroke cycle, when compared to his partner.

This theory had been contradicted by several biomechanists (Asami et al. 1977;

Mason, Shakespear & Doherty 1988; Wing & Woodburn 1995) who assumed that

the optimal boat propulsion would result from a uniform force-time pattern from all

crew members. In order to test the theory, 10 established pair combinations were

monitored in both the original and reversed seating arrangements. Furthermore,

43

two new crew combinations were created after analysing each of the rower’s

technique to provide two extreme cases to test the theory. One of these crews

consisted of rowers who demonstrated the appropriate “seat specific” technique

while the other crew consisted of rowers with similar rowing technique. For the

established pair combinations it was discovered that the crews exhibited a full

spectrum of individual and crew technique rather than the hypothesis that the

rowers would exhibit “seat specific” technique. Comparison of data collected from

the original and reverse positioned crews revealed trends of technique modification

that were in accordance with the theory of seat specific rowing technique. Finally,

as hypothesised by McBride, performance was enhanced when two rowers who

demonstrated the appropriate seat specific technique were paired, while it was

detrimental to performance to pair two rowers with similar rowing technique.

Despite this important finding, McBride stated that since the experiment only

consisted of two created pairs, the sample size was much too small to make any

substantiated conclusions. Nevertheless, this work was a very important

preliminary step in verifying the theory of seat specific rowing technique.

4. Evaluation of an elite (Olympic level) rowing pair

An evaluation of two male heavyweight rowers who won the silver medal at the

1996 Atlanta Olympic Games was conducted. Comparing this elite pair to the other

sub-elite crews, it was found that their superior speed was primarily due to their

ability to produce greater work with every stroke. Although the biomechanical

analysis identified aspects of elite rowing technique, which could account for their

superior performance, there was little support for the theory of seat specific rowing

technique from this pair of rowers.

McBride’s PhD research identified some of the key elements in rowing technique

needed to optimise shell velocity and verified that the continuous monitoring of

shell velocity and specific biomechanical variables is essential in the development

of optimisation strategies for any rowing crew. McBride acknowledged that it would

be speculative to make any technique recommendations from her studies, since

44

they were based entirely upon data collected from sub-elite crews and only one

elite crew. Although some of the data supported the theory of seat specific

technique, there was not enough data to provide conclusive statistical verification.

Holger Hill (2002) conducted a study that complemented on McBride’s

investigation on the theory of “seat specific rowing technique”. He hypothesised

that since rowers show individual force patterns, they have to adapt their

movements when rowing as a crew. The study was based on the force patterns of

six elite coxless four crews for a total of 11 training runs. The force curves were

assessed based on smoothness, the location of a centre line that halves the force

curve area to determine early or late force production and computational

differences between force curves (i.e. subtracting one curve from another). His two

conclusions were that crews should be composed of rowers with similar force

patterns (with some exceptions due to the specific demands of the coxed and

coxless pairs, which require asymmetric force patterns) and in order to reduce

force pattern differences, more effective rowing training should be performed at

high force output. He added that due to the exploratory nature of the study, the

non-systematic crew combinations and training run content created much variation

in the force pattern analysis, and therefore, hampered the statistical analysis.

Soper (2004) investigated the relationship between foot stretcher angle and rowing

performance for her PhD project. She conducted her study with both ergometer

rowing and on-water rowing. First, she investigated the ability of rowers to replicate

their on-water rowing performance to determine the variability of rower

performance when no intervention takes place and under ideally controlled

circumstances (i.e. no wind, fatigue had not set in, etc.). The results indicated that

up to 5% variation should be expected for 90-second trials at a self-selected high

intensity stroke rate during on-water sculling. Due to repeated failures of the on-

water measurement system, Soper was only able to conduct two successful trials.

The two case studies indicated that changing the foot stretcher angle changed the

total oar excursion for both scullers, but the effect on the shell velocity was

45

inconsistent. The ergometer rowing tests indicated that a steeper angle resulted in

higher output power. Soper’s research showed that significant performance

improvements occurred with a foot-stretcher angle of 46°, compared with 36° or

41°.

Baudouin and Hawkins (2004) hypothesised that rowing performance was

predictable using a simple linear model that takes into account the total propulsive

power, synchrony (a real time comparison of rower propulsive force magnitudes)

and total drag contribution (a measure of the rowers’ effect on shell drag forces

during recovery). Four port and four starboard subjects participated in two rounds

of data collection: Round 1 trials were random pair assignments and round 2

pairings were based on the results of round 1 to test specific aspects of the

hypothesis and to maximise the range of the explanatory variables. They

concluded that performance could not be predicted using their proposed simple

linear model and that subtle biomechanical factors may play a critical role in

performance. They also noted that the rowers’ force-time profiles were repeatable

between trials, with some but not all rowers adapting their force-time profile

dependent on their pair partner.

The measurement system developed by Kleshnev was used to study rowing

biomechanics of elite rowers at the Australian Institute of Sport. In one study

(Kleshnev 2000), he introduced a new method of the power calculation in rowing.

Kleshnev pointed out that the traditional method of calculating rower input power

as oar handle force multiplied by the linear velocity of the point of force application

(Fukunaga et al. 1986; Zatsiorsky & Yakunin 1991) is only applicable to stationary

systems and not on-water rowing. According to Kleshnev, this method “cannot be

used in the real on-water rowing because the reference point of the system (gate

pin) moves with acceleration together with the boat shell and Newton’s laws are

not applicable in this system”. However, with the introduction of the relevant so-

called fictitious forces, Newton’s laws can be applied in any frame of reference. To

calculate the total rowing power correctly, it is necessary to take into account the

46

foot stretcher force and shell velocity in addition to traditional oar handle force and

oar angle. Measurements were taken from 88 elite singles, pairs and doubles.

Kleshnev found that his proposed power calculation method produced a 16.8%

higher total rowing power than the traditional method. In other studies, the

propulsive efficiency of rowing for 21 crews (a total of 71 rowers) were determined

(Kleshnev 1999) and on-water data was collected to verify a rowing model

developed by Cabrera et al. (2006). Cabrera’s rowing model will be discussed in

section 2.4.

2.4 EXISTING ROWING MODELS

Six rowing models were found from the literature. All of the models simulated the

fore-aft motion (1-D) only and ignored the rotational motions of the shell. They

assumed that the effort in keeping the boat balanced is negligible. Furthermore, the

oars were assumed to be infinitely stiff and environmental conditions such as wind

and water current were ignored. Essentially, they employed the same governing

equation that describes the rowing system, with minor differences based on

specific assumptions.

Millward’s (1987) model was one of the earlier rowing models developed. The

model was used to explore the effect of changes in the rowing force on the boat

speed. Millward assumed that the force at the oar lock in the direction of boat

motion had the shape of the square of a sine wave as a function of time and that

this force acts for exactly half of the stroke period. Due to the lack of relevant data

at the time, Millward further assumed that the movement of the rower within the

boat did not significantly affect the overall motion. Although the model was shown

to match FISA championship performance data, this model was overly simplified

and would not be adequate to study rowing biomechanics.

Brearley and de Mestre (1996) developed a mathematical rowing model to predict

race times for various boat types. A differential equation was derived to represent

the motion of the rowing system (much like Equation 2.19). It was assumed that

47

the forward force at the oar lock and the rower motion were in the form of half-cycle

simple harmonic motion (i.e. sinusoidal). The limitation with this model was that it

assumed force and kinematic profiles that differ in many respects from those in real

rowing. Thus, it was not realistic to use this model to analyse the forces and

motions experienced during actual rowing.

The 1-D model developed by van Holst (1996) was simple and restricted to the

steady state rowing cycle, yet it contained the important components of a real

rowing system, which was sufficient for parametric studies. The model used

quadratic force-velocity relationships to represent shell resistance, and oar blade

hydrodynamic drag and lift forces. The model prescribed the rower’s centre of

mass position and the component of the oar blade force in the direction of shell

motion as functions of oar angle. The kinematics of the rower was coupled to the

forces on the blade by a rationalised mathematical description based on the oar

angle during the stroke cycle. The drag and lift coefficients needed to calculate the

hydrodynamic forces at the oar blade was based on Hoerner’s aerodynamics

experimental data (Hoerner 1965). A mathematical relationship was set up to

determine the drag and lift coefficients once the angle of attack had been

calculated. In simple terms, the model accounted for the fact that the force on the

blade varies throughout its trajectory. The model assumed that the blade force

throughout the stroke was known and an iterative process was set up to determine

the oar angle that would match the specified blade force. The rower kinematics

was then calculated based on the oar angle. Although the input data were not

actual measured data, van Holst attempted to match as many parameters to

measured data as possible, such as peak blade force, rower velocity and stroke

rate. He compared the simulated shell velocity against measured data and

basically confirmed that simple modelling was sufficient to match the average shell

velocity in magnitude reasonably. Nevertheless, it was apparent that in order to

match the form of the shell velocity trace the model required real data as inputs. In

particular, the assumed rower motion as a function of scull angle, set as a

48

sinusoidal relationship, produced simulated rower motion that was quite different to

the real data.

Atkinson’s (2001) rowing model was possibly the most comprehensive one to date.

Although it was also a 1-D mechanical model, it took many factors that affect the

mechanics of rowing into consideration. It accounted for added mass, oar inertia,

oar flexibility, blade cant angle, arm bend, rower reach, and even difference in

friction at different water temperature. Like van Holst, Atkinson modelled the oar

blade force and shell drag using quadratic force-velocity relationships. It required a

look up table (based on Hoerner’s (1965) experimental data) to determine the drag

and lift coefficients once the angle of attack had been calculated. Unlike many

models, Atkinson did not make any assumption of the nature of the rowing shell

velocity profile (such as defining it as a half sine wave). Atkinson’s modelling

program divided a single stroke cycle into segments and in each of which oar force

and rower motions were allowed to be specified by the user. Thus, the user must

interpolate their measured data and then manually enter them into the program as

inputs. The model was able to simulate shell velocity similar to the measured shell

velocity in general shape, even though Atkinson did not have access to a full set of

measured data and had to manipulate the values in the model. Nevertheless, there

were still apparent deviations between the simulated and measured shell velocity

curves throughout the rowing cycle. As the report was a personal pursuit and not a

scientific publication, the author did not conduct an error analysis for the rowing

model.

Lazauskas first constructed a simple rowing model (Lazauskas 1997) by deriving

from the work of Brearley and de Mestre (1996) to predict the performance of a

crewed rowing shell. The modifications Lazauskas’ made included: the maximum

force applied by the rower to the oar was a squared sinusoidal curve, the drive

phase duration was modelled as an equation in terms of stroke rate and that the

coefficient of drag was estimated from empirical formulae and fundamental

theorem rather than experimentally measured. This model was used to simulate

49

double sculls, quad sculls and coxed eights to examine difference between

difference classes – lightweight men, heavyweight men, lightweight women and

heavyweight women.

Some years later, Lazauskas updated his model and published it on his website

(Lazauskas 2004). The same differential equation was still employed to represent

the motion of the rowing system. The model had been extended by representing

the rower’s body as a number of segments and that an experimental oar blade

force-time curve (assumed that it is known) was able to be used in place of a

simple mathematical function. The lengths, masses and centres of gravity of the

rower’s body segments were estimated from the work of Clauser et al. (1969) and

also from Dempster’s (1955) anthropometric studies. To model the effect of the

movement of the body segments, body joint angles were specified at different time

instants during the stroke phase and during the recovery phase. The movement of

the body segments were approximated from measured data. The model was tested

against experimental data supplied by Valery Kleshnev (of the Australia Institute of

Sport at that time). The data included oar angles, handle forces, foot-stretcher

forces, seat and trunk position, and boat speed and acceleration. The agreement

between the model’s shell velocity predictions and experimental data was

satisfactory, but like Atkinson’s model, there were apparent deviations between the

simulated and measured shell velocity curves throughout the rowing cycle. Again,

Lazauskas did not do an error analysis to quantify the error and examine the cause

of the deviations.

The model by Cabrera et al. (2006) is based upon the model proposed by

Alexander (1925). The model was based on writing state space equations

describing all of the rowing components. For fluid forces, the model took into

account large angular displacement of the oar in a plane parallel to the water

surface. The direction of the resultant force on the oar blade was assumed to be

normal to the longitudinal oar axis. The oars inertia was taken into account.

Quadratic relationships were used to model shell drag and the oar blade drag and

50

lift forces. All rowers were assumed to be identical in size, strength and

coordination; they row together in perfect synchrony. The rower was represented

by a point mass and the rower coordination defined by the fore-aft positioning of

the arms, back and legs. The rower’s centre of mass was assumed to be

concentrated in her gut and the height of the rower’s centre of mass from the

sliding seat was assumed to be constant. The model was validated for both

sculling and sweep rowing using numerical optimisation to construct reasonable fits

to on-water force and kinematics data. Solving the set of state space equations to

obtain the variables of interest required the minimisation of the net error, which

turned out to be a root finding problem. In summary, Cabrera’s best fit simulation of

singles produced the following results: residuals were less than 2.1° for oar angle,

0.35 cm for seat slide, 0.13 ms-1 for boat velocity, 11 N for oar handle force and

0.11 cm for back position (horizontal distance from hip to shoulder). Besides

quantifying the model error, a sensitivity analysis was also carried out where all the

mechanical constants were varied and looked for the minimum error. It was also

found that oar flexibility has very little effect on the force and kinematics prediction.

The testing of the model was based on an averaged stroke (many strokes of data

were interpolated and then combined). The predicted shell velocity was found to be

very close to the measured shell velocity. However, since the data was based on

an average stroke, a lot of the fine details from stroke to stroke would have been

lost and the ability of the model to predict these fine details was not tested.

All of these models, with the exception of Lazauskas, have all shown that

modelling the shell and rower as point masses can reasonably predict race times

based on measured oar forces. That is, balancing average oar propulsive force

with boat drag, which is dependent on average boat speed, gives reasonable

predictions for average boat speed. Nevertheless, estimating a single sculler’s

centre of mass motion using a multi-segment rower model does not assume any

waveform, therefore, is a much more accurate representation. Table 2.2 compares

the similarities and differences between the models.

51

Table 2.2: Rowing models found in the literature.

Model Shell resistance Oar blade drag/lift

representation

Applied force

assumption

Rower mass

representation

Rower motion

modelling

Verification with

measured data

(Atkinson 2001) Quadratic

force/velocity

relationship.

Estimated with

empirical

formulae.

Yes Defined the oar

handle force (four

point linear

interpolation or

parabolic) as a

function of time.

2 lumped masses The velocity of the

2 lumped masses

were divided into

time segments

and then fitted

(linear or

parabolic).

Inputs were

estimated from

measured data.

There was no

actual verification

against

experimental data.

(Brearley & de

Mestre 1996)

Quadratic

force/velocity

relationship

No. Sinusoidal 1 lumped mass Half cycle simple

harmonic motion

No

(Cabrera, Ruina &

Kleshnev 2006)

Quadratic

force/velocity

relationship

Yes Used real

measured data

Assumed the

rower’s centre of

mass was fixed in

height and in the

abdomen.

Estimated the

rower’s centre of

mass with torso

and seat

measurement.

Yes.

52

Model Shell resistance Oar blade drag/lift

representation

Applied force

assumption

Rower mass

representation

Rower motion

modelling

Verification with

measured data

1. (Lazauskas

1997)

2. (Lazauskas

2004)

Quadratic

force/velocity

relationship.

Estimated with

empirical formula

and fundamental

theory.

No. Asserted that

it warrants

computational

fluid dynamics

modelling.

1. Square of a

sinusoid

2. Assumed that

the propulsive

force was known

1. Single lumped

mass

2. All body

segments

represented

1. Half cycle

simple harmonic

motion

2. Estimated from

real data

Inputs were

estimated from

measured data.

There was no

actual verification

against

experimental data.

(Millward 1987) Polynomial

force/velocity

relationship, but it

is essentially

equivalent to

quadratic

No Square of a

sinusoid

It was ignored, as

it was assumed

that the rower

motion did not

have a significant

effect on the

overall motion.

No No

(van Holst 1996) Quadratic

force/velocity

relationship

Yes Blade force was

defined as a

function of oar

angle with five

point linear

interpolation.

1 lumped mass Assumed to be

sinusoidal

(function of oar

angle) during the

drive, and

triangular (function

of time) during

recovery.

No.

53

2.5 CONCLUSION

In this literature review, the optimum approach in rowing from a mechanics

perspective has been identified. The crew should row at a constant velocity

throughout the whole race. However, from a practical sense, this is not the

optimum because rowing is not only based on mechanics. It also involves the

rowing crews’ physiology and psychology. It has also been established that

efficiency is one of the most crucial aspects in rowing, especially when the physical

capacity of the crews are very similar. However, there is no standard or

comprehensive way to monitor and quantify rowing efficiency. Many researchers

have found different methods to assess rowing technique and like many sports,

there is no such thing as the definitive method to identify good technique. It was

found that there was a very limited amount of publications on using accelerometers

to measure rowing motion and virtually none on the methodology of using

acceleration data for rowing technique assessment. Therefore, it is believed that

examining the use of accelerometers as a tool for rowing technique assessment

and understanding how the shell acceleration trace is generated is a contribution to

knowledge in rowing biomechanics. Several researchers have constructed rowing

models and use them to study rowing technique. These models all have their

merits and purposes. It was identified that none of these models looked at how

changes in the propulsion, resistance and rower motion affected the shell

acceleration trace, which reflects the resultant force on the rowing system. This

particular aspect is identified as a subject that should be researched. Chapter 3 will

discuss the development of an improved calibration technique and the static

measurement testing for the triaxial accelerometer.

2.6 REFERENCES

Alexander, FH 1925, 'The theory of rowing', in Proceedings of the University of Durham Philosophical Society, pp. 160-79. Asami, T, Adachi, N, Yamamoto, K, Ikuta, K & Takahashi, K 1977, 'Biomechanical analysis of rowing skill', in E Asmussen & K Jorgensen (eds), Sixth International Congress of Biomechanics, Copenhagen, Denmark, vol. B, pp. 109-14.

54

Atkinson, WC 2001, Modeling the dynamics of rowing - A comprehensive description of the computer model ROWING 9.00, viewed 1 May 2004, <http://www.atkinsopht.com/row/rowabstr.htm>. Baudouin, A & Hawkins, D 2004, 'Investigation of biomechanical factors affecting rowing performance', Journal of Biomechanics, vol. 37, no. 7, pp. 969-76. Baudouin, A, Hawkins, D & Seiler, S 2002, 'A biomechanical review of factors affecting rowing performance', Br J Sports Med, vol. 36, no. 6, pp. 396-402. Brearley, M & de Mestre, NJ 1996, 'Modelling the rowing stroke and increasing its efficiency', in 3rd Conference on Mathematics and Computers in Sport, Bond University, Queensland, Australia, pp. 35-46. Cabrera, D, Ruina, A & Kleshnev, V 2006, 'A Simple 1+ Dimensional Model of Rowing Mimics Observed Forces and Motions', Human Movement Science, vol. 25, no. 2, pp. 192-220. Clauser, CE, McConville, JT & J.W., Y 1969, Weight, volume, and centre of mass of segments of the human body, AMRL-TR-69-70, Aerospace Medical Research Library, Aerospace Medical Division, Air Force Systems Command, Wright-Patterson Air Force Base, Dayton, Ohio, <http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0710622>. Dempster, WT 1955, Space requirements of the seated operator : geometrical, kinematic, and mechanical aspects of the body, with special reference to the limbs, WADC-TR-55-159, Wright Patterson Air Force Base, Dayton, OH, <http://deepblue.lib.umich.edu/handle/2027.42/4540>. Dudhia, A 2001, Physics of Rowing, viewed 10 May 2004, <http://www.atm.ox.ac.uk/rowing/physics/>. Ferguson, S 2004, 'Breaking Waves at the Olympics', Dynamics (CD-adapco customer magazine), no. 23, 2004, viewed 2006/12/11, <http://www.cd-adapco.com/press_room/dynamics/23/olympics.html>. Fukunaga, T, Matsuo, A, Yamamoto, K & Asami, T 1986, 'Mechanical efficiency in rowing', European Journal of Applied Physiology, vol. 55, no. 5, pp. 471-5. Hase, K, Kaya, M, Zavatsky, AB & Halliday, SE 2004, 'Musculo-skeletal loads in ergometer rowing', Journal of Applied Biomechanics, vol. 20, no. 3, pp. 317-23. Hawkins, D 2000, 'A new instrumentation system for training rowers', Journal of Biomechanics, vol. 33, pp. 241-5.

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Hill, H 2002, 'Dynamics of coordination within elite rowing crews: evidence from force pattern analysis', Journal of Sports Sciences, vol. 20, no. 2, pp. 101-17. Hoerner, SF 1965, Fluid-dynamic drag, S. F. Hoerner, New York. Hofmijster, M, De Koning, J & Van Soest, AJ 2010, 'Estimation of the energy loss at the blades in rowing: Common assumptions revisited', Journal of Sports Sciences, vol. 28, no. 10, pp. 1093 - 102. Hofmijster, MJ, Landman, EHJ, Smith, RM & Van Soest, AJK 2007, 'Effect of stroke rate on the distribution of net mechanical power in rowing', Journal of Sports Sciences, vol. 25, no. 4, pp. 403 - 11. Hofmijster, MJ, Van Soest, AJ & De Koning, JJ 2008, 'Rowing Skill Affects Power Loss on a Modified Rowing Ergometer', Medicine & Science in Sports & Exercise, vol. 40, no. 6, pp. 1101-10 10.249/MSS.0b013e3181668671. —— 2009, 'Gross Efficiency during Rowing Is Not Affected by Stroke Rate', Medicine & Science in Sports & Exercise, vol. 41, no. 5, pp. 1088-95 10.249/MSS.0b013e3181912272. Jones, CJFP & Miller, CJN 2002, The Mechanics and Biomechanics of Rowing, viewed 2004/10/19 2004, <http://www.yorkshirerowing.co.uk/biomechanics.htm>. Kleshnev, V 1999, 'Propulsive efficiency of rowing', in RH Sanders & BJ Gibson (eds), 17th International Symposium on Biomechanics in Sports, Edith Cowan University, Perth, Western Australia, Australia, pp. 224-8. —— 2000, 'Power in rowing', in Y Hong, DP Johns & R Sanders (eds), 18th International symposium on biomechanics in sports, Chinese University of Hong Kong, Hong Kong, pp. 662-6. —— 2001a, 'Racing strategy in rowing during Sydney Olympic games', Australian Rowing, vol. 24, no. 1, 2001/04, pp. 20-3, viewed 2004/06/24, <http://www.coachesinfo.com/index.php?option=com_content&view=article&id=393:racingstrategy-article&catid=107:rowing-general-articles&Itemid=207 http://www.biorow.com/Papers_files/2000RaceStrat.pdf>. —— 2001b, 'Stroke rate vs distance in rowing during the Sydney Olympics', Australian Rowing, vol. 24, no. 2, 2001/09, pp. 18-22, viewed 2004/06/24, <http://www.coachesinfo.com/index.php?option=com_content&view=article&id=394:strokerate-article&catid=107:rowing-general-articles&Itemid=207>. —— 2005, Biorow.com, viewed 2006/06/01, <http://www.biorow.com>. Kuchler, M & Gföhler, M 2003, 'Development of a biomechanical model of the human body including the upper and the lower extremities used to simulate the

56

motion on a rowing ergometer - The inverse dynamic problem', in International Society of Biomechanics XIXth Congress, Dunedin, New Zealand, pp. 122-5. Lazauskas, L 1997, A performance prediction model for rowing races, viewed 2004/05/01, <http://www.cyberiad.net/library/rowing/stroke/stroke.htm>. —— 2004, Michlet rowing 8.08, viewed 2004/12/01 2004, <http://www.cyberiad.net/library/rowing/rrp/rrp1.htm>. Leroyer, A, Barré, S, Kobus, J-M & Visonneau, M 2008, 'Experimental and numerical investigations of the flow around an oar blade', Journal of Marine Science and Technology, vol. 13, no. 1, pp. 1-15. Lin, A, Mullins, R, Pung, M & Theofilactidis, L 2003, Application of accelerometers in sports training, viewed 2004/05/03 2004, <http://www.analog.com/Analog_Root/sitePage/mainSectionContent/0%2C2132%2Clevel4%253D%25252D1%2526ContentID%253D8079%2526Language%253DEnglish%2526level1%253D212%2526level2%253D213%2526level3%253D%25252D1%2C00.html>. Mason, BR, Shakespear, P & Doherty, P 1988, 'The use of biomechanical analysis in rowing to monitor the effect of training', Excel, vol. 4, no. 4, pp. 7-11. McBride, ME 1998, 'The role of individual and crew technique in the enhancement of boat velocity in rowing', PhD thesis, University of Western Australia. Millward, A 1987, 'A study of the forces exerted by an oarsman and the effect on boat speed', Journal of Sports Sciences, vol. 5, no. 2, pp. 93 - 103. Roth, W 1991, 'Physiological-biomechanical aspects of the load development and force implementation in rowing', FISA Coach, vol. 2, no. 4, pp. 1-9. Sanderson, B & Martindale, W 1986, 'Towards optimizing rowing technique', Medicine and Science in Sports and Exercise, vol. 18, no. 4, pp. 454-68. Schneider, E, Angst, F & Brandt, JD 1977, 'Biomechanics in rowing', in E Asmussen & K Jorgensen (eds), Sixth International Congress of Biomechanics, Copenhagen, Denmark, vol. B, pp. 115-9. Smith, RM & Loschner, C 2002, 'Biomechanics feedback for rowing', Journal of Sports Sciences, vol. 20, no. 10, pp. 783 - 91. —— 2004a, Boat orientation & skill level in sculling boats, viewed 2004/06/24 2004, <http://www.coachesinfo.com/index.php?option=com_content&view=article&id=390:boatrotation-article&catid=107:rowing-general-articles&Itemid=207>.

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—— 2004b, Net power production and performance at different stroke rates and abilities during sculling, viewed 2004/06/24 2004, <http://www.coachesinfo.com/index.php?option=com_content&view=article&id=391:netpower-article&catid=107:rowing-general-articles&Itemid=207>. Soper, C 2004, 'Foot-stretcher angle and rowing performance', PhD thesis, Auckland University of Technology, <http://repositoryaut.lconz.ac.nz/theses/3>. Tuck, EO & Lazauskas, L 1996, Low Drag Rowing Shells, viewed 2004/05/01 2004, <http://www.cyberiad.net/library/rowing/misbond/misbond.htm>. van Holst, M 1996, Simulation of rowing, viewed 2010/2/22 2010, <http://home.hccnet.nl/m.holst/report.html>. Wing, AM & Woodburn, C 1995, 'The coordination and consistency of rowers in a racing eight', Journal of Sports Sciences, vol. 13, no. 3, pp. 187 - 97. Young, K & Muirhead, R 1991, 'On-board-shell measurement of acceleration', RowSci, vol. 91-5. Zatsiorsky, VM & Yakunin, N 1991, 'Mechanics and biomechanics of rowing: A review', International Journal of Sport Biomechanics, vol. 7, pp. 229-81.

58

3. ACCELEROMETERS FOR ROWING TECHNIQUE

ANALYSIS

3.1 OVERVIEW

The motivation for using accelerometers for rowing technique assessment is

discussed in section 3.2. This is followed by the presentation of a triaxial

accelerometer calibration technique (Lai et al. 2004) that avoids the systematic

errors that are inherent with conventional calibration technique of aligning with

gravity (Analog Devices Inc. 2000). Section 3.3 provides the background to the

proposed calibration technique and section 3.4 summarises the sources of

errors that contaminates this calibration technique. Section 3.5 explains how the

calibration technique was assessed. The results for the calibration technique

assessment are presented in section 3.6. The accuracy of the triaxial

accelerometer when used for static measurements is assessed in section 3.7.

Finally, section 3.8 concludes this chapter.

3.2 MOTIVATION FOR USING MEMS ACCELEROMETERS FOR

ROWING TECHNIQUE ASSESSMENT

Inertial acceleration sensors have been applied to study biomechanics in many

sports (Anderson, Harrison & Lyons 2002), ranging from swimming (Ichikawa et

al. 2002; Ohgi & Ichikawa 2002) to javelin throwing (Maeda & Shamoto 2002).

The measurement of rowing kinematics is very suitable for triaxial

accelerometer because they are small, self contained and can be sampled at a

high rate, typically in the order of 100 Hz (Lin et al. 2003; Smith, Richard M. &

Loschner 2002); ample to cover the frequency content of rowing kinematics.

The main intention to employ Micro-Electro-Mechanical System (MEMS) inertial

sensors for motion sensing in rowing was because these sensors could be

made into a miniaturised unit and would pose virtually no hindrance to rowing

technique/performance. According to the coaches and rowers at the Australian

Institute of Sport (A Rice 2003, pers. comm., 12 June), they believed that they

could feel the difference in weight with instrumented boats and particularly the

59

drag from the shell velocity impeller sensor. Further, these measurement

systems are definitely not suitable for regattas (international rowing races)

because of their hindrance. For this reason, MEMS inertial sensors became a

very appealing option for technique and performance monitoring during races.

There are basically two types of Micro-Electro-Mechanical System (MEMS)

inertial sensors: accelerometers that measure linear acceleration and

gyroscopes that measure angular rate. Naturally, the accelerometer was

chosen because heading acceleration is much more apparent than rotation in a

rowing shell. The heading shell acceleration is typically ranged within ±1g

(Cabrera, Ruina & Kleshnev 2006; Smith, Richard M. & Loschner 2002; Young

& Muirhead 1991). Smith and Loschner (2004) have measured the boat

orientation of 13 single scullers rowing at four ascending rating steps (20, 24, 28

and above 32 strokes per minute) for 20 strokes. It was found that the range of

motion for the pitch was from 0.3 to 0.5 degrees, the yaw ranged from 0.1 to 0.6

degrees and the roll was the highest of all three dimensions, ranging from 0.3 to

2.0 degrees. Thus, the change in angular rates of the rowing system is very

subtle and it was anticipated that the employment of accelerometers would yield

a better reflection of rowing performance, since the linear motion of the rowing

system is much more observable. At the commencement of this PhD project in

2002, accelerometers were generally smaller, more rugged and less expensive

than gyroscopes (Zorn 2002). The difference in cost between the two types of

sensors was significant. The cost of accelerometers was about US$10 per unit

compared to about US$100 per unit for gyroscopes in 2002.

It was contemplated whether we should combine accelerometers and

gyroscopes into an Inertial Measurement Unit (IMU) or Inertial Navigation

System (INS) because the accuracy would be substantially improved. This

would enable the location and the orientation (i.e., dead reckoning) of the

rowing system to be monitored much more accurately. It was decided that the

complexity for combining accelerometers with gyroscopes and the expensive

cost of gyroscopes meant that it was not ideal for our application at the time.

The chosen option was to incorporate a Global Positioning System (GPS) unit

with the accelerometers. The justifications were that: rowing takes place

60

outdoors (i.e., suitable for GPS); combining GPS with accelerometers is much

more straightforward, since they are both linear kinematics measurements;

there was GPS expertise within the Cooperative Research Centre; rotation of

the rowing system is subtle; and both accelerometers and gyroscopes have

issues with drift, and combining GPS with accelerometers would resolve the

problem with drift.

Combining GPS with accelerometers resolved the problem with drift when the

acceleration measurement was integrated to obtain velocity. This is because

data sampled from accelerometers must be integrated to yield velocity and

displacement, and the integration process accumulates error. Since GPS

measures position, it avoids the integration process, and therefore,

accumulating error. The highest sampling rate for commercially available GPS

units was 10 Hz in 2002, so it was not a viable option on its own to measure

rowing kinematics. Thus, the use of GPS was basically to supplement

accelerometers, as the latter provided the higher temporal resolution needed to

monitor rowing kinematics.

The application of accelerometers required many issues, including calibration

and errors caused by noise and drift, to be resolved. These application issues

were well documented for all the different types of accelerometers (Yazdi, Ayazi

& Najafi 1998). It was widely established that accelerometers are particularly

applicable to inertial navigation given that the application issues could be

resolved (Franco & Nosenchuk 2000; Mao & Gu 2000). The accuracy and

reliability of accelerometers for sporting applications have been established as

satisfactory. Anderson et al. (2002) have compared MEMS accelerometers

(ADXL202) against a motion analysis system (Panasonic AGDP800 broadcast

quality cameras with the Motus 2000 motion analysis software package) and

concluded that the former offered more accurate acceleration data than the

latter. Maeda and Shamoto (2002) have verified that a semi-conductor strain

gauge accelerometer (Kyowa ASP-2000GA) recorded data that were in good

agreement with a piezoelectric accelerometer (Teac 708-type) and a force

sensor (PCB 208A05).

61

The first task in using the accelerometers was calibration. The accelerometers

must be calibrated in order to relate the arbitrary output from the sensors to a

meaningful parameter, which was shell acceleration in this case. An improved

calibration technique for accelerometers is discussed in the next section.

3.3 CALIBRATION TECHNIQUE

Calibration is needed for any sensor to relate the arbitrary sensor output to the

measured variable. The conventional method to calibrate an accelerometer

(Analog Devices Inc. 2000) is by aligning each measurement axis parallel (a = +

9.80 ms-2 and -9.80 ms-2) and perpendicular (a = 0 ms-2) to the Earth’s gravity

vector (Figure 3.1). However, there are inevitable systematic errors in this

approach. First, it is very difficult to achieve exact alignment, especially when it

has to be consistently repeated. Second, the user has to assume that the

accelerometer packaging (usually in the shape of a rectangular prism) axes are

perfectly aligned to the accelerometer’s true axes, which is not true. Analog

Device’s ADXL series of accelerometers, in 2002, specified the alignment error

as up to 1°. Further, there is also the alignment of the accelerometer on the

printed circuit board, as well as the alignment of the printed circuit board inside

the packaging for application. Thus, there are multiple causes for alignment

error to occur and the assumption that the user is able to align the

accelerometer’s sensing axes to the gravity vector exactly is the problem.

Figure 3.1: Conventional calibration technique for accelerometers. The z-axis is being

calibrated in the figure. This process is repeated for the other two axes.

62

An improved accelerometer calibration technique was employed that eliminated

the need to have exact alignment to the gravity vector. This technique is based

on the principle that when the triaxial accelerometer is stationary the vector sum

of acceleration from the three orthogonal sensing axes is equal to the gravity

vector, as illustrated in Figure 3.2 and represented in Equation 3.1. The method

requires 6 static measurements (i.e. the triaxial accelerometer had to be

stationary) at 6 different orientations to determine the 3 scale factors and 3

offsets for the x, y and z axes, as described in Equation 3.2. That is, six

measurements to set up six equations to solve for the six unknowns.

2222

zyxaaag ++=

( 3.1 )

where g is the gravity vector, [0 -9.80 0] ms-2, in the global 3 dimensional

Cartesian coordinate system.

xa , y

a , za are the acceleration magnitudes as measured by the triaxial

accelerometer’s three orthogonal axes (i.e., local 3 dimensional

Cartesian coordinate frame, which can translate and rotate freely within

the global coordinate system ).

2

2

2

2

−

+

−

+

−

=

z

zz

y

yy

x

xx

s

ov

s

ov

s

ovg

( 3.2 )

where g is the gravitational acceleration (set to 9.80 ms-2)

xv is the x-axis sensor arbitrary output (likewise for y

v and zv )

xo is the x-axis sensor zero input - output offset (likewise for y

o and

zo )

xs is the x-axis sensor output scale factor (likewise for y

s and zs )

63

Figure 3.2: Calibration of the triaxial accelerometer using the principle that the vector

sum of the three axes’ inputs equals to the gravity vector. The calibration technique

requires six measurements to resolve the six unknowns: scale factors and offsets in all

three axes.

This approach have also been used by Lötters et al. (1998) for in-use calibration

of triaxial accelerometer in medical applications. The accelerometer unit was

programmed to re-calibrate itself (without any manual intervention) consistently

to overcome the problem of drift of the scale factors and offsets. Whenever the

unit detected a quasi-static state (i.e. the triaxial accelerometer was established

as stationary after satisfying some specified conditions), it stored the

acceleration data until there was sufficient information to resolve the three scale

factors and three offsets. For the rowing application, it was decided that the

calibration should be carried out manually, while the software should only

provide the user with a step-by-step calibration procedure and processing of the

data. The manual intervention was maintained because the stationary

requirement of the accelerometers would be better controlled, therefore,

resulting in a more accurate calibration.

Six gravity measurements were taken with the triaxial accelerometer and the

data was substituted into Equation 3.2 to determine the scale factors and

offsets for the three axes. The variations in the measured data were resolved by

g

x

y

z

2222

zyxaaag ++=

x

y

z

x y

z

x

y z

x

y

z

x

y

z

64

taking an average of a few seconds worth of data, which were manually

checked to ensure that there was no drift. Since Equation 3.2 is non-linear, it

cannot be solved using linear methods such as Gaussian elimination or LU

decomposition. The Generalised Newton-Raphson method was chosen to

resolve the non-linear equations, which amounts to finding the zeros of

continuously differentiable functions. The two distinct requirements for the

Generalised Newton-Raphson method are that the system of equations is

analytically differentiable (or at least the derivative could be represented by a

series) and a set of initial values that is close to the solution could be obtained.

Both of these requirements could be fulfilled for this application. Furthermore,

this method has a high computational efficiency as a result of its fast quadratic

convergence to the solution, which was found to be advantageous when

calibrating the triaxial accelerometer. For these reasons, the method was

employed for the application.

The Generalised Newton-Raphson method (Cheney & Kincaid 1985) is based

on a Taylor Series expansion operated to the first order derivative (Equation

3.3). The left hand side of Equation 3.3 is set to zero to convert it into a root

finding problem, as shown in Equation 3.4. In the case of the triaxial

accelerometer calibration, the system of equations had six unknown variables,

three offsets and three scale factors and required six sets of measurement data

to provide a solution, as shown in Equation 3.5. In matrix form and with the

substitution of the scale factors and offsets, the system of equations became

Equation 3.6.

( ) ( )

( )

x

xfhxfhxf

∂

∂+≈+

( 3.3 )

where ( )xf is a generalised function

h is the small correction to the root and is used to measure the

convergence to a solution

( )

x

xfhxf

∂

∂=− )(

( 3.4 )

65

( )( ) ( ) ( )

( )( ) ( ) ( )

( )( ) ( ) ( )

6

6216

6

2

6216

2

1

6216

16216

6

6212

6

2

6212

2

1

6212

16212

6

6211

6

2

6211

2

1

6211

16211

,...,,

...

,...,,,...,,

,...,,

,...,,

...

,...,,,...,,

,...,,

,...,,

...

,...,,,...,,

,...,,

x

xxxfh

x

xxxfh

x

xxxfhxxxf

x

xxxfh

x

xxxfh

x

xxxfhxxxf

x

xxxfh

x

xxxfh

x

xxxfhxxxf

∂

∂

++

∂

∂

+

∂

∂

=−

∂

∂

++

∂

∂

+

∂

∂

=−

∂

∂

++

∂

∂

+

∂

∂

=−

M

( 3.5 )

where each equation (i.e., 621

,,, fff K ) corresponds to each of the six

measurements needed to solve for the six unknowns (i.e., three offsets and

three scale factors of the triaxial accelerometer, 621

,,, xxx K ).

( )

( )

( )

( )

( )

( )

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

=

−

6

5

4

3

2

1

666666

555555

444444

333333

222222

111111

6

5

4

3

2

1

,,,,,

,,,,,

,,,,,

,,,,,

,,,,,

,,,,,

h

h

h

h

h

h

s

f

s

f

s

f

o

f

o

f

o

f

s

f

s

f

s

f

o

f

o

f

o

f

s

f

s

f

s

f

o

f

o

f

o

f

s

f

s

f

s

f

o

f

o

f

o

f

s

f

s

f

s

f

o

f

o

f

o

f

s

f

s

f

s

f

o

f

o

f

o

f

sssooof

sssooof

sssooof

sssooof

sssooof

sssooof

zyxzyx

zyxzyx

zyxzyx

zyxzyx

zyxzyx

zyxzyx

zyxzyx

zyxzyx

zyxzyx

zyxzyx

zyxzyx

zyxzyx

( 3.6 )

where ( )T

ffffff654321

,,,,, is the function vector

( )T

hhhhhh654321

,,,,, is the correction vector

zyxzyxsssooo ,,,,, are as defined in Equation 3.2

Equation 3.2 was rearranged to Equation 3.7, so that it could be substituted into

Equation 3.6 to solve for the three offsets and scale factors of the triaxial

accelerometer. The system of equations in Equation 3.6 was solved to find the

corrections to the six unknowns, i

h . The chosen exit criteria for the iterative

process were that the root mean square of the elements in the correction vector

converged to lower than 0.01 ( 01.0

2

6

2

2

2

1

<+++ hhh L ) AND the absolute value

66

of the elements in the function vector converged to below 0.005

( 005.0,,,

621

<fff K ). The offsets and scale factors were found to be around

490 and 6.5 Analogue-Digital-Converter units, respectively. Thus, when the

correction vector converged to lower than 0.01, the order of magnitude for the

correction would be lower than 0.15% (that is, 0.01/6.5×100% is 0.15%).

Similarly, when the function vector converged to below 0.005, the x, y and z

components of the acceleration measurement matched the gravity vector of

9.80 ms-2 to an accuracy of 0.005% (that is, referring to Equation 3.7,

difference/actual × 100% = 0.005/9.82 × 100% is 0.005%). Thus, the numerical

process was stopped when the change in the correction vector was negligible

and the function vector was sufficiently close to zero. Further, these exit criteria

were chosen to be significantly smaller in comparison to the absolute error and

noise floor of the accelerometer, which are in the order of a few percent. The

maximum estimation error for the scale factors and offsets was limited by these

exit criteria.

0

2

2

2

2

=−

−

+

−

+

−

= gs

ov

s

ov

s

ovf

z

zzi

y

yyi

x

xxi

i

( 3.7 )

3.4 ERRORS IN THE CALIBRATION TECHNIQUE

There were several sources of error that degraded the accuracy in the

evaluation of the scale factors and offsets using the proposed calibration

technique. These included the errors from the accelerometer itself, variations in

gravity and non-orthogonality between the three sensing axes. Each of these

errors is addressed below.

3.4.1 ERRORS FROM THE ACCELEROMETER

Noise in the acceleration sensor presented an erroneous signal to the

recordings, and thus, decreased the accuracy of the scale factor and offset

evaluation. This error is prevalent to all calibration techniques. The

accelerometers used were Analog Devices’ ADXL202JE with a typical noise

density of 200mg√Hz rms (Analog Devices Inc. 2000). The 3 dB bandwidths of

the accelerometers were set at 2.26 Hz, therefore, the rms noise level was 0.38

67

mg (milli-gravity) and the peak to peak noise estimate 95% probability (rms × 4)

was 1.52 mg. The highest resolution that the ADXL202JE was capable of

achieving was 0.4 mg. Non-linearity in the accelerometer’s output also

contributed to the inaccuracy in the calibration. The non-linearity of the

ADXL202JE was 2 % of the full scale according to the data sheet. Thus, non-

linearity and the, relatively lower, error due to noise contributed to the

calibration error, which consequently set the limit on the accuracy of the

acceleration measurements.

3.4.2 VARIATIONS IN THE GRAVITY FIELD VECTOR

The variation in gravity presents the problem of a calibration mechanism that

change in space and time. Temporal based variations of the Earth's gravity field

are caused by various complex phenomena including lunar-solar tides,

atmospheric and oceanic mass redistribution, variations in groundwater storage

and snow cover/ice thickness, earthquakes, post-glacial rebound in the Earth's

mantle, long-term mantle convection and core activities, and other geophysical

phenomena (Chao 1993). Spatial based variations of the Earth’s gravity field

include latitude variation (caused by the ellipsoidal shape and the rotation of the

earth), elevation variation (caused by the increased distance between the

Earth’s centre and the observation point) and topographic effects (e.g. the

observation point is inside a cave hundreds of metres below sea level or at the

top of a mountain thousands of metres above sea level)(Telford, Geldart &

Sheriff 1990).

The Earth's gravitational acceleration is approximately 980 gal, where a gal is

defined as a centimetre per second squared (i.e. 1g = 9.80 ms-2 = 980 gal =

980000 mgal) (Telford, Geldart & Sheriff 1990; Wahr 1996). Table 3.1

summarises the order of magnitude for some of the sources of variations that

cause the Earth’s gravity field to vary. As can be seen in Table 3.1, the order of

magnitude for the sources of variations of the Earth’s gravity field is below the

highest resolution of the ADXL202JE (0.4 mg or 392 mgal) under normal

circumstances for the rowing application. That is, the standard 2 km rowing

races would not be subjected to any dramatic change, both spatial and

temporal, in the local gravity vector. So, the change in gravity field vector is of

68

Table 3.1: Summary of the order of magnitudes for some of the sources of variations that affect the Earth’s gravity field.

Source of variations Order of magnitude Reference/Description

Tidal variations ± 0.1 mgal (Morrison, Gasperikova & Washbourne 2004)

Latitude variations φ2sin817.0≈

ds

dg

(mgal/km)

where φ is latitude (°) and ds

dg is the change in gravitational acceleration from the

latitude location (mgal/km) (Morrison, Gasperikova & Washbourne 2004)

At a latitude of 45°, 817.0=

ds

dg mgal/km, i.e. gravity changes by approximately 0.01

mgal every 12 m near the latitude location of 45°.

Gravity is less at the equator than at the poles by about 5 gal (Morrison, Gasperikova

& Washbourne 2004; Telford, Geldart & Sheriff 1990; Wahr 1996).

Elevation variations -0.308 mgal/m at

the equator

(Morrison, Gasperikova & Washbourne 2004; Wahr 1996)

Seasonal

groundwater

movement,

atmospheric

processes and polar

motion.

< ± 0.01 mgal Peak to peak gravity variations

(Lambert et al. 1995)

69

little concern in rowing, and other sports that are short term (e.g., several hours

duration) and in a confined geographical area (e.g., less than 50 km radius with

no dramatic change in terrain).

3.4.3 NON-ORTHOGONALITY BETWEEN THE THREE SENSING

AXES

Finally, the x, y and z axes cannot be exactly mutually orthogonal in practice

and this introduced errors into the measurement. This type of error is termed

cross axis sensitivity error and it affected the accurate evaluation of the 3 scale

factors and 3 offsets, and therefore, all measurements made with the triaxial

accelerometer. According to the data sheet, the typical alignment error between

the x and y axes was 0.01º, which was sufficiently accurate for the rowing

application. However, the z axis of the triaxial accelerometer was obtained by

soldering an ADXL202JE on its side on the printed circuit board (PCB), which

was susceptible to several alignment errors. First, the z-axis accelerometer

(soldered on its side) and the x-y accelerometer (placed level on the PCB)

might not have been perfectly orthogonal because of size of components and

hand assembly process. Second, the data sheet specified that the alignment

error between the true and indicated (i.e. packaging) axis of sensitivity was

typically ± 1º. Third, since the z-axis accelerometer was on its side, there might

have been a slight possibility that it was being flexed during application, and

therefore, contributed to further inaccuracy in the calibration. Typical errors that

arose from the non-orthogonality between the x, y and z axes are illustrated in

Figure 3.3.

70

Figure 3.3: Errors due to the non-orthogonality between the sensing axes (x’, y’, z’) and

the reference axes (x, y, z).

Figure 3.3 illustrates the steps to determine the non-orthogonality error. First,

one of the three axes must be chosen as the reference axis that contains no

error (this was chosen to be the x axis), so that the number of unknowns are

reduced to a minimum. Next, the second axis is chosen (y axis) and the non-

orthogonality between the x and y’ axes within their plane (x-y plane) is taken

into account by evaluating the projection of the acceleration vector onto the y’

axis. Finally, the third axis (z-axis) takes into account the non-orthogonality

between the x and z axes, and y and z axes. Again, the difference is

determined by evaluating the projection of the acceleration vector onto the z’

axis. Table 3.2 summarises the difference in the measurement between a

triaxial accelerometer with an orthogonal set of axes and one that has a non-

orthogonal set of axes.

γγβγβ sincossincoscos

'

'

zyxaaa

az

z

++

=•

αα sincos

'

'

yxaaa

y

y+=•

x

y

z

y’

z’

a

ax ay

az

α

β

γ

71

Table 3.2: Summary of the difference in measurement between an orthogonal and a non-

orthogonal triaxial accelerometer.

Orthogonal Non-orthogonal

x x

y y’

αα sincos

'

'

yxaaa

y

y+=•

where ( ) °=−∠+ 90'yyα

z z’

γγβγβ sincossincoscos

'

'

zyxaaaa

z

z++=•

where ( ) °=−∠+−

90'

planexyzyβ

and ( ) °=−∠+ 90'zzγ

Ideally, α, β and γ should all be 90º, in which case the non-orthogonal outputs in

Table 3.2 would reduce to the orthogonal outputs. A simple simulation was

carried out to get an indication of the magnitude of the calibration error due to

the non-orthogonality between the sensing axes. The simulation used the

Monte Carlo method to generate a million uniformly distributed pseudo-random

acceleration vectors (within ± 2g) and used the equations in Table 3.2 to

generate the non-orthogonal x, y and z values to quantify the error. Specifically,

the difference between each orthogonal set of values and its corresponding

non-orthogonal set of values was evaluated as an error percentage. As a simple

case, the non-orthogonal errors were assumed to equal to one degree for all

three planes (i.e. α= β = γ = 89°), and the simulation results indicated that the

average measurement error for any acceleration vector was 0.56 %. The non-

orthogonal errors for the triaxial accelerometer were actually closer to α error of

1°, β error of 1° and γ error of 3°. In this case, the simulation indicated that the

mean measurement error for an acceleration vector would be 2.08 %.

Misalignment is an inherent error that is very difficult to factor out, especially in

the case here when two dual-axis accelerometers were used to make up the

72

third axis. However, from year 2006 onwards three-axis accelerometers were

readily available and were comparable in price to single and dual axis

accelerometers. Thus, the uncertainty in the third axis was significantly

improved with advanced accelerometer technology. It is theoretically possible to

make additional calibration measurements to solve for the non-orthogonality

error between the x, y and z axes. However, this idea was not investigated for

this PhD thesis.

3.5 CALIBRATION TECHNIQUE ASSESSMENT

The calibration technique was tested by manually calibrating the triaxial

accelerometer a few times per day over several days. Table 3.3 is the

calibration log showing exactly when the calibrations were conducted. The

triaxial accelerometer was always calibrated in the same room at a fixed spot on

a bench (within a 5 cm radius), so the spatial variation in the gravity field vector

was negligible. The room temperature was consistent at 20 ± 3 ºC.

Table 3.3: Calibration log.

Calibration

number

Date Time (hh:mm)

1–6 2003-10-15 19:16,19:19,19:23,19:26,19:29,19:32

7–11 2003-10-16 14:46,14:48,14:51,14:59,17:27

12–17 2003-10-17 12:03,16:41,16:44,16:47,16:58

18–23 2003-10-21 14:42,14:46,14:50,14:53,14:55,14:57

24–29 2003-10-22 14:14,14:17,14:20,14:22,14:24,14:33

30–37 2003-10-23 17:09,17:12,17:14,17:16,17:18,17:20,17:22,17:25

38–42 2003-10-24 19:18,19:20,19:23,19:27,19:29

43–48 2003-10-31 16:33,16:36,16:39,16:41,16:43,16:45

The precision of the calibration technique and the calibration accuracy were

both assessed. First, the precision of the calibration technique was assessed by

using each of the 48 evaluated sets of scale factors and offsets to check how

close each set re-calculated their six gravity measurements to the assumed

value of 9.80 ms-2. The results are presented in section 3.6.3.

73

Next, the calibration accuracy was assessed and the results are presented in

section 3.7. The triaxial accelerometer was calibrated 48 times and since each

calibration consisted of six gravity measurements, a total of 288 gravity

measurements were made. For each of the 288 gravity measurements, the

analogue-to-digital units were recorded. Using the 48 sets of calibration scale

factors and offsets, each of the 288 gravity measurements were converted from

analogue-to-digital units to acceleration, ms-2 (i.e., 288 acceleration values for

each of the 48 calibrations). If the calibration was accurate, it produced a set of

scale factors and offsets that calculated the vector sum of the x, y and z axes to

be very close to 9.80 ms-2 for all 288 gravity measurements.

Effectively, this calibration accuracy assessment also quantified the accuracy of

the triaxial accelerometer when used for static measurement, because the

triaxial accelerometer was basically measuring a constant acceleration (i.e.

gravity) for 288 times. The accuracy of EACH set of evaluated scale factors and

offsets was dependent on whether the individual calibration was performed

accurately. On the other hand, the accuracy of ALL the sets of evaluated scale

factors and offsets was dependent on the accuracy of the triaxial accelerometer.

In other words, if the triaxial accelerometer was only subjected to a negligible

amount of combined error during calibration, then the triaxial accelerometer

would have measured the gravity magnitude as (the assumed value of) 9.80

ms-2 no matter which set of evaluated scale factors and offsets it was using.

The combined error included analogue-to-digital quantisation error, alignment

error, noise, non-linearity, non-orthogonality, and calibration error (calibration

cannot possibly be free from the aforementioned errors and all measurements

are contaminated with this inherent calibration error). As it was difficult to

resolve the combined effect of all these errors, quantifying the combined error

directly with static measurements was a more straightforward approach.

3.6 CALIBRATION TECHNIQUE RESULTS

The results for the calibration technique are presented below. First, section

3.6.1 presents the rate of convergence for solving the accelerometer offsets and

scaling. This is followed by section 3.6.2, which discusses the variations in the

74

device offsets and scaling. Finally, the precision of the calibration technique is

assessed in section 3.6.3.

3.6.1 RATE OF CONVERGENCE

Figure 3.4: Offset calibration of the triaxial accelerometer.

Figure 3.5: Scale factor calibration of the triaxial accelerometer.

Figure 3.4 and Figure 3.5 show the rate of convergence of the Generalised

Newton-Raphson method in solving the scale factors and offsets for the triaxial

accelerometer (Equation 3.6). As can be seen, it only took five iterations for the

scale factors and offsets to converge to the criteria of 01.0

2

6

2

2

2

1

<+++ hhh L

75

and 005.0,,,

621

<fff K as discussed in section 3.3, which only took 1.04 ms

on average for the 48 calibrations. There were only 3 cases, when there were

connection problems with the electronics, which took longer than 5 iterations to

converge to the chosen exit criteria. One of the main criteria for using the

Generalised Newton-Raphson method is that the initial guess for the scale

factors and offsets must be relatively close to the true value or else the

iterations will diverge from the solutions. Thus, the initial guess could be based

on the data sheet estimation or a calibration using the conventional gravity

alignment technique. The initial guess only needs to be obtained once for the

triaxial accelerometer, since it is unlikely that scale factors and offsets differ

dramatically throughout its application life.

3.6.2 VARIANCE IN THE OFFSETS AND SCALE FACTORS

Figure 3.6 and Figure 3.7 show the evaluated offsets and scale factors for each

of the calibration sessions (described in Table 3.3), respectively. Table 3.4

tabulates the mean and standard deviation for the offsets and scale factors for

all the calibration sessions.

Figure 3.6: Offsets throughout the calibration sessions.

76

Figure 3.7: Scale factors throughout the calibration sessions.

From Figure 3.6 and Figure 3.7, it is apparent that the z-axis acceleration

measurement had the largest variance. This z-axis measurement corresponded

to the ADXL202JE integrated-circuit chip soldered on its side (as the

ADXL202JE chips were dual axis accelerometers). As expected, this axis was

susceptible to the largest alignment error, therefore, the standard deviation was

the largest for both its offset and scale factor (see Table 3.4).

Table 3.4: Mean and standard deviation

for the offsets and scale factors.

Symbols are as defined in Equation 3.2

Factor Mean Standard

deviation (σ)

xo 488.72 1.4311

yo 484.22 1.0792

zo 494.80 4.3109

xs 6.6672 0.0374

ys 6.6750 0.0406

zs 6.5013 0.1331

Table 3.5: Mean and standard deviation

for the offsets and scale factors omitting

the defective calibrations.

Factor Mean Standard

deviation (σ)

xo 488.50 1.2839

yo 484.01 0.8664

zo 493.78 2.6087

xs 6.6679 0.0358

ys 6.6751 0.0409

zs 6.5100 0.1353

77

It was noted that the z-axis measurement was contaminated with calibration

error in calibration number 35 to 37 and 42, which was evident in the offset

values in Figure 3.6, but somehow this was not reflected in the scale factors in

Figure 3.7. The actual reason for the large calibration error in the z-axis

measurement for calibration number 35 to 37 and 42 was due to a bad

connection in the z-axis accelerometer. When the z-axis accelerometer had a

faulty connection, the standard deviation of the gravity measurement error was

measured as 0.69 % (ideally, gravity should be measured consistently as 9.80

ms-2, and therefore, standard deviation is zero and the error percentage is also

zero). On the contrary, when the z-axis accelerometer was working properly,

the standard deviation of the gravity measurement error was reduced to 0.38 %.

This problem with the z-axis was highly susceptible, due to the difficulty in

producing a good solder joint with the accelerometer instrumented on its side.

Omitting the four defective calibrations, the mean and standard deviations were

recalculated and shown in Table 3.5. The major notable differences between

Table 3.4 and Table 3.5 were the reduced standard deviations of the offsets for

all three axes. This indicated that the calibration error in the z-axis affected the

determination of the offset more than the scale factor. On the other hand, it is

suspected that the alignment error (i.e., the z-axis accelerometer not orthogonal

to the x and y axes accelerometer) had a more significant effect on the accurate

estimation of the z-axis scale factor. Also, the reduction in standard deviation for

the x-axis and y-axis offsets, when the four defective calibrations were omitted,

indicated that error in only one axis affected the calibration of all three axes (i.e.,

all the scale factors and offsets).

3.6.3 PRECISION OF THE CALIBRATION TECHNIQUE

The precision of each calibration was assessed by using its evaluated scale

factors and offsets to check how close they re-calculated their respective six

gravity measurements in analogue-to-digital units to the acceleration value of

9.80 ms-2. Figure 3.8 shows the self-verification for each of the calibrations.

There were six gravity measurements in each calibration, so six data points

(numbered 1 to 6 with different markers for the six orientations) were plotted to

each calibration number. As can be seen in Figure 3.8, all the calibrations

78

evaluated the gravity vector magnitude very close to the assumed value of 9.80

ms-2. For the worst case, calibration number 36 orientation number 2, the value

was within 2 × 10-6 ms-2 from 9.80 ms-2, which meant the error was less than

one in 4.9 million. Figure 3.8 provided an indication of how well the calibration

algorithm converged to accurate values for the scale factors and offsets ONLY

with respect to its six measurements. That is, the calibration algorithm

determined the scale factors and offsets that satisfied the 6 equations to a high

precision, despite the possibility that these 6 equations (i.e. each calibration

data set) could have been contaminated with large amount of noise and

alignment errors. This important aspect was uncovered by the satisfactory self-

verification results for calibration number 35 to 37 and 42 in Figure 3.8, even

though it was known that the connection problem in the z-axis produced a

significant amount of error during these calibrations. Thus, this confirmed that a

limitation with the calibration technique is that error in only one axis affects the

evaluation accuracy of all the scale factors and offsets.

Figure 3.8: Self-verification of the calibrations. The precision of each calibration was

assessed by using its evaluated scale factors and offsets to check how close they re-

calculated their respective 6 gravity measurements in analogue-to-digital units to the

gravity magnitude of 9.80 ms-2

. The 6 measurements (numbered 1 to 6 with different

markers) were plotted against its own calibration number. The vertical axis is the

difference from the gravity magnitude of 9.80 ms-2

in units of 10-6

ms-2

.

79

The analysis so far has not provided any information on the accuracy of the

scale factors and offsets. The accuracy of the calibration technique is examined

in section 3.7 below, which coincidently, also examined the static measurement

error for the triaxial accelerometer, since they are interrelated.

3.7 ACCURACY OF THE TRIAXIAL ACCELEROMETER WHEN

USED FOR STATIC MEASUREMENTS

In order to assess the accuracy of each calibration, each of the 48 sets of

evaluated scale factors and offsets was used to convert the 288 gravity

measurements in analogue-to-digital units to acceleration, ms-2, and the

accuracy of each calibration was dependent on how close it calculated the

gravity acceleration magnitude to the assumed value of 9.80 ms-2. Since the

calibrations are actually static acceleration measurements, it also assessed the

static measurement accuracy of the triaxial accelerometer.

Figure 3.9: Verification of the calibration accuracy. The accuracy of the 48 calibrations

was assessed by using their scale factors and offsets to calculate the gravity vector

magnitude with all 288 gravity measurements (from the calibration data).

Figure 3.9 shows the accuracy of each of the 48 calibrations. The graph shows

the mean and standard deviation of all 288 gravity magnitude estimations for

each of the 48 calibrations. That is, each data point and corresponding error

bars represent 288 estimations of the gravity magnitude. As expected, the

mean for all the calibrations were fairly close to 9.80 ms-2, ranging from 9.64 to

80

10.40 ms-2, with varying standard deviations ranging from ± 0.43 to ± 1.50 ms-2.

Figure 3.9 confirmed that calibration number 35 to 37 and 42 were not accurate

calibrations (already discussed in section 3.6.2 and 3.6.3), as their mean were

all above 10 ms-2 and their standard deviations were about double that of the

other calibrations. Omitting those four defective calibrations, since it was known

that there were connection problems with the z-axis accelerometer, the mean

was much closer to 9.80 ms-2, ranging from 9.64 to 9.96 ms-2, and the standard

deviation decreased significantly, ranging from ± 0.43 to ± 0.72 ms-2.

The mean and standard deviation for the best calibration (calibration number

22) was 9.82 ± 0.43 ms-2, which corresponded to an error of 4.6 % from the

assumed gravity magnitude of 9.80 ms-2 (i.e. (9.82+0.43-9.8)/9.8×100%). For

the worst calibration (number 28 – disregarding the four defective calibrations),

the mean and standard deviation was 9.96 ± 0.66 ms-2, which equated to an

error of 8.4 % (i.e. (9.96+0.66-9.8)/9.8×100%). An average of all the means and

standard deviations for the 44 calibrations was taken, which showed that the

average calibration calculated the gravity vector magnitude to 9.80 ± 0.51 ms-2.

This equated to an error of 5.2 % (i.e. (9.80+0.51-9.8)/9.8×100%) in using the

triaxial accelerometer for static measurement. Although the error appeared to

be quite large, one has to bear in mind that this was the total combined error,

which included analogue-to-digital quantisation error, alignment error, noise,

non-linearity, non-orthogonality, and calibration error. In particular, as

mentioned at the end of section 0, the alignment errors for the triaxial

accelerometer was estimated to be α error of 1°, β error of 1° and γ error of 3°,

which resulted in a 2.08 % error on average in the acceleration vector

measurements. This error in the acceleration vector propagated to the scale

factor and offset determination, therefore, contributed to the error for all

subsequent acceleration measurements.

81


number 22.


number 37.

The remaining of this section highlights how much difference there was in using

the triaxial accelerometer for measurement with a good calibration compared to

a defective calibration. Figure 3.10 shows the gravity measurements when an

accurate set of scale factors and offsets (calibration number 22) was used, and

Figure 3.11 shows that of an inaccurate set (calibration number 37). Calibration

number 22 and 37 were chosen based on the information in Figure 3.9. As can

82

be seen in Figure 3.10, the scale factors and offsets derived from calibration

number 22 consistently evaluated the gravity magnitude fairly close to 9.80 ms-

2, with a mean and standard deviation of 9.82 ± 0.43 ms-2. The large fluctuations

between calibration data set number 200 and 250 in Figure 3.10 were actually

the calibration measurements for calibration session 35 to 37 and 42

(corresponding to calibration data set number 205 to 222 and 247 to 252). The

large amount of error in the z-axis in these calibration sessions is further

reflected here. Calibration number 37 produced a very inaccurate set of scale

factors and offsets as shown in Figure 3.11. The mean and standard deviation

were 10.40 ± 1.50 ms-2, which indicated that the derived set of scale factors and

offsets were unacceptable.

Figure 3.11 confirmed once again that error in only one axis had a critical effect

on the accurate determination of all the scale factors and offsets. This was a

disadvantage with calibrating all three axes simultaneously; however, it is still

less susceptible to error than the conventional calibration technique, which

assumes that each of the three axes is aligned perfectly to the gravity vector

during each measurement. Nevertheless, no matter what calibration technique

is used, the calibration must be sufficiently accurate as the accuracies of all

subsequent measurements are dependent upon it. That is, the evaluated scale

factors and offsets from a defective calibration made all the measurements

erroneous, as illustrated by Figure 3.11. This signified the importance of

checking for peculiarities in the calibration data, such as calibration error due to

a faulty connection. As discussed earlier in this section, the calibration accuracy

of a triaxial accelerometer can be validated by making static measurements of

the gravity vector. If the vector sum of the three axes is not close to the gravity

acceleration magnitude, then the evaluated scale vectors and offsets are not

accurate. Perhaps the most straightforward solution is to make several

calibrations (i.e. redundancy) to identify any peculiarities and reduce the

possibility of introducing large errors.

83

3.8 CONCLUSION

In conclusion, a method of calibrating accelerometers that eliminated the need

to align to gravity had been demonstrated. The calibration method requires the

triaxial accelerometer to be oriented and stationary in 6 different orientations.

The Newton-Raphson method was used to solve the non-linear equations in

order to obtain the scale factors and offsets for the triaxial accelerometer. The

iterative process was fast, with an average of 5 iterations required to solve the

system of equations and only took 1.04 ms on average for the 48 calibrations.

The precision of the derived scale factors and offsets determined from each

calibration session were assessed by using them to re-calculate the gravity

vector magnitude for their own six calibration measurements. The precision was

found to be better than one in 4.9 million.

The accuracy of the 48 sets of derived scale factors and offsets were

determined by using them to calculate the gravity vector magnitude for each of

the 288 calibration measurements (i.e. each calibration consisted of 6 gravity

measurements, so 6 gravity measurements per calibration × 48 calibrations =

288 gravity measurements). On average, the calibrated triaxial accelerometer

measured the gravity vector magnitude as 9.80 ± 0.51 ms-2. This equated to an

error of 5.2 % from the assumed gravity magnitude of 9.80ms-2. This error was

the total combined error for the triaxial accelerometer, which included analogue-

to-digital quantisation error, alignment error, noise, non-linearity, non-

orthogonality, and calibration error. It was found that the accuracy in the

evaluation of the scale factors and offsets was significantly dependent on the

accelerometer measurement error, like any other calibration technique.

Because of the principle behind the proposed calibration technique, it has the

disadvantage that error in only one axis will cause an inaccurate determination

of all the scale factors and offsets. This effect was observed in calibration

number 35 to 37 and 42, when the third sensing axis (i.e. the second dual-axis

accelerometer soldered to its side) had a connection problem and dramatically

affected the accuracy of the calibration. On the other hand, the conventional

method of calibrating an accelerometer by aligning each of the three axes to

84

gravity is still more prone to error because of the practical limitation that

alignment cannot be exact. With the availability and comparable cost of single

package three-axis MEMS accelerometers (from 2006 onwards), the proposed

calibration technique would be much more accurate than the conventional

calibration technique, because there is no need to align the axes of the

accelerometer to the gravity vector.

3.9 REFERENCES

Analog Devices Inc. 2000, 'ADXL202E datasheet', <http://www.analog.com/static/imported-files/data_sheets/ADXL202E.pdf>. Anderson, R, Harrison, AJ & Lyons, GM 2002, 'Accelerometer based kinematic biofeedback to improve athletic performance', in SJH S. Ujihashi (ed.), The 4th International Conference on the Engineering of Sport, Kyoto, Japan, pp. 803-9. Cabrera, D, Ruina, A & Kleshnev, V 2006, 'A simple 1+ dimensional model of rowing mimics observed forces and motions', Human Movement Science, vol. 25, no. 2, pp. 192-220. Chao, BF 1993, 'The Geoid and Earth Rotation', in P Vaníček & NT Christou (eds), Geoid and Its Geophysical Interpretations, CRC Press, pp. 285-98. Cheney, W & Kincaid, D 1985, Numerical Mathematics and Computing, Brooks/Cole Publishing Co. Franco, PC & Nosenchuk, EH 2000, 'Determination of integrated navigation system requirements for a landing craft using off the shelf hardware', in Position Location and Navigation Symposium, IEEE 2000, San Diego, CA, USA, pp. 207-12. Ichikawa, H, Ohgi, Y, Miyaji, C & Nomura, T 2002, 'Application of a mathematical model of arm motion in front crawl swimming to kinematical analysis using an accelerometer', in SJH S. Ujihashi (ed.), The 4th International Conference on the Engineering of Sport, Kyoto, Japan, pp. 645-51. Lai, A, James, DA, Hayes, JP & Harvey, EC 2004, 'Semi-automatic calibration technique using six inertial frames of reference', in D Abbott, K Eshraghian, CA Musca, D Pavlidis & N Weste (eds), Proceedings of the SPIE - The International Society for Optical Engineering, vol. 5274, pp. 531-42. Lambert, A, James, TS, Liard, JO & Courtier, N 1995, 'The role and capability of absolute gravity measurements in determining the temporal variations in the Earth's gravity field', in RH Rapp, AA Cazenave & RS Nerem (eds), G3 Symposium (Global and Gravity Field and Its Temporal Variations), Boulder, Colorado, USA, vol. 116, pp. 20-9.

85

Lin, A, Mullins, R, Pung, M & Theofilactidis, L 2003, Application of accelerometers in sports training, viewed 2004/05/03 2004, <http://www.analog.com/Analog_Root/sitePage/mainSectionContent/0%2C2132%2Clevel4%253D%25252D1%2526ContentID%253D8079%2526Language%253DEnglish%2526level1%253D212%2526level2%253D213%2526level3%253D%25252D1%2C00.html>. Lötters, JC, Schipper, J, Veltink, PH, Olthuis, W & Bergveld, P 1998, 'Procedure for in-use calibration of triaxial accelerometers in medical applications', Sensors and Actuators A: Physical, vol. 68, no. 1-3, pp. 221-8. Maeda, M & Shamoto, E 2002, 'Measurement of acceleration applied to javelin during throwing', in SJH S. Ujihashi (ed.), The 4th International Conference on the Engineering of Sport, Kyoto, Japan, pp. 553-9. Mao, G & Gu, Q 2000, 'Design and implementation of microminiature inertial measurement system and GPS integration', in National Aerospace and Electronics Conference, 2000. NAECON 2000. Proceedings of the IEEE 2000, Dayton, OH, USA, pp. 333-8. Morrison, F, Gasperikova, E & Washbourne, J 2004, The Berkeley course in applied geophysics, viewed 2003/10, <http://appliedgeophysics.berkeley.edu:7057/>. Ohgi, Y & Ichikawa, H 2002, 'Microcomputer-based data logging device for accelerometry in swimming', in SJH S. Ujihashi (ed.), The 4th International Conference on the Engineering of Sport, Kyoto, Japan, pp. 638-44. Smith, RM & Loschner, C 2002, 'Biomechanics feedback for rowing', Journal of Sports Sciences, vol. 20, no. 10, pp. 783 - 91. Smith, RM & Loschner, C 2004, Boat orientation & skill level in sculling boats, viewed 2004/06/24 2004, <http://www.coachesinfo.com/index.php?option=com_content&view=article&id=390:boatrotation-article&catid=107:rowing-general-articles&Itemid=207>. Telford, WM, Geldart, LP & Sheriff, RE 1990, Applied geophysics, Cambridge University Press. Wahr, J 1996, Geodesy and Gravity Course Notes, Samizdat Press, <http://samizdat.mines.edu/geodesy/geodesy.pdf>. Yazdi, N, Ayazi, F & Najafi, K 1998, 'Micromachined inertial sensors', Proceedings of the IEEE, vol. 86, no. 8, pp. 1640-59. Young, K & Muirhead, R 1991, 'On-board-shell measurement of acceleration', RowSci, vol. 91-5.

86

Zorn, AH 2002, 'A merging of system technologies: all-accelerometer inertial navigation and gravity gradiometry', in Position Location and Navigation Symposium, IEEE, pp. 66-73.

87

4 A SINGLE SCULL ROWING MODEL

This chapter is comprised of a book section (Lai, Hayes et al. 2005), the book

includes refereed contributions presented at the Asia-Pacific Congress on

Sports Technology held at Tokyo Institute of Technology in September 2005,

and an abstract presented at the International Society of Biomechanics XXth

Congress 2005 (Lai, James et al. 2005).

4.1 INTRODUCTION

Researchers have investigated the measurement of rowing shell acceleration

for a long time. The earliest publication found on rowing acceleration

measurement was (Young & Muirhead 1991). Shell acceleration is proportional

to the net resultant force on the rowing system and it should reflect the

effectiveness of a rower’s performance. However, even to this day, rowing

coaches are still only analysing the shell velocity, and not both the shell velocity

and acceleration, to gauge a rower’s technique and performance. The shell

acceleration profile must contain additional technical insight, especially when

one remembers that shell acceleration is the rate of change of shell velocity.

A single-scull rowing model was developed to interpret the shell acceleration

data to provide further insight into a rower’s technique. The goal was also to

enable a parameter to gauge the effectiveness of a single sculler to be

extracted. In regards to the interpretation of the shell acceleration data, the

motivation was to learn how the changes in the rower motion and the applied

force affect the shell acceleration profile. None of the existing models (Atkinson

2001; Brearley & de Mestre 1996; Cabrera, Ruina & Kleshnev 2006; Millward

1987; van Holst 1996) have looked at this aspect. This understanding is

essential in order to use the shell acceleration data directly as feedback to the

rowers about their rowing technique.

The single-scull rowing model (Lai, Hayes et al. 2005; Lai, James et al. 2005)

was developed in Matlab®, in which the motion of the rowing system was

represented by a differential equation that will be discussed in section 2.2.5.

The rower model was developed in Matlab SimMechanics in which the rower

88

body segments were modelled in great detail, including length, weight and

inertial properties.

This chapter will present the development of the single-scull rowing model and

some results to assess how well the model represented a real single sculler.

Detailed analysis of the model will be discussed in subsequent chapters.

4.2 DEVELOPMENT OF THE ROWING MODEL

As with any model, boundary conditions, assumptions and simplifications are

made to simplify a real world problem. The conditions for the single-scull rowing

model are listed in Table 4.1 below. The rowing model was composed of two

parts: an equation of motion that was used to simulate the single scull rowing

system (discussed in section 4.2.2) and a rower model that simulated the rower

kinematics (discussed in section 4.2.3).

4.2.1 ASSUMPTIONS

Table 4.1: Rowing model assumptions.

Assumptions Reasons

The rower body could be accurately

represented by a rigid linkage system.

Simplified the complex motion of all

the different body segments.

The anthropometric properties of the

rower body segments could be

accurately represented from cadaver

data, where actual measurements

could not be made from the subjects.

Eliminated the need to directly

measure the inertial properties of each

body segment for the subjects.

The rower did not make any lateral

movement.

Reduced the rower motion to two

dimensions. The legs, trunk and head

of the rower’s body have minimal

lateral movement during the rowing

stroke, while the rower’s arms do have

a significant amount of lateral

movement. The mass of the arms is

small in comparison to the mass of the

rest of the body, so neglecting the

89

lateral movement of the arms should

only have a small effect on the

estimation of the motion of the rower’s

centre of mass.

The rowing shell did not have any

rotational motion.

Simplified the complicated effect of

rotational motion on the forward

motion. Specifically, the variation of

the gravity vector and resistance, due

to rotation, was assumed to have

negligible effect on the acceleration

measurement.

The rower motion could be estimated

from the video data with minimal error

without the use of a motion capture

system by placing markers on the

rower’s body

The measurements were taken on-

water; therefore, it was not viable to

use a motion capture system. In

common to all video analysis, no point

of reference exists to determine the

systematic error, but the random error

was accounted for in section 4.3.3 with

a reliability analysis of the rower body

angles.

The resistive force on the rowing

system could be represented with a

single drag coefficient with minimal

error.

The effort of creating a computational

fluid dynamics model to account for

the complex interaction between the

rowing system and the surrounding

fluid (water and air) would be

extremely substantial. It was decided

that it would be more sensible to first

identify whether there was a need to

model this aspect in such great detail.

No internal energy loss (in the rower’s

body and oar lever system).

The internal losses were ignored

because it would be extremely difficult

to measure them.

90

The oars had infinite stiffness. It has been shown that oar stiffness

has minimal effect on shell velocity

(Atkinson 2001; Cabrera, Ruina &

Kleshnev 2006), so an infinite spring

constant was assumed for the oars to

simplify the oar force calculations.

There was no wind and no water

current during the rowing session.

The constant change in magnitude

and direction of the wind and water

current would not be easy to measure,

so they were ignored. The rowing

sessions were carried out during

relatively calm days when there was

not much wind.

4.2.2 EQUATION OF MOTION FOR THE SINGLE-SCULL ROWING

MODEL

In section 2.2.5, an equation (Equation 2.19) was derived that represents the

motion of a single scull as a result of all the forces acting on it. This differential

equation is reproduced here for convenient reference.

( )

shellrowerrowershellblade

shell

rowershellamvcF

dt

dvmm

_

2

⋅−⋅−=⋅+

( 4.1 )

where shell

m is the mass of the rowing shell (kg)

rowerm is the mass of the rower (kg)

shellv is the absolute velocity of the shell (ms-1)

blade

F is the reaction force at the oar blade’s centre of pressure in the

forward direction (N)

c is the coefficient of drag taking into account both the aerodynamic

and hydrodynamic component

shellrower

a_

is the acceleration of the rower with respect to the shell (ms-2)

91

Equation 4.1 describe rowing shell motion as a result of the propulsive force at

the oar blade, the drag force on the rowing system and the motion of the

rower’s centre of gravity relative to the rowing shell.

The water reaction force at the oar blade in the forward direction is the force

that propels the rowing system. Initially, oar blade force was calculated from

applied oar handle force and oar lever inboard-outboard ratio:

( ) ( )ϕϕ coscos

_

out

in

handlebladeforwardblade

L

LFFF ==

( 4.2 )

where forwardblade

F_

is the forward component of the blade force (N)

blade

F is the reaction force at the oar blade’s centre of pressure (N)

ϕ is the oar angle in the plane parallel to the water surface (°). Zero

degree is perpendicular to the length of the rowing shell.

handleF is the handle force applied by the rower (N)

in

L is the inboard oar length (m)

out

L is the outboard oar length (m)

Using the propulsive force calculated from Equation 4.2, it was found that the

simulated shell acceleration was very different in shape to the measured shell

acceleration and the peak shell acceleration was out by a significant magnitude.

These results will be presented and discussed in section 4.4.1. The discrepancy

between the simulated and measured shell acceleration was due to the

inadequacy of calculating the blade force using Equation 4.2, which in turn was

ascribed to the inadequacy of the assumptions underlying Equation 4.2.

Equation 4.2 reconstructs the blade force on the basis of:

1. measurement of the oar handle force, where only the component normal

to the oar is measured;

92

2. knowledge of the inboard-outboard oar length ratio, which requires an

assumption regarding the point of application of the handle force and the

point of application of the net blade force;



5. the assumption that the blade force has no component in the direction of

the oar.

Thus, a hydrodynamic blade model was used to directly determine the force

acting on the blade. The hydrodynamic blade model intrinsically accounts for

the hydrodynamic phenomenon of slip. To explain the concept of slip, if the oar

blades are leveraging off a solid medium, then there is no slip, however, as

water is fluid and does yield (i.e., accelerate aft), slip must be taken into account.

The hydrodynamics blade force model reconstructs the net blade force on the

basis of:

1. measurement of the oar angle in the plane parallel to the water surface

and shell velocity;

2. knowledge of the outboard oar length, which requires an assumption

regarding the point of application of the net blade force;



Thus, the main difference between Equation 4.2 and the hydrodynamic blade

model is that the latter does not make the assumption that there is no axial

force in the oar.

The hydrodynamic interaction between the oar blades and water is analogous

to the aerodynamic interaction between the wings of an airplane and air. The

propulsive force on the rowing system is actually the forward component of the

water reaction force (Figure 4.1 and Equation 4.3). Equation 4.3 states that the

water reaction force is the vector sum of the oar blade drag and lift forces

(Figure 4.1). The oar blade drag force is opposite in direction (i.e., parallel) to

the oar blade velocity relative to the water and the oar blade lift force is

perpendicular to the oar blade velocity relative to the water.

93

Figure 4.1: Vector diagram of the oar blade slip velocity and the resultant propulsive

force.

2

_

2

__ liftbladedragbladereactionwaterFFF +=

( 4.3 )

where reactionwaterF

_

is the water reaction force (N)

dragbladeF

_

is the oar blade drag force (N)

liftblade

F_

is the oar blade lift force (N)

The equations of the drag and lift forces on the blade are of the form:

2

2

1

_ slipDbladedragbladevCAF ⋅⋅⋅⋅= ρ

2

2

1

_ slipLbladeliftbladevCAF ⋅⋅⋅⋅= ρ

( 4.4 )

where ρ is the water density = 999.1 kg m-3 at 15 °C

bladeA is the blade area in the plane orthogonal to the direction of relative

motion (m2). Note that during the blade entry and exit, when a portion of

the blade is not immersed in water, it is accounted for by multiplying the

area by a fraction as discussed in section 4.4.3 below.

vshell

vslip Fblade_lift

Fblade_drag

Fwater_reaction

Fpropulsive

vshell

ϕ

•

ϕ

α

outL

•

ϕ

94

slip

v is the relative velocity of the blade’s centre of pressure with respect

to water, known as the slip velocity (ms-1)

D

C is the drag coefficient for the oar blade

L

C is the lift coefficient for the oar blade

The drag and lift coefficients are functions of the angle of attack, α , the

angle between the slip velocity and the longitudinal oar axis.

Equation 4.4 indicates that the force acting at the blade’s centre of pressure is a

function of the blade velocity respective to water, also called the slip velocity.

The slip velocity, slip

v , is the vector sum of the contribution of the oar angular

velocity to the velocity vector of the centre of the blade (the term “oar angular

velocity vector” will be used as a shorthand from here on in the thesis), out

L

•

ϕ ,

and the rowing shell velocity vector, shell

v , as shown in Figure 4.1. Note that the

oar angular velocity vector is the velocity of the blade relative to the rowing shell,

while the slip velocity is the velocity of the blade relative to water.

Equation 4.4 is based on the fundamental concept that the application of a

mechanical force between a solid and a fluid occurs at every point on the

surface of the solid body by the means of fluid pressure. For a sectional area of

an object immersed in a fluid, the magnitude of the force acting is given by:

APF ⋅= ( 4.5 )

where F is the resultant force at the pressure centre of the sectional area of

the object (N)

P is the pressure acting normal to the sectional area of the object (Pa)

A is the sectional area of the object (m2)

From Bernoulli’s equation, the dynamic pressure, which is the pressure term

associated with the velocity, v , of the flow of the fluid, is given by:

95

2

2

1 vPdynamic

⋅⋅= ρ ( 4.6 )

where dynamic

P is the dynamic pressure (Pa)

ρ is the fluid density (kg m-3)

v is the relative velocity of the fluid with respect to the object (ms-2)

Combining Equation 4.5 and Equation 4.6, and substituting in a coefficient that

models all of the complex dependencies of shape, inclination and flow

conditions, one would arrive at Equation 4.4. The coefficient representing the

complex dependencies of the object’s shape, angle between the object’s

velocity relative to the fluid and the longitudinal axis of the object’s surface (i.e.,

angle of attack, α in Figure 4.1) and flow conditions (i.e., Reynolds Number for

viscosity and Mach Number for compressibility) is usually determined by

experiments.

The oar blade drag and lift coefficients, D

C and L

C , are functions of the angle

of attack, α . Figure 4.2 and Figure 4.3 show the oar blade drag and lift

coefficients plotted against the angle of attack, respectively. Since there was no

published drag and lift coefficient data for oar blades at the time of their rowing

model development, van Holst (1996) and Atkinson (2001) used the only

available data – for a totally immersed flat plate at various angles of attack from

Hoerner (1965). Atkinson used Hoerner’s data without modification, but van

Holst decided to remove the discontinuities and smoothed the coefficient plots.

The reason for the modification was that van Holst (1996) believed that the

sharp decrease of the coefficients (although a well known phenomenon) at

about 42° was only observed in experiment with the plate in static positions and

that no sudden decrease of the force on the blade is observed during the pull

through in practice because flowing patterns belonging to this decrease have no

time to develop. Cabrera et al. (2006) used the drag and lift coefficient

formulation based on Wang et al. (2004). More recently, Caplan and Gardner

(2005) have developed a new measurement system to determine the fluid

forces generated by the oar blades using quarter scale model oar blades in a

water flume. The determination of the drag and lift coefficients was based on a

96

quasi-static approach, with the oar blade being held static at a range of angles

relative to the fluid flow direction. As the data of Caplan and Gardner were

obtained using a scale model, it should be noted that it is not guaranteed that

drag and lift measurements are scaling-independent. All four sets of coefficients

were used in the rowing model and it was found that the generated propulsive

forces had only minor differences. Lazauskas, through personal communication,

pointed out that he left out the oar blade modelling altogether in his rowing

model (Lazauskas 2004) because he believed that the interaction between the

oar blade and water (i.e., hydrodynamic interaction) is too complex and it should

only be represented with realistic experimental data or detailed computational

fluid dynamics modelling. Nevertheless, with the lack of resources and expertise

to carry out such an experiment or fluid dynamics modelling, it is in the author’s

opinion that one should first find out how close such a simplification can

represent the real phenomenon. Caplan and Gardner’s data on the drag and lift

coefficients (Caplan & Gardner 2005) were chosen for the rowing model

because it was the most “realistic” at the time of the rowing model development.

Figure 4.2: Drag coefficient as a function of the angle of attack from the literature

(Atkinson 2001; Cabrera, Ruina & Kleshnev 2006; Caplan & Gardner 2005; van Holst

1996).

97

Figure 4.3: Lift coefficient as a function of the angle of attack from the literature

(Atkinson 2001; Cabrera, Ruina & Kleshnev 2006; Caplan & Gardner 2005; van Holst

1996).

4.2.3 ROWER MODEL

In order to examine how the rower motion interacts with the shell motion, the

rower was modelled in great detail. That is, the motion of each body segment’s

centre of mass was simulated and combined to determine the motion of the

rower’s centre of mass. This approach enabled the motion of the rower’s centre

of mass to be determined more accurately, in contrast to many of the existing

models (Atkinson 2001; Brearley & de Mestre 1996; Cabrera, Ruina & Kleshnev

2006; Millward 1987; van Holst 1996). This section explains how the rower

model was developed.

The anthropometric properties (length, weight, centre of mass position, and

inertial properties of all the body segments) of a rower were measured where

possible, or otherwise, acquired from anthropometric data in the literature (de

Leva 1996; Winter 2004). Figure 4.4, taken from (Winter 2004), is a diagram

illustrating the average body segment lengths expressed as a fraction of the

body height, H. It was used to calculate the body segment lengths that were not

measured.

98

Figure 4.4: Diagram of the body segment lengths expressed as a fraction of the body

height, H, (Winter 2004).

Table 4.2 summarises the mass and inertial properties of the body segments of

an average female (de Leva 1996). The moment of inertia of each body

segment (see Equation 4.7) is calculated from its radius of gyration, which is a

dimensionless parameter specifying how the mass is distributed around the

centre of mass in a particular rotational axis (assuming constant density). Thus,

three radii of gyration are needed to represent the inertial properties of a body

segment in three dimensions.

( )2

axissegmentsegmentrLmI ⋅⋅=

( 4.7 )

where I is inertia of the body segment (kg m2)

segment

m is the mass of the body segment (kg)

segment

L is the length of the body segment (m)

axis

r is the mean relative radius of gyration of the segment about the

axis under consideration (sagittal, transverse or longitudinal)

0.186H

0.146H

0.108H

0.332H

0.245H

0.246H

0.039H

0.138H

Figure is not to scale.

0.383H

0.191H

99

Table 4.2: Mass and inertial properties of female body segments (de Leva 1996).

Body

segment

(abbreviated

anatomical

location^)

Mass

(fraction of

body

mass)

r sagittal r

transverse

r

longitudinal

Longitudinal

Centre of

Mass*

(fraction of

segment

length)

Trunk

(CERV-

MIDH)

0.4257 0.307 0.292 0.147 0.4964

Upper arm

(SJC-EJC) 0.0255 0.278 0.26 0.148 0.5754

Forearm

(EJC-STYL) 0.0138 0.263 0.259 0.095 0.4592

Hand

(STYL-

DAC3)

0.0056 0.241 0.206 0.152 0.3502

Thigh (HJC-

KJC) 0.1478 0.369 0.364 0.162 0.3612

Shank

(KJC-

SPHY)

0.0481 0.275 0.271 0.094 0.4481

Foot (HEEL-

TTIP) 0.0129 0.299 0.279 0.139 0.4014

Head

(VERT-

CERV)

0.0668 0.271 0.295 0.261 0.4841

^The exact anatomical locations marking the end points of each body segment are abbreviated

and shown in brackets. See (de Leva 1996) for the definitions of the abbreviated anatomical

locations.

*Segment centre of mass positions are referenced either to proximal or cranial endpoints

(origin).

100

On-water rowing data of four Australian national level heavyweight female

rowers were collected. Data was collected during the rowers’ training sessions

ran by Dr. Anthony Rice, a senior sport physiologist at the Australian Institute of

Sport. The subjects were informed and agreed that the data would be used for

research purposes. A large range of anthropometric properties were measured

from the rowers and documented as part of their anthropometric reporting as

athletes at the Australian Institute of Sport. Table 4.3 shows the anthropometric

properties of the subjects that were relevant to the rower model development.

Table 4.3: Measured anthropometric properties of the rowing subjects.

Subject 1 2 3 4

Height (cm) 183.3 177.2 181.2 171.4

Weight (kg) 75.22 71.9 70.7 77.9

Upper arm

length (cm) 34.6 34.2 36.5 34.4

Forearm

length (cm) 25.4 25.5 28.2 25.9

Thigh length

(cm) 46.7 44.5 47.8 45.2

Lower leg

length (cm) 47 49.3 50.3 45.2

Shoulder

breadth (cm) 38.3 38.3 38.3 38.8

Since the length of the trunk, foot and head were not measured directly from the

subjects, they were estimated from Figure 4.4 using the subject’s height. The

length of the trunk, foot and head had to be multiplied by a scale factor so that

the sum of these lengths and the measured length of the thigh and shank would

equal to the rower’s height.

The rower model in the catch position of the rowing cycle is shown in Figure 4.5.

The ellipsoids representing the inertial properties of each body segment is

displayed.

101

Figure 4.5: Rower model in the catch position. The x-axis is the longitudinal axis of the

rowing shell, y-axis is the vertical axis and z-axis is the transverse axis. The graph is in

units of metres and the coordinate (0,0) on the graph is the rower’s ankle and assumed to

be stationary relative to the rower shell (i.e., a non-inertial reference frame).

The motion of the rower’s centre of mass was obtained by summing the motion

of all the moving segments (based on the conservation of momentum). This is

described by:

TOTAL

SEATSEATTRUNKTRUNKHEADHEAD

FISTFISTFOREARMFOREARMUPPERARMUPPERARM

THIGHTHIGHSHANKSHANK

COMm

mxmxmx

mxmxmx

mxmx

x

⋅+⋅+⋅+

⋅+⋅+⋅⋅+

⋅+⋅⋅

=

•••

•••

••

•

2

2

( 4.8 )

where m is the mass of the body segment or rowing seat, as defined by the

subscript (kg)

102

•

x is the velocity of the moving mass, defined by the subscript, in the

forward direction relative to the rowing shell, that is, a non-inertial

reference frame (ms-1)

COMx

•

is the velocity of the combined centre of mass in the forward

direction relative to the rowing shell (ms-1)

TOTAL

m is the sum of all the masses that move relative to the rowing

shell (kg)

4.3 MODEL VERIFICATION WITH ON-WATER DATA

In order to verify the rowing model, on-water data of single scullers (n = 4) were

collected. The data consisted of rowing shell acceleration and velocity, oar

angle, seat position and side-view video recording of the rower. The propulsive

force was calculated from the shell velocity and oar angle data using Equation

4.3 and Equation 4.4. The seat position data and video data were used to

calculate the rower motion. The propulsive force and rower motion were

subsequently used as inputs into Equation 4.1 to simulate the shell acceleration.

This simulated shell acceleration was compared to the measured shell

acceleration to find out how accurate the rowing model was able to represent a

single sculler.

Section 4.3.1 provides the details of the data collected and section 4.3.2

discusses the step-by-step model verification process.

4.3.1 ON WATER DATA COLLECTION

On-water data was collected for the variables in Equation 4.1 to simulate the

shell acceleration, shell

a or dt

dvshell . Table 4.4 shows how the time dependent

variables were measured.

103

Table 4.4: Methods for obtaining the time dependent variables for the rowing model

simulation.

Variable Obtained from:

i) Oar angle, ϕ

ii) Oar angular velocity, •

ϕ

i) Servo potentiometers for the oar

angle.1

ii) Calculated the derivative of the oar

angle data to determine the oar

angular velocity.

Hydrodynamic coefficients

i) Drag coefficient for the total

resistive force on the rowing system,

c

ii) Oar blade drag coefficient, D

C and

oar blade lift coefficient, L

C

Empirical data in the literature

i) (Lazauskas 1998)

ii) (Caplan & Gardner 2005)

Shell velocity, shell

v Velocity data measured with the

Rover system (deduced from GPS

and MEMS triaxial accelerometer

data).2

Rower acceleration relative to the

shell, shellrower

a_

Multi-turn potentiometer for the seat

position 1 and video recording (with

no compression) for the rower motion.

Shell acceleration, shell

a Shell acceleration data measured

with MEMS triaxial accelerometers.2 1

Rowing biomechanics measurement system developed in-house at the Australian Institute of

Sport (Kleshnev 1999, 2000, 2005).

2 Rover rowing kinematics measurement system developed by the Cooperative Research

Centre for microTechnology and the Australian Institute of Sport. It is an integrated GPS and

MEMS triaxial accelerometer measurement system (Grenfell 2007; James, Davey & Rice 2004).

The oar angle, seat position and shell acceleration were measured using a

rowing biomechanics measurement system (Kleshnev 1999, 2000, 2005)

developed by the department of biomechanics of the Australian Institute of

Sport. The system sampled the data at 25 Hz. The rowing biomechanics system

could actually measure a range of other parameters including shell velocity by

104

attaching impellers underneath the shell, applied force at the oar handles using

calibrated strain gauges and trunk orientation deduced from a potentiometer

connected to the rower at the back of the neck at the top of the rowing jersey

via a clip and fishing line. However, these parameters were not needed for the

rowing model. An additional and independent kinematics measurement system,

Rover – developed by the Cooperative Research Centre for microTechnology in

conjunction with the Australian Institute of Sport, was also used. Rover

incorporates high sensitivity 10 Hz Global Positioning System (GPS) and triaxial

accelerometers at a sample rate of 100 Hz. Rover has on board data logging,

as well as telemetry capabilities to allow real time data viewing using a wireless

Personal Computer (PC) or Personal Digital Assistant (PDA). Rover and the

rowing biomechanics system were not synchronised, so the two sets of

acceleration data had to be aligned manually. The shell velocity was measured

with Rover, which derived the shell velocity from combining its GPS data with

the acceleration data. The video camera frame rate was 25 frames per second

and was not synchronised to either Rover or the rowing biomechanics system,

so the video data also required manual alignment.

Data was collected from the rowers performing four rowing sessions at different

stroke rates. For the first and second sessions, the rowers sculled at the

nominal rates of 20 and 28 strokes/min, respectively. For the third and fourth

sessions, the rowers sculled at a nominal rate of 32 strokes/min.

Since the measurements were taken on water, an automated motion capture

system could not be used. We could have placed reflective markers on the

rowers for the video recording, but it was considered that it would not make

much difference when the rower motion was processed manually and not with

an automated motion analysis software. Further, it is well established that skin

artefacts do contribute to errors in motion analysis (Benoit et al. 2005; Lu et al.

2005), and the reflective markers would have been placed on the rowers’

clothing, which would have been even worse.

Video was recorded by the sports physiologist on a power boat cruising next to

the rowing shell. A much better solution would have been to mount the video

105

camera on the outrigger; ideally one on each side of the rowing shell to obtain

both side views of the rower motion. However, there wasn’t such a set up at the

time, so the quality of video data was severely limited because a fixed side view

could not be consistently maintained.

4.3.2 MODEL VERIFICATION METHOD

The model verification method is summarised in Figure 4.6. Three typical

consecutive rowing strokes worth of data was analysed for each of the rowers

from steady state (nominally constant stroke rate) rowing. Rower motion data

was extracted by manually processing the video frames. The selection of the

rowing strokes, as well as the rowing session, for analysis was primarily based

on the video frame quality. The video frames were checked to ensure that the

zoom was maintained at a level where the rower motion was clearly observable

and the capture angle of the rower was consistently orthogonal to the rower

motion (i.e., good side view of the rower motion) throughout the strokes. It was

very difficult to keep a consistent side view of the rower with the video camera

because the rowing shell velocity fluctuated within the stroke whereas the boat

used to film the rowing shell was powered by a motor and had a much more

constant velocity. The three consecutive rowing strokes were simulated and the

generated shell velocity and acceleration were compared to the measured shell

velocity and acceleration.

The simulation of single scullers involved a five step process. First, the rower’s

upper body motion, which included trunk orientation, shoulder angle and elbow

angle, was extracted from the video data. Along with the seat position

measurement, they make up all the components of rower motion. Second, the

rower motion data was filtered. Third, the rower motion data were combined to

estimate the motion of the rower’s centre of mass. The fourth step was to

calculate the propulsive force. Finally, the motion of the rower’s centre of mass

and the propulsive force were used to simulate the shell motion. The details of

all the steps are listed below.

106

Figure 4.6: Model verification method.

Step 1

Step 2

Step 3

Solving Equation 4.1

( )

shellrowerrowerdragpropulsive

shellrowershell

amFF

amm

_

⋅−−=

⋅+

vrower Step 5

ashell

Fpropulsive

Step 4

107

STEP 1 – Extracting rower motion from the data

UTHSCSA ImageTool (Wilcox et al. 2002) was used to measure the trunk

orientation, shoulder angle and elbow angle from the video frames (Figure 4.7).

The rower motion was derived from the change in the rower’s joint angles,

which were manually measured by marking the respective points on the rower’s

body frame by frame:

• Trunk orientation (relative to the seat) – was measured by marking the

shoulder joint, hip joint and the horizontal line corresponding to the seat.

• Shoulder angle (the angle of the rower’s upper arm relative to the trunk)

– was measured by marking the elbow joint, shoulder joint and hip joint.

• Elbow angle (the angle of the rower’s forearm relative to the upper arm)

– was measured by marking the wrist joint, elbow joint and shoulder joint.

Figure 4.7: Image analysis of the video data to determine body segment rotation.

As mentioned in section 4.2.1 and summarised in Table 4.1, it was assumed

that the rower did not make any lateral movement to reduce the rower motion to

108

two dimensions. The legs, trunk and head of the rower’s body have minimal

lateral movement during the rowing stroke, but the rower’s arms do have a

significant amount of lateral movement (i.e., out-of-plane motion of the elbow).

Since the mass of the arms is small in comparison to the mass of the rest of the

body, neglecting the lateral movement of the arms should only have a small

effect on the estimation of the motion of the rower’s centre of mass.

Nevertheless, if an accurate representation of the arm motion is needed, then it

is a good idea to reconstruct this on the basis of wrist and shoulder position,

and the known lengths of upper arm and forearm.

The initial trunk orientation, shoulder angle and elbow angle were recorded to

set up the rower starting posture (i.e., the rower in the catch position) in

SimMechanics. The seat position was measured with a multi-turn potentiometer

in the rowing biomechanics measurement system. The rower motion data are

shown in Figure 4.8.

(a) Seat position

(b) Trunk orientation

(c) Shoulder angle

(d) Elbow angle

Figure 4.8: Rower motion raw data (3 strokes of measured data). (a) Seat position. (b)

Trunk orientation. (c) Shoulder angle. (d) Elbow angle.

109

STEP 2 – Rower motion data conditioning

Three consecutive strokes were simulated at a time to avoid the problem of

large deviations at the start and end of the simulated traces. The deviations are

due to mathematical boundary condition problems when solving the differential

equation of motion. In particular, large deviations at the beginning of the first

stroke and the end of the third stroke were evident, but the second stroke had

completely avoided the boundary condition induced error since it was

continuous with the first and third stroke and were far away from the boundaries.

If the whole rowing session had been simulated (i.e., started from when the

rowing system, both rower and shell, was stationary until it came to a stop at the

end), then the boundary condition problems would have been avoided since all

the variables started and ended with zeros. However, since the video data

quality was not consistent, this could not be accomplished.

The rower motion data was then low passed filtered (i.e., smoothed). This was

particularly important because the differentiation process (i.e., from position to

velocity to acceleration and from angle to angular velocity to angular

acceleration) would amplify the high frequency noise. A 5th-order Butterworth

low pass filter was selected to minimise the spikes in the data. A cut-off

frequency of 4 Hz was chosen based on residual analysis (Winter 2004) and the

Butterworth filter was applied bi-directionally (i.e., zero-phase-shift filter), which

resulted in a cut-off frequency of 3.7 Hz (i.e., -3 dB at 3.7 Hz). Since the highest

stroke rate that was analysed was 32 strokes/min, which equated to 0.53 Hz,

the low pass filter cut-off frequency was about 7 times higher and should cover

the bandwidth of the rower motion. Furthermore, the video frame rate was only

25 frames per second anyway, and that over-sampling by a factor of 4 to 5 is

usually needed to help avoid aliasing, improve resolution and reduce noise, so

the highest frequency content that could be extracted from the video frames

was about 5 to 6 Hz. The filtered rower motion data were subsequently used as

inputs for the rower model. It should be noted that extra points at the start and

end of the three consecutive strokes were included for filtering and then omitted

to avoid the start up transients during filtering.

110

STEP 3 – Calculating the motion of the rower’s centre of mass

The initial posture of the rower and the filtered rower motion data (representing

the motion of the body segments) were entered into the rower model to

calculate the motion of the rower’s centre of mass. Subsequently, the position of

the rower’s centre of mass (i.e., rower model output) was differentiated twice

with respect to time, and became the rower motion input, shellrowera

_

or

dt

dvshellrower _

, for the rowing system differential equation (Equation 4.1). Although

it was not carried out in this thesis, one way to check to what extent the

reconstructed rower motion is a valid representation of the actual rower motion

is to check if in the reconstructed rower motion, the position of the wrist follows

the handle of the oar as calculated from the oar angle.

STEP 4 – Calculating the propulsive force

The forward component of oar blade force was calculated using Equation 4.3

and Equation 4.4, with the oar angle data. Oar angular velocity was calculated

from the oar angle data using the finite backward difference (Equation 4.9). The

truncation error of the backward difference approximation has the order of O(h),

whereas the truncation error of the central difference approximation has the

order of O(h2), where h is the step size. Nevertheless, the backward difference

approximation was used based on the idea that real-time calculation of the

propulsive force would be applied in the future, although central difference

approximation can be applied in real-time with a sample delay. The measured

shell velocity corresponding to the start of the three consecutive strokes of data

was required to initiate the rowing model simulation (i.e., the initial boundary

value for the differential equation). This was because the rowing system had

already attained a certain shell velocity. That is, if the simulation was started

from when the rowing system was stationary, then the initial shell velocity could

have just been set to zero without the need for the measured shell velocity. It

should be noted that the propulsive force was calculated from the solved shell

velocity and not the measured shell velocity. That is, the propulsive force was

dependent on the solution to the differential equation representing the rowing

system. The left and right (forward component) oar blade forces were summed

111

to obtain the total propulsive force. The evaluated total propulsive force was

used as the propulsive force input, propulsive

F , for the rowing system differential

equation (Equation 4.1).

t

fff

nn

n

∆

−

=−1

'

,

='

1

f 0 and =n 2 to N

( 4.9 )

where n is the sample index

f is a generalised function

'

f is the derivative of the function

t∆ is the sampling interval (s)

STEP 5 – Single-scull rowing model simulation

The velocity of the rower’s centre of mass (from step 3) and the forward

component of the total propulsive force (from step 4) were then fed into the

rowing system differential equation (Equation 4.1) to simulate the rowing system

and generate the shell acceleration and velocity data. Specifically, the

differential equation representing the rowing system was solved to determine

the shell motion (i.e., shell velocity, and therefore, shell acceleration are the

variables of interest in the differential equation).

4.3.3 RELIABILITY ANALYSIS OF THE ROWER BODY ANGLES

MEASURED FROM VIDEO FRAMES

As discussed previously, rower motion was estimated from the video data

manually, as the measurements were taken on-water; therefore, it was not

viable to use a motion capture system. For subjects 1, 2, 3 and 4, a total of 157,

248, 245 and 243 video frames were analysed (corresponding to 3 consecutive

rowing strokes for each subject), respectively. For each of these video frames,

the elbow angle, shoulder angle and trunk orientation were each measured

three times (i.e., 3 of 3 different rower body angle measurements per video

frame). A total of 8037 measurements were taken, i.e., 9 measurements per

video frame by 893 (157 + 248 + 245 + 243) frames. One can appreciate how

112

labour intensive the task was, and therefore, the error analysis that could be

performed was quite limited. A makeshift standard deviation was calculated for

each of the three rower angles: elbow, shoulder and trunk. This was done by:

1. The rower body angle measurements of the four subjects were

concatenated together as shown in Equation 4.10.

2. The mean of the trials were then taken, resulting in a column vector

containing the mean value of each row. This is because each row

corresponds to the measurement of a particular angle, so it only makes

sense to take the mean this way. That is, it is incorrect to take the mean

of different video frames and different rower subjects, since each angle

that was measured was distinctively different.

3. The mean was subtracted from the trials and then squared as shown in

Equation 4.11.

4. All the elements of stdev

A in Equation 4.11 were summed, divided by the

total amount of elements in stdev

A and then the resultant value square

rooted resulting in a makeshift standard deviation measure.

The makeshift standard deviation provides an idea of the variance expected

in the measurement of each rower body angle and the results are shown in

Table 4.5. It was found that the makeshift standard deviation of the rower

body angles measured from video frames was about 3.8 degrees on

average.

113

=

3,243,42,243,41,243,4

3,1,42,1,41,1,4

3,245,32,245,31,245,3

3,1,32,1,31,1,3

3,248,22,248,21,248,2

3,1,22,1,21,1,2

3,157,13,157,11,157,1

3,1,12,1,11,1,1

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

A

MMM

MMM

MMM

MMM

( 4.10 )

where A is a vector representing the measurements of a particular rower body

angle: elbow angle, shoulder angle or trunk orientation.

a is a measurement. The first subscript corresponds to the subject

number, the second subscript corresponds to the video frame number,

and the third subscript corresponds to the measurement trial number.

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

−−−

−−−

−−−

−−−

−−−

−−−

−−−

−−−

=

2

243,43,243,4

2

243,42,243,4

2

243,41,243,4

2

1,43,1,4

2

1,42,1,4

2

1,41,1,4

2

245,33,245,3

2

245,32,245,3

2

245,31,245,3

2

1,33,1,3

2

1,32,1,3

2

1,31,1,3

2

248,23,248,2

2

248,22,248,2

2

248,21,248,2

2

1,23,1,2

2

1,22,1,2

2

1,21,1,2

2

157,13,157,1

2

157,13,157,1

2

157,11,157,1

2

1,13,1,1

2

1,12,1,1

2

1,11,1,1

µµµ

µµµ

µµµ

µµµ

µµµ

µµµ

µµµ

µµµ

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

Astdev

MMM

MMM

MMM

MMM

( 4.11 )

114

where stdev

A is vector A , as described in Equation 4.10, that has been

manipulated in order to estimate a makeshift standard deviation measure

of all the measurements taken.

a is as described in Equation 4.10 above

µ is the mean of the trials. The first subscript corresponds to the subject

number and the second subscript corresponds to the video frame

number.

Table 4.5: Makeshift standard deviation for the rower body angle measurements.

Rower body angle Makeshift standard deviation (deg)

Elbow angle 3.7261

Should angle 4.0083

Trunk orientation 3.8140

4.4 RESULTS AND DISCUSSION

4.4.1 PROPULSIVE FORCE CALCULATED FROM THE

HYDRODYNAMICS OAR BLADE MODEL VERSUS THE FORCE

CALCULATED FROM THE OAR HANDLE FORCE, OAR LEVER

RATIO AND COSINE OF THE OAR ANGLE

This section will explain the difference in the force calculated from the

measured oar handle force, oar lever ratio and cosine of the oar angle (referred

to as forward applied force from here on) and the propulsive force calculated

from the hydrodynamics oar blade model (referred to as forward propulsive

force from here on). The difference between the two is of fundamental

significance. Analysis of the forward applied force reveals the effort of the

rower’s strokes, while the analysis of the forward propulsive force reveals how

the effort is effectively used to propel the rowing shell forward.

Figure 4.9 and Figure 4.10 show the forward applied force plotted with the

forward propulsive force for subject 1 and 2, respectively. It should be noted

that the graphs show the total force; sum of the left and right forces. The

forward applied force at the oar blade was calculated using Equation 4.2. The

115

forward propulsive force was calculated using Equation 4.3 and Equation 4.4

(i.e., the hydrodynamics oar blade model as illustrated in Figure 4.1).

The forward applied force was completely different in shape to the forward

propulsive force for both subjects. The inadequacy of the forward applied force

is ascribed to the inadequacy of the assumptions underlying its calculation as

discussed in section 4.2.2. On the contrary, the forward applied force does not

make the assumption that there is no axial force in the oar. The hydrodynamics

oar blade model accounted for all the forces on the rowing system including the

rower motion, shell drag, propulsive force at the oar blade, and braking force at

the blade during the catch and release. It took into account the effort applied by

the rower using the oar angle and oar angular velocity. It accounted for the

hydrodynamics effects at the oar blade with the immersed oar blade area,

coefficient of drag and lift and the oar blade’s slip velocity. Most importantly, it

accounted for the constant change in the kinematics of the rowing system with

the shell velocity vector, which affects the oar blade’s slip velocity vector, and

therefore, the blade force.

Referring to the graphs of the forward applied force, the difference between

subject 1 and subject 2 (blue curves marked with dots in Figure 4.9 and Figure

4.10, respectively) looked as if it could be accounted for by a scale factor. That

is, the relationship between the forward applied force curves of the two subjects

seemed almost linear. In comparison, referring to the graphs of the forward

propulsive force (red curves marked with circles in Figure 4.9 and Figure 4.10),

subject 1’s force curve varied non-linearly over time relative to subject 2’s force

curve. In particular, subject 1’s first peak was about double the magnitude of

subject 2’s, while the third peak was lower by about 100 N on average.

116

Figure 4.9: Comparing the total forward blade force derived from the measured handle force using the oar lever ratio against the forward blade

force calculated from oar blade hydrodynamics model. Results for subject 1.

117

Figure 4.10: Comparing the total forward blade force derived from the measured handle force using the oar lever ratio against the forward blade

force calculated from oar blade hydrodynamics model. Results for subject 2.

118

The forward applied force was initially used as the input into the differential

equation describing the motion of the rowing system (as discussed in section

4.2.2), but the simulated shell acceleration curve just didn’t follow the curvature

of the measured shell acceleration. Figure 4.11 and Figure 4.12 show the shell

acceleration plots for subject 1 and 2, respectively. This led to the blade

hydrodynamics modelling, which simulated a shell acceleration trace that

followed the curvature of the measured shell acceleration.

In Figure 4.11 and Figure 4.12, the ‘Biomech’ trace is the measured shell

acceleration obtained using the rowing biomechanics measurement system.

The ‘Simulated’ trace is the shell acceleration simulated with the rowing model

and used the hydrodynamics oar blade model to calculate the blade force.

Lastly, the ‘Oar leverage’ trace is the shell acceleration simulated with the

rowing model and used Equation 4.2 to calculate the blade force.

Table 4.6 compares the sum of squared error (Equation 4.12) and absolute

mean error (Equation 4.13) in the simulated shell acceleration using

hydrodynamics modelling against using oar leverage calculation. Table 4.6

shows that there was actually less error in the simulated shell acceleration

using oar leverage calculation than when the hydrodynamics modelling was

used for both subjects. This was mainly due to the excessive deceleration at the

catch and particularly at the release (highlighted by the black arrows in Figure

4.11 and Figure 4.12). The sources of error that contributed to the simulation

error at the catch and release will be discussed in section 4.4.3.

2

1

∑=

∧

−=⋅⋅⋅

n

i

ii xxerrorsquaredofSum ( 4.12 )

∑

=

∧

−=⋅⋅

n

i

ii xxn

errormeanAbsolute

1

1

( 4.13 )

where ix

∧

is the estimated data

i

x is the measured data

119

i is the index of the data points

n is the total number of data points

Table 4.6: Error in the simulated shell acceleration using hydrodynamics modelling

versus oar leverage calculation.

Difference

between:

Sum of squared

error (m2s-4)

Absolute mean

error (ms-2)

Hydrodynamics

model & measured

524.6426 1.2848 Subject 1

Oar leverage &

measured

475.0548 1.1861

Hydrodynamics

model & measured

320.4653 0.8565 Subject 2

Oar leverage &

measured

216.1651 0.6851

Hydrodynamics

model & measured

135.6637 1.1442 Subject 1 – drive

phase only, with

catch and

release omitted

Oar leverage &

measured

191.3858 1.4084

Hydrodynamics

model & measured

178.7851 1.3174 Subject 2 – drive

phase only, with

catch and

release omitted

Oar leverage and

measured

121.2474 0.9881

The errors were recalculated for only during the drive phase with the catch and

release omitted, as the blade force only occurs during the drive phase and it

was known that the hydrodynamics modelling had limitations in modelling the

catch and release. As shown in the bottom half of Table 4.6, it can be seen that

there was less error in the simulation shell acceleration using the

hydrodynamics modelling than when oar leverage calculation was used for

subject 1, but not for subject 2. This gave more assurance that the

hydrodynamics modelling is a good representation of the force at the oar blade.

In particular, being able simulate the shell acceleration more accurately for

subject 1 than subject 2, when the force applied by subject 1 (Figure 4.9) was

120

much greater than subject 2 (Figure 4.10) due to the difference in stroke rate, is

much more important. Specifically, the oar blade force derived from oar

leverage calculation can only have a single peak, and the only way for the

simulated shell acceleration to match the measured shell acceleration

accurately is for the blade force to have multiple peaks with a very sharp peak

right at the start of the drive, which was found to be the case using

hydrodynamics modelling.

In Figure 4.11, the ‘biomech’ acceleration had two peaks (the peaks are

highlighted with the red ovals) separated by a large dip during the drive phase.

However, in the ‘oar leverage’ trace the first peak had merged with the second

peak, so the large dip between the peaks was missing. Further, the rise to the

first peak was not sharp enough and the second peak was overestimated by a

significant margin (with an average of 1.38 ms-2 overestimation for the three

second peaks for ‘oar leverage’ versus 0.50 ms-2 for ‘simulated’) In Figure 4.12,

the ‘simulated’ shell acceleration matched both the first and second peaks of

the ‘biomech’ shell acceleration better than the ‘oar leverage’ shell acceleration.

In particular, the ‘oar leverage’ shell acceleration underestimated the first and

second peaks by an average of 1.50 ms-2 and 1.79 ms-2 over the three strokes,

respectively. This underestimation actually resulted in an underestimated shell

velocity (graphs not shown). In contrast, the ‘simulated’ shell acceleration

underestimated the first and second peaks by an average of 1.00 ms-2 and 0.65

ms-2 over the three strokes, respectively.

121

Figure 4.11: Comparing two sets of simulated shell acceleration against the measured shell acceleration for subject 1. ‘Simulated’ was the shell

acceleration calculated using the hydrodynamics model, while ‘oar leverage’ was the shell acceleration calculated using the measured oar handle

force, oar lever ratio and cosine of the oar angle.

122

Figure 4.12: Comparing two sets of simulated shell acceleration against the measured shell acceleration for subject 2. ‘Simulated’ was the shell

acceleration calculated using the hydrodynamics model, while ‘oar leverage’ was the shell acceleration calculated using the measured oar handle

force, oar lever ratio and cosine of the oar angle.

123

4.4.2 COMPARISON BETWEEN THE SIMULATED SHELL

ACCELERATION AND THE MEASURED SHELL

ACCELERATION

Figure 4.13 shows the simulated forward shell acceleration compared against

the measured acceleration using the biomechanics system (25 Hz) and the

Rover (100 Hz) for the 4 subjects. Subject 1 (Figure 4.13a) sculled at a nominal

stroke rate of 32 strokes per minute, while the other 3 subjects (Figure 4.13b, c

and d) sculled at a nominal stroke rate of 20 strokes per minute. Initially, only

one stroke was simulated. However, it was realised that the mathematical

boundary conditions became a problem for the simulation as the end points to

the simulated acceleration could not match the measured acceleration. If the

quality of the video data was consistently good to estimate the rower motion

from the start to the end of the rowing session (i.e., from a stand still start to a

stand still finish), then there would have been no problem. However, since the

start and end of the simulation did not correspond to zero net acceleration and

zero velocity, the simulated and measured rowing shell acceleration did not

match up. This occurred despite the fact that the simulated shell velocity was

set to the measured shell velocity for the first data point. To avoid the boundary

condition problem, three consecutive strokes were simulated, so that the

second stroke was completely free from the problems associated with the

boundary conditions.

124

(a) Subject 1

(b) Subject 2

Figure 4.13: Comparison of simulated shell acceleration with measured shell acceleration.

(a) Subject 1, (b) Subject 2, (c) Subject 3, (d) Subject 4. Three consecutive strokes are

shown. Subject 1 rowed at a higher nominal stroke rate of 32 strokes per minute.

Subjects 2, 3 and 4 rowed at a nominal stroke rate of 20 strokes per minute.

125

(c) Subject 3

(d) Subject 4

126

Three consecutive strokes of shell acceleration results are shown in Figure

4.13a for subject 1 who sculled at the higher, nominal rate of 32 strokes per

minute. Referring to Figure 4.13a, the troughs at 0, 1.8, 3.6 and 5.4 s (as

indicated by the arrows) correspond to the instances when the rower was in the

catch position, and the rower was in the release position at about 0.8, 2.6 and

4.4 s (as indicated by the arrows) when the shell acceleration was near zero.

The drive phase is from the trough at the start of the trace to the release, and

the recovery phase is from the release to the trough at the end of the trace (i.e.,

the next catch). Figure 4.13b, c and d show the shell acceleration for the three

other subjects who sculled at the lower, nominal rate of 20 strokes per minute.

As indicated in Figure 4.13b, c and d, a catch approximately corresponds to a

trough in the acceleration trace and a release corresponds to the beginning of

the flat period of the trace (i.e., zero net acceleration). It can be seen in Figure

4.13a that there are several notable differences compared to Figure 4.13b, c

and d because of the difference in stroke rating. First, at the faster stroke rating

(Figure 4.13a), the first peak was almost as high as the second peak because

of the stronger leg drive. Second, at the slower stroke rating (Figure 4.13b, c

and d), the net acceleration was essentially zero during the recovery phase

because the slow recovery did not generate enough momentum to overcome

the resistance and accelerate the rowing shell. Finally, the drive to recovery

ratio was much higher at 32 strokes per minute (almost 1:1) compared to 20

strokes per minute (about 1:2).

It can be seen that the simulated shell acceleration data are similar in shape to

the measured data. This indicated that the rowing model is a reasonable

representation of the real rowing system. Table 4.7 lists the cross correlation

coefficients (also known as Pearson’s correlation, Equation 4.14) between the

three sets of shell acceleration data. This was done to quantify the closeness

(i.e. strength of the linear relationship) between the simulated and the measured

acceleration data. The coefficient is 1 if the relationship between two data sets

is perfectly linear regardless of scaling and offset. As expected, the two sets of

measured data were highly correlated with cross correlation coefficients all

above 0.95. The main difference between the two sets of measured data was

their magnitude. This was most likely due to a difference in the calibrated gain.

127

The cross correlation coefficients between the simulated data and the

Biomechanics (25 Hz) measured data ranged from 0.7499 to 0.8488, while the

coefficients between the simulated data and the Rover (100 Hz) measured data

ranged from 0.7442 to 0.8333. This showed that there was some sign of

correlation between the simulated and the measurements, but it was definitely

not sufficient to infer that the simulated data was strongly linear-correlated to

the measured data. A correlation coefficient of about 0.95, like those between

the two sets of measured data, would be needed in order to draw such a

conclusion.

( )( )

( ) ( )∑∑

∑

==

=

−⋅−

−−

=n

i

i

n

i

i

n

i

ii

yyxx

yyxx

r

1

2

1

2

1

( 4.14 )

where r is the correlation coefficient

i

x is data set one

x is the mean of data set one

i

y is data set two

y is the mean of data set two

i is the index of the data points

n is the total number of data points


simulated rowing shell acceleration data.

Cross correlation coefficient Subject

Biomech (25 Hz)

– Rover (100 Hz)

Simulated –

Biomech (25 Hz)

Simulated –

Rover (100 Hz)

1 0.9930 0.7499 0.7442

2 0.9793 0.8488 0.8333

3 0.9547 0.8003 0.7821

4 0.9634 0.8448 0.8324

128

It was expected that the error would be more significant in the drive phase than

the recovery phase for the simulated acceleration data. The logic for this was

that the propulsive force generation at the blade and water interface is complex

and it had been simplified using a static representation in the rowing model. On

the contrary, the interaction of forces during the recovery is much more

straightforward, when rower motion is the only active force and the resistance

on the shell is the reactive force. Thus, it was expected that with no propulsive

force in the recovery phase, there should be less error. Table 4.8 shows that

this was indeed the case. Nevertheless, the error in the simulated acceleration

during the recovery phase was still about 46% of the error during the drive

phase on average across the four subjects, which signified the importance of

modelling the rower motion and the shell resistance on the rowing system

accurately as well.

Table 4.8: Error in the simulated shell acceleration during the drive phase versus

recovery phase.

Absolute mean error (ms-2) in the simulated shell

acceleration compared to the ‘biomech’ shell

acceleration measurement.

Subject

Drive phase Recovery phase

1 1.8584 1.5963

2 1.4134 0.4728

3 1.9843 0.5249

4 1.2886 0.4811

4.4.3 SOURCES OF ERROR THAT CONTRIBUTED TO THE

SIMULATION ERROR DURING THE DRIVE PHASE

There were many possible sources of error that contributed to the simulation

error because the rowing model involved multiple data inputs and many

measured and assumed constants (A sensitivity analysis for the model

constants and model inputs was conducted and presented in the following

chapter). The sources of error that contributed to a significant proportion of the

simulation error during the drive phase included:

129

1. differentiation of the oar angle to obtain oar angular velocity, when the

oar angle was sampled at a relatively low rate of 25 Hz;

2. estimation of the immersed oar blade area for the blade entry and exit

from the video frames based on human inspection, along with the

assumption that both blades entered and exited the water simultaneously,

since only one side of the rower was video recorded, and;

3. drag and lift coefficients being unavailable for when the oar blade velocity

vector was actually in the direction towards the back of the oar blade,

which occurred around blade entry and exit when the shell velocity vector

was more dominant than the oar angular velocity vector.

4. The action of feathering was not taken into account. During the blade exit,

the rower actually rotates the blade so that it becomes horizontal to

minimise air drag, called feathering. Thus, since the pitch of the blade is

not aligned vertically at the blade exit, the braking force should be

reduced

Each of these sources of error is discussed in further detail below.

The oar angular velocity data was obtained by differentiating (Equation 4.9) the

measured oar angle (angle of the oar shaft relative to a line perpendicular to the

shell at the oarlock in the horizontal plane) data. Since the oar angle was

sampled at 25 Hz, which was relatively low, the accuracy of the derived oar

angular velocity data was perhaps insufficient. Furthermore, the oar shaft

vertical angle was ignored, because the biomechanics measurement system did

not measure this variable. In particular, when the blade is submerged into the

water during blade entry and taken out of the water during blade exit, the pitch

of the oar shaft changes and should be employed to empirically determine the

change in the oar outboard length and immersed oar blade area. This three

dimensional representation would allow the force at the oar blade to be

estimated more accurately.

During blade entry and exit, the oar blade was only partially immersed in the

water, so the effective blade area was only a fraction of the whole blade area in

Equation 4.4. To account for this, the immersed blade area was estimated from

the video frames (Figure 4.14). Since the oar blade surface was not orthogonal

130

to the view of the video camera, the area estimation feature in the image

analysis software could not be used to estimate the immersed blade area, but

was judged by human eye instead. A rough estimate of the immersed blade

area fraction was recorded for each of the blade entry and exit video frames

(The immersed blade area fraction is graphed in chapter 7, which shows and

discusses the relationship between shell acceleration and all the other variables

of the rowing system). This fraction was used to scale the oar blade area, and

therefore, the oar blade force in Equation 4.4. This method corrected for the

immersed blade area, but it also introduced systematic error because it is based

on crude human observation. Moreover, the immersed blade area was

assumed to be symmetrical for the left and right oar blades, because only one

side of the rowing motion was video recorded. Even though there were separate

left and right oar angle data recorded using the biomechanics system, error was

introduced at the blade entry and exit points with the assumption that the left

and right blades were symmetrically immersed into the water, as this is not true

in practice.

131

Figure 4.14: Three consecutive video frames showing blade exit.

132

It was found that the blade velocity vector was in the direction towards the back

of the blade at the catch and release (or blade entry and exit) of the rowing

cycle, as illustrated in Figure 4.15. This phenomenon is known as backsplash,

as discussed in (Macrossan & Macrossan 2006) and it posed a problem

because Caplan and Gardner’s (2005) data only covered drag and lift

coefficients when the blade velocity vector was in front of the blade (0° to 180°).

As shown in Figure 4.15, the oar angular velocity component is small during

blade entry and exit. This is because the oar has just changed its rotational

direction during blade entry and has to slow down to change its rotational

direction during blade exit. Thus, the blade velocity vector is dominated by the

shell velocity at the blade entry and exit, and points in the direction behind the

blade (180° to 360°). Note that in this situation, the blade is actually acting as a

brake and the blade force decelerates the rowing system. Since the back of the

blade is usually convex, it is very streamlined, so the drag and lift coefficients

would be different to the front of the blade or even a flat plate. Due to the lack of

data, the drag and lift coefficients behind the blade (180° to 360°) was assumed

to be the same as in front of the blade (0° to 180°). This inevitably introduced

error into the simulation when the blade velocity vector was pointing in the

direction behind the blade.

Figure 4.15: Blade velocity vector at the catch and release.

vshell

vslip

vshell

•

ϕ

outL

•

ϕ

outL

•

ϕ

vshell

vslip

CATCH RELEASE

133

Referring to Figure 4.13 again, the maximum deviations between the simulated

acceleration trace and the two measured acceleration traces were evaluated

and the results are summarised in Table 4.9 (The mean error between the

simulated and measured shell acceleration data will be presented and

discussed in the next chapter, as it is required for comparison with results from

the sensitivity analysis). The results in Table 4.9 revealed that the largest

deviations either occurred at the catch or release. For subject 1, 3 and 4, the

maximum deviation occurred at the release. For subject 2, the maximum

deviation occurred at the catch. As discussed previously, the blade entry and

exit were particularly affected by error because of the additional step of having

to estimate the immersed blade area fraction and the lack of data for the drag

and lift coefficients when the blade velocity vector pointed in the direction

behind the blade (i.e., when the blades had a braking effect on the rowing

system). Thus, it was expected that the largest deviations between the

simulated acceleration and the measured acceleration occurred at the catch

and release of the rowing stroke.

It was beyond anticipation that the magnitude of the maximum deviation would

be so large. In the case of subject 3 (Figure 4.13c), the simulation error at the

release resulted in a dip (less than -6 ms-2) that was even larger in magnitude

than the drive acceleration peaks (about 5 ms-2) and the catch deceleration dips

(about -5 ms-2). It is not understood exactly why there was such a large error.

One reason could be the pitch of the blade, the vertical angle of the blade as it

travels through the water. During the release, or blade exit, the rower actually

rotates the blade so that it becomes horizontal to minimise air drag, called

feathering, as can be seen in Figure 4.14. The pitch of the blade would

definitely change the hydrodynamic force generation during release. In

particular, since the pitch of the blade is not aligned vertically at the blade exit,

the braking force should be reduced. To reduce the simulation error at the blade

entry and exit to a tolerable level, the first step would be to obtain experimental

drag and lift coefficients when the blade velocity vector points in the direction

behind the blade and increase the sampling rate of the oar angle (say, 100 Hz).

If further improvement is required, then a more accurate method to estimate the

134

immersed oar blade area needs to be developed and the pitch of the oar blade

(i.e., the action of feathering) needs to be taken into account.

If the simulation error at the blade entry and exit (i.e., over-estimation of the

braking force) is still not within a tolerable level, then perhaps the hydrodynamic

interaction during the blade entry and exit is too complex for a static

representation and requires a computational fluid dynamic model.


acceleration data. Over-estimation is positive and under-estimation is negative. The

actual measured acceleration value is shown in the bracket. The percentage of error was

not calculated because some of the actual measured values were very close to zero,

which produced excessively large error percentages.

Maximum deviations between the simulated and

measured acceleration data

Subject

Simulated – Biomech

(25 Hz)

Simulated – Rover (100

Hz)

1 -3.70 ms-2 at 0.84

seconds (-0.07 ms-2).

-3.78 ms-2 at 0.84

seconds (0.00 ms-2).

2 -4.37 ms-2 at 6.16


-3.84 ms-2 at 6.16


3 -6.08 ms-2 at 1.04


-6.26 ms-2 at 3.96


4 -3.74 ms-2 at 1.16


-4.17 ms-2 at 1.12


Figure 4.16 shows the simulated forward shell velocity compared against the

shell velocity measured using Rover (deduced from GPS and accelerometer)

for the four subjects. Again, subject 1 rowed at the nominal rate of 32 strokes

per minute, while the other three subjects rowed at the nominal rate of 20

strokes per minute. As can be seen in the graphs, the simulated velocity

generally followed the measured velocity, but there were some significant

deviations that corresponded to the catch and release not being modelled

accurately in the hydrodynamics model. The cross correlation coefficients in

135

Table 4.10 indicated that the simulated velocity data were strongly linear-

correlated with the measured velocity data. For subjects 3 and 4 (Figure 4.16c

and d), the simulated velocity trace drastically deviated from the measured

velocity trace just after the peak velocity. This was due to the simulation error at

the release as discussed previously. The deviation between the simulated

velocity and the measured velocity for subject 1 (Figure 4.16a) was also due to

the simulation error at the release.


simulated velocity data.

Subject Cross correlation coefficient

Simulated – Rover (100 Hz)

1 0.9548

2 0.9770

3 0.9296

4 0.9734

Table 4.11 shows the maximum deviations between the simulated and the

measured velocity data (The mean error between the simulated and measured

shell velocity data will be presented and discussed in the next chapter, as it is

required for comparison with results from the sensitivity analysis). With the

exception of subject 1, the largest deviations occurred at the catch or release.

For subject 1, the maximum deviation occurred during the recovery phase at t =

1.48 s (between the release and the end of the stroke). For subjects 2 and 3,

the maximum deviations occurred at the catch, while it occurred at the release

for subject 4. It is should be noted that the simulated acceleration error is

accumulated in the velocity data because velocity is the integral of acceleration.

This is most apparent in Figure 4.16c and d when the simulation error at the

release caused the simulated shell velocity trace to deviate from the measured

trace for the whole of the recovery periods. Likewise, the maximum deviation for

subject 1 at t = 1.48 s in Figure 4.16a was accumulated from the three separate

under estimations in acceleration at about t = 0.8, 1.1 and 1.4 s in Figure 4.13a.

136

The higher cross correlation coefficients and the lower maximum deviations

compared to the acceleration data indicated that it was more difficult to simulate

the shell acceleration accurately compared to the shell velocity. This highlighted

that acceleration data has more detailed features concealed in its profile than

the velocity data.

Table 4.11: The maximum deviations between the simulated and the measured velocity

data. Over-estimation is positive and under-estimation is negative. The actual measured

velocity value is shown in the bracket. The percentage of error was calculated and shown

in the last column.

Maximum deviations between the simulated and

the measured velocity data

Simulated – Rover (100 Hz)

Subject

Magnitude and time of

occurrence. Actual

measure value shown in

the bracket

Percentage of error

1 -0.46 ms-1 at 1.48

seconds (4.98 ms-1)

-9.2 %

2 0.39 ms-1 at 0.60

seconds (2.68 ms-1)

14.7 %

3 -0.73 ms-1 at 7.12

seconds (4.50 ms-1)

-16.2 %

4 0.43 ms-1 at 6.36

seconds (2.72 ms-1)

15.9 %

137

(a) Subject 1

(b) Subject 2

Figure 4.16: Comparison of simulated shell velocity with measured shell velocity. (a)

Subject 1, (b) Subject 2, (c) Subject 3, (d) Subject 4.

138

(c) Subject 3

(d) Subject 4

139

4.5 CONCLUSION

The development of the single-scull rowing model was explained in this chapter.

On-water data was collected to verify the model and the model verification steps

were outlined.

The rowing model generated a shell acceleration data that was fairly close the

measured data, based on cross correlation coefficients ranging from 0.7442 to

0.8488. The largest deviation between the simulated acceleration and the

measured data was an under-estimation of 6.26 ms-2 at the release of the

stroke cycle for subject 3. This deviation was substantial as the peak measured

shell acceleration was about 5 ms-2, while the minimum acceleration was about

-5 ms-2 for subject 3. The simulation revealed that the model was reasonable in

representing the true motion of the rowing system, despite many assumptions

that introduced errors into the simulation. The simulation results showed that

the error in simulated shell acceleration was significantly dependent on the

propulsive force and rower motion data. This highlighted that the shell

acceleration reflects even the slight changes in the propulsive force and rower

motion. The relationship between rower motion, propulsive force and shell

acceleration is non linear and intricate, and perhaps analysing them together

would provide additional insight into a rower’s technique.

The simulated velocity data was more similar to the measured data than the

simulated acceleration, with cross correlation coefficients ranging from 0.9296

to 0.9770. The fact that the simulated acceleration data was not as close to the

measured acceleration as the simulated velocity data was to the measured

velocity, even though they are directly related, demonstrated that shell

acceleration was more difficult to simulate and has more detailed features

concealed in its profile. As mentioned in the introduction of this chapter, the

shell acceleration profile must contain additional technical insight, especially

when one remembers that shell acceleration is the rate of change of shell

velocity. From a signal processing point of view, acceleration contains the high

frequency information of velocity. Thus, the acceleration data contains

140

information about the instantaneously changes in the rowing motion, while the

velocity data contains the cumulative information in the rowing motion.

In the subsequent chapter, the focus is the sensitivity analysis of the rowing

model, where the rowing model error is analysed in greater detail. A sensitivity

analysis was carried out to look at the variation of the model constants and their

effects on the simulated acceleration. Also, a sensitivity analysis was conducted

to look at introducing normally distributed random error into the time varying

model inputs and observe their effects on the simulation output. The sensitivity

analysis revealed which of the variables and parameters had the most

significant effect on the rowing motion. The contribution of all the uncertainties

in the model inputs and model constants were combined to determine the total

uncertainty in the rowing model output. Comparing the total uncertainty to the

rowing model error (i.e., difference between the simulated shell motion and the

measured shell motion) indicated whether the rowing model was a satisfactory

representation of a real single sculler.

The goal of developing the rowing model was not just for the sake of modelling

the single sculler accurately. It was to understand the mechanics of a single

sculler and how the motion of the rowing system develops. In particular, it was

developed to show how the shell acceleration trace is generated. This topic will

be discussed in detail in the biomechanics analysis chapter in chapter 7.

4.6 REFERENCES

Atkinson, WC 2001, Modeling the dynamics of rowing - A comprehensive description of the computer model ROWING 9.00, viewed 1 May 2004, <http://www.atkinsopht.com/row/rowabstr.htm>. Benoit, DL, Ramsey, DK, Lamontagne, M, Xu, L, Wretenberg, P & Renstrom, P 2005, 'Skin movement artifact during gait and cutting movements measured in vivo', in Proceedings of the International Society of Biomechanics XXth Congress and American Society of Biomechanics 29th Annual Meeting, Cleveland, Ohio, U.S.A., p. 89. Brearley, M & de Mestre, NJ 1996, 'Modelling the rowing stroke and increasing its efficiency', in 3rd Conference on Mathematics and Computers in Sport, Bond University, Queensland, Australia, pp. 35-46.

141

Cabrera, D, Ruina, A & Kleshnev, V 2006, 'A simple 1+ dimensional model of rowing mimics observed forces and motions', Human Movement Science, vol. 25, no. 2, pp. 192-220. Caplan, N & Gardner, TN 2005, 'A new measurement system for the determination of oar blade forces in rowing', in MH Hamza (ed.), Proceedings of the Third IASTED International Conference on Biomechanics, Benidorm, Spain, pp. 32-7. de Leva, P 1996, 'Adjustments to Zatsiorsky-Seluyanov's segment inertia parameters', Journal of Biomechanics, vol. 29, no. 9, pp. 1223-30. Grenfell, RM, AU), Zhang, Kefei (Melbourne, AU), Mackintosh, Colin (Bruce, AU), James, Daniel (Nathan, AU), Davey, Neil (Nathan, AU) 2007, Monitoring water sports performance, Sportzco Pty Ltd (Victoria, AU), patent, United States, <http://www.freepatentsonline.com/7272499.html>. Hoerner, SF 1965, Fluid-dynamic drag, S. F. Hoerner, New York. James, DA, Davey, N & Rice, T 2004, 'An accelerometer based sensor platform for insitu elite athlete performance analysis', in Sensors, 2004. Proceedings of IEEE, pp. 1373-6 vol.3. Kleshnev, V 1999, 'Propulsive efficiency of rowing', in RH Sanders & BJ Gibson (eds), 17th International Symposium on Biomechanics in Sports, Edith Cowan University, Perth, Western Australia, Australia, pp. 224-8. —— 2000, 'Power in rowing', in Y Hong, DP Johns & R Sanders (eds), 18th International symposium on biomechanics in sports, Chinese University of Hong Kong, Hong Kong, pp. 662-6. —— 2005, Biorow.com, viewed 2006/06/01, <http://www.biorow.com>. Lai, A, Hayes, JP, Harvey, EC & James, DA 2005, 'A single-scull rowing model', in A Subic & S Ujihashi (eds), The Impact of Technology on Sport, Australasian Sports Technology Alliance Pty. Ltd., Tokyo, Japan, pp. 466-72. Lai, A, James, DA, Hayes, JP & Harvey, EC 2005, 'Validation Of A Theoretical Rowing Model Using Experimental Data ', in Proceedings of the International Society of Biomechanics XXth Congress and American Society of Biomechanics 29th Annual Meeting, Cleveland, Ohio, U.S.A., p. 778. Lazauskas, L 1998, Rowing shell drag comparisons, viewed 2008/09/02 2008, <http://www.cyberiad.net/library/rowing/real/realrow.htm>. —— 2004, Michlet rowing 8.08, viewed 2004/12/01 2004, <http://www.cyberiad.net/library/rowing/rrp/rrp1.htm>. Lu, TW, Lin, YS, Kuo, MY, Hsu, HC & Chen, HL 2005, 'A kinematic model of the upper extremity with globally minimized skin movement artefacts', in

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Proceedings of the International Society of Biomechanics XXth Congress and American Society of Biomechanics 29th Annual Meeting, Cleveland, Ohio, U.S.A., p. 452. Macrossan, MN & Macrossan, NW 2006, Back-splash in rowing-shell propulsion, University of Queensland, Brisbane. Millward, A 1987, 'A study of the forces exerted by an oarsman and the effect on boat speed', Journal of Sports Sciences, vol. 5, no. 2, pp. 93 - 103. van Holst, M 1996, Simulation of rowing, viewed 2010/2/22 2010, <http://home.hccnet.nl/m.holst/report.html>. Wang, ZJ, Birch, JM & Dickinson, MH 2004, 'Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations vs robotic wing experiments', J Exp Biol, vol. 207, no. 3, pp. 449-60. Wilcox, CD, Dove, SB, McDavid, WD & Greer, DB 2002, UTHSCSA ImageTool, 3.0 edn, Department of Dental Diagnostic Science at The University of Texas Health Science Center, San Antonio, Texas, U.S.A. Winter, D 2004, Biomechanics and Motor Control of Human Movement, 3rd edn, Wiley, New York. Young, K & Muirhead, R 1991, 'On-board-shell measurement of acceleration', RowSci, vol. 91-5.

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5. ROWING MODEL SENSITIVITY ANALYSIS

5.1 INTRODUCTION

This chapter documents the findings from the sensitivity analysis of the rowing

model. The main purpose for doing the sensitivity analysis was to determine

whether the difference between the measured and simulated rowing shell

motion (i.e., the simulation error) could be accounted for by the uncertainty in

the rowing model output. Specifically, if the simulation error is within the

uncertainty in the rowing model output, then the simulation error can be

accounted for by the uncertainties in the rowing model constants and model

inputs, and confirms that the rowing model is an adequate representation of the

rowing system.

The equation representing the motion of the rowing system is a differential

equation that has no analytic solution, and had to be solved numerically. Thus,

it is not feasible to propagate the uncertainties in the rowing model inputs to

determine the uncertainty in the model output (i.e., cannot analytically evaluate

the uncertainty in the rowing model output by finding the partial derivatives of all

the model variables). To resolve this, a sensitivity analysis was carried out to

quantify the variations in the model output caused by variations in each of the

model constants and variables. The resulting contributions, from each of the

model constants and variables, to the uncertainty in the rowing model output

were combined in quadrature as an estimate of the total uncertainty.

5.2 METHOD

In rowing, the rower moves back and forth within the rowing shell in order to

generate propulsive force to the rowing shell to overcome the various sources

of resistance. Thus, the forces acting on the rowing system can be grouped into

three components: the propulsive force (i.e. applied force at the oar blades), the

resistive force (i.e. mainly shell drag) and the motion of the rower’s centre of

gravity. In order to determine the shell motion (i.e., shell velocity and

acceleration); these three force components have to be resolved in the rowing

model. Figure 5.1 summarises how the shell velocity and acceleration were

144

measured and the input variables (i.e., measurements) required by the rowing

model to simulate (or numerically solve for) the shell velocity and acceleration.

The motion of the rower’s centre of gravity was calculated from the video (trunk

orientation, shoulder angle and elbow angle) and seat position data. The

propulsive force and resistive force are dependent on the shell velocity, the

model output, thus, they were determined by numerically solving the rowing

system’s differential equation. Further, the propulsive force required measured

oar angle data and known oar blade drag and lift characteristics, while the

resistive force required a known shell drag coefficient. Table 5.1 provides a

summary of the measurements used as model inputs. Since the propulsive

force is proportional to the vector sum of the shell velocity vector and the “oar

angular velocity vector” (shorthand for the contribution of the oar angular

velocity to the velocity vector of the centre of the blade as discussed in chapter

4) at the blade, and the forward component of the propulsive force is dependent

on the oar angle, it introduces a complicated term into the rowing system’s

differential equation making it unfeasible to find an analytic solution. Moreover,

the rower’s centre of mass motion is dependent on many variables (including

body segment length and mass, seat position and body segment rotation angle)

that are inter-related, along with physical and timing constraints specific to each

rower. Thus, it is not possible to find an analytic solution to the uncertainty in the

rowing model output with all these complicating factors.

A sensitivity analysis was carried out for the various constant parameters in the

rowing model. Table 5.2 summarises the details about these model parameters.

The main reason for this analysis was because some of these constants were

only estimated or taken from the literature as they could not be directly

measured. The sensitivity analysis revealed how sensitive the model was to

variations in these model constants. The model constants were varied to these

percentages of uncertainty: ±1, ±2, ±3, ±4, ±5, ±10%. Table 5.3 presents the

measured/estimated values of the model parameters and their uncertainties at

the different percentage levels. The expected uncertainties are highlighted in

bold and italic.

145

The grounds on which the uncertainties of the model constants where chosen

will now be explained. The uncertainty of the weight measurements was chosen

to be 0.5 kg. This seems very large, but it was because the rowers did not get

weighed at every rowing session. As for the weight of the non-sliding mass of

the rowing system, a combined uncertainty of 0.5 kg seemed reasonable, since

there were many components including the rowing shell, oars (assumed to be

part of the non-sliding mass) and the rower’s feet. The uncertainty of the density

of water was chosen to be less than 1% because the main variable of concern

was temperature and the temperature was always about 15 degrees when the

rowing sessions took place. Although the area of the oar blade was difficult to

estimate, it was deemed that it could still be estimated quite accurately, so an

uncertainly of 1% was assumed. The oar blade drag and lift coefficients and the

shell drag coefficient were based on data in the literature as summarised in

Table 5.2. The uncertainties of these coefficients were assumed to be 5%,

which was a conservative estimate, given that an error well over 5% doesn’t

seem totally unreasonable. The outboard oar length was difficult to measure

accurately because it was difficult to determine the exact location of the centre

of pressure at the oar blade. Nevertheless, it was expected that the error should

be less than 2 cm, which was about 1% of the total oar length.

146

Figure 5.1: Rowing model flow chart. The rowing model numerically solves for the shell velocity and acceleration with measured rower motion and

oar angles as the inputs. The colour coding is as follows: red boxes are the measurement systems, purple boxes are the force components on the

rowing system, green boxes are constants, the blue boxes are the measured variables and the filled yellow boxes are the measured and simulated

shell velocity and acceleration.

Rover

Biomechanics system Video

Accelerometer GPS

Servo

potentiometers

Servo

potentiometers

Simulated

shell velocity

Simulated shell

acceleration Shell

velocity

Shell

position

Shell

acceleration

Oar angle

(left and right)

Seat

position

Trunk

orientation

Shoulder

angle

Elbow

angle

Propulsive

force

Motion of the

rower’s centre

of gravity

Resistive

force

Drag

coefficient

Initial shell

velocity

Single scull rowing model

147

Table 5.1: Rowing model input variables.

Measured model input variables

Measurement method Derived variables

Elbow angle, shoulder angle, trunk orientation

Rower body segment angles estimated from video frames manually with UTHSCSA ImageTool (Wilcox et al. 2002).

Seat position Seat position measured with potentiometers.

Joint rotation angles and seat position were combined to calculate the motion of the rower’s centre of mass.

COM

SEATTRUNKHEADFIST

FOREARMUPPERARMTHIGHSHANK

x

xxxx

xxxx

•

••••

••••

⇒

⇒

,,,

,,,,

Dependent on the rowing style (i.e. rower’s posture and timing), and body segment length, mass and moment of inertia.

Oar angle, ϕ Oar angle measured with potentiometers

Oar angular velocity, •

ϕ ,

was obtained by differentiating the oar angle with respect to time. The oar angle and oar angular velocity were then used to calculate the propulsive force.

148

Table 5.2: Constant parameters of the rowing model.

Constants Units Details

shellm (measured) kg Mass of the shell

(movement relative to the start line)

rowerm (measured) kg Mass of the rower

(movement relative to the shell)

ρ (estimated – based on a water

temperature of about 15 °C)

kg/m3 Density of water

A (estimated with image analysis (Wilcox et al. 2002))

m2 Oar blade area

DC and

LC (based on experimental

data in (Caplan & Gardner 2005))

Dimensionless Oar blade drag and lift coefficient – function of the angle of attack, α

c (based on simulation data in (Lazauskas 1998))

kg/m Shell drag coefficient – assumed to be constant

L (measured) m Oar outboard length

149

Table 5.3: Model parameters and their uncertainty (used for sensitivity analysis). The expected uncertainties are shown in red bold italic.

Measured/estimated values

±1% ±2% ±3% ±4% ±5% ±10%

Shell non-sliding mass (kg)

18.86 (measured) 0.1886 0.3772 0.5658 0.7544 0.943 1.886

Rower sliding mass (kg)

71.04 (measured) 0.7104 1.4208 2.1312 2.8416 3.552 7.104

Density of water (kg/m3)

999.1 (estimated) 9.991 19.982 29.973 39.964 49.955 99.91

Oar blade area (m2) 0.0903 (estimated) 0.000903 0.001806 0.002709 0.003612 0.004515 0.00903

Oar blade drag coefficient (largest magnitude) (dimensionless)

2.13 (estimated) 0.0213 0.0426 0.0639 0.0852 0.1065 0.213

Oar blade lift coefficient (largest magnitude) (dimensionless)

1.43 (estimated) 0.0143 0.0286 0.0429 0.0572 0.0715 0.143

Shell drag coefficient (kg/m)

3.00 (estimated – based on (Kleshnev 1999) and personal communication with van Holst)

0.03 0.06 0.09 0.12 0.15 0.3

Oar length (m) 1.805 (measured) 0.01805 0.0361 0.05415 0.0722 0.09025 0.1805

150

A sensitivity analysis was also carried out to see how random error in the inputs

to the rowing model affected the rowing model output. It is random error, and

not just a fixed uncertainty, because the model inputs are time series data.

More specifically, fixed offset errors would not propagate to the rate of change

of the model inputs (i.e., oar angle to oar angular velocity, and the position of

the rower’s centre of mass to the velocity of the rower’s centre of mass).

It should be noted that the biomechanical/physiological relationship between the

rower motion and force generation was not explicitly represented in the rowing

model. In particular, the rower motion and propulsive force generation were

measured independently (video and seat position for the former, and oar angle

for the latter) and were used as separate inputs for the rowing model. Thus,

when normally distributed random error was added to each set of the rower

motion data, the propulsive force remained the same without any added random

error, as if the rower motion measurement (i.e., video analysis) was

contaminated with error while the force measurement (i.e., Biomechanics

measurement system to measure the oar angle) was free from error. Likewise,

when normally distributed random error was added to the oar angle

measurement, no error was added to the rower motion data.

The error magnitude was set at various percentage levels of each

measurement’s peak to peak range. For example, a 1% random error for seat

position is 1% of the 0.5 m maximum seat excursion, which is equal to 0.005 m

or 5 mm. Then, a normally distributed random error with a mean of 0 mm and

one standard deviation of 5 mm (i.e., about 67% of the error falls within 5mm)

was added to the seat position data for the sensitivity analysis. The error

percentage levels chosen were 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10% of the peak to

peak measured range.

Table 5.4 shows the peak to peak range of the measured inputs for the rowing

model and the actual magnitudes at the different percentages of error.

Estimates of the expected error are highlighted in bold and italic. Prior to adding

error to the measurement, the Nyquist limit was obeyed by filtering the error

with the same filter settings as for the measured data.

151

The oar angle uncertainty was based on the potentiometer specification of 3

degrees uncertainty. The seat position uncertainty was based on the

potentiometer specification of 1.5 cm uncertainty. The elbow angle, shoulder

angle and trunk orientation uncertainties were based on the makeshift standard

deviation values presented in section 4.3.3.

A total of 20 sets of random errors were generated and used in the rowing

model simulation. The results from the 20 simulations were combined to

quantify the effects of random error in the inputs of the rowing model on the

rowing model output. In particular, the mean error from the 20 simulations was

used for analysis.

After finding numerically the variations in the rowing model output caused by

variations in each measured input/model parameter through the sensitivity

analysis, the individual contributions were combined in quadrature (i.e.,

combined uncertainty: ...

2222

+∂+∂+∂+∂=∂dcba

xxxxx ) to estimate the total

uncertainty (Bevington & Robinson 1992) in the model output – simulated shell

acceleration and velocity. The model output uncertainty was needed to compare

it against the difference observed between the measured and the simulated

shell motion. In other words, if the simulation error (i.e. the mean difference

between the simulated and measured shell acceleration) is less than the model

output uncertainty, then the simulation results are within tolerance; indicating

that the rowing model is an adequate representation of the real rowing system.

152

Table 5.4: Measurement data and the added random error used for sensitivity analysis. The values calculated from the percentage change were

used as the standard deviation of the normally distributed random error with mean values of zero. The expected error magnitudes are shown in red

bold italic. Note that the seat position was limited to a maximum of ± 7 % random error, because of the physical limit of the rower’s leg length.

Peak to peak range 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

L oar angle (deg) 111.39 1.1139 2.2278 3.3417 4.4556 5.5695 6.6834 7.7973 8.9112 10.0251 11.139

R oar angle(deg) 114.50 1.145 2.29 3.435 4.58 5.725 6.87 8.015 9.16 10.305 11.45

Elbow (deg) 111.10 1.111 2.222 3.333 4.444 5.555 6.666 7.777 8.888 9.999 11.11

Shoulder (deg) 135.39 1.3539 2.7078 4.0617 5.4156 6.7695 8.1234 9.4773 10.8312 12.1851 13.539

Trunk (deg) 62.09 0.6209 1.2418 1.8627 2.4836 3.1045 3.7254 4.3463 4.9672 5.5881 6.209

Seat position (m) 0.529 0.00529 0.01058 0.01587 0.02116 0.02645 0.03174 0.03703 – – –

153


First, in section 5.3.1, the rowing model simulation error (i.e. the difference

between the simulated and measured rowing shell motion) is examined to

identify how accurate the rowing model was able to represent the real rowing

system. This is followed by an examination of the results from the sensitivity

analysis of the rowing model in relation to the uncertainties in the model

constants in section 5.3.2. Section 5.3.3 presents the results from the sensitivity

analysis of the effects of random error in the rowing model inputs on the model

output. The combined effect of the uncertainties in the model constants and

random error in the measured input variables is examined in 0. Finally, the

effect of synchronisation error is discussed in 5.3.5.

5.3.1 ROWING MODEL SIMULATION ERROR

Figure 5.2a shows the simulated shell acceleration with the two measured shell

acceleration traces (measured with the biomechanics measurement system and

the Rover system) for subject 2. The general shape of the simulated shell

acceleration trace matched the measured traces quite well. The main deviations

were in the drive phases at t = 0 to 1.2 s, 3.0 to 4.2 s, and 6.0 to 7.2 s in Figure

5.2b. This was expected because force generation is the most complex

component of the rowing model and the blade-water interface was represented

with a simple static model, instead of a full computational fluid dynamics model.

In particular, large deviations occurred at the blade entries and exits. For the

blade entries, the deviations were -3.94 ms-2 (131 % error) at 0.2 s, -2.95 ms-2

(92 %) at 3.12 s and -4.37 ms-2 (146 %) at 6.16 s. For the blade exits, the

deviations were -4.26 ms-2 (316 %) at 1.16 s, -1.90 ms-2 (2540 %) at 4.20 s, and

-2.47 ms-2 (660 %) at 7.24 s. The difficulty in calculating the forces accurately

when the oar blades entered and came out of the water was the reason for

these large deviations. As mentioned in chapter 4, the immersed oar blade area

was estimated by human visual assessment of the video frames during blade

entry and exit. Further, it was assumed that both the oar blades entered and

exited the water symmetrically because the video only captured the rowing

motion from one side. This was likely to be the reason for the over-estimate of

the deceleration magnitude (i.e. simulated acceleration was significantly lower

154

than the measured acceleration) at the blade entries and exits. It should be

noted that the large error percentages (calculated using the standard formula of

%100/)( ×− measuredmeasuredsimulated ) was because sometimes the

measured acceleration was very close to zero, but the simulated acceleration

was not. The most prominent example of this was the deviation of -1.90 ms-2

(2540 %) at 4.20 s. This problem was avoided in subsequent analyses by using

a different scaling approach as discussed in the next paragraph.

During the recovery periods (at t= 1.2 to 3.0 s, 4.2 to 6.0 s, and 7.2 to 9.1 s in

Figure 5.2), the deviations between the simulated and measured traces were

much smaller than in the drive phase, as shown in Figure 5.2b. In particular, the

simulated trace was much smoother in the recovery phase than the measured

traces, because the rowing model did not account for random noise in the

measurements, waves or turbulence of the water or any jerking movement in

the rower’s sculling. Further, the only active force on the rowing system during

this time was the rower’s recovery, since the propulsive force was zero, so the

main source of error was in the rower motion data. The other sources of error,

which affect both the drive and recovery phase, include error in the model

constants and synchronisation error from using data acquired with two separate

measurement systems. Table 5.5 shows the mean error between the simulated

and the measured shell acceleration traces for all the data points throughout the

three strokes. The mean error as a percentage of the range of shell acceleration

(i.e. maximum acceleration minus minimum acceleration) was about 7 %.

Percentage of error relative to the range of shell acceleration was used

because, as discussed previously, sometimes the measured acceleration was

very close to zero and the use of the standard error formula of

%100/)( ×− actualactualestimated resulted in extremely large error percentages

(actually over 106 % for some data points). These data points biased the mean

error towards an excessively large percentage that was not useful for

interpretation.

155

(a)

(b)

Figure 5.2: (a) plot of the simulated shell acceleration and the two sets of independently

measured shell acceleration data for subject 2. (b) plot of the simulation error (simulated

data minus the “Biomech” measured data).

156

Table 5.5: Mean error between the simulated and the two measured acceleration data.

Difference between simulated and measured shell acceleration data:

Mean error (ms-2) Mean error as a percentage of the range of shell acceleration (%)

Rover 0.825 ms-2 6.79%

Biomech 0.857 ms-2 7.02%

Figure 5.3 shows the simulated and the measured shell velocity traces. Again,

the simulated shell velocity trace matched the measured trace quite well. The

simulated shell velocity trace deviated from the measured velocity most

apparently towards the end of the blade entries (at t = 0.25 to 0.75 s, 3.25 to

3.75 s and 6.25 to 6.75 s) and the end of the blade exits (at t = 1.0 to 1.5 s, 4.0

to 4.5 s and 7.0 to 7.5 s). These deviations between the shell velocity traces are

slighted delayed in relation to the deviations in the shell acceleration plot in

Figure 5.2. This is logical because velocity is the integral of acceleration, so the

error in velocity is accumulated from the error in acceleration. Table 5.6 shows

the mean error between the simulated and the measured shell velocity traces

for all the data points for the three strokes. The mean error as a percentage of

the range of shell velocity was approximately 4.7 %. The mean error as a

percentage of the range of shell velocity was used to be consistent with the

mean error percentage for shell acceleration.

In the measured shell velocity trace in Figure 5.3, there were two abrupt

changes in the data at t = 2.0 s and 8.0 s. This was due to the GPS correcting

the shell velocity obtained by integrating the accelerometer data.

Table 5.6: Mean error between the simulated and measured velocity data.

Mean error (ms-1) Mean error as a percentage of the range of shell velocity (%)

Difference between simulated and measured shell velocity data:

0.105 ms-1 4.70%

157

Figure 5.3: Plot of the simulated and measured shell velocity data.

5.3.2 THE EFFECT OF VARIATIONS IN THE MODEL CONSTANTS

ON THE SIMULATION OUTPUT

Figure 5.4 and Figure 5.5 show how the variations in the model parameters

affected the propulsive force and rower velocity, respectively. These two

variables are the active (i.e. applied) forces on the rowing system, as opposed

to the drag force, which is a reactive force. Figure 5.4 shows the graphs of all

the model constants, with the exception of oar blade area, water density, and

oar blade drag and lift coefficients, which share the same graph because they

have identical traces (explained below). Some of the model constants had such

a small effect on the simulation that it was difficult to observe the difference in

the plots without zooming in by at least ten times the scale, thus most of those

plots were omitted in Figure 5.5 to Figure 5.7. Figure 5.6 and Figure 5.7 show

how the variations in the model constants affected the simulated shell

acceleration and velocity, respectively. These two variables are the resultant

motion of the rowing system, which were the model outputs. Note that only one

rowing stroke was selected for the graphs to provide a better view of the

changes, since some of them are so small. The effects of each of the model

constants against the four rowing system variables (propulsive force, rower

velocity, shell acceleration and shell velocity) are summarised in Table 5.7

158

In order to realistically replicate the error in the experimentally determined oar

blade drag and lift coefficients, random error had to be added to the coefficients

at different angles of attack. It is beyond the scope of this thesis to analyse the

effect of the oar blade characteristics, with independent variations in the drag

and lift coefficients at different angles of attack, on the motion of the rowing

system. The oar blade drag and lift coefficients were varied collectively because

the main objective was to cause the propulsive force to increase or decrease in

magnitude, thereby being able to determine the error that resulted in the

simulation, and not to analyse the hydrodynamic effects. When the oar blade

drag and lift coefficients were varied collectively, it had the same effect as

varying the oar blade area and water density, since they all scaled the blade

force proportionally (see Equation 4.4 in chapter 4).

Note that the results reflect what happened when error was added to one of the

model parameters, while the rest of the model parameters were kept

unchanged. The results here did not take physiological effects into account, so

it is not realistic to use them to analyse biomechanical factors. For example, an

increase in shell drag resistance by 10 % would increase the rower’s work load

dramatically, hence the force applied by the rower should decrease over time

for physiological reasons, but this was not accounted for in the simulations.

159

(a)

(b)

Figure 5.4: Propulsive force variation with a change in a selected model parameter: (a)

oar blade area (water density, and blade drag and lift coefficients had the exact same

effect); (b) oar length; (c) rower mass; (d) shell mass; and (e) shell drag coefficient.

160

(c)

(d)

Figure 5.4 continued.

161

(e)


162

(a)

(b)

Figure 5.5: Rower (centre of mass) velocity variation with a change in a selected model

parameter: (a) oar blade area had no effect on rower velocity (water density, and blade

drag and lift coefficients had no effect either); (b) rower mass had an imperceptible effect

on rower velocity graph. The graphs for oar length, shell mass and shell drag coefficient

were omitted because they had no effect on the rower velocity in the rowing model.

163

(a)

(b)

Figure 5.6: Shell acceleration variation with a change in a selected model parameter: (a)

oar blade area (water density, and blade drag and lift coefficients had the exact same

effect); (b) oar length. The graphs for rower mass, shell mass and shell drag coefficient

were omitted because the change in the shell acceleration graph were too small to see,

like the oar blade area graph.

164

(a)

(b)

Figure 5.7: Shell velocity variation with a change in a selected model parameter: (a) oar

blade area (water density, and blade drag and lift coefficients had the exact same effect);

(b) oar length; (c) rower mass; and (d) shell drag coefficient. The graph for shell mass

was omitted because the change in the shell velocity graph was too small to see.

165

(c)

(d)


166

Table 5.7: A summary for the effect of each of the model parameters against the four rowing system variables.

Rowing system

variable

Model

Parameter

Propulsive force, bladeF

(N) Velocity of the rower’s

centre of mass, rowerv

(ms-1)

Simulated shell

acceleration, shella

(ms-2)

Simulated shell velocity,

shellv

(ms-2)

Oar blade area,

bladeA

(m2)

Figure 5.4a

Directly scaled the propulsive force by a fixed percentage change. That is, an increase in oar blade area made the propulsive force larger when it was positive and even more negative when it was negative.

Reminder:

2

2

1

_ slipDbladedragbladevCAF ρ=

2

2

1

_ slipLbladeliftbladevCAF ρ=

2

_

2

__ liftbladedragbladereactionwaterFFF +=

Figure 5.5a

No effect on the rower motion.

Figure 5.6a

The increased propulsive force caused the shell acceleration to reach higher peaks and lower minimums, but with an overall increased acceleration in the drive phase. The lower shell acceleration (unnoticeable in the plot) in the recovery phase was due to the increased shell velocity, which increased the drag force.

Figure 5.7a

The increased oar blade area increased the oar blade force, which resulted in an increased shell velocity.

Water density, ρ (kg m-3)

Same effect as oar blade area. Same as oar blade area. No effect.

Same effect as the oar blade area.


167

Blade drag and lift coefficients,

DC & L

C (dimensionless)

Same effect as oar blade area. Same as oar blade area. No effect.



Oar length, oarL

(m)

Figure 5.4b

A change in the oar length resulted in the largest propulsive force scaling (larger magnitude for both positive and negative force). The reason was that it significantly changed the velocity vector at the oar blade by increasing the oar angular velocity, and hence, the propulsive force curve. The propulsive force was more significantly increased in magnitude when it was positive (i.e., when the oar angular velocity vector was more dominant than the shell velocity vector) than when it was negative (i.e. during the blade entry and exit when the shell velocity vector was more dominant).

No effect. Figure 5.6b

The overall increased propulsive force caused the shell acceleration to be much higher in the drive phase. More negative accelerations were reached during blade entry and exit (or catch and release). The increased shell velocity resulted in a larger drag force, hence, reduced the shell acceleration slightly in the recovery phase.

Figure 5.7b

An increased oar length dramatically increased the propulsive force, which resulted in a much faster shell velocity curve.

168

Rower mass,

rowerm

(kg)

Figure 5.4c

The effect that the increased rower mass had on the propulsive force throughout the stroke was not intuitive. It was lower from 0 to 0.48 seconds, higher from 0.48 to 1.18 seconds, and lower from 1.18 to 1.24 seconds. (The end of the drive phase, or the release, was at 1.24 seconds)

Figure 5.5b

Logically, if the rower’s mass was inaccurately measured, the rower motion should still remain the same (i.e., the measurement of the rower’s motion is independent of rower mass). Unexpectedly, an increased rower mass resulted in a minuscule decrease in rower velocity (imperceptible on the plot). The rower’s centre of mass travels a shorter distance than the sliding seat, which was combined into the rower’s sliding mass, so an increase in rower mass reduces the full excursion of the combined centre of mass.

No graph shown because the variation was too small to see.

Variation in the rower mass had a complex effect on the shell acceleration. With an increased rower mass, shell acceleration was lower from 0 to 0.72 seconds, higher from 0.72 to 0.82 seconds, lower from 0.82 to 0.93 seconds, higher from 0.93 to 2.9 seconds, and lower from 2.9 to 3 seconds.

Figure 5.7c

An increased rower mass reduced shell velocity range because of the increased inertia in the rowing system. With an increased rower mass, the shell velocity was higher from 0 to 0.48 seconds (i.e., less significant dip) and lower from 0.48 to 1.18 seconds (i.e., lower peak). The increased shell velocity during the recovery phase, from 1.18 to 3 seconds, was due to the shell surging forward faster with the increased rower momentum. In contrast, a decreased rower mass made it easier for the shell velocity to vary.

169

Shell mass,

shellm

(kg)

Figure 5.4d

A change in the shell mass caused an unnoticeable change in the propulsive force graph. With an increased shell mass, the propulsive force was actually lower during the first 0.58 seconds, but for the rest of the drive phase (up to 1.24 seconds), the propulsive force was increased by a small amount.

No effect. No graph shown because the variation was too small to see.

Increased shell mass basically scaled the shell acceleration amplitude down. The curve had lower peaks and less significant dips, corresponding to the increased inertia, which reduced the variation in acceleration.

No graph shown because the variation was too small to see.

With an increased shell mass, the inertia in the rowing system was increased. Thus, the peak and trough of the shell velocity trace were lower in magnitude. On the contrary, a lower shell mass allowed the rowing shell to reach a higher peak velocity, and because of the higher drag force (proportional to the shell velocity) encountered, the minimum velocity was lower.

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Shell drag coefficient, c (dimensionless)

Figure 5.4e

An increase in the shell drag coefficient resulted in a larger propulsive force. This is because with an increased resistive force on the rowing system, a larger propulsive force was generated in the simulation to “balance” the motion of the rowing system. The feedback nature of the differential equation describing the motion of the rowing system where the propulsive force (i.e., input) is dependent on the shell velocity (i.e., output) is the mechanism which brings about the “balance”. The most apparent increase in the propulsive force graph was during 0.2 to 0.7 seconds.

No effect. No graph shown because the variation was too small to see.

An increased shell drag coefficient resulted in a higher acceleration during most of the drive phase (0.04 to 1.00 seconds); well into the blade entry and early part of the blade exit when the oar angular velocity vector was more dominant than the shell velocity vector. Again, this was because the propulsive force had to compensate for the higher drag in the differential equation. Shell acceleration was decreased during the recovery phase (1.00 to 3.00 seconds) with the increased shell drag.

Figure 5.7d

An increased drag coefficient made the shell travel slower throughout the whole stroke. However, the effect was more pronounced during the recovery phase when the propulsive force was absent and there was nothing to counter the drag force.

171

Figure 5.8 is a plot of the mean error in the shell acceleration against the

amount of uncertainty in the model parameters. It shows the sensitivity of the

model to each of the modelling constants. Evidently, variation in each of the

model constants was linearly proportional to the change in the simulated shell

acceleration. It can be seen from Figure 5.8 (also noted in Table 5.7) that oar

blade coefficients (i.e., drag and lift collectively), blade area and water density

have the same effect on the rowing model simulation. This is because when any

one of these constants is changed by a given percentage, it changes the drag

and lift force at the blade proportionally.

Figure 5.8: Plot of the mean error in the shell acceleration output against uncertainty in

the model parameters.

Figure 5.9 is a plot of the mean error in the shell velocity against the amount of

uncertainty in the model parameters. It also shows the sensitivity of the model

to each of the modelling constants like Figure 5.8. The difference is that Figure

5.9 reflects the effect on the shell velocity, which is the integral of shell

acceleration, so it represents the accumulated error in the shell acceleration.

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Figure 5.9: Plot of the mean error in the shell velocity output against error in the model

parameters.

Table 5.8 ranks the model parameters in the order of influence on the simulated

shell acceleration and velocity outputs. The ranking is based on the change in

the simulation outputs with a ±10% error in each of the model parameters. That

is, ranking 1 has the largest effect on the simulation outputs.

Table 5.8: Ranking table for the model parameters based on their influence on the

simulated shell motion (based on a ±10% error in the model parameters).

Ranking Model parameter and the percentage change instigated in the simulated shell acceleration

Model parameter and the percentage change instigated in the simulated shell velocity

1 Oar length (1.42 %) Oar length (13.73 %)

2 Rower mass (0.50 %) Shell drag coefficient (2.00 %)

3 Shell drag coefficient (0.33 %) Rower mass (1.59 %)

4 Oar drag coefficient, blade area and water density (0.31 %)

Oar drag coefficient, blade area and water density (0.78 %)

5 Shell mass (0.18 %) Shell mass (0.20 %)

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From Table 5.8, one would notice that the percentage change in the simulated

velocity is much more significant than the simulated acceleration. This was

because the range (i.e., peak to peak value) of the shell acceleration was much

larger than the range of the shell velocity. That is, acceleration error percentage

was lower because it was divided by a larger value. Further, shell velocity is the

integral of shell acceleration, so error in the shell acceleration is accumulated

into shell velocity. Thus, if the error introduced to the shell acceleration is

consistently above, or below, for a considerable time interval (as opposed to

fluctuating above and below), then the error will accumulate into the shell

velocity.

Note that the only difference in the ranking between the shell acceleration and

velocity outputs in Table 5.8 is rower mass. Error in the rower mass caused the

second largest change in the shell acceleration output (Figure 5.8), but it was

only third for the shell velocity output (Figure 5.9). This was because the ±10 %

shell velocity curves actually crossed over the control curve twice at

approximately t = 0.5 and 1.2 s in Figure 5.7c. The “crossing-over points” were

due to the increased inertia in the rowing system as a result of the increased

rower mass (as discussed in Table 5.7). With the increased rower mass, the

shell velocity reached a less significant dip at t = 0.2 s and a lower peak at t =

1.1 s. That is, it was more difficult for the rowing system to reach a higher

velocity and slow down to a lower velocity (i.e., more difficult to accelerate and

also to decelerate). Further, the increased rower mass resulted in a larger

sliding momentum, so the rowing shell was actually faster during the recovery

phase as can be seen in Figure 5.7c. Thus, in comparison to the shell drag

coefficient, which shifted the whole velocity curve either up or down (as shown

in Figure 5.7d), the mean error in shell velocity was lower with the error in rower

mass because of the “cross-over points”.

Table 5.8 gives an indication of the sensitivity of the model to each of the model

parameters, but the expected uncertainty was not 10 % for any of the constants.

Table 5.9 provides the error propagation results for the expected uncertainty for

each of the model parameters. As can be seen, the three model parameters of

most concern (shaded cells) are the outboard oar length, shell drag coefficient,

174

and the oar blade drag and lift coefficients. An outboard oar length uncertainty

of about ± 2 cm would actually be expected, which was mainly due to the

difficulty in determining the centre of pressure at the blade. The oar length

uncertainty was simulated at ± 1 % (or ± 1.805 cm as specified in Table 5.1) to

be consistent with all the other parameters. Hence, the uncertainty in the oar

length propagated to the error in the simulated shell acceleration and velocity

would actually be slightly higher than ±0.14 % and ±1.38 %, respectively. This

meant that oar length basically had the most significant effect on the simulation

output out of all the model parameters.

Table 5.9: Expected uncertainties of the model parameters and the corresponding error

propagation in the simulated shell acceleration and simulated shell velocity.

Model parameter Expected uncertainty

Mean error as a % of the shell acceleration range

Mean error as a % of the shell velocity range

Shell mass (kg) ±3% ±0.06% ±0.06%

Rower mass (kg) ±1% ±0.05% ±0.17%

Density of water (kgm-3)

±1% ±0.03% ±0.09%

Oar blade area (m2)

±1% ±0.03% ±0.09%

Oar blade drag and lift coefficients (scaled) (kgm-1)

±5% ±0.16% ±0.45%

Shell drag coefficient (kgm-1)

±5% ±0.17% ±1.02%

Oar length (m) ±1% ±0.14% ±1.38%

In summary, when a 10 % uncertainty was assumed for all the model

parameters, the motion of the rowing system was most sensitive to an

uncertainty in oar length, while the shell mass error had the least effect. When

realistic uncertainties were considered, oar length, shell drag coefficient, and

oar blade drag and lift coefficients were the most significant contributing model

parameters for simulation error.

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5.3.3 THE EFFECT OF RANDOM ERRORS IN THE MODEL INPUTS

ON THE SIMULATION OUTPUT

Figure 5.10 is a plot of the mean error in the shell acceleration against the

amount of added error in the model inputs (time series measurements).

Figure 5.10: Plot of the mean error in the shell acceleration output against error in the

model inputs.

As expected, the amount of error in the shell acceleration was more significant if

the rower motion measurement accounted for a larger moving mass. That is, in

ascending order: elbow angle, shoulder angle, trunk orientation and seat

position. It is apparent in Figure 5.10 that the elbow angle error was basically

negligible. This was because the elbow angle error only had an effect on a

small fraction of the total rower momentum and did not have any effect on the

propulsive force generation. The shoulder angle and trunk orientation also had

no effect on the propulsive force generation.

With the same percentage of input error, oar angle error resulted in a larger

mean error in shell acceleration than the seat position error. A comparison of

the shell acceleration profiles, Figure 5.11 for seat position error and Figure

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5.12 for oar angle error, revealed that the oar angle error affected the shell

acceleration trace in the drive phase and had no effect in the recovery phase,

while the seat position error affected the shell acceleration trace throughout the

whole stroke. The reason for this is that the oar angle only affects the propulsive

force, which is only present during the drive phase. So, the oar angle error had

a very significant effect on the simulated rowing shell motion, even though it

only affected the drive phase of the rowing stroke.

Figure 5.11: Plot of the simulated shell acceleration data with increasing amount of error

added to the seat position data. Note that only 1 of the 20 sets of random errors, but with

all the scaled levels of error percentages, is shown.

Figure 5.13 is a plot of the mean error in the shell velocity against the amount of

added error in the model inputs (time series measurements). It confirms the

findings observed in Figure 5.10 that if the rower motion measurement

accounted for a larger portion of the rower’s mass, the error in the simulated

shell motion would be larger. That is, the same order of influence for the rower

motion measurements (in ascending order): elbow, should, trunk and seat

position.

177

Figure 5.12: Plot of the simulated shell acceleration data with increasing amount of error

added to the oar angle data. Note that only 1 of the 20 sets of random errors, but with all

the scaled levels of error percentages, is shown.

In comparison to the mean acceleration error (Figure 5.10), the oar angle error

had an even larger effect on the mean velocity error than the seat position

(Figure 5.13). As discussed before, the oar angle error had a very significant

effect on the simulated rowing shell motion. It is evident from Figure 5.12 that

the oar angle error changed the shell acceleration profile significantly because

there was a dramatic change in the net impulse (integral of force with respect to

time) – area under the propulsive force curve during the drive phase.

Consequently, the motion of the rowing system was perturbed throughout the

whole rowing stroke, not just during the drive phase, and drastically altered the

shell velocity profile, as shown in Figure 5.14. The oar angle error had a much

more significant effect on the simulated shell velocity than the seat position

error (comparing Figure 5.14 and Figure 5.15). Note that Figure 5.12 and Figure

5.14 were graphed from the same one out of twenty sets of random errors

added to the oar angle data. Likewise, Figure 5.11 and Figure 5.15 were

graphed from the same one out of the twenty sets of random errors added to

the seat position data. Table 5.10 ranks the measurement inputs in their order

of influence on the simulated shell motion. Namely, in descending order, oar

178

angle, seat position, trunk orientation, shoulder angle and elbow angle.

Figure 5.13: Plot of the mean error in the shell velocity output against error in the model

inputs.

Figure 5.14: Plot of the simulated shell velocity data with increasing amount of error

added to the oar angle data. Note that only 1 of the 20 sets of random errors, but with all

the scaled levels of error percentages, is shown

179

Figure 5.15: Plot of the simulated shell velocity data with increasing amount of error

added to the seat position data. Note that only 1 of the 20 sets of random errors, but with

all the scaled levels of error percentages, is shown.

Table 5.10: Ranking table for the measurements based on the effect of their errors on the

rowing model output error.

Ranking (largest error in the rowing model output is ranked number 1)

Expected error in the measurement

Mean error as a % of the shell acceleration range

Mean error as a % of the shell velocity range

1

Oar angle

3% 5.32% 6.16%

2

Seat position

3% 5.05% 1.61%

3

Trunk orientation

6% 4.12% 1.60%

4

Shoulder angle

3% 0.23% 0.08%

5

Elbow angle

3% 0.04% 0.02%

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5.3.4 COMBINED UNCERTAINTY

As explained in the methods in section 5.2, the resultant uncertainty in the

rowing model output (i.e., shell acceleration and velocity) was estimated by

finding the variations in the model output caused by variations in each of the

measured inputs/model parameters, and then combining them in quadrature

(i.e., combined uncertainty: ...

2222

+∂+∂+∂+∂=∂dcba

xxxxx ) (Bevington &

Robinson 1992). In other words, the combined uncertainty of the rowing model

is based on the expected uncertainty in each of the model parameters and the

expected error in each of the measured inputs. The results are shown in Table

5.11. The rowing model simulation errors for shell acceleration in Table 5.5 and

for shell velocity in Table 5.6 are duplicated in Table 5.11 for ease of reference.

Comparing the combined uncertainty and the simulation error, it was found that

the simulation had an acceptable amount of error for the shell velocity

estimation (4.70% simulation error compared to a combined uncertainty of

6.84%), as well as being adequately accurate for the shell acceleration

estimation (7.02% simulation error compared to a combined uncertainty of

8.39%). The velocity simulation error was well within the combined uncertainty,

while the acceleration simulation error had a narrower margin. This once again

highlighted the intricacy of simulating the shell acceleration compared to

simulating the shell velocity. Velocity is essentially the accumulative addition of

the acceleration data points, so while the acceleration profile contains a lot of

the sharp high frequency details, they are lost in the velocity profile through the

integration process.

The fact that the mean error between the measured data and the simulated

data (i.e., simulation error) was within the combined uncertainty of the rowing

model meant that the simulation error could be accounted for by the

uncertainties in the rowing model constants and model inputs, and confirmed

that the rowing model is an adequate representation of the real rowing system.

In particular, the model contained all the necessary components, including force

generation at the oar blades, rower motion and total resistance on the rowing

system, and the representations of these components are sufficiently accurate.

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Table 5.11: Combined uncertainty of the rowing model simulation compared against the

mean error between the simulated and measured data (the latter is shown in brackets).

Shell motion variable Uncertainty and error in original units

Uncertainty and error as percentages of the magnitude range (%)

Mean acceleration error

(Rover)

(Biomech)

1.06 ms-2

(0.825 ms-2)

(0.857 ms-2)

8.39 %

(6.79 %)

(7.02 %)

Mean velocity error

(Rover)

0.15 ms-1

(0.105 ms-1)

6.84 %

(4.70 %)

5.3.5 SYNCHRONISATION ERRORS

One of the main sources of error was that the measurements were made using

two separate measurement systems, as illustrated in Figure 5.1 (Refer to

Chapter 4 for a description of the measurement systems). The biomechanics

measurement system (used to measure oar angle and seat position) and the

video camera (used to measure trunk orientation, shoulder angle and elbow

angle) were not synchronised and the time discrepancy between them was not

known. The two data sets were manually aligned to the nearest sample, but

since the measurement systems were not synchronised electronically, their

samples could be off by anything between 0 to 0.04 seconds (i.e. 0.04 s, since

the sampling rate was 25 Hz for the biomechanics measurement system and

the video frame rate was also 25 Hz). Thus, a simple simulation was

undertaken to study the effects of having the data misaligned by one data point.

The reason for shifting by one data point and not by a fraction of a data point

was that the latter required the data to be interpolated and resolving the

proportions of the synchronisation error caused by the misalignment of the two

data sets and by the interpolation error is very difficult.

Figure 5.16 shows the simulated shell acceleration traces for the original

aligned data, video data lagging and the biomechanics data lagging. Similarly,

Figure 5.17 shows the simulated shell velocity traces for the same three

conditions. When the biomechanics data was lagging, the deviation seemed to

be more pronounced in the drive phase as shown in Figure 5.16. This seemed

logical since the biomechanics data was used for modelling the force

182

generation, which is only involved with the drive phase of the rowing cycle.

When the video data was lagging, the misalignment exacerbated the blade exit

error at about t = 1.1 s in Figure 5.16. This was because the misaligned rower

motion data combined with the braking effect of the blades made the

deceleration at the release even worse. That is, at the release, the rower motion

should have started recovering, so the rower’s momentum should accelerate

the rowing shell and help cancel out the braking effect of the blades. In Figure

5.17, the velocity trace corresponding to the video data lagging deviated from

the actual data considerably for the rest of the recovery period because of the

large erroneous deceleration at 1.1 seconds.

Figure 5.16: Plot of the simulated shell acceleration for the original aligned data and with

synchronisation error (out by 1 data point).

Table 5.12 shows the mean shell acceleration error as a result of the introduced

misalignment between the two measured data sets that are the model inputs.

Table 5.13 shows the mean shell velocity error as a result of the

synchronisation error between the two measured data sets. The mean

acceleration error was larger when the biomechanics data was lagging than

when the video data was lagging; 3.47 % compared to 2.53 %, respectively, as

shown in Table 5.12. This was in accordance with the observation discussed

183

previously that when the biomechanics data was lagging, it affected the force

generation more significantly, so the error in the simulated acceleration was

larger. The mean velocity error was smaller when the biomechanics data was

lagging than when the video data was lagging; 4.49 % compared to 5.26 %,

respectively, as shown in Table 5.13. This was because of the large deviation

between the video lagging velocity trace and the original data during the

recovery phase in Figure 5.17, which was caused by the large deceleration

error at the release in Figure 5.16 at around t = 1.1 s.

Figure 5.17 Plot of the simulated shell velocity for the original aligned data and with

synchronisation error (out by 1 data point).

The effect that the synchronisation error had on the simulated motion was

considerable in comparison to the combined uncertainty presented in section 0.

The mean acceleration error was 3.47 % when the biomechanics data was

lagging and 2.53 % when the video data was lagging compared to 8.39 %

combined uncertainty in the simulated acceleration. The mean velocity error

was 4.49 % when the biomechanics data was lagging and 5.26 % when the

video data was lagging compared to 6.84 % combined uncertainty in the

simulated velocity. It is very difficult to analytically quantify the effects of the

synchronisation error on the rowing simulation, as the error propagates through

184

the model’s equations in a very complicated manner. Nevertheless, this simple

synchronisation error simulation provided an indication that the misalignment

between the measured data had a significant effect on the simulation accuracy.

Table 5.12: Mean error between the simulated acceleration data and the out of

synchronisation acceleration data.

Difference between the original simulated shell acceleration data and:

Mean error (ms-2) Mean error as a percentage of the peak to peak shell acceleration range (%)

Simulated shell acceleration with the Biomechanics measurement system’s data lagging by one data point

0.44 ms-2 3.47 %

Simulated shell acceleration with the Video data lagging by one data point

0.32 ms-2 2.53 %

Table 5.13: Mean error between the simulated velocity data and the out of

synchronisation velocity data.

Difference between the original simulated shell velocity data and:

Mean error (ms-1) Mean error as a percentage of the peak to peak shell velocity range (%)

Simulated shell velocity with the biomechanics measurement data lagging by one data point

0.10 ms-1 4.49 %

Simulated shell velocity with the video data lagging by one data point

0.12 ms-1 5.26 %

As the biomechanics measurement system and the video camera were not

electronically synchronised, synchronisation error was present and it did

contribute to the rowing simulation error. This further supported that the rowing

model was an adequate representation of the real rowing system. By

185

electronically synchronising the video camera and the biomechanics

measurement system, the simulated results should improve and the simulation

error should reduce accordingly.

5.4 CONCLUSION

In conclusion, it has been shown that the rowing model can generate simulated

shell acceleration and velocity data that are within tolerance to the measured

data. The simulated shell acceleration data deviated from the two sets of

measured acceleration data by an average of 6.91 %, while the simulated

velocity data deviated from the measured velocity data by 4.70 %. The

sensitivity analysis indicated that the expected error in the shell acceleration

and velocity were 8.39 % and 6.84 %, respectively. The error in the simulated

acceleration and velocity were within these tolerance limits. Further, the

difference in the measured shell acceleration between the Rover system and

the biomechanics measurement system was 2.98 % (mean error as a

percentage of the range of shell acceleration). Although the simulated shell

acceleration deviated from the measured acceleration data by an average of

6.91 %, which is more than double the 2.98 % difference between the two sets

of measured acceleration, the rowing model was reasonably accurate in

representing the real rowing system, especially when considering that a lot of

the model parameters were based on empirical data.

It has been shown that the misaligned data from the two unsynchronised

measurement systems could generate an acceleration error between 2.53 %

and 3.47 %, and a velocity error between 4.49 % and 5.26 %. The

synchronisation error cannot be summed to the total uncertainty directly

because it has a complicated error propagation relationship with all of the model

inputs.

Another error to point out was the boundary condition problems in solving the

system differential equation, which caused large errors at the start and end of

the simulated data. However, the simulation was done with extra data points at

the start and end, and then omitted, to minimise the error associated with the

boundary effects.

186

The sensitivity analysis showed that, of all the time series measured data, the

rowing model was most sensitive to oar angle and seat position, as the former

accounts for the propulsive force and the latter accounts for a significant

component of the rower motion. Thus, it is recommended that these variables

are measured as accurately as possible, such as doubling the sampling rate

and increasing the resolution of the analogue to digital conversion. In particular,

the oar angle and seat position measurements can be combined with the shell

acceleration measurement to estimate the propulsive force on the rowing

system, which gives a good indication on the rower’s efficiency and technique.

This topic will be discussed in chapter 7.

5.5 REFERENCES

Bevington, PR & Robinson, DK 1992, Data reduction and error analysis for the physical sciences, 2 edn, McGraw-Hill, New York. Caplan, N & Gardner, TN 2005, 'A new measurement system for the determination of oar blade forces in rowing', in MH Hamza (ed.), Proceedings of the Third IASTED International Conference on Biomechanics, Benidorm, Spain, pp. 32-7. Kleshnev, V 1999, 'Propulsive efficiency of rowing', in RH Sanders & BJ Gibson (eds), 17th International Symposium on Biomechanics in Sports, Edith Cowan University, Perth, Western Australia, Australia, pp. 224-8. Lazauskas, L 1998, Rowing shell drag comparisons, viewed 2008/09/02 2008, <http://www.cyberiad.net/library/rowing/real/realrow.htm>. Wilcox, CD, Dove, SB, McDavid, WD & Greer, DB 2002, UTHSCSA ImageTool, 3.0 edn, Department of Dental Diagnostic Science at The University of Texas Health Science Center, San Antonio, Texas, U.S.A.

187

6. MOTION OF THE ROWER’S CENTRE OF MASS

6.1 OVERVIEW

In this chapter, the motion of the rower’s centre of mass will be examined. From

here on, the “motion of the rower’s centre of mass” will be referred to as “rower

c.o.m. motion” for convenience, where motion includes position, velocity and

acceleration. Likewise, the “acceleration of the rower’s centre of mass” will be

referred to as “rower c.o.m. acceleration”, and so forth for velocity and position.

Instead of using the rower model that required video analysis and seat position

data to determine the rower c.o.m. motion, which was discussed in chapter 4, a

simplified method is proposed in this chapter. The rower c.o.m. motion

determined using the rower model that required video analysis for the rower’s

upper body movement combined with the seat position data will be referred to

as “video-derived rower c.o.m. motion”. Also, the rower c.o.m. motion

determined using the simplified method will be referred to as “estimated rower

c.o.m. motion” for convenience from here on.

Section 6.2 introduces the motivation for estimating the rower c.o.m. motion,

which was mainly because video analysis was too labour intensive and time

consuming. Section 6.3 describes the simplified methodology for estimating the

rower c.o.m. motion. The proposed method basically calculated the “average

difference” between the time series data of the rower c.o.m. position and that of

the seat position for several rowing strokes, and this “average difference curve”

was then used in an inverse manner to estimate the rower c.o.m. position from

the seat position data. The estimated rower c.o.m. motion was compared

against the video-derived rower c.o.m. motion to assess its accuracy. Further,

the estimated rower c.o.m. motion data was used in the rowing model

simulation to calculate the shell acceleration and velocity, and then compared to

those calculated using the video-derived rower c.o.m. motion data. That is,

compare the simulation outputs (simulated shell acceleration and velocity) using

the two sets of rower c.o.m. motion data. Section 6.4 shows the results that

indicated that the proposed method was sufficiently accurate in estimating the

rower c.o.m. motion. Section 6.5 concludes the chapter.

188

6.2 INTRODUCTION

Many rowing models in the literature used a point mass (Brearley & de Mestre

1996; Lazauskas 1997; van Holst 1996) or two point masses (Atkinson 2001) to

represent rower c.o.m. motion. In most cases, the rower c.o.m. motion was

represented with a simple mathematical equation. On the other hand, there

were two models (Cabrera, Ruina & Kleshnev 2006; Lazauskas 2004) that

estimated rower c.o.m. motion with more accurate methods. Cabrera et al.

(2006) estimated the rower c.o.m. motion from seat position and trunk position

with the assumption that the rower’s centre of mass was “concentrated in her

gut”. While, Lazauskas (2004) developed a multi-segment rower model to

estimate the rower c.o.m. motion, similar to the one developed in this thesis.

The main point here is that the rowing shell motion is strongly influenced by the

rower c.o.m. motion, which required a lot of work and resources to collect and

process the data in order to calculate it accurately.

In the author’s case, it was very labour intensive and time consuming to develop

a multi-segment rower model specifically for each rower, video record the

rowing shell from an adjacent boat, and to process the video data and seat

position data to determine the rower c.o.m. motion. A simpler methodology that

would be practical to be implemented on a routine basis was needed. Thus, it

was set out to investigate whether it was sufficiently accurate to estimate the

rower c.o.m. position from the seat position measurement and an “average

difference curve”. The “average difference curve” was generated from the

difference between the seat position data and the rower c.o.m. data.

If the “average difference curve” proved to be sufficiently accurate as a

simplified methodology, it would be generated from a single session of video

analysis and then used repeatedly to estimate the rower c.o.m. motion from the

seat position measurement. The equipment required to generate the “average

difference curve” include the rowing shell and oars that the rower uses in

training, seat position measurement, a video camera mounting mechanism on

the outrigger, and a motion capture system (including motion analysis software,

video camera and reflective markers). The seat position data would then be

189

subtracted from the rower c.o.m. position data over many strokes and averaged

to obtain the “average difference”.

The motivation for developing a simple method to relate seat motion to rower

c.o.m. motion was because it was too inconvenient to obtain the rower c.o.m.

motion with video recording out in the water on a routine basis. Nevertheless,

the rower c.o.m. motion provides a more realistic and accurate biomechanical

representation of how the rower moves, as it includes the upper body

movement, compared to using only the seat position data. Further, it was

discovered that it would be useful to develop a methodology, with minimal

hindrance to the rower that could be used everyday during training, to estimate

the propulsive force for rowing technique assessment using the Rover

GPS/accelerometer measurement device. This method of estimating the

effective propulsive force requires the rower c.o.m. motion data. The idea of

estimating the effective propulsive force will be discussed in further details in

chapter 7.

6.3 METHOD

This section presents the process of relating the seat position data to the rower

c.o.m. motion. The five step process outlined below details the reason for using

a “difference curve” to estimate the rower c.o.m. position from the seat position

data, the actual methodology, and the error analysis of using the “difference

curve”.

190

STEP 1 – Determine the relationship between the seat position data and the

rower c.o.m. position data.

Figure 6.1 shows the seat position data and the rower c.o.m. position data for

subject 2 (from a total of 4 subjects, as detailed in Chapter 4) who sculled at a

nominal rate of 20 strokes per minute. As can be seen, the seat position and the

rower c.o.m. position had very similar upward and downward slopes, but

differed with their peaks. While the seat position curve had plateau-like peaks,

the rower c.o.m. position curve had higher rounded peaks. This difference

corresponded to when the seat position reached its maximum when the rower’s

legs were fully extended (i.e. seat position reached the plateau), but the rower’s

upper body was still moving away from the foot stretcher (i.e. rower c.o.m.

position kept increasing). Based on the average of 3 rowing strokes for each of

the 4 subjects, the rower c.o.m. position (average of 0.679 m) travelled 29.6%

further than the seat position (average of 0.524 m), which was a substantial

difference that could not be neglected.

Figure 6.1: Plot of the seat position and the rower c.o.m. position for subject 2 of the four

subjects.

191

The pattern observed in Figure 6.1 was prevalent for all four rowers and

regardless of stroke rating (subject 1 sculled at a faster nominal rate of 32

strokes per minute compared to the other three subjects, who sculled at a

nominal rate of 20 strokes per minute). The rower c.o.m. position data were

plotted against the seat position data in Figure 6.2 to examine their relationship.

It can be seen in Figure 6.2 that the relationship between the two sets of data

was linear, but with hysteresis, at the top right end of the graphs. The hysteresis

in Figure 6.2 corresponds to the difference in the peaks of the seat position and

rower c.o.m. position in Figure 6.1. It can be seen in Figure 6.2 that the

hysteresis loops are not symmetrical, and the physical reason for this was that

each of the rower’s motion through the drive phase was not the exact reversal

of the motion through the recovery phase. This was as expected since a rower

has to overcome substantial resistance to power the rowing shell during the

drive phase and experiences significantly less resistance during recovery. An

interesting feature to note was that the hysteresis loops were quite different for

subject 2, 3 and 4, even though they all sculled at a nominal rate of 20 strokes

per minute. This indicated that the upper body movement of each rower was

quite different from one another.

Using a regression curve to represent the relationship between the seat position

and rower c.o.m. position would be straightforward, but it would not account for

the hysteresis, which represents a key aspect of the rower motion. So, the seat

position was simply subtracted from the rower c.o.m. position to work out the

“difference” from stroke to stroke, and then averaged to produce an “average

difference curve”. The “average difference curve” was subsequently used to

relate the seat position data to the rower c.o.m. position data. The assumption

was that the “average difference curve” would be sufficiently accurate in

compensating for the difference between the seat position and rower c.o.m.

position, even though the difference varies from stroke to stroke.

192

Figure 6.2: Plot of the rower c.o.m. position data against the seat position data

STEP 2 – Set up the seat position data and rower c.o.m. position data to work

out the difference curves.

The seat position data and rower c.o.m. position data had to be normalised and

interpolated before they were subtracted from one another:

i) The seat position and rower c.o.m. position time series data were split

into individual strokes at the instant that the oar blade dipped into the

water in the video frame.

ii) The offsets of the time series data of all the individual strokes were then

removed (i.e., each set of time series data was subtracted from its initial

value, so that they all start at zero).

iii) The data of all the strokes were normalised in magnitude (divided by the

individual stroke’s maximum seat position value), and temporally

normalised between 0 and 1.

iv) The data were then spline interpolated to the highest number of data

points out of all the different strokes, so that they could be compared.

193

Figure 6.3 shows the processed seat position and rower c.o.m. position data

(there were 3 consecutive strokes from 4 single scullers equating to a total of 12

strokes).

Figure 6.3: Plot of all the normalised and interpolated seat position and rower c.o.m.

position data.

STEP 3 – Evaluate the difference between the seat position and rower c.o.m.

position.

Evaluating the difference curves involved:

i) All the normalised seat position data sets were averaged to produce a

“combined means seat position curve” (i.e., an average over the

combined 12 rowing strokes for all the rowers). The three normalised

seat position data sets for each rower were averaged to produce an

“individual mean seat position curve” (i.e., an average over the 3 rowing

strokes for each individual rower).

ii) As in (i), a combined mean rower c.o.m. position curve and individual

mean rower c.o.m. position curves were calculated.

194

iii) The mean seat position curves were then subtracted from the

corresponding mean rower c.o.m. position curves to obtain the difference

curves.

The mean seat position curves, mean rower c.o.m. position curves and

difference curves are plotted in Figure 6.4

Figure 6.4: Plot of the mean seat position curves, mean rower c.o.m. position curves and

the difference curves.

STEP 4 – Estimation of rower c.o.m. position by adding the difference curve to

the seat position data.

Next, the difference curve and seat position data were summed to estimate

rower c.o.m. position. To generate estimated data for the rower c.o.m. position:

i) The difference curve was spline interpolated to the same number of

points as each stroke of the seat position data.

ii) Subsequently, the difference curve was added to the seat position data

stroke by stroke. That is, it was assumed that the difference between the

seat position data and the rower c.o.m. data was the same every stroke.

195

Two sets of rower c.o.m. position data were estimated: one with the individual

difference curve for each of the rowers and the other with the combined

difference curve for all four rowers. The data estimated with the individual

difference curve will be referred to as “individual-estimated” and the data

estimated with the combined difference curve will be referred to as “combined-

estimated” from here on.

STEP 5 – Error analysis.

The error in estimating the rower c.o.m. position data by adding the difference

curve to the seat position data was assessed. This was done by comparing the

estimated rower c.o.m. position data against the video-derived rower c.o.m.

position data. Also, the estimated rower c.o.m. position data was used in the

rowing model simulation to see how much difference there was in the simulated

rowing shell velocity and acceleration compared to using the video-derived

rower c.o.m. position data originally. The error in the simulated shell velocity

and acceleration were quantified to determine whether the estimated rower

c.o.m. position data was sufficiently accurate to justify replacing the rower

model (that requires labour intensive video analysis) with the simplified method

(that requires seat position measurement and the average difference curves).

Four measures were used for the error analysis, which included:

i) The sum of squared error, described by the generalised equation of

Equation 4.12. The sum of squared error provides an indication of the

total error between each estimated data set and its corresponding video-

derived data set.

ii) The absolute mean error, described by the generalised equation of

Equation 4.13. The absolute mean error provides an indication of the

average error between the two sets of data.

iii) The similarity between the two curves (i.e. the two sets of data) was

assessed by calculating the correlation coefficient, as described by

Equation 4.14.

196

iv) The maximum deviation between the two sets of data, along with its time

of occurrence, was evaluated to see how significant the difference

reached in the most extreme case. In order to appreciate the magnitude

of the maximum deviation in the rower c.o.m. position, it was also

specified as a percentage of error relative to the largest rower c.o.m.

excursion (i.e. how far the rower’s centre of mass moved from catch to

release) out of the three strokes for each rower. For example, subject 1’s

centre of mass travelled a total distance of 0.690 m for the first stroke,

0.689 m for the second stroke and 0.690 m for the third stroke, therefore,

the largest rower c.o.m. excursion was 0.690 m. The percentage of error

was the error value divided by 0.690 m and multiplied by 100%. For the

acceleration curves, the percentage of error was relative to the range of

the acceleration values (i.e. maximum acceleration minus minimum

acceleration) rather than the conventional method of dividing by the

relative acceleration value. This was done because sometimes the

measured acceleration was close to zero, but the simulated acceleration

was not, which produced excessively large error percentages. To be

consistent, the percentage of error for velocity was also relative to the

range of the velocity (i.e. maximum velocity minus minimum velocity).


Figure 6.5 are plots for the estimated rower c.o.m. position (i.e. using the

difference curve) compared against the video-derived rower c.o.m. position (i.e.

using the rower model). As mentioned in the methods section, two sets of rower

c.o.m. position data were produced: the individual-estimated rower c.o.m.

position data and the combined-estimated rower c.o.m. position data. As can be

seen in Figure 6.5 , the individual-estimated rower c.o.m. position curves are

indistinguishable from the video-derived curves almost all of the time. On the

other hand, the combined-estimated curves deviated from the video derived

curves quite apparently in Figure 6.5(a), (c) and (d) (subjects 1, 3 and 4,

respectively).

197

(a) Subject 1

(b) Subject 2

Figure 6.5: Plots for the video-derived and estimated rower c.o.m. position. Video was

calculated from seat position data and video analysis (i.e. using the rower model).

Individual was the estimated data using each subject’s individual difference curve.

Combined was the estimated data using the combined difference curve. (a) Subject 1. (b)

Subject 2. (c) Subject 3. (d) Subject 4.

198

(c) Subject 3

(d) Subject 4


199

An interesting feature to note was that the stroke rating changed the timing of

the rower c.o.m. motion. This can be seen in Figure 6.5(a) for subject 1, who

sculled at a nominal rating of 32 strokes per minute compared to a nominal

rating of 20 strokes per minute for the other 3 rowers. The rower c.o.m. position

curve for subject 1 (Figure 6.5(a)) was more symmetrical than the other 3

subjects (Figure 6.5(b), (c) and (d)), who had curves that were skewed to the

right (i.e. longer tail on the right). In practice, when a rower increases the stroke

rate, time is mainly conserved by recovering faster. Thus, a higher stroke rating

would have a more symmetrical rower c.o.m. position curve, compared to a

lower stroke rating, which would have a recovering period that is much longer

than the drive phase (i.e. the rower c.o.m. position peaks earlier in the stroke).

It was anticipated that the combined difference curve would not work well for

subject 1, and that the error would be comparable for subject 2, 3 and 4, since

subject 1 was rowing at a nominal rate of 32 strokes per minute, while the other

three rowers were rowing at a nominal rate of 20 strokes per minute. This was

not the case. The estimated rower c.o.m. motion using the combined difference

curve worked well for subject 2 (Figure 6.5(b)), but not subject 1, 3 and 4

(Figure 6.5(a) (c) and (d)). This finding suggested that each individual rower has

a characteristic rower c.o.m. motion. This effect has actually been discussed in

step one of the methods section (section 6.3), where the hysteresis loops in

Figure 6.2 were quite different between the subjects. The difference in the

hysteresis loops between the subjects is related to the deviation between the

video-derived and combined-estimated rower c.o.m. position curves around the

peaks in Figure 6.5. The varying amount of deviation between the combined-

estimated rower c.o.m. position curve and the video-derived rower c.o.m.

position curves of subjects 2, 3 and 4 (Figure 6.5(b), (c) and (d)) indicated that

the upper body movement of each rower was quite different from one another

even at the same stroke rate. These observations indicated that the rower

c.o.m. motion can only be accurately estimated using an individual difference

curve that is also stroke rate dependent.

200

The estimation error will now be examined. Table 6.1 summarises the goodness

of fit and the error for the two sets of estimated data compared to the video-

derived data. Comparing the correlation coefficients in Table 6.1, the correlation

between the individual-estimated rower c.o.m. position data and the video-

derived data was higher than the correlation between the combined-estimated

rower c.o.m. position data and the video-derived data for all four rowers.

In accordance to the correlation coefficients, the sum of squared error and the

absolute mean error in the combined-estimated rower c.o.m. position data were

several and up to many folds larger than the individual-estimated rower c.o.m.

position data. The absolute mean error percentage ranged from 1.26 to 2.68%

for the combined-estimated data, while it ranged from 0.40 to 0.85% for the

individual-estimated data. Further, the absolute maximum deviation percentage

ranged from 3.71 to 7.30% for the combined-estimated data, while the absolute

maximum deviation percentage ranged from 1.33 to 2.48% for the individual-

estimated data. Therefore, the combined difference curves are not adequate for

rower c.o.m. motion estimation, especially when the absolute maximum

deviation was as high as 7.30%. On the other hand, the error in the individual-

estimated rower c.o.m. motion was quite reasonable. These results confirmed

that the rowers, each with a different body build, moved their centre of mass

according to their own timing and technique.

201

Table 6.1: Comparison of the estimated rower c.o.m. position against the video-derived rower c.o.m. position.

Rower c.o.m. position estimation error using combined

difference curve

Rower c.o.m. position estimation error using individual

difference curve

Correlation

coefficient

Sum of

squared

error (m2)

Absolute

mean error

(m) and as a

percentage

of full rower

c.o.m.

excursion in

brackets

Maximum

deviation (m),

time of

occurrence (s) &

as a percentage

of full rower

c.o.m. excursion

in brackets

Correlation

coefficient

Sum of

squared

error (m2)

Absolute

mean error

(m) and as a

percentage

of full rower

c.o.m.

excursion in

brackets

Maximum

deviation (m),

time of

occurrence (s) &

as a percentage

of full rower

c.o.m. excursion

in brackets

Subject 1 0.9945 0.0688 0.0171

(2.68%)

0.0453 at 4.24 s

(7.10%)

0.9999 0.0019 0.0031

(0.48%)

0.0085 at 1.12 s

(1.33%)

Subject 2 0.9990 0.0252 0.0087

(1.26%)

-0.0256 at 4.00 s

(-3.71%)

0.9999 0.0027 0.0028

(0.40%)

0.0112 at 9.08 s

(1.62%)

Subject 3 0.9988 0.0626 0.0138

(1.94%)

0.0398 at 1.64 s

(5.59%)

0.9997 0.0123 0.0060

(0.85%)

-0.0176 at 7.00

s (-2.48%)

Subject 4 0.9993 0.1121 0.0183

(2.63%)

-0.0507 at 4.16 s

(-7.30%)

0.9999 0.0042 0.0036

(0.52%)

-0.0098 at 3.64

s (-1.41%)

202

It was interesting to note in Table 6.1 that subject 4 had a sum of squared error

for the combined-estimated data of 0.1121, while subject 1 had 0.0688, but yet

they had about the same absolute mean error. That is, subject 4 had an

absolute mean error of 0.0183 compared to 0.0171 for subject 1. The reason for

this discrepancy was identified by comparing Figure 6.5(a) and Figure 6.5(d) for

subjects 1 and 4, respectively. The deviation between the combined-estimated

curve and the video-derived curve for subject 1 was smaller in magnitude but

relatively longer in duration than for subject 4. For subject 1, the deviation was

almost half of the rowing stroke cycle and the absolute maximum deviation was

0.0453 m (at 4.24 s), whereas for subject 4, the deviation was about 40% of the

rowing stroke cycle and the absolute maximum deviation was 0.0507 m (at 4.16

s). Further, the combined-estimated curve and the video-derived curve crossed

over at about 0.9, 2.7 and 4.5 s for subject 1 (Figure 6.5(a)), whereas the

combined-estimated curve was consistently below the video-derived curve for

subject 4 (Figure 6.5(d)). Thus, the two error statistics, sum of squared error

and absolute mean error, were useful in revealing the characteristics of the

deviation between data curves.

As the combined-estimated rower c.o.m. position data were not sufficiently

accurate, they were not used in the rowing model simulation. In particular, it had

already been established in chapter 5 that the rowing model is sensitive to error

in the motion of the rower’s centre of mass, when error was added to the rower

motion data to observe the effect on the simulated shell acceleration. Figure

6.6, Figure 6.7, Figure 6.8 and Figure 6.9 are the shell acceleration and velocity

plots for subjects 1, 2, 3 and 4, respectively. The ‘video’ traces were the

simulation results that used the video-derived rower c.o.m. motion (i.e., rower

model). The ‘estimated’ traces were the simulation results that used the

individual-estimated rower c.o.m. motion. The measured shell acceleration data

acquired with the ‘Rover’ accelerometer/GPS system and the biomechanics

(‘Biomech’) measurement system were also plotted in the shell acceleration

graphs. Similarly, the measured shell velocity data acquired with the Rover

system were also plotted in the shell velocity graphs.

203

The simulated shell acceleration traces compared well, which indicated that the

individual-estimated rower c.o.m. position data were comparable to the video-

derived rower c.o.m. position data. In the velocity plots, the differences between

the simulated shell velocity traces were more noticeable. This was expected

because the shell velocity data reflects the accumulative error in the shell

acceleration data. The individual-estimated shell velocity traces deviated from

the video-derived shell velocity traces most significantly during the recovery

phase for all four subjects. For example, in Figure 6.7(b) for subject 2, the

deviations occurred during the intervals: t = 2 to 3, 5 to 6, and 8 to 9 s. The

reason for this observation was that during the recovery, when rower motion is

the main active force on the rowing system, even the small error in the rower

c.o.m. position data resulted in very apparent deviations in the shell motion

traces. On the contrary, during the drive phase, the propulsive force at the blade

is the dominant force, so error in the rower motion was not as apparent in the

shell motion traces.

Another error to highlight was the large deviation at the blade entry, where the

shell acceleration was at its minimum acceleration. For example, in Figure

6.7(a) (subject 2) the individual-estimated shell acceleration trace deviated from

the video-derived shell acceleration trace by approximately 3.0 ms-2 at around t

= 3.2 and 6.2 s. At these times, the difference between the individual-estimated

rower c.o.m. position trace and the video-derived rower c.o.m. position trace

was hardly noticeable in Figure 6.5(b). At these times, the rower c.o.m. position

was at the minimum, which corresponded to the end of the recovery when the

rower’s body was fully tucked in. As the rower c.o.m. motion was changing

direction from the recovery phase to the drive phase at these times, the rower

c.o.m. velocity was zero; changing from negative to positive. Moreover, this

actually corresponded to the maximum in the rower c.o.m. acceleration. The dip

in the shell acceleration trace during the blade entry is highly dependent on the

corresponding maximum rower c.o.m. acceleration (this point will be explained

in further details in chapter 7 – the biomechanical analysis chapter). Thus, the

simulated shell acceleration and velocity are very sensitive to the error in the

rower c.o.m. motion at the blade entry. Deviation between the individual-

estimated and video-derived shell acceleration traces during blade entries were

204

also observed for the other three subjects (Figure 6.6(a), Figure 6.8(a) and

Figure 6.9(a)), although they were not as significant as subject 2 (Figure 6.7(a)).

The same error statistics used in Table 6.1 were calculated for the comparison

of the shell acceleration data in Table 6.2 and the shell velocity data in Table

6.3. These statistics quantified how much the error in the individual-estimated

rower c.o.m. position affected the rowing model simulation. The four statistics:

correlation coefficient, sum of squared error, absolute mean error and maximum

deviation along with its time of occurrence, are shown along the rows,

respectively, in both Table 6.2 and Table 6.3.

Table 6.2 compares the similarities and differences between the four sets of

shell acceleration data, which includes the measured shell acceleration using

the Rover system, measured shell acceleration using the biomechanics system,

simulated shell acceleration that used the video-derived rower c.o.m. motion

and simulated shell acceleration that used the individual-estimated rower c.o.m.

motion. Table 6.3 compares the three sets of shell velocity data against one

another, which includes the measured shell velocity using the Rover system,

the video-derived simulated shell velocity and the individual-estimated

simulated shell velocity. These two tables display the results of the individual

subjects separately in columns. The absolute mean error and maximum

deviation were also given as percentages relative to the acceleration or velocity

range (i.e. maximum value minus the minimum value), as discussed in the

methods in section 6.3.

205

(a)

(b)

Figure 6.6: Subject 1’s shell acceleration (a) and velocity (b) plots. Video is the simulation

result that used the rower c.o.m. motion calculated from the video data and seat position

data. Estimated is the simulation result that used the rower c.o.m. motion estimated from

the seat position data and individual difference curve. Rover is the measured data using

the Rover accelerometer/GPS measurement system. Biomech is the measured shell

acceleration using the biomechanics measurement system.

206

(a)

(b)

Figure 6.7: Subject 2’s shell acceleration (a) and velocity (b) plots. The figure legend is

the same as Figure 6.6.

207

(a)

(b)



208

(a)

(b)



209

Table 6.2: Comparison of the measured and simulated sets of shell acceleration data for all 4 subjects, along the columns, respectively. The 4 error

quantification statistics (as detailed in section 6.3 – STEP 5) are shown along the rows, respectively.

Acceleration

data

Biomechanics system (measured)

acceleration

Rover (measured) acceleration Simulated acceleration using video-derived

rower c.o.m. motion

0.9955 0.9793 0.9547 0.9634

37.1160 74.8180 90.7080 90.5980

0.4574

(2.98%)

0.4595

(3.76%)

0.4364

(4.70%)

0.5002

(4.71%)

Rover

(measured)

acceleration

-1.6865

at 1.72 s

(10.99%)

-2.7931

at 0.00 s

(22.88%)

-3.5778

at 4.12 s

(38.53%)

-2.6811

at 6.16 s

(25.21%)

Colu

mn 1

is s

ubje

ct

1

Colu

mn 2

is s

ubje

ct

2

Colu

mn 3

is s

ubje

ct

3

Colu

mn 4

is s

ubje

ct

4 Note: Error was calculated as row relative to

column (e.g. Rover data minus biomechanics

data for the block of results Rover versus

Biomechanics system).

0.8583 0.8359 0.7071 0.8338 0.8624 0.8393 0.7337 0.8510 Row 1 is correlation coefficient

524.6400 320.4700 839.4500 295.7700 538.0300 311.3400 836.0900 292.9000 Row 2 is sum of squared error (m2s

-4)

1.2848

(8.37%)

0.8565

(7.02%)

1.0892

(11.73%)

0.8070

(7.59%)

1.3486

(7.69%)

0.8254

(5.58%)

1.0676

(10.68%)

0.8341

(7.21%)

Row 3 is absolute mean error (ms-2

).

Percentage of error in brackets

Simulated

acceleration

using video-

derived

rower c.o.m.

motion

10.5145

at 0.00 s

(68.49%)

-4.3738

at 6.16 s

(35.83%)

-18.0347

at 0.04 s

(194.2%)

-4.4791

at 8.88 s

(42.12%)

10.8172

at 0.00 s

(61.66%)

6.5114 at

0.00 s

(44.00%)

-17.6890

at 0.04 s

(177.0%)

-4.1695

at 1.12 s

(36.06%)

Row 4 is maximum deviation (ms-2

), its time

of occurrence (s) and percentage of error

relative to full acceleration range in brackets

0.8635 0.8225 0.7106 0.8392 0.8681 0.8286 0.7276 0.8528 0.9904 0.9696 0.9763 0.9864

497.8700 347.0000 804.4800 276.6600 504.8300 335.8700 820.0400 278.7500 38.5210 60.5130 77.2950 25.9780

1.2423

(8.09%)

0.8269

(6.77%)

1.0657

(11.48%)

0.7843

(7.38%)

1.3139

(7.49%)

0.8018

(5.42%)

1.0892

(10.90%)

0.8000

(6.92%)

0.3299

(1.79%)

0.2949

(2.33%)

0.3646

(1.61%)

0.2451

(1.86%)

Simulated

acceleration

using

individual-

estimated

rower c.o.m.

motion.

10.5145

at 0.00 s

(68.49%)

-6.9756

at 6.16 s

(57.15%)

-16.7074

at 0.04 s

(179.9%)

-4.0692

at 1.16 s

(38.27%)

10.8172

at 0.00 s

(61.66%)

6.5114 at

0.00 s

(44.00%)

-16.3616

at 0.04 s

(163.7%)

-4.6400

at 1.12 s

(40.12%)

2.9178 at

3.68 s

(15.86%)

3.4016 at

3.16 s

(26.89%)

3.8257 at

6.00 s

(16.88%)

1.7596 at

8.88 s

(13.38%)

210

Table 6.3: Comparison of the 3 sets of rowing shell velocity data for all 4 subjects, along the columns, respectively. The 4 error quantification

statistics are shown along the rows, respectively, following the format of Table 6.2.

Velocity

data

Rover (measured) velocity Simulated velocity using video-derived rower c.o.m.

motion

0.9548 0.9770 0.9296 0.9734

10.0140 4.2246 35.3240 6.0742

0.2228

(9.77%)

0.1048

(4.64%)

0.3357

(16.22%)

0.1347

(7.05%)

Simulated

velocity

using

video-

derived

rower

motion

-0.61544 at

5.12 s

(26.99%)

0.48242 at

9.08 s

(21.35%)

-0.72698 at

7.12 s

(35.12%)

0.43184 at

6.36 s

(22.61%)

Note: Error was calculated as row relative to column (e.g.

simulated data using estimated rower motion minus

simulated data using video analysis in the block of entries

below this note).

0.9545 0.9763 0.9338 0.9726 0.9976 0.9974 0.9959 0.9968

7.3627 4.2219 32.8250 4.7596 0.9630 0.7205 0.9434 0.6551

0.1895

(8.31%)

0.1089

(4.82%)

0.3281

(15.85%)

0.1198

(6.27%)

0.0659

(3.33%)

0.0460

(2.05%)

0.0515

(2.01%)

0.0444

(2.48%)

Simulated

velocity

using

individual-

estimated

rower

c.o.m.

motion

-0.51216 at

5.08 s

(22.46%)

0.44846 at

9.08 s

(19.84%)

-0.77551 at

7.12 s

(37.46%)

-0.38197 at

1.24 s

(20.00%)

0.24802 at

1.64 s

(12.53%)

-0.1378 at

6.20 s

(6.13%)

-0.19426 at

5.96 s

(7.59%)

-0.12331 at

3.24 s

(6.87%)

211

Table 6.2 and Table 6.3 were reduced to Table 6.4 and Table 6.5, respectively,

by combining the results for all four subjects. The cross correlation coefficient,

sum of squared error and absolute error were averaged, while the largest

maximum deviation was selected from the four rowers. This was done to obtain

a combined result for the comparison of the measured and simulated shell

motion data.

The shell acceleration simulated with the individual-estimated rower c.o.m.

motion was comparable to the shell acceleration simulated with the video-

derived rower c.o.m. motion. This was deduced from comparing the two sets of

simulated shell acceleration data against the two sets of measured shell

acceleration data in Table 6.4. That is, in Table 6.4, video against biomech (row

2 column 1) and video against Rover (row 2 column 2) compared to estimated

against biomech (row 3 column 1) and estimated against Rover (row 3 column

2). The cross correlation coefficients ranged from 0.8088 to 0.8216, while the

sum of squared errors ranged from 481.5037 to 495.0821 m2s-4. The absolute

mean error percentages ranged from 7.68 % to 8.68 %. Even the maximum

deviations were comparable for the two sets of simulated acceleration data with

under-estimated values ranging from -16.3616 ms-2 to -18.0347 ms-2 (77.37 %

to 85.96 %), when they all occurred at 0.04 second.

The difference between the two simulated shell acceleration data sets

(individual-estimated against video-derived) was actually less than the two

measured shell acceleration data sets (Rover against biomech). The two

simulated data sets (row 3 column 3 in Table 6.4) had a cross correlation of

0.9807, sum of squared error of 50.5768 m2s-4, absolute mean error of 0.3086

ms-2 (1.90%), and a maximum deviation of 3.8257 ms-2 (18.25%, over-

estimation). The two measured data sets (row 1 column 1 in Table 6.4) had a

cross correlation of 0.9732, sum of squared error of 73.3100 m2s-4, absolute

mean error of 0.4634 ms-2 (4.04%), and a maximum deviation of 3.5778 ms-2

(24.40%, under-estimation). Thus, the two simulated data sets had a higher

cross correlation, lower sum of squared error, lower absolute mean error, but a

higher maximum deviation between them compared to the two measured sets.

The main point here is that since the difference between the individual-

212

estimated data and video-derived data was less than the difference between the

Rover data and biomech data, then the individual-estimated rower c.o.m.

motion should be justifiable as a substitute to the rower model that requires

video analysis and seat position data.

Table 6.4: Shell acceleration comparison table. The correlation coefficient, sum of

squared error and absolute mean error are the mean values for the four subjects (row 1,

2 and 3, respectively, in each cell block). The largest maximum deviation value among

the four subjects was selected for display in this table (row 4 in each cell block).

Acceleration

data

Biomechanics

system (measured)

acceleration

Rover (measured)

acceleration

Simulated

acceleration using

video-derived rower

c.o.m. motion

0.9732 Row 1 is correlation coefficient

73.3100 Row 2 is sum of squared error (m2s-4)

0.4634 (4.04%) Row 3 is absolute mean error (ms-2)

Rover

(measured)

acceleration

-3.5778 at 4.12 s

(24.40%)

Row 4 is maximum deviation (ms-2) along

with its time of occurrence (s)

0.8088 0.8216

495.0821 494.5881

1.0094 (8.68%) 1.0189 (7.79%)

Simulated

acceleration

using video-

derived

rower c.o.m.

motion

-18.0347 at 0.04 s

(85.17%)

-17.6890 at 0.04 s

(79.67%)

Note: Error was

calculated as row

relative to column

0.8090 0.8193 0.9807

481.5037 484.8747 50.5768

0.9798 (8.43%) 1.0012 (7.68%) 0.3086 (1.90%)

Simulated

acceleration

using

individual-

estimated

rower c.o.m.

motion

-16.7074 at 0.04 s

(85.96%)

-16.3616 at 0.04 s

(77.37%)

3.8257 at 6.00 s

(18.25%)

213

Table 6.5: Shell velocity comparison table. The correlation coefficient, sum of squared

error and absolute mean error are the mean values for the four subjects (row 1, 2 and 3,

respectively, in each cell block). The largest maximum deviation value among the four

subjects was selected for display in this table (row 4 in each cell block).

Velocity data Rover (measured)

velocity

Simulated velocity using

video-derived rower

c.o.m. motion

0.9587 Correlation coefficient

13.9092 Sum of squared (m2s-2)

0.1995 (9.42%) Absolute mean (ms-1)


video-derived rower

c.o.m. motion

-0.7270 at 7.12 s

(26.52%)

Maximum dev. (ms-1)

time of occurrence (s)

0.9593 0.9969

12.2923 0.8205

0.1866 (8.81%) 0.0520 (2.47%)


individual-estimated

rower c.o.m. motion

-0.7755 at 7.12 s

(24.94%)

0.2480 at 1.64 s

(8.28%)

Referring to Table 6.5, the difference between the individual-estimated shell

velocity data set and Rover shell velocity data set (row 2 column 1) was

comparable to the difference between the video-derived shell velocity data set

and Rover shell velocity data set (row 1 column 1). The cross correlation

coefficients were comparable, with 0.9593 for individual-estimated against

Rover and 0.9587 for video-derived against Rover. The other error statistics

were also comparable. The difference between the individual-estimated shell

velocity data set and Rover shell velocity data set had a sum of squared error of

12.2923 m2s-2, absolute mean error of 0.1866 ms-1 (8.81%) and a maximum

deviation of -0.7755 ms-1 (24.94%, under-estimation). In comparison, the

difference between the video-derived and Rover data sets had a sum of

squared error of 13.9092 m2s-2, absolute mean error of 0.1995 ms-1 (9.42%)

and a maximum deviation of -0.7270 ms-1 (26.52%, under-estimation). These

results indicated that the simulated shell velocity that used the individual-

estimated rower c.o.m. motion had a comparable amount of error compared to

214

the simulated shell velocity that used the rower model with video analysis,

where the error was relative to the measured shell velocity.

Further, comparing the individual-estimated shell velocity against the video-

derived shell velocity, they were highly correlated according to their correlation

coefficient of 0.9969, sum of squared error of 0.8205 m2s-2 and absolute mean

error of 0.0520 ms-1 (2.47%). These results are significantly better than those

comparing the simulated data (i.e., both individual-estimated and video-derived

data) against the Rover measured data, as discussed in the previous

paragraph. The maximum deviation between the individual-estimated data set

and the video-derived data set was 0.2480 ms-1 (8.28%, over-estimation), which

was about three times smaller than the maximum deviation values of 0.7755

ms-1 (24.94%) for individual-estimated against Rover and 0.7270 ms-1 (26.52%)

for video-derived against Rover. Thus, the results indicated that the two sets of

simulated shell velocity were comparable.

The velocity results also confirmed that the individual-estimated rower c.o.m.

motion data, evaluated from the seat position data and the individual difference

curves, was sufficiently accurate as a substitute for the rower c.o.m. motion

data determined from the rower model, which required video analysis and seat

position data.

6.5 CONCLUSION

From the analysis of the 12 rowing strokes, it was recognised that the rowers

were very consistent with their movements and it was reasonably accurate to

estimate the rower c.o.m. position from the seat position data and a pre-

determined difference curve. This difference curve was obtained by subtracting

the seat position data from the rower c.o.m. position data, which was estimated

from video analysis of rower body angles combined with seat position data. A

combined difference curve for all four rowers and individual difference curves

for each rower were generated, and their accuracy in reproducing the rower

c.o.m. position data by combining with seat position data was assessed. The

estimated rower c.o.m. position that used the individual difference curve had an

absolute maximum error of 2.48%, while the estimated rower c.o.m. position

215

that used the combined difference curve had an absolute maximum error of

7.30%. This indicated that each rower has their own characteristic timing and

technique, so the difference curve must be specific to the rower in order to

accurately estimate the rower c.o.m. position. It was also observed that stroke

rating changed the shape of the rower c.o.m. position curve. Thus, each rower

must have their own difference compensation graphs for different stroke ratings.

Estimating the rower c.o.m. position using the seat position data and the rower

specific difference curves was found to be comparable to the rower c.o.m.

position calculated from the rower model that required video analysis and seat

position data. The rower c.o.m. position estimated with the individual difference

curves had an absolute maximum error of 2.48% and a mean error of 0.85 %

relative to the rower c.o.m. position calculated from the rower model, which was

actually the worst case out of the four subjects.

It was also found that the individual-estimated rower c.o.m. motion was

sufficiently accurate for rowing model simulation. In particular, the simulated

shell acceleration error of the individual-estimated rower c.o.m. motion was

comparable to the simulated shell acceleration error of the video-derived rower

c.o.m. motion. On average across the 4 subjects, the absolute mean error and

absolute maximum error in the simulated shell acceleration that used the

individual-estimated rower c.o.m. motion were 7.68% and 77.37%, respectively,

relative to the Rover measured shell acceleration. In comparison, the absolute

mean error and absolute maximum error in the simulated shell acceleration that

used the video-derived rower c.o.m. motion were 7.79% and 79.67%,

respectively, relative to the Rover measured shell acceleration.

Since there was a very limited amount of good quality video data to estimate the

motion of the rower’s upper body, the analysis in this chapter was very limited.

For future work, the rower motion analysis should be conducted by using a

motion capture system (including motion capture software, reflective markers

and a video camera mounted on the outrigger). This will ensure that the video

will have a fixed field of view and the data of good quality. Further, a validation

of the difference curve on data that are not part of the fitting procedure should

216

be conducted. The absence of a validation on out of sample data implied that

no significant conclusion could be drawn from this chapter. At this point it could

only be concluded that it was possible to come up with a difference curve that

adequately described the data of an individual rower at a specific stroke rate

during a specific rowing session. Nevertheless, the data analysis in this chapter

showed that elite rowers have very consistent rowing motion, which implies that

constructing an empirical curve to represent the motion of the rower’s upper

body relative to the sliding seat is a reasonable approach.

In practice, the individual difference curves would be determined with a once off

video analysis session, where the rower would scull at a range of different

stroke rates for a specified number of strokes. For example, 28, 30 and 32

strokes/min for 30 strokes at each of these stroke rates. As it was established in

chapter 5, seat position accounts for the majority of the rower c.o.m. motion, so

measuring the seat position with a sensor, but using a rower and stroke rate

specific difference curve to account for the upper body movement should

enable a good estimate of the rower c.o.m. motion.

Estimating the rower c.o.m. motion using the individual difference curve method

will be useful for calculating the propulsive force on the rowing system. This

topic will be discussed in chapter 7.

6.6 REFERENCES

Atkinson, WC 2001, Modeling the dynamics of rowing - A comprehensive description of the computer model ROWING 9.00, viewed 1 May 2004, <http://www.atkinsopht.com/row/rowabstr.htm>. Brearley, M & de Mestre, NJ 1996, 'Modelling the rowing stroke and increasing its efficiency', in 3rd Conference on Mathematics and Computers in Sport, Bond University, Queensland, Australia, pp. 35-46. Cabrera, D, Ruina, A & Kleshnev, V 2006, 'A simple 1+ dimensional model of rowing mimics observed forces and motions', Human Movement Science, vol. 25, no. 2, pp. 192-220. Lazauskas, L 1997, A performance prediction model for rowing races, viewed 2004/05/01, <http://www.cyberiad.net/library/rowing/stroke/stroke.htm>.

217

—— 2004, Michlet rowing 8.08, viewed 2004/12/01 2004, <http://www.cyberiad.net/library/rowing/rrp/rrp1.htm>. van Holst, M 1996, Simulation of rowing, viewed 2010/2/22 2010, <http://home.hccnet.nl/m.holst/report.html>.

218

7. ANALYSIS OF THE MECHANICS OF ROWING

7.1 INTRODUCTION

This chapter will examine the mechanics of rowing in detail. In particular, graphs

will be presented to clarify the relationship between all the rowing mechanics

variables and how they affect the motion of the rowing system. First, the data of

subject 2, who sculled at a nominal rate of 20 strokes per minute, will be

examined in detail. This set of data will then be compared to that of subject 1,

who sculled at a nominal rate of 32 strokes per minute. Please note that the

comparison was by no means an analysis of the ‘optimal technique’, but just to

highlight the similarities and differences between two different rowers who

sculled at different stroke ratings. A more conclusive comparison would warrant

a significant improvement in the experimental set up in terms of equipment and

resource. Finally, the last section of the chapter will discuss the use of the

Rover system and the differential equation describing the motion of the rowing

system to calculate the propulsive force.

The chapter will be presented as follows:

1. First, the results of the hydrodynamics model for calculating the forward

propulsive force at the oar blade are presented in section 7.3.1. The

results were from subject 2, who sculled at a nominal rate of 20 strokes

per minute. Six vector diagrams at different times during the drive phase

were plotted to explain all the hydrodynamics variables at the oar blade.

The aim here was to explain the concepts visually to make it easier to

understand the graphs of the hydrodynamics variables.

2. Next, the graphs of the hydrodynamics variables are presented in section

7.3.2. These will complete the discussion on oar blade hydrodynamics. In

particular, the graphs show how all of the hydrodynamics variables affect

the forward propulsive force generation.

219

3. The graphs of the rower model are presented in section 7.3.3 (the

explanation on how the motion of the rower’s centre of mass was

calculated was already discussed in Chapter 6). The main intention was

to emphasise to the reader how much the elbow angle, shoulder angle,

trunk orientation and seat position each contribute to the motion of the

rower’s centre of mass.

4. The shell acceleration was plotted with all the components that

contributed to the shell acceleration including the forward propulsive

force, the motion of the rower’s centre of mass and the shell drag

(section 7.3.4). This was done to examine the contribution of each of

these components on the shell motion.

5. Another complete set of data at a different stroke rate (subject 1 at a

nominal rate of 32 strokes per minute) is presented in section 7.4 to

highlight some differences in force generation, the motion of the rower’s

centre of mass and the resultant shell motion.

6. Finally, section 7.5 will discuss the use of the Rover system, seat

position measurement and the differential equation describing the motion

of the rowing system to calculate the propulsive force at the oar blade. In

particular, it is an alternative to instrumented boats with the advantages

of being unobtrusive, inexpensive and easy to set up.

7.2 BACKGROUND

The discussions in this chapter will refer to some of the background theory

presented in the previous chapters. These include:

1. The differential equation describing the motion of the rowing system

(Equation 2.19 and presented again as Equation 4.1).

2. The vector diagram of the oar blade slip velocity and the resultant

propulsive force (Figure 4.1). The associated equation of the water

reaction force (Equation 4.3) and the equations of the oar blade drag and

lift forces (Equation 4.4).

220

3. The equation describing the motion of the rower’s centre of mass as a

result of the motion of all the body segments (Equation 4.8).

4. The graphs showing the oar blade drag (Figure 4.2) and lift (Figure 4.3)

coefficients as a function of the angle of attack.

5. The rowing model flow chart (Figure 5.1) illustrating the measurements

required by the rowing model in order to simulate the shell velocity and

acceleration.

The calculation of the propulsive force at the oar blade was the most

complicated aspect of the rowing model. Thus, one of the main focus of this

chapter is to use the simulation results to explain how the blade force was

calculated. Figure 7.1 summarises how all the rowing system variables interact

in the determination of the blade force.

221

Figure 7.1: Flow diagram illustrating the interaction of the hydrodynamic variables. The

x-component is in the heading direction, while the y-component is orthogonal to the

heading in the plane of the water.

Drag force

(x-component)

Oar angle

Oar angular

velocity

Shell

velocity

Slip velocity

(x-component)

Slip velocity

(y-component)

Slip velocity

magnitude

Angle of

attack

Coefficient

of lift

Slip velocity

direction

Drag force

magnitude

Lift force

magnitude

Drag force

direction

Lift force

direction

Drag force

(y-component)

Lift force

(x-component)

Lift force

(y-component)

Blade force

(y-component)

Blade force

(x-component)

Blade force

magnitude

Blade force

direction

Oar angular

velocity

(y-component)

Oar angular

velocity

(x-component)

Coefficient

of drag

222

7.3 ANALYSIS OF THE ROWING MODEL SIMULATION FOR

SUBJECT TWO

7.3.1 VECTOR ANALYSIS OF THE HYDRODYNAMICS MODELLING

A series of vector diagrams graphed from measured data is presented here to

explain the generation of the hydrodynamics forces at the oar blade. Note that

the vector diagrams (except the rowing shell) were actually plotted to scale on

the graph. The oar length is in units of m, the velocity vectors are in units of ms-

1 and the force vectors are in units of N; so for example, 1 unit on the graph is 1

m in length and 1 ms-1 in velocity. The force vectors were scaled down by a

factor of 30 to make them fit well on the graph with the oar length and velocity

vectors.

Figure 7.2 shows all the oar blade vectors during the catch of the rowing cycle.

When the blade first touched the water during the catch, the oar angular velocity

vector (shorthand for the contribution of the oar angular velocity to the velocity

vector of the centre of the blade as discussed in chapter 4) was small since the

oar rotation had just started changing direction and the shell velocity vector was

much larger in magnitude. The slip velocity (or oar blade velocity), is the vector

sum of the oar angular velocity and the shell velocity, thus, the slip velocity

vector was very similar to the shell velocity vector at this instant of the stroke.

Since the drag force vector is opposite in direction to the slip velocity vector by

definition, the drag force was actually creating a negative thrust or braking effect.

The lift force, perpendicular to the drag force by definition, contributed

insignificantly to the forward propulsion of the rowing shell when its direction

was almost orthogonal to the rowing shell’s heading. Further, the transverse

force component on the rowing shell due to this lift force was predominantly

cancelled out by symmetry with the left oar. As the blade was not fully

immersed into the water at this earliest stage of the catch, this braking force

was not large to start off with, but it increased very quickly as more of the blade

was immersed. (Hofmijster, De Koning & Van Soest 2010) presented

comparable graphs on the basis of inverse dynamical analysis of the oar

behaviour and their findings will be compared to the findings in this section.

Hofmijster et al. showed that the drag component of the blade force was

223

Figure 7.2: Oar blade vector diagram during the catch of the rowing cycle. Oar (on the

right hand side) is the blue line connected to the rowing shell, which is the long and

narrow oval. Vshell is the shell velocity vector, Oar ang v is the oar angular velocity vector,

Vslip is the slip velocity (or blade velocity), FD is the drag force at the oar blade, FL is the

lift force at the blade, Fblade is the resultant force (from the drag and lift forces) at the

blade and Fblade-f is the forward component (in the heading direction) of the resultant

force at the blade.

actually towards the heading, although very small in magnitude, with the lift

component of the blade force correspondingly pointing towards the rowing shell.

The difference is that the oar blade did not create a breaking force in

Hofmijster’s results, whereas it did in the results presented here. As it was

discussed in previous chapters, the braking effect at the blades during the catch

and release was somehow exaggerated in the hydrodynamics model. According

224

to the measured shell acceleration results, there should be a small braking

effect at the blades during the catch in order for the forces to balance out, but it

shouldn’t have been so large and lasted for so long. In fact, the braking effect

was still present in the next two vector plot sequences after Figure 7.2 (figures

not shown). That is, the braking effect lasted 0.12 s (3 samples at 25 Hz sample

rate).

Figure 7.3: Oar blade vector diagram during the early phase of the drive when the drag

force was relatively small.

Figure 7.3 shows the oar blade vectors during the early stage of the drive phase,

when the drag force was relatively small. The slip velocity vector was almost

parallel with the oar, so the angle of attack was low. From the drag and lift

225

coefficients’ relationship with the angle of attack (Figure 4.2 and Figure 4.3), this

means that lift was high compared to the drag in this early phase of the drive.

Again, as the drag force vector is opposite in direction to the slip velocity vector

by definition, it was contributing to a negative thrust. On the contrary, the lift

force was generating a large positive thrust, since a significant component of

the lift force was in the same direction as the shell’s heading. The goal in this

phase is to maximise lift and minimise drag as much as possible. The results of

(Hofmijster, De Koning & Van Soest 2010) also confirmed that lift is the

dominant component that contributes to the propulsion during this period.

Figure 7.4 illustrates the velocity and force vectors before the oar was

orthogonal to the shell heading, when the lift force was almost parallel to the

shell’s heading. The slip velocity vector was almost orthogonal to (i.e. away

from) the rowing shell and was making an angle of approximately 30° with the

face of the oar blade, thus, the angle of attack was about 30°. Lift was

contributing almost all the forward thrust, while drag was not doing any useful

work (i.e. produced a transverse force component on the rowing shell, which

was mostly cancelled out by symmetry with the left oar). Again, the aim in this

phase of the drive is to maximise lift and minimise drag. The results here are in

accordance to (Hofmijster, De Koning & Van Soest 2010).

226

Figure 7.4: Oar blade vector diagram before the oar was orthogonal to the shell’s heading

and when the lift force was almost parallel to the shell’s heading.

Figure 7.5 shows all the oar blade velocity and force vectors when the oar was

(almost exactly) orthogonal to the shell heading. During this period, the slip

velocity vector was orthogonal to the face of the oar blade and parallel (i.e.

opposite direction) to the shell velocity. Thus, drag, opposite in direction to the

slip velocity vector, was contributing almost all the forward thrust. Lift was

negligible at this instant in time when the oar was orthogonal to the shell’s

heading. The goal in this period is to maximise drag. The results here agree

with (Baudouin, Hawkins & Seiler 2002; Caplan & Gardner 2007; Sykes-Racing

2009), but it contradicted the results in (Hofmijster, De Koning & Van Soest

2010).

227

Figure 7.5: Oar blade vector diagram when the oar was orthogonal to the shell’s heading.

Figure 7.6 is actually very similar to Figure 7.4, except that they are opposite in

direction. The slip velocity vector was roughly orthogonal to (i.e. into) the rowing

shell. Again, drag was not contributing to any useful work, while lift was

contributing to almost all the forward thrust. The aim in this period is also to

maximise lift and minimise drag. In comparison to (Hofmijster, De Koning & Van

Soest 2010), the direction of the lift and drag components still corresponded

well, but the magnitude change was different. In particular, Hofmijster et al.

showed that once the oar passed the point of being perpendicular to the

heading, the lift force and drag force consistently reduced in magnitude. On the

contrary, it was found that the lift force and drag force still maintained similar

magnitude after the oar passed the point of being perpendicular to the heading

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in comparison to before being perpendicular. In fact, the blade force (vector

sum of the drag force and lift force) was larger in Figure 7.6 than in Figure 7.4.

Nevertheless, there are many factors that could give rise to this observation

including rower technique, rigging and stroke rate (the rower was sculling at a

nominal rate of 20 strokes per minute in the graphs presented here, while the

rower was sculling at 30-32 strokes per minute in the study of (Hofmijster, De

Koning & Van Soest 2010)).

Figure 7.6: Oar blade vector diagram half way between when the oar was orthogonal to

the shell’s heading and the release of the rowing cycle.

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Figure 7.7 is similar to Figure 7.2, except that they are opposite in direction.

When the blade was coming out of the water at the release, the oar angular

velocity was small since the oar rotation had to slow down, and the shell

velocity vector dominated the slip velocity. Thus, the slip velocity vector was

very similar to the shell velocity vector, much like during the catch. Also similar

to the catch, the drag force was producing a braking effect, while the lift force

was not doing much useful work since its direction was almost orthogonal to the

shell’s heading (but into the shell now, as opposed to during the catch). The

goal of the release is to withdraw the blade from the water as quickly as

possible to minimise the braking effect. In contrast, Hofmijster et al. (2010)

showed that towards the end of the drive phase, the lift force and drag force

magnitudes were very small and eventually reached zero at the release. Again,

the braking effect at the blades during the release was somehow exaggerated

in the hydrodynamics model. According to the measured shell acceleration

results, there should be minimal braking effect at the blades during the release

in order for the forces to balance out. However, it was found that the braking

effect was too large and for too long. The braking effect was actually present in

the three vector plot sequences prior to Figure 7.7, which are not shown here.

This corresponded to the braking effect lasting 0.16 s (4 samples at 25 Hz

sample rate).

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Figure 7.7: Oar blade vector diagram at the release phase of the rowing cycle.

In practice, both the blade drag and lift force vectors are always pointing away

on the opposite side of the blade’s surface to the slip velocity vector. For

example if the slip velocity vector is pointing away from the back (convex side)

of the blade, then the blade drag and lift force vectors should be pointing away

from the front (concave side) of the blade. The vector diagrams (Figure 7.2 to

Figure 7.7) presented in this section are in accordance to oar blade theory

(Sykes-Racing 2009). The only exception was the excessive braking force due

to modelling error at the catch and release.

Another interesting point to note was that the blade force (vector sum of the

blade drag and lift forces) was consistently very close to being orthogonal to the

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oar’s longitudinal axis; ranging from 88.10 to 91.48° for subject 2 and ranging

from 88.13 to 91.27° for subject 1. Thus, most of the blade force was orthogonal

to the oar’s longitudinal axis. In accordance to (Hofmijster, De Koning & Van

Soest 2010), blade force parallel to the oar’s longitudinal axis was non-

negligible ranging from -2.62 to 2.02 N for subject 2 and ranging from -4.61 to

2.68 N for subject 1. However, the magnitude of the parallel oar blade force

measured by the oar shaft force sensors in that study ranged from about -13 to

10 N, which was about 4 folds higher than was found for subject 1 here. It

should be noted that subject 1 sculled at a nominal rate of 32 strokes per

minute, and her height and weight were 183 cm and 75 kg, respectively, while

the subject in the study of (Hofmijster, De Koning & Van Soest 2010) sculled at

30 to 32 strokes per minute, and her height and weight were 173 cm and 70 kg,

respectively. So, the two rowers sculled at about the same stroke rate and were

both in the heavyweight weight class, but were quite different in height. Further,

the data measured by (Hofmijster, De Koning & Van Soest 2010) showed that

during the stroke phase, parallel blade force was acting inwards on the blade

during the first half of the stroke, and outwards during the second half of the

stroke. In contrast, the blade force parallel to the oar shaft’s longitudinal axis

fluctuated inwards and outwards throughout the drive phase for both subject 1

and subject 2. As the data here was calculated using many assumed constants

and estimated data, it was not expected to be as accurate as the data

presented in (Hofmijster, De Koning & Van Soest 2010).

7.3.2 DATA ANALYSIS OF THE HYDRODYNAMICS VARIABLES

This section continues on the theme of hydrodynamics from the previous

section. The hydrodynamics variables derived from empirical data and

measurements from subject 2, who sculled at a nominal rate of 20 strokes per

minute, are plotted below for discussion. Since three consecutive rowing

strokes were simulated in the rowing model, all three consecutive rowing

strokes were also plotted here to illustrate the transition from cycle to cycle.

First, the graphs that are concerned with the direction of the hydrodynamics

variables have to be interpreted according to Figure 7.8. The main point is that

when the velocity or force vector at the oar blade is pointing away from the

rowing shell, the angle is 90°, whereas when the vector is pointing into the

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rowing shell, the angle is 270°. Further, if the vector is pointing in the heading

direction, the angle is 0°, and when the vector is pointing opposite to the

heading, the angle is 180°. Please also note that sometimes the graphs were

plotted in the angle range 180° to 360° and at other times in the range -180° to

0°, even though they are equivalent. This is because in the former case, it was

done for the ease of interpretation for the graphs, while in the latter case, it was

to follow convention.

Figure 7.8: Diagram illustrating how to interpret the vector direction of the

hydrodynamics variables at the oar blades.

Please note that the plots in this section (Figure 7.9 to Figure 7.22) had the

recovery phase data points hidden by masking them with zeroes to highlight

only the drive phase data points.

Figure 7.9 illustrates that the oar angular velocity was numerically derived from

the oar angle, along with oar angular velocity separated into x and y

components. Figure 7.9a shows the measured oar angles, which indicate the

position of the oars as they rotated and the oar blades moved through an arc

path. When the oars were orthogonal to the longitudinal shell axis or heading

direction, the oar angles were defined as zero. At the catch, the oar blades were

closer to the bow or pointing towards the heading direction, and the oar angles

Rowing shell Heading

Right oar

Left oar

0º/360º

0º/360º

180º

180º

90º

90º

270º

270º

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were defined as negative. Similarly, towards the release, when the oar blades

were closer to the stern or pointing away from the heading direction, the oar

angles were defined as positive. The oar angular velocity was obtained by

taking the time derivative of the oar angle data. The direction of the oar angular

velocity vector is orthogonal to the oar’s longitudinal axis at the blade’s centre of

pressure. Thus, the x and y components of the oar angular velocity are

dependent on the magnitude of the oar angular velocity as well as the oar angle.

The x component of the oar angular velocity is negative all the time because it

always points away from the heading direction. The x component of the oar

angular velocity was at its largest magnitude (i.e. most negative) close to when

the oar angular velocity was at its maximum, just after when the oar was

orthogonal to the rowing shell. The y component was initially positive and then

negative. Positive values meant the vector was pointing away from the rowing

shell and negative values meant the vector was pointing into the shell. The y

component was zero when the oar angle was zero. This is because when the

oar is orthogonal to the heading direction, there is only forward and no lateral

component (i.e. only x and no y component) for the oar angular velocity.

The slip velocity vector is the vector sum of the velocity components at the oar

blade, which consists of the oar angular velocity and the shell velocity. As the

shell velocity vector is in the heading direction (x direction), it does not

contribute to the lateral (y direction) component of the slip velocity vector. Thus,

the lateral component of the slip velocity vector is only composed of the y

component of the oar angular velocity vector (so Figure 7.9d is equivalent to

Figure 7.11b). On the other hand, the x component of the slip velocity is the

sum of the shell velocity and the x component of the oar angular velocity, as

shown in Figure 7.10. At the start and end of the drive (i.e. catch and release),

the x-component of the slip velocity vector was predominantly determined by

the shell velocity because the oar angular velocity was small during these times

and had little influence.

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Figure 7.9: Derivation of the oar angular velocity vector from the measured oar angle. (a) Oar angle. (b) Oar angular velocity. (c) x-component of the

oar angular velocity. (d) y-component of the oar angular velocity.

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Figure 7.10: The x component of the slip velocity is the sum of the shell velocity vector and the x component of the oar angular velocity. (a) Shell

velocity. (b) x-component of the oar angular velocity. (c) x-component of the slip velocity.

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Figure 7.11 shows the x and y components of the slip velocity vector

transformed to polar form. This step was required to calculate the other

hydrodynamics variables at the oar blade. As the slip velocity magnitude is the

vector sum of its x and y components, any non-zero values in the x or y

component would contribute to the magnitude regardless of direction. This was

exactly the case when one compares Figure 7.11a and Figure 7.11b against

Figure 7.11c. The direction of the slip velocity vector (Figure 7.11d) completed

almost one revolution throughout the drive phase. This corresponds to the

vector diagrams from Figure 7.2 to Figure 7.7. The direction of the slip velocity

vector started at just above 0° at the catch and finished at just below 360° at the

release, when the slip velocity was predominantly determined by the shell

velocity at these instants during the rowing cycle. The graph of the slip velocity

direction (Figure 7.11d) was verified by comparing it to the x and y component

graphs (Figure 7.11a & b, respectively). The polarity of the x and y components

determine the quadrant the slip velocity is pointing. That is, when the x and y

components are both positive, the direction is between 0° and 90°, while when

they are both negative, the direction is between 180° and 270°. Similarly, when

the x component is positive and y component is negative, the direction is

between 270° and 360°, and when the x component is negative and the y

component is positive, the direction is between 90° and 180°.

Figure 7.12 shows the calculation of the angle of attack, which is the direction of

the slip velocity vector relative to the oar’s longitudinal axis. Explicitly, the angle

of attack (Figure 7.12c) is equal to the slip velocity vector direction (Figure

7.12a) minus the oar axis direction (Figure 7.12b). The angle of attack has to be

specified in the range -180° to 180° because that is the convention. Thus, the

angle of attack was re-drawn in Figure 7.12d in accordance to convention.

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Figure 7.11: Transformation of the slip velocity from Cartesian form to polar form. (a) x-component of the slip velocity. (b) y-component of the slip

velocity. (c) Slip velocity magnitude. (d) Slip velocity direction.

238

Figure 7.12: The angle of attack is the angle between the slip velocity vector and the oar’s longitudinal axis. (a) Slip velocity direction. (b) Oar

direction. (c) Angle of attack (plotted from 0° to 360°). (d) Angle of attack (plotted from -180° to 180°).

239

When the angle of attack is between 0° and 180° it is termed positive, and

correspondingly, it is negative when the angle of attack is between -180° and 0°.

The angle of attack determines how the blade interacts with the water to

produce the drag and lift forces. In the rowing model, this was based on Caplan

and Gardner’s (2005) experimental data, as shown in Figure 4.2 and Figure 4.3.

Figure 4.2 and Figure 4.3 only show the relationship between the angle of

attack and coefficients of drag and lift in the range 0° to 180°. The curves are

basically repeated (to the left) for the angles between -180° and 0°. Please note

that the direction of rotation in calculating the angle of attack were different for

the left and right oars. For the right oar, the angle of attack was positive when

the slip velocity vector was anti-clockwise from the oar axis and vise versa. For

the left oar the angle of attack was positive when the slip velocity vector was

clockwise from the oar axis and vice versa. This follows the explanation in

Figure 7.8.

Figure 7.12d revealed that the angle of attack essentially went through three

stages during the drive phase. Initially during the catch, the oar angular velocity

was small, so the slip velocity vector was behind the blade resulting in a

negative angle of attack. During the middle of the drive phase, the oar angular

velocity vector was larger than the shell velocity vector so that the resultant slip

velocity vector was in front of the blade, which meant a positive angle of attack.

Then during the release, the oar angular velocity had to slow down to change

direction, so the larger shell velocity vector resulted in a negative angle of attack

again.

Figure 7.13 shows the coefficient of drag and coefficient of lift for the three

rowing strokes. The angle of attack started at about -30° and finished at around

-150°, but for most of the drive phase, the angle of attack was within the range

of 0° to 180°. Thus, the shape of the drag coefficient graph (Figure 7.13b) and

the lift coefficient graph (Figure 7.13c) showed some resemblance to Figure 4.2

and Figure 4.3, respectively. The main difference was that they had some data

points at the two ends that corresponded to the negative angles of attack.

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Figure 7.14 shows the coefficient of drag, the slip velocity, immersed blade area

fraction and the blade drag force. The blade drag force is proportional to the

coefficient of drag and the square of the slip velocity (as described by Equation

4.4 in chapter 4 – the rowing model chapter). Visual inspection of Figure 7.14

confirmed this relationship. Referring to each of the three strokes in Figure

7.14d, the first spike in the blade drag force corresponds to the catch, the main

bump in the middle corresponds to the pull through and the last peak

corresponds to the release. The peaks at the start and end of each drive phase

in the blade drag force (Figure 7.14d) were the result of the peaks in the

coefficient of drag (Figure 7.14a) and slip velocity (Figure 7.14b), but their

magnitudes were reduced by the immersed oar blade area (Figure 7.14c).

During the catch and release, the oar blades were only partially immersed into

the water, so the contact area between the water and the oar blade was

reduced. The immersed blade area fraction was crudely estimated by visual

estimation of the video frames. The immersed blade area is very important for

calculating the blade force accurately at the catch and release, but it is very

difficult to measure accurately.

It was also noted that there were large differences between the right and left

drag forces (Figure 7.14d), which must be due to the differences in the

coefficient of drag and slip velocity, since the density of water and (it was

assumed that) the immersed blade area were the same for both the left and

right sides. Just based on visual inspection of Figure 7.14, it could be seen that

the main source of the differences between the left and right drag forces was

the coefficient of drag, which is a function of the angle of attack. Ultimately, the

differences in the left and right drag forces were due to the differences in the

oar angle and oar angular velocity, as the shell velocity vector is always the

same for both the left and right oar.

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Figure 7.13: The coefficient of drag and lift are functions of the angle of attack. (a) Angle of attack. (b) Coefficient of drag. (c) Coefficient of lift.

242

Figure 7.14: The blade drag force is proportional to the coefficient of drag and the square of the slip velocity. (a) Coefficient of drag. (b) Slip

velocity magnitude. (c) Immersed blade area fraction. (d) Blade drag force.

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Blade lift force generation is analogous to the blade drag force. That is, the

blade lift force is proportional to the coefficient of lift and the square of the slip

velocity (Equation 4.4). Figure 7.15 shows the coefficient of lift, the slip velocity,

immersed blade area fraction and the blade lift force. Referring to each of the

three strokes in Figure 7.15d, the initial dip in the blade lift force corresponds to

the catch and the final peak corresponds to the release. The blade lift force had

negative values because its direction changes depending on the coefficient of

lift, which, in turn, is dependent on the angle of attack (Figure 4.3). The blade

drag force only had positive values, because the coefficient of drag is positive

for all angles of attack (Figure 4.2). By definition, the lift force is orthogonal to

the drag force. If one follows the convention that the direction of the blade lift

force is always an additional 90° from the direction of the blade drag force (see

Figure 7.8), then a negative coefficient of lift would shift the direction of the

blade lift force by 180°. Thus, a negative coefficient of lift actually results in the

direction of the blade lift force being minus 90° from the direction of the blade

drag force. The magnitude of the blade lift force had been plotted with negative

values in Figure 7.15d to make it more straightforward to relate it to Figure

7.15a, b & c. The direction of the blade lift force had to be resolved to determine

whether it was acting as a propulsive or resistive force on the rowing system.

By definition, the blade drag force is opposite in direction (180° out of phase) to

the slip velocity. Figure 7.16 shows that blade drag force vector completed

about one revolution starting at around 180° and finished at approximately the

same angle.

244

Figure 7.15: The blade lift force is proportional to the coefficient of lift and the square of the slip velocity. (a) Coefficient of lift. (b) Slip velocity

magnitude. (c) Immersed blade area fraction. (d) Blade lift force.

245

Figure 7.16: The blade drag force is opposite in direction to the slip velocity. (a) Slip velocity direction. (b) Blade drag force direction.

246

The direction of the blade lift force throughout the three rowing strokes is shown

in Figure 7.17. The direction of the blade drag force was also plotted to illustrate

that the direction of the drag and lift are always orthogonal to one another.

Further, Figure 7.17 show that when the coefficient of lift is positive, the

direction of the blade lift force is an additional 90° to the direction of the blade

drag force, and when it is negative, the lift direction is minus 90° from the drag

direction. The physical explanation for this 180° phase shift in the direction of

the blade lift force based on the coefficient of lift is that the resultant blade force

always has to come out on the opposite side of the blade to the slip velocity

vector. This point had already been discussed towards the end of section 7.3.1,

when it was stated that the resultant blade force is always orthogonal to the

oar’s longitudinal axis. Looking at Figure 7.3 to Figure 7.6 (the diagrams show

the right oar rotating anti-clockwise during the drive phase), see how the slip

velocity vector is pointing out from the front of the blade and the drag and lift

force vectors are pointing out from the back of the blade. Likewise, the slip

velocity vector is pointing out from the back of the blade in Figure 7.2 and

Figure 7.7, and correspondingly, the drag and lift force vectors are pointing out

from the front of the blade.

Figure 7.18 shows the blade drag force transformed from polar form to

Cartesian form for the three rowing strokes. This was needed to calculate the

forward propulsive force and the lateral force on the rowing system. As with the

discussion of Figure 7.11, the x and y components of the blade drag force

(Figure 7.18c & d) can be checked by comparing them against the blade drag

direction graph (Figure 7.18b). That is, the quadrant that the drag force direction

is in should correspond to the polarity of the x and y components. The x

component of the drag force was mostly positive around the time when the oar

was orthogonal to the rowing shell, and was negative at the start and end of the

drive (i.e. catch and release). This made sense because it was during the

middle of the drive that the oar angular velocity dominated over the shell

velocity, resulting in the x component of the slip velocity vector pointing away

from the heading, and therefore, the x component of the blade drag force vector

pointing towards the heading (Figure 7.5). As it should, the y component of the

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Figure 7.17: The blade lift force is orthogonal to the blade drag force. The coefficient of lift determines whether it is 90° clockwise or anti-clockwise.

(a) Blade drag force direction. (b) Coefficient of lift. (c) Blade lift force direction.

248

Figure 7.18: Transformation of the blade drag force from polar form to Cartesian form. (a) Blade drag force magnitude. (b) Blade drag force

direction. (c) x-component of the blade drag force. (d) y-component of the blade drag force.

249

blade drag force (Figure 7.18d) was opposite in direction to the y (i.e. lateral)

component of the slip velocity. The lateral component of the slip velocity was

pointing away from the rowing shell (positive) for approximately the first half of

the drive phase (Figure 7.2 to Figure 7.4) and then pointing into the shell

(negative) for the rest of the drive phase (Figure 7.5 to Figure 7.7).

Correspondingly, the y component of the blade drag force was pointing into the

shell (negative) first and then pointed away from the shell (positive) later. The

peak in the x component of the blade drag force lined up with the zero crossing

in the y component, which corresponded to the time when the oar was

orthogonal to the heading and the blade drag force was completely aligned to

the heading. That is, only x and no y component, as illustrated in Figure 7.5.

Figure 7.19 shows the blade lift force transformed from polar form to Cartesian

form. As with the blade drag force, this was done to calculate the forward

propulsive force and the lateral force on the rowing system. The very small dips

(i.e. negative values) at the start and end of the drive phase in the x component

graph, in Figure 7.19c, corresponded to the catch and release when the slip

velocity vector was pointing out from the back of the blade (i.e., convex side)

and the blade lift force vector was pointing out from the front of the blade (i.e.,

concave side), as shown in Figure 7.2 and Figure 7.7. The zero point between

the two peaks (about two thirds into the drive phase) corresponded to the time

when the oar was orthogonal to the shell and the lift force was zero and only the

drag force was present (Figure 7.5). For the y component graph (Figure 7.19d),

it changed polarity so many times because the lift force kept alternating

between pointing away from and into the rowing shell (Figure 7.2 to Figure 7.7).

The third zero crossing of each stroke in the y component graph lined up with

the zero point in the x component graph, when the blade lift force was zero, as it

had been discussed just before.

Figure 7.20 shows that the forward blade force is the sum of the x components

of the blade drag and lift forces. As expected, the forward propulsive force was

negative at the catch and the release. This was because the rower needed time

to increase the force to overcome the braking effect when the blades entered

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Figure 7.19: Transformation of the blade lift force from polar form to Cartesian form. (a) Blade lift force magnitude. (b) Blade lift force direction. (c)

x-component of the blade lift force. (d) y-component of the blade lift force.

251

Figure 7.20: The forward propulsive force is the sum of the forward components of the blade drag and lift forces. (a) x-component of the blade drag

force. (b) x-component of the blade lift force. (c) x-component of the blade force (i.e. forward propulsive force).

252

the water at the catch, and similarly, needed time to slow down the oar’s

rotation to pull the blades out of the water at the release. Throughout the middle

of the drive phase, a positive force was maintained to provide propulsion to the

rowing system.

Figure 7.21 shows that the lateral blade force is the sum of the y components of

the blade drag and lift forces. The lateral blade force, as illustrated in Figure

7.21c, went through four phases during the drive phase. In the first phase, at

the start of the drive phase (i.e. the catch), the lateral blade force was pointing

away from the shell (see Figure 7.2), which corresponded to the first peak in

each stroke in Figure 7.21c (this figure will be referred to for the remaining three

phases, but will not be explicitly referenced). Then in the second phase, up to

the point when the oar was orthogonal to the heading, the lateral blade force

was pointing into the shell (see Figure 7.3 and Figure 7.4), which corresponded

to the dip with a gradual return to zero. Again, when the oar was orthogonal to

the heading, the blade force only had a forward component and no lateral

component, which corresponded to the zero crossing about two thirds into the

drive phase. In the third phase, just after when the oar was orthogonal to the

heading, the lateral blade force was pointing away from the shell once again

(see Figure 7.6), which corresponded to the small peak towards the end of the

drive phase in each stroke. Finally in the fourth phase, during the release, the

lateral blade force was pointing into the shell (Figure 7.7), which corresponded

to the last dip.

Figure 7.22 shows the resultant blade force, the vector sum of the blade drag

and lift forces, transformed from Cartesian form to polar form. The resultant

blade force magnitude is the vector sum of the x and y components (i.e.,

22

yx + ), and this relationship can be recognised by comparing Figure 7.22c

with Figure 7.22a and, b. The resultant blade force direction, Figure 7.22d, was

around 120° to 130° (second quadrant) at the catch and was around -150° to -

140° (third quadrant) at the release. That is, the resultant blade force pointed

away from the heading. This was when the angular velocity was small and the

shell velocity dominated, which resulted in the oar blades producing a

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Figure 7.21: The lateral blade force is the sum of the lateral components of the drag and lift forces. (a) y-component of the drag force. (b) y-

component of the lift force. (c) y-component of the blade force (i.e. lateral blade force).

254

Figure 7.22: Transformation of the blade force from Cartesian form to polar form. (a) x-component of the blade force. (b) y-component of the blade

force. (c) Blade force magnitude. (d) Blade force direction.

255

braking force. For most of the pull through, the direction of the resultant blade

force was always in the first and fourth quadrant between -60° to 45°, which

corresponded to the resultant blade force being a propulsive force.

Figure 7.23 confirmed that the resultant blade force direction was always

orthogonal to the oar direction. It also verified that during the middle of the drive

phase, the resultant blade force was propulsive with the resultant blade force

lagging the oar’s axis by 90°. On the other hand, the resultant blade force was

resistive during the catch and release, when the resultant blade force was

leading the oar’s axis by 90° (note: –270° is equivalent to 90°).

Figure 7.24 shows the total forward and lateral forces on the rowing shell by

summing the left and right blade forces. It is apparent in the graphs that the

force on the right blade was larger than that on the left. Ideally, the lateral force

on the left and right side should sum to zero so that there is no lateral motion

overall. Figure 7.24b shows that this was not the case, as the sculler cannot

generate an identical force profile on the left and right sides in practice. The

non-symmetrical aspect was also observed in the left and right oar angle

measurements and their derived angular velocities, shown in Figure 7.27b & c,

although the differences in the left and right profiles are quite difficult to spot in

the graphs.

Further, the net lateral force observed in Figure 7.24b was quite large; about

150 N at 0.3 s. It is suspected that the actual net lateral force was smaller and

that this was likely due to factors that had not been accounted for. Perhaps if

there were video cameras mounted on the outriggers to synchronously record

both the left and right oars, then it would have been possible to see the exact

rotation of the oars throughout rowing stroke and work out whether the large net

lateral force was due to asymmetry of the rower’s technique or data

synchronisation problems, or may be both of these factors.

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Figure 7.23: Verifying that the direction of the blade force vector was consistently orthogonal to the oar direction. (a) Blade force direction. (b) Oar

direction. (c) Angle between the blade force vector and the oar.

257

Figure 7.24: The total forward and lateral forces on the rowing shell. (a) Forward force on the rowing shell. (b) Lateral force on the rowing shell.

258

7.3.3 ANALYSIS OF ROWER MOTION

Figure 7.25 shows the graphs of the rower motion with the stick figures showing

approximately the stance of the rower throughout the three strokes. The elbow,

shoulder and trunk curves hit their turning points, which corresponded to the

rower’s full body extension, at about the same times (t = 1.2, 4.2 and 7.2 s). In

contrast, the seat position curve reached its plateau much earlier (t = 0.9, 3.9

and 6.9 s). The position of the rower’s centre of mass followed closely to the

seat position much of the time except around its peak. The peak of the rower’s

centre of mass position curve was due to the movement of the elbows,

shoulders and trunk to the full body extension position after the seat position

reached its maximum.

The graphs corresponding to the position, velocity and acceleration of the

rower’s centre of mass relative to the rowing shell are shown in Figure 7.26. As

each variable is the time derivative of the preceding variable, each one

depended on the gradient of the preceding curve. The stick figure illustrates the

stance of the rower throughout the three strokes. As expected, the rower’s

centre of mass velocity was positive in the drive phase, zero at the catch and at

the release, and negative in the recovery phase. The rower centre of mass

acceleration had a large peak (t = 0.1, 3.1 and 6.1 s), a smaller peak (t = 0.6,

3.6 and 6.6 s), and followed by a dip (t = 0.9, 4 and 7 s) throughout each drive

phase. The first peak in acceleration was due to the acceleration with the leg

effort, the second peak was due to the acceleration with the upper body effort,

and the minimum was due to the deceleration of the rower when the seat

position reached its maximum extension and the rower was moving into the fully

extended position. Thus, the fact that there were two peaks in the rower centre

of mass acceleration profile showed that there was a transition between the leg

and upper body effort.

The measured oar angles and derived oar angular velocities are shown in

Figure 7.27b & c, respectively. The position of the rower’s centre of mass and

the seat position were also plotted in Figure 7.27a to highlight the timing of the

stroke cycles. The oar angles changed the direction of rotation at the times

259

Figure 7.25: Graphs for the rower motion. (a) Rower body angles. (b) Seat position and rower centre of mass position.

260

Figure 7.26: Graphs for the rower’s centre of mass motion. (a) Position. (b) Velocity. (c) Acceleration.

261

Figure 7.27: Comparing the rower centre of mass position and the seat position against the oar angle and oar angular velocity. (a) Rower centre of

mass position and seat position. (b) Oar angle. (c) Oar angular velocity.

262

when the position of the rower’s centre of mass changed direction (i.e. the

maxima and minima of Figure 7.27a and b are aligned). The oar angular

velocity was the steepest at the start, which indicated that leg drive played a

significant part in generating the oar angular velocity. The oar angular velocity

continued to increase, with a lower gradient, until it reached its peak. This

second phase of increase in the oar angular velocity corresponded to the latter

part of the leg drive and the upper body force generation. The zero crossings in

the oar angular velocity graph correspond to the time when the oar angle

changed its direction of rotation and when the rower reached the full body

extension position.

263

7.3.4 PROPULSIVE FORCE, ROWER MOTION AND SHELL DRAG –

THEIR CONTRIBUTIONS TO THE RESULTANT SHELL

ACCELERATION

Figure 7.28 illustrates that the shell acceleration is the sum of the propulsive

force at the oar blades, acceleration of the rower’s centre of mass and the shell

drag. Note that all the variables were graphed in acceleration units, ms-2. This

was done by rearranging Equation 4.1 to produce Equation 7.1 with terms that

are in acceleration units and then graphing the three terms on the right hand

side of Equation 7.1 in Figure 7.28a, b and c, respectively. Graphing it in this

way demonstrates how the three components contributed to the overall shell

acceleration (Figure 7.28d).

( ) ( ) ( )rowershell

shell

rowershell

shellrowerrower

rowershell

blade

shell

mm

cv

mm

am

mm

Fa

+

−

+

⋅

−

+

=

2

_

( 7.1 )

The dip in the shell acceleration curve at the catch was due to the deceleration

caused by the acceleration of the rower’s centre of mass, the braking effect of

the blades and the shell drag, in descending order of significance. This order

can be explained with the following examination. First, the point that the shell

deceleration was primarily due to the rower’s motion made sense because in

order for the rower to accelerate during the catch, there must have been a

reaction force to the rower’s acceleration. This reaction force was the large

negative force on the shell; particularly, each of the rower’s mass was about 4

times heavier than the rowing shell. The shell drag contributed the least to the

shell deceleration because the shell velocity was near its minimum during the

catch, so the resistive force was proportionally reduced.

264

Figure 7.28: The shell acceleration curve compared with each of the components in the system equation. (a) Acceleration due to propulsive force.

(b) Acceleration due to rower motion. (c) Acceleration due to shell drag. (d) Shell acceleration.

265

After the shell deceleration, the following sharp increase in shell acceleration

was primarily due to the rapid increase in propulsive force (mainly work done by

the legs). At the same time, the contribution due to the acceleration of the

rower’s centre of mass was around zero (the transition point from the legs

generating the propulsive force to the upper body), and the shell drag was at its

maximum (i.e., lowest magnitude, because the shell velocity was at its minimum

after the considerable shell deceleration at the catch).

The oscillations before reaching the highest peak in the shell acceleration were

due the oscillations in the propulsive force and rower motion. The oscillations in

the propulsive force were due to the fluctuating magnitude of the blade force.

The oscillations in the rower motion up to the point of the highest peak in the

shell acceleration were due to the acceleration and deceleration of the rower’s

body segments as described for Figure 7.26c. Referring to Figure 7.28b, the

contribution from the rower acceleration had two periods of deceleration from

the catch to the highest peak in the shell acceleration. These negative

contributions corresponded to the acceleration of the rower with the leg effort

and then with the upper body. Remember that when the rower accelerates, the

shell decelerates because of the conservation of momentum. Thus, the

transition of effort from the legs to the upper body was reflected in the shell

acceleration profile, which shows its importance as a tool for the analysis of a

rower’s technique.

The highest peak in the shell acceleration towards the end of the drive phase

was the result of the propulsive force and, less intuitively, the acceleration of the

rower’s centre of mass. The rower acceleration contributed to the highest peak

in the shell acceleration curve by the braking motion of the rower towards the

release, which resulted in the acceleration of the shell because of the transfer of

momentum. The recovery period basically had a net shell acceleration close to

zero because of the balance of acceleration between the shell surging forward

caused by the rower’s recovery and the shell drag.

266

7.4 COMPARING THE ROWING MODEL SIMULATION

RESULTS BETWEEN TWO SINGLE SCULLERS ROWING

AT DIFFERENT STROKE RATES

Three consecutive strokes of data were plotted for the full range of rowing

mechanics variables (Figure 7.29 to Figure 7.38). The two sets of graphs,

respectively, had the same general shape even though they belonged to two

different rowers rowing at different stroke ratings. Subject 2 was sculling at a

nominal rate of 20 strokes per minute while subject 1 was sculling at a nominal

rate of 32 strokes per minute. The time difference can be seen in all of the

graphs when it took subject 2 about 9.0 seconds to complete 3 strokes, while it

only took subject 1 about 5.5 seconds.

Figure 7.29 compares the two subjects’ rower angles (elbow, shoulder and

trunk), seat position and position of the rower’s centre of mass. Looking at the

rower angles, subject 2’s curves were skewed to the right and subject 1’s

curves were more centred. This was because subject 2 spent a larger

proportion of the rowing cycle for recovery, with a drive to recovery ratio of

about 0.33, while subject 1’s drive to recovery ratio was about 0.5.

Consequently, the position curve of subject 2’s centre of mass was skewed to

the right, while subject 1’s curve was more centred.

Figure 7.30 compares the position, velocity and acceleration graphs of the two

rowers’ centre of mass. Subject 2 was shorter than subject 1 by 6.1 cm, with

heights of 1.772 m and 1.833m, respectively, but subject 2’s centre of mass

travelled a further distance of 0.690 m compared to 0.638 m for subject 1.

Subject 1’s velocity and acceleration curves were higher in magnitude because

of a much shorter stroke period, even though subject 1’s centre of mass

travelled 5.2 cm less than subject 2. The magnitude difference in the velocity

and acceleration curves was actually more significant during the recovery phase

(when the rower velocity was negative in Figure 7.30 c and d). This is because

a rower speeds up the stroke by recovering faster while the time to complete

the drive remains relatively unchanged. The recovery time can be significantly

267

Figure 7.29: Inter-subject comparison for rower angles (elbow, shoulder and trunk), seat

position and position of the rower’s centre of mass. (a) Subject 2’s rower angles. (b)

Subject 1’s rower angles. (c) Subject 2’s seat position and position of the rower’s centre

of mass. (d) Subject 1’s seat position and position of the rower’s centre of mass.

Figure 7.30: Inter-subject comparison for rower centre of mass position, velocity and

acceleration. (a) Subject 2’s position. (b) Subject 1’s position. (c) Subject 2’s velocity. (d)

Subject 1’s velocity. (e) Subject 2’s acceleration. (f) Subject 1’s acceleration.

268

reduced because there is minimal resistance on the rower motion during

recovery, while the timing of the drive phase is constrained by the rower’s force

application on the oar handles to generate the propulsive force at the blade in

the water. Moreover, subject 1’s rower velocity and acceleration curves had

fewer oscillations during the recovery phase than those of subject 2. This

highlighted that the rower’s recovery motion is actually smoother at a higher

stroke rate.

Note that the graphs of the hydrodynamics variables from Figure 7.31 to Figure

7.37 had the data points during the recovery phase masked with zeroes to show

only the data points during the drive phase.

Figure 7.31 shows the oar angle and oar angular velocity plots for both subject

1 and 2. Since subject 1 was sculling at a nominal stroke rate of 32 strokes per

minute and subject 2 was sculling at a nominal rate of 20 strokes per minute,

the oar angle plots for the two rowers were different in timing. Subject 2 had an

oar angle range of -66° to 47°, which was larger than subject 1’s oar angle

range of -61° and 42°. This corresponded to the point discussed previously that

subject 2’s centre of mass travelled a further distance than subject 1 (0.690 m

for subject 2 and 0.638 m for subject 1). Although subject 2 kept the blades

immersed in the water for a larger angle range, it can be observed from the oar

angular velocity plots that subject 1 had put more energy into the rowing system.

Subject 1 only had a slightly higher peak oar angular velocity of 2.7 rad/s

compared to 2.6 rad/s for subject 2, but the oar angular velocity of subject 1

was above 1.75 rad/s (100°/s) for a longer percentage of time than that of

subject 2. This indicated that at the higher stroke rating, subject 1 exerted force

with the legs right from the start of the drive and made the oars rotate more

rapidly earlier on in the drive phase, as the peak oar angular velocity was

probably close to the physical limit and could not be increased much further.

Lastly, for both of the rowers, the peak oar angular velocity occurred when the

oar was orthogonal to the heading (i.e. when oar angle was zero).

269

Figure 7.31: Inter-subject comparison for oar angle and oar angular velocity. (a) Subject

2’s oar angle. (b) Subject 1’s oar angle. (c) Subject 2’s oar angular velocity. (d) Subject

1’s oar angular velocity.

Figure 7.32: Inter-subject comparison for slip velocity magnitude and direction. (a)

Subject 2’s slip velocity magnitude. (b) Subject 1’s slip velocity magnitude. (c) Subject

2’s slip velocity direction. (d) Subject 1’s slip velocity direction.

270

Referring to plots of the slip velocity magnitude, Figure 7.32a and b, subject 1’s

maximum slip velocity was not significantly larger than that of subject 2, given

that subject 1’s stroke rate was 60% higher (i.e., 32 strokes per minute

compared to 20 strokes per minute). However, looking at the slip velocity

direction plots in Figure 7.32, one can observe that the inflexion points in Figure

7.32d (t = 0.1, 2 and 3.9 s) are much more pronounced, and almost like a step,

than those in Figure 7.32c (t = 0.5, 3.5 and 6.5 s). This is the same effect as

discussed in the previous paragraph; subject 1 got the oars to a high angular

velocity sooner. The slip velocity vector went through one revolution (from 0° to

180°, then -180° back to 0°) in approximately 1 second for both subjects,

regardless of the stroke rating. Again, this was due to subject 2 taking a

comparable amount of time for the drive phase, but increasing the time for

recovery at the slower stroke rate.

Figure 7.33 are the plots of the angle of attack for the two rowers. They have

the same general shape because of the similarity between the two rowers’ oar

angle plots (Figure 7.31a and b) and slip velocity direction plots (Figure 7.32c

and d). The most obvious difference is the size of the inflection after the initial

dip at the start of each drive phase. The more pronounced inflection for subject

1 was again due to the large initial effort with the legs, getting the oar angular

velocity up to a high velocity sooner. As the coefficient of drag and lift are

dependent on the angle of attack, the plots of these coefficients (Figure 7.34)

were also similar between the two rowers. For the coefficient of drag, subject 1

had rounded peaks during the initial third of each drive phase (Figure 7.34b),

while there was only a very small bump in subject 2’s coefficient of drag curve

during this time (Figure 7.34a). At the end of each drive phase, subject 1 had

larger peaks than subject 2; magnitude of about 1.5 compared to 1. For the

coefficient of lift, the main difference was in the magnitude of the peak following

the dip at the start of each drive phase. For subject 2, this peak was around 0.7

(Figure 7.34c), whereas it was about 1.3 for subject 1 (Figure 7.34d). Again, the

larger peaks at the start of the drive phase in both of the drag and lift coefficient

plots was due to subject 1 getting the oar angular velocity up to a high velocity

sooner.

271

Figure 7.33: Inter-subject comparison for the angle of attack. (a) Subject 2’s angle of

attack. (b) Subject 1’s angle of attack.

Figure 7.35 and Figure 7.36 show the drag and lift forces at the oar blade for

the two rowers, respectively. The direction plots of the blade drag and lift force

vectors were similar for both rowers. The main difference was in the magnitude

plots. For both the drag and lift forces, the magnitude differences were mainly at

the start and end of each drive phase (i.e. the catch and release) rather than the

middle. The difference here is much more significant than the slip velocity

magnitude plots (Figure 7.32a and b) and coefficient plots (Figure 7.34)

because the force at the oar blade is proportional to the coefficient of drag and

lift and the square of the slip velocity (Equation 4.4). Correspondingly, the

forward and lateral blade forces (i.e. the x and y components of the blade force)

were larger at the start and end of each drive phase, as shown in Figure 7.37.

As it has been discussed many times now, the larger peak in the blade force

during the catch was due to subject 1 applying a greater effort at the start of the

drive phase. The larger deceleration at the release (i.e. the dip at the end of

each drive phase) was the result of the increased shell velocity, thus, the

braking effect with the blades at the release was more significant. Beside the

increased force in the forward axis, it can be seen when comparing Figure 7.37

c and d, that the force in the transverse axis was also increased. This increase

272

Figure 7.34: Inter-subject comparison for the blade drag and lift coefficients. (a) Subject 2’s coefficient of drag. (b) Subject 1’s coefficient of drag. (c)

Subject 2’s coefficient of lift. (d) Subject 1’s coefficient of lift.

273

Figure 7.35: Inter-subject comparison for the blade drag force magnitude and direction. (a) Subject 2’s blade drag force magnitude. (b) Subject 1’s

blade drag force magnitude. (c) Subject 2’s blade drag force direction. (d) Subject 1’s blade drag force direction.

274

Figure 7.36: Inter-subject comparison for the blade lift force magnitude and direction. (a) Subject 2’s blade lift force magnitude. (b) Subject 1’s

blade lift force magnitude. (c) Subject 2’s blade lift force direction. (d) Subject 1’s blade lift force direction.

275

Figure 7.37: Inter-subject comparison for the blade force’s x and y component. (a) Subject 2’s x-component of the blade force. (b) Subject 1’s x-

component of the blade force. (c) Subject 2’s y-component of the blade force. (d) Subject 1’s y-component of the blade force.

276

of the lateral forces does not do any useful work and it is an inevitable

consequence of the increased effort.

The shell velocity traces of the two rowers are shown in Figure 7.38. During the

drive phase, the two shell velocity curves shared many common features. The

shell velocity dipped at the start of each drive phase corresponding to the

braking effect of the blades and the acceleration of the rower at the catch. The

velocity then increased to a maximum with the rower’s pull through. The

difference in the two shell velocity curves during the drive phase was that

subject 2 had a lower minimum velocity at the catch; about 3 ms-2 for subject 2

compared to 3.25 ms-2 for subject 1 on average. Both rowers reached about the

same maximum velocity of 4.5 ms-2 during the drive phase, so subject 2’s

velocity curve was actually steeper than subject 1’s. The most significant

difference was in the recovery phase. For subject 2, who rowed at a nominal

rate of 20 strokes per minute and with a slow recovery, the shell velocity

decreased gradually until the sharp drop in gradient that corresponded to the

rower‘s initial acceleration just before the blades entered the water. For subject

1, who rowed at a nominal rate of 32 strokes per minute, the shell velocity

actually increased because the rower was recovering so fast that it propelled

the shell forward because of the conservation of momentum. The drop off in

velocity at the end of the recovery was even more rapid because the shell

velocity actually reached a higher maximum than during the drive phase. Finally,

subject 1 had a higher mean velocity of about 4 ms-2 while subject 2 had a

mean velocity of about 3.5 ms-2.

It should be noted that the drop in the velocity curve at the release (most

apparent in Figure 7.38b at t = 0.9, 2.75 and 4.6 s) was not observed in the

measured shell velocity. This was due to an over-estimation of the braking force

at the blade during the release. This will be discussed in further details in

section 7.5 below.

277

Figure 7.38: Inter-subject comparison for the shell velocity. (a) Subject 2’s shell velocity.

(b) Subject 1’s shell velocity.

Looking at all the contributions to the shell acceleration in Figure 7.39, there

were some apparent differences. The differences in the blade force and the

rower centre of mass acceleration have already been discussed (Figure 7.37

and Figure 7.30, respectively). The shell drag contributions to the shell

acceleration were also different for the two rowers. During the drive phase, the

shape of the shell drag contribution curves were similar, but during the recover

phase, the slopes were opposite in direction. This was because of the

difference in the shell velocity profile as discussed in the previous paragraph for

Figure 7.38.

The analysis of the rowing model data highlighted that the shell acceleration

can be decomposed into three components, namely, the oar blade propulsion,

rower motion and shell drag. One should bear in mind that these three terms

are all inter-related with shell acceleration, as it had been shown in the

derivation of the equation representing the motion of the single scull in section

4.2.2. Thus, the use of these components as feedback to the coaches,

biomechanists and rowers require further research. In particular, the difference

in the shell acceleration and velocity profiles, and the three decomposed terms

278

between scullers of different skill levels (i.e., elite versus sub-elite) needs to be

investigated. Nevertheless, presenting these components as feedback would be

much more intuitive and provide a better insight than just the resultant shell

acceleration profile. From the knowledge gained in this PhD project, a

methodology to quantitatively assess rowing technique was conceived. This will

be discussed in Section 7.5 below.

279

Figure 7.39: Inter-subject comparison for the acceleration contributions from each component of the rowing system. (a) Subject 2’s propulsive

component. (b) Subject 1’s propulsive component. (c) Subject 2’s rower motion. (d) Subject 1’s rower motion. (e) Subject 2’s shell drag. (f) Subject

1’s shell drag. (f) Subject 2’s shell acceleration. (g) Subject 1’s shell acceleration.

280

7.5 CALCULATING THE PROPULSIVE FORCE AT THE OAR

BLADE WITH THE DIFFERENTIAL EQUATION DESCRIBING

THE MOTION OF THE ROWING SYSTEM

The differential equation describing the motion of the rowing system can be

used for rowing technique assessment. As has been shown in this thesis, the

differential equation describing the motion of the rowing system is an adequate

representation of a single sculler. It has also been pointed out that the force at

the oar blade calculated from the measured oar handle force applied by the

rower, the oar leverage and cosine of the oar angle is not equivalent to the

blade force that propels the rowing system. The propulsive force at the oar

blade has to account for the hydrodynamic interaction between the blade and

the water. Based on these findings, it was discovered that the differential

equation describing the motion of the rowing system, Equation 4.1 could be

rearranged to Equation 7.2 and used to calculate the propulsive force at the oar

blade, thereby, allowing coaches, biomechanists and rowers to gauge the force

that actually propels the rowing system.

( )

shellrowerrowershell

shell

rowershellbladeamcv

dt

dvmmF

_

2

⋅++⋅+= ( 7.2 )

Equation 7.2 was rearranged from Equation 4.1 to make the propulsive force at

the oar blade the variable of interest. The rowing shell mass and rower mass

can be readily measured. The shell drag coefficient can be assumed to be a

constant using data from the literature (Lazauskas 1998) as has been shown in

this thesis. If the shell drag characteristics of a particular rowing shell does not

exist, it can be estimated using the method described by (Lazauskas 1998), or

experimentally determined (Wellicome 1967). The shell velocity and

acceleration can be measured using the Rover system used in this research

project (Grenfell 2007; James, Davey & Rice 2004). Finally, the motion of the

rower's centre of mass relative to the rowing shell can be estimated using seat

position measurement and a difference curve as discussed in chapter 6.

281

Figure 7.40 and Figure 7.41 show the acceleration contributions from each

component of the rowing system (as described by Equation 7.1) for subject 1

and subject 2, respectively. These two figures contain the same variables as

Figure 7.39, but the difference was that all the variables except for the

propulsive force at the oar blade were determined from measured data for the

former figures. In Figure 7.39, Equation 4.1 was solved to simulate the shell

motion (velocity and acceleration, or the rate of change of velocity). The

propulsive force at the oar blade and shell drag were dependent on the shell

velocity, so in effect they were also determined from solving Equation 4.1. The

rower motion was directly evaluated from measured data. For Figure 7.40 and

Figure 7.41, shell acceleration, shell drag and rower motion were determined

using measured data, and then used to calculate the propulsive force at the oar

blade according to Equation 7.2. Specifically, the initial objective of the research

was to prove that the differential equation describing the motion of the rowing

system is an adequate representation of the real rowing system. This objective

was achieved by successfully simulating the shell acceleration using the rowing

model with on-water rowing data. With this objective achieved, the variable of

interest was no longer shell acceleration, but the propulsive force at the oar

blade, as shell acceleration could be measured using the Rover system. The

methodology proposed here to monitor the propulsive force provides great

insight to a rower's technique, as all the forces acting on the rowing system and

the resultant shell motion (Equation 4.1, Figure 7.40 and Figure 7.41) are

collectively monitored.

282

Figure 7.40: The acceleration contributions from each component of the rowing system.

The propulsive component was determined from the other three components as

described above using Equation 7.2. (a) Subject 1’s propulsive component. (b) Subject

1’s rower motion. (c) Subject 1’s shell drag. (d) Subject 1’s shell acceleration.

Figure 7.41: The acceleration contributions from each component of the rowing system.

The propulsive component was determined from the other three components as

described above using Equation 7.2. (a) Subject 2’s propulsive component. (b) Subject

2’s rower motion. (c) Subject 2’s shell drag. (d) Subject 2’s shell acceleration.

283

Impulse of force (i.e., integral of force over time) at the oar handle has

traditionally been analysed to assess the rower's effort (Baudouin, Hawkins &

Seiler 2002; Celentano et al. 1974; Hill & Fahrig 2009). It is not the rower's total

energy input to the rowing system, as the force at the foot stretcher and the

rower's motion are also the rower's energy input to the rowing system. However,

the oar handle force is important because the oars are the mechanism that

provides the propulsion to the rowing system. If the rowing shell is instrumented

with the apparatus to measure the applied force at the oar handle in addition to

the proposed methodology, then it is possible to compare the 'applied impulse

of force' against the 'propulsive impulse of force' to gauge how well the rower's

effort is effectively directed to propelling the rowing system. The ratio of the

impulse of force at the oar blade to the impulse of force at the oar handle can

be calculated. This ratio index (Equation 7.3), which will now be referred to as

the impulse of force effective index, is related to the ‘effectiveness of oar

propulsion’ (Equation 7.4) as defined by Zatsiorsky and Yakunin (1991), which

is the ratio of work expended to propel the boat over the sum of works at oar

handles. More specifically, it is the ratio of the hydrodynamic losses at the oar

blade due to energy consumed in the propulsion of water in the direction

opposite to the way of the rowing shell and to the rotation of the oar which

includes work expended to move water in the lateral direction over the energy

applied at the oar handle. Figure 7.42 compares the applied force at the oar

handle against the propulsive force at the oar blade. The impulse of force

effective indices are also shown for the 3 consecutive strokes for all the

subjects in Table 7.1. Figure 7.42 demonstrates how the Rover system, along

with seat position and oar handle force measurements, could be used to assess

the effectiveness of a single sculler in transferring the applied impulse of force

at the oar handle to the propulsive impulse of force at the oar blade. Due to the

limited amount of data analysed because of limitations with the experimental

setup (Table 7.2), no definitive conclusions could be drawn regarding the results

of Figure 7.41 , Figure 7.42 and Table 7.1. Nevertheless, the results highlighted

that the proposed methodology to monitor all the forces acting on the rowing

system and the resultant shell motion, and using the impulse of force effective

index to assess rower performance warrant further research.

284

==

handle

blade

J

JI

dtF

dtF

T

handle

T

blade

∫

∫ ⋅

0

0

( 7.3 )

where I is referred to as the impulse of force effective index

blade

J is the impulse of force at the oar blade (N s)

handle

J is the impulse of force at the oar handle (N s)

T is the stroke period (s)

blade

F is the force at the oar blade’s centre of pressure (N)


==

handle

blade

ef

W

WK

( )

dtLF

dtvLF

T

inhandle

T

shelloutblade

∫

∫•

•

⋅

⋅

+

0

0

cos

ϕ

ϕϕ

( 7.4 )

where ef

K is the effectiveness of oar propulsion

blade

W is the energy consumed at the oar blade (J)

handle

W is the energy applied by the rower at the oar handles (J)

T is the stroke period (s)

blade

F is the force at the oar blade’s centre of pressure (N)


in

L is the inboard oar length (m)

out

L is the outboard oar length (m)

ϕ is the oar angle in the plane parallel to the water surface (°)

•

ϕ is the oar angular velocity (rads-1)

shell

v is the velocity of the rowing shell (ms-1)

285

Figure 7.42: Comparing the propulsive force at the oar blade (calculated from

measurements and using the equation describing the motion of the rowing system)

against the applied force measured at the oar handle. (a) Results for subject 1. (b)

Results for subject 2. (c) Results for subject 3. (d) Results for subject 4.

286


Table 7.1: Impulse of force effective index for the three rowing strokes of all four subjects.

Impulse of force effectiveness index

Subject First rowing

stroke

Second

rowing stroke

Third rowing

stroke

1 0.3481 0.3550 0.3637

2 0.3200 0.3764 0.3943

3 0.6177 0.5053 0.5030

4 0.4236 0.4550 0.4648

287

Table 7.2: Limitations with the experimental setup.

Limitations

Manually aligned the data from the three systems as they were not

synchronised: Rover system (shell velocity and acceleration),

Biomechanics measurement system (oar handle force and seat position)

and video (rower motion).

Difficulty in maintaining a fixed orthogonal view when video recording

the rower's motion on water and manually processing the video frames

to estimate rower motion.

Due to the previous two limitations, the amount of data that could be

processed was limited. That is, only 3 strokes for each of the 4 subjects.

Low sampling rate of 25 Hz with the Biomechanics measurement

system and video, compared to 100 Hz with the Rover system. In

particular, higher accuracy would be obtained if all the measurements

were synchronised and sampled at 100 Hz.

7.6 CONCLUSION

A full analysis of the rowing model simulation, which included actual

measurements, for one of the subjects was presented in this chapter. The

analysis revealed the relationship between all the variables of the rowing

system and their effect on the resultant shell motion.

The calculation of the propulsive force at the oar blade was the most

complicated aspect of the rowing model. Thus, a significant proportion of this

chapter was dedicated to explaining how the blade force was calculated with

the simulation results. It was established that the oar blade force estimated

using the hydrodynamics model was consistent with oar blade theory (Sykes-

Racing 2009). The hydrodynamics oar blade model accounted for all the forces

on the rowing system which included the rower motion, shell drag, propulsive

force at the oar blade, and braking force at the blade during the catch and

release. It took into account the effort applied by the rower using the oar angle

and oar angular velocity. It accounted for the hydrodynamics effects at the oar

blade with the immersed oar blade area, coefficient of drag and lift and the oar

blade’s slip velocity. Most importantly, it accounted for the constant change in

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the kinematics of the rowing system with the shell velocity vector, which affects

the oar blade’s slip velocity vector, and consequently, blade force. Further it

was confirmed by the sensitivity analysis presented in chapter 5 that the shell

acceleration was adequately simulated, thus, it substantiated that the

hydrodynamics modelling is an adequate representation of the blade-water

interaction.

Shell acceleration is the result of the combined contributions from the propulsive

force at the oar blade, the motion of the rower’s centre of gravity and the shell

drag. This was explicitly shown with a graph of the shell acceleration along with

the three contributing components in the differential equation describing the

motion of the rowing system.

The rowing model simulation results, which included actual measurements, for

two rowers sculling at different stroke rates have been presented. Their

similarities and differences were highlighted. The comparison was by no means

a definitive analysis, but it demonstrated that the rowing model was able to

relate all of the rowing mechanics variables to the shell acceleration.

Improvement in the experimental set up and more extensive data collection is

needed to enable detailed comparisons between rowers and between different

stroke ratings.

During the development of the rowing model, it was realised that the oar blade

force calculated using the measured oar handle force, oar leverage and cosine

of the oar angle is not equivalent to the blade force that propels the rowing

system, as it is ascribed to the inadequacy of the assumptions underlying the

calculation as discussed in section 4.2.2.

It was shown in chapter 5 that the differential equation describing the motion of

the rowing system is an adequate representation of a single sculler. It was also

shown in chapter 6 that motion of the rower’s centre of mass relative to the shell

can be estimated to sufficient accuracy using seat position measurement and a

compensating difference curve. In the last section of this chapter, the propulsive

force at the blade was calculated using the shell motion measurements

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obtained using the Rover system and the estimated motion of the rower’s centre

of mass relative to the shell, based on the differential equation describing the

motion of the rowing system. This proposed methodology of evaluating the

propulsive force provides great insight to a rower's technique, as all the forces

acting on the rowing system and the resultant shell motion are collectively

monitored. It is an important tool for gauging the effectiveness of a single sculler.


oar handle was calculated, as the force applied at the oar handle was also

measured. This ‘impulse of force effective index’ is related to the ‘effectiveness

of oar propulsion’ defined in (Zatsiorsky & Yakunin 1991) and shows how much

of the rower’s effort is effectively used to propel the rowing system forward. The

results, albeit slight, showed that it warrants further research. In the conclusion

chapter, suggestions on how to improve the measurement set up and the

methodology to conduct an extensive assessment of the proposed methodology

to gauge the effectiveness of a single sculler will be discussed.

7.7 REFERENCES

Baudouin, A, Hawkins, D & Seiler, S 2002, 'A biomechanical review of factors affecting rowing performance', Br J Sports Med, vol. 36, no. 6, pp. 396-402. Caplan, N & Gardner, T 2007, 'A mathematical model of the oar blade - water interaction in rowing', Journal of Sports Sciences, vol. 25, no. 9, pp. 1025 - 34. Caplan, N & Gardner, TN 2005, 'A new measurement system for the determination of oar blade forces in rowing', in MH Hamza (ed.), Proceedings of the Third IASTED International Conference on Biomechanics, Benidorm, Spain, pp. 32-7. Celentano, F, Cortili, G, Di Prampero, PE & Cerretelli, P 1974, 'Mechanical aspects of rowing', J Appl Physiol, vol. 36, no. 6, pp. 642-7. Grenfell, RM, AU), Zhang, Kefei (Melbourne, AU), Mackintosh, Colin (Bruce, AU), James, Daniel (Nathan, AU), Davey, Neil (Nathan, AU) 2007, Monitoring water sports performance, Sportzco Pty Ltd (Victoria, AU), patent, United States, <http://www.freepatentsonline.com/7272499.html>. Hill, H & Fahrig, S 2009, 'The impact of fluctuations in boat velocity during the rowing cycle on race time', Scandinavian Journal of Medicine & Science in Sports, vol. 19, no. 4, pp. 585-94.

290

Hofmijster, M, De Koning, J & Van Soest, AJ 2010, 'Estimation of the energy loss at the blades in rowing: Common assumptions revisited', Journal of Sports Sciences, vol. 28, no. 10, pp. 1093 - 102. James, DA, Davey, N & Rice, T 2004, 'An accelerometer based sensor platform for insitu elite athlete performance analysis', in Sensors, 2004. Proceedings of IEEE, pp. 1373-6 vol.3. Lazauskas, L 1998, Rowing shell drag comparisons, viewed 2008/09/02 2008, <http://www.cyberiad.net/library/rowing/real/realrow.htm>. Sykes-Racing 2009, Oar Theory (Presented by Pete and Dick Dreissigacker at the XXIX FISA Coaches Conference, Sevilla, Spain 2000), viewed 2009/02/01, <http://www.sykes.com.au/content/view/51/46/>. Wellicome, JF 1967, Report on resistance experiments carried out on three racing shells., 184, National Physics Laboratory, London. Zatsiorsky, VM & Yakunin, N 1991, 'Mechanics and biomechanics of rowing: A review', International Journal of Sport Biomechanics, vol. 7, pp. 229-81.

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8 CONCLUSIONS AND RECOMMENDATIONS

8.1 CONTRIBUTIONS TO KNOWLEDGE

This thesis reports an investigation into the application of triaxial accelerometers

for rowing technique assessment. The two aims of this thesis were a

comprehensive rowing biomechanics model and solving the inverse problem to

determine rower biomechanics using Micro-Electro-Mechanical Systems

(MEMS) accelerometers. These aims were achieved and they were

contributions to knowledge in the field of rowing biomechanics.

First, this thesis revealed the relationship between the combination of

propulsion, resistance and rower motion against the resultant shell acceleration.

This was achieved with the development of a rowing model to represent a

single scull. The forces acting on the single scull and the resultant motion of the

rowing shell was represented with a differential equation. A detailed multi-

segment rower model was created to represent the rower motion. Also, a

hydrodynamic model was developed to calculate the force at the oar blade,

which is the propulsive force on the rowing system. On-water rowing data was

collected and used as inputs to the rowing model to ‘simulate’ the rowing shell

motion. The rowing model revealed how the rowing shell acceleration trace was

generated from all the variables and parameters of the rowing system.

The second contribution to knowledge of this research was the development of

a methodology to use accelerometers with shell velocity and seat position

measurements to monitor all the forces acting on a single scull and the resultant

shell acceleration. The proposed methodology is based on a differential

equation describing the motion of a single scull, which basically states that the

force acting on the single scull is the sum of the force due to rower motion and

the propulsive and resistive forces on the rowing system. The resultant force on

the single scull was measured using a triaxial accelerometer, that is, product of

the mass of the rowing system and the shell acceleration. The resistive force on

the single scull was estimated from the shell velocity measurement and a

coefficient representing the drag characteristics on the rowing system, that is,

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product of the drag coefficient and square of the shell velocity. The force due to

the motion of the rower’s centre of mass relative to the rowing shell was

estimated using seat position measurement and a compensation difference

curve to account for the motion of the upper body, including the arms. The

resultant force and resistive force on the single scull and the force due to the

motion of the rower’s centre of mass were then used to calculate the propulsive

force on the rowing system. The proposed methodology of calculating the

propulsive force provides great insight to a rower's technique, as all the forces

acting on the rowing system and the resultant shell motion are collectively

monitored

It was discovered during the research that the established method of calculating

the forward oar blade force using the oar handle force, oar lever ratio and oar

angle is not equivalent to the forward propulsive force on the rowing system, as

it is ascribed to the inadequacy of the assumptions underlying the calculation as

discussed in section 4.2.2. The proposed methodology of calculating the

propulsive force on the rowing system resolves the inadequacy, as it does not

make the assumption that there is no axial force in the oar.

Additionally, when the proposed methodology is combined with oar handle force

and oar angle measurements, a ratio of the impulse of force at the oar blade to

the impulse of force at the oar handle can be calculated and could be used to

gauge the rower’s effectiveness. This ‘impulse of force effective index’ is related

to the ‘effectiveness of oar propulsion’, as defined in (Zatsiorsky & Yakunin

1991), and could be used to indicate how much of the rower’s effort is

effectively used to propel the rowing system forward. Due to the limited amount

of data analysed because of limitations with the experimental setup, no

definitive conclusions could be drawn. Nevertheless, the preliminary results

highlighted that the proposed methodology to monitor all the forces acting on

the rowing system and the resultant shell motion, and using the impulse of force

effective index to assess rower performance warrant further research

The proposed methodology of using MEMS accelerometers to analyse rower

technique included the advantages of being unobtrusive and easy to set up,

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because micromechanical sensors were inherently small and light, and their

reliability, precision and accuracy have significantly improved over the decade

since 2000. It offered an attractive alternative to instrumented boats, which were

expensive and difficult to set up. At the time this research was conducted, the

application of micromechanical sensors had already become quite common in

the automotive industry and in consumer electronics including gaming devices

and mobile phones. It was anticipated that MEMS sensors would be commonly

applied for the analysis of sports biomechanics in the near future. This thesis

detailed the methodology to employ this revolutionary sensor technology for the

analysis of biomechanics in the sport of rowing.

8.2 RESEARCH FINDINGS

The findings of this thesis can be summarised as:

1. The biomechanics of a single sculler could be examined using a rowing

model.

a. The relationship between the rowing shell acceleration and the

forces acting on the rowing system could be represented by a

single differential equation.

b. The resistance on the rowing shell could be represented by a drag

coefficient.

c. The propulsive force could be calculated using a static

hydrodynamic model of the oar blades (using experimental drag

and lift coefficients found in the literature).

d. The motion of the rower’s centre of mass relative to the rowing

shell could be calculated using a multi-segment rower model, with

video analysed data for the rower angles (trunk orientation,

shoulder angle and elbow angle) and seat position data for the

sliding motion.

2. The effectiveness of a single sculler could be assessed and quantified by

employing accelerometers to monitor the rowing shell motion.

a. All the forces acting on the rowing system and the resultant shell

motion could be analysed using accelerometers and additional

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measurements (shell velocity, and rower motion estimated from

seat position, as described in hypothesis 2b) based on a

differential equation describing the motion of the rowing system.

b. The motion of the rower’s centre of mass relative to the rowing

shell could be estimated using a simplified methodology as a

simplification to the method described in hypothesis 1d. This

simplified methodology estimates the motion of the rower’s centre

of mass relative to the rowing shell from seat position data, and a

rower and stroke rate specific compensation curve.

c. A parameter can be deduced to gauge the effectiveness of a

single sculler. The propulsive force on the rowing system (i.e.,

blade force) could be estimated using the methodology as

described in hypothesis 2a. Combined with oar handle force

measurement, the ratio of the impulse of force at the blade to the

impulse of force at the oar handle could be calculated. This

‘impulse of force effective index’ can be used to show how much

of the rower’s effort is effectively used to propel the rowing system

forward.

Hypothesis 1 and its sub-hypotheses were substantiated with the sensitivity

analysis of the rowing model detailed in chapter 5. It was found that the

simulated shell acceleration data deviated from the two sets of measured

acceleration data, measured with the biomechanics system and Rover, by 7.02

% and 6.79 %, respectively (an average of 6.91 %). Further, the simulated

velocity data deviated from the shell velocity measured with Rover by 4.70 %.

The sensitivity analysis indicated that the expected simulation error (i.e., the

uncertainty in the model output due to the combined contributions from the

uncertainties in the model input variables and constants) in the shell

acceleration and velocity were 8.39 % and 6.84 %, respectively. This showed

that the error in the simulated shell motion were within the expected simulation

error, and therefore, indicating that the rowing model is an adequate

representation of a single sculler. It should also be noted that the triaxial

accelerometer had an error of 5.2% when used for static acceleration

measurements as discussed in chapter 2, so it further suggested that the

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simulated shell acceleration emulated the measured shell acceleration

adequately.

Further, the difference in the measured shell acceleration between the Rover

system and the biomechanics measurement system was 2.98 %. Although the

simulated shell acceleration deviated from the measured acceleration data by

an average of 6.91 %, which is more than double the 2.98 % difference

between the two sets of measured acceleration, the rowing model could still be

considered adequate in representing the real rowing system, especially when

considering that many of the model parameters were based on empirical data

from literature (such as oar blade drag and lift coefficients) or rough estimations

(such as immersed oar blade area). In chapter 7, a full examination of all the

biomechanical and hydrodynamics variables was performed on the data of

subject 1, who sculled at a nominal rate of 20 strokes per minute. The intricate

relationships between all the variables were clarified with graphs of selectively

grouped variables.

Hypothesis 2a was substantiated in chapter 7, which analysed the mechanics of

rowing using data collected on-water. All the forces acting on the single scull

was monitored based on the differential equation describing the motion of the

rowing system, as previously mentioned in the second contribution to

knowledge of this thesis. This proposed methodology of evaluating the

propulsive force provides great insight to a rower’s technique, as all the forces

acting on the rowing system and the resultant motions are collectively

monitored.

An attempt was made to substantiate hypothesis 2b in chapter 6, which detailed

a methodology of estimating the motion of the rower’s centre of mass relative to

the rowing shell using seat position measurement and a compensation

difference curve to account for the motion of the upper body, including the arms.

This method is unobtrusive and can be readily implemented on-water. The

proposed method is based on the idea that the “average difference” between

the position of the rower’s centre of mass and the seat position can be

evaluated from one recording session and then used for subsequent rowing

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sessions. The method assumes that the rower’s motion is highly consistent,

which was found to be true for elite rowers from the analysis of a total of 12

rowing strokes (3 strokes for 4 rower subjects). The compensation difference

curve has to be rower and stroke rate specific, as each rower has a

characteristic motion, which varies depending on the stroke rate. It was found

that the position of the rower’s centre of mass estimated from the ‘rower and

stroke rate specific’ difference curve and seat position data had a maximum

error of 2.48 % and a mean error of 0.85 % relative to that calculated from the

rowing model, which required video analysis of the rower’s upper body

movement. These error percentages were actually the worst case of the 4

subjects. The estimated motion of the rower’s centre of mass relative to the

rowing shell was then used to re-simulate the shell acceleration using the

rowing model to examine the error propagation effect. On average across the 4

subjects, the absolute mean error and maximum error in the re-simulated shell

acceleration using the estimated rower motion were 7.68% and 77.37%,

respectively, relative to the shell acceleration measured by the Rover system. In

comparison, the absolute mean error and maximum error in the original

simulated shell acceleration using the video-derived rower motion were 7.79%

and 79.67%, respectively, relative to the Rover measured shell acceleration. As

no out-of-sample validation was performed, it could only be stated that it was

possible to come up with a compensation curve that accurately described the

data of an individual rower at a specific stroke rate during a specific rowing

session. Nevertheless, the low amount of error in the estimated motion of the

rower’s centre of mass indicated that elite rowers have very consistent rowing

motion and that using a rower and stroke rate specific compensation curve to

estimate the motion of the rower’s centre of mass relative to the rowing shell

from seat position measurement is a reasonable approach.

It was found that hypothesis 2c was feasible using the proposed method

described in hypothesis 2a to calculate the propulsive force on the rowing

system (i.e., blade force) and combined with oar handle force and oar angle

measurements. The ratio of the impulse of force at the blade to the impulse of

force at the oar handle was calculated. This ratio, referred to as ‘impulse of

force effective index’, is related to the ‘effectiveness of oar propulsion’, as

297

defined in (Zatsiorsky & Yakunin 1991), and can be used to show how much of

the rower’s effort is effectively used to propel the rowing system forward. No

conclusions could be drawn because of the limited amount of data analysed,

but it warrants further research into use of the ‘impulse of force effective index’

as a parameter to gauge the effectiveness of a single sculler and correlate the

index to performance.

In conclusion, it was found that a single differential equation is a good

representation of the relationship between all the forces acting on the single

scull and the resultant shell motion. A methodology was developed to monitor

the variables of this differential equation using the Rover measurement system

and allow the remaining variable, the propulsive force, to be calculated. The

proposed methodology of calculating the propulsive force provides great insight

to a rower's technique, as all the forces acting on the rowing system and the

resultant shell motion are collectively monitored. Most importantly, the sensors

pose no hindrance to the rower and are easy to set up, so the method can be

readily applied on a routine basis.

8.3 RECOMMENDATIONS FOR FURTHER RESEARCH

As with any research, there were limitations with this research project and this

section details the author’s ideas on how to improve and extend on the

research. The recommendations for improvements and/or extensions to the

research for each of the thesis chapters are presented below.

8.3.1 ACCELEROMETERS FOR ROWING TECHNIQUE ANALYSIS

• Since the triaxial accelerometers were only tested for static

measurements, dynamic testing is the logical step for further assessment.

This could be achieved by using a three-dimensional vibration generator

and three laser interferometers as reported in (Umeda et al. 2004). It is

important to know the amount of error expected when the triaxial

accelerometer is used in a dynamic sense because shell acceleration is

not static, but dynamic. However, with the significant improvements in

the reliability, precision and accuracy of MEMS accelerometers over the

decade from 2000, this issue might not be as essential.

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• An alternative approach is to construct a rotation rig and use the

combination of centripetal acceleration (the radial component of the

rotational acceleration), tangential acceleration and gravity to assess the

dynamic measurement accuracy of the triaxial accelerometers. In

particular, the rotation should be at a constant speed (i.e., uniform

circular motion), so that the tangential acceleration is zero and the

centripetal acceleration has a constant magnitude, and it is the change in

direction of the resultant acceleration (i.e., sum of the centripetal

acceleration and gravity vectors) that allows the dynamic measurement

accuracy of the triaxial accelerometers to be assessed.

8.3.2 A SINGLE SCULL ROWING MODEL

First, there are several aspects of the data collection methodology that should

be improved:

• Increase the sample rate of the biomechanics measurement system and

the video from 25Hz to 100Hz to match the Rover data, instead of having

to low pass filter and resample the Rover data down to 25 Hz. This is

particularly important because some of the data required the evaluation

of its derivatives (e.g., rower angles and oar angles), and for accurate

differentiation, the input signal needs to be sampled at a higher sampling

rate.Synchronise the three measurement systems electronically: the

biomechanics measurement system, the video recording and the

Rover.Conduct the rowing model validation in an indoor water tank to

eliminate environmental factors including water current and wind.

• Calculate the rower motion using a motion capture software package

with body markers by mounting video cameras on both the port and

starboard outriggers, instead of manually processing the video recording.

• A more extensive data set – Collect on-water data from rowers of

different skill levels (amateur versus national level) in a water tank, from

a stationary start, for a predetermined distance (say, 100m). Each rower

would repeat this at different stroke rates, such as 20, 25, 32 strokes per

minute.

299

Improvements to make the rowing model more realistic and accurate include:

• Experimentally determine the hydrodynamic characteristics of the rowing

shell and oar blades. This would need to be performed at a

hydrodynamics laboratory; inside a water tank with equipment to

measure the forces that the water exerts on the rowing equipment. An

alternative is to do computational fluid dynamics simulations of the

rowing shell and oar blades. In any case, better hydrodynamics

representation is needed.

• Account for rotational motion of the rowing shell in the rowing model.

This will require the use of gyroscope sensors to verify the rowing model.

Triaxial gyroscopes were actually incorporated into the next generation of

Rover (its name was changed, when the Rover design was sold).

8.3.3 ROWING MODEL SENSITIVITY ANALYSIS

The simulation error should be re-calculated after implementing the

recommendations suggested previously for the development and validation of

the rowing model in section 8.3.2. Synchronising the biomechanics

measurement system, Rover and video, sampling all the data at 100 Hz, and

conducting the rowing sessions in an indoor water tank to eliminate

environmental factors would improve the data accuracy. Using motion capture

would improve the accuracy of determining the motion of the rower’s centre of

mass relative to the rowing shell. Further, collecting data from a stationary start

would eliminate the need to set the initial shell velocity, which inevitably has an

uncertainty as it is a measurement.

From the sensitivity analysis, it was found that the simulation was most

sensitive to oar angle out of all the time series data used as inputs to the rowing

model. This is because oar angle accounted for the propulsive force on the

rowing system, while the remaining variables accounted for portions of the force

due to the rower motion. By using experiments or numerical simulations to

determine the hydrodynamic characteristics of the oar blades more accurately,

along with increased sampling rate of the oar angle measurement to 100 Hz

and synchronisation with the shell velocity measurement, the accuracy of

calculating the propulsive force using the hydrodynamic model of the oar blades

300

would improve significantly. It would be very interesting to find out how much

the simulated shell velocity and acceleration improves after these

implementations.

8.3.4 MOTION OF THE ROWER’S CENTRE OF MASS

• More data will have to be collected to further confirm the results of the

rower motion study, which showed that the motion of the rower’s upper

body was highly consistent at a fixed stroke rate and that an average

difference curve was a reasonable approach in estimating the motion of

the rower’s centre of mass relative to the rowing shell from seat position

measurement.

• As mentioned previously in section 8.3.2, the motion of the rower should

be measured with a motion capture system. This would reduce the

amount of manual work in calculating the motion of the rower’s centre of

mass significantly, as well as improve the accuracy.

• Seat position could be measured with accelerometers, which would

make the measurement system much more straightforward and

consistent, but the average difference compensation curve will be in the

units of acceleration, instead of position. Specifically, the acceleration of

the rower’s upper body, estimated from motion capture studies of the

rower motion, is combined with seat acceleration measured data to

estimate the acceleration of the rower’s centre of mass.

8.3.5 ANALYSIS OF THE MECHANICS OF ROWING

As discussed in section 8.3.2, a more extensive data set sampled at 100 Hz

from rowers of different skill levels (amateur versus national level) should be

collected. This data will allow us to analyse the difference between rowers of

different skill levels with the proposed methodology of using the differential

equation describing the motion of the rowing system to assess rowing technique

and performance. By comparing the variables in the differential equation, which

includes propulsive force, resistive force, force due to the rower motion and

resultant force (i.e., product of shell acceleration and rowing system mass),

between the rowers of different skill levels, the cause and effect relationship

between the variables and how it relates to performance can be revealed.

301

Further, the propulsive force estimated by evaluating the other force variables in

the differential equation describing the motion of the rowing system was limited

to 25 Hz. This was because the rower motion data was sampled at 25 Hz (i.e.,

25 frames per second video recording to measure the rower’s trunk orientation,

shoulder angle and elbow angle, and 25 Hz sampling rate for the seat position

measurement). At the stroke rate of 32 strokes per minute, the drive to recovery

ratio was approximately 0.5 for subject 1, which equated to the drive phase

lasting only 0.94 s. At the sampling rate of 25 Hz, this meant that there were

only about 23 data points representing the propulsive force profile. Thus,

sampling the data at a higher rate of 100 Hz would be of significant value in

analysing the difference in the propulsive force profile between the rowers of

different skill levels. This will allow more in-depth analysis and more definitive

conclusions to be drawn.

Due to the limitations with the experimental setup as discussed in chapter 7, no

definitive conclusions could be drawn regarding the ‘impulse of force effective

index”, the ratio of the impulse of force at the oar blade to the impulse of force

at the oar handle, evaluated for each of the four subjects. Thus, it is strongly

recommended that more research should be conducted to investigate the use of

the ‘impulse of force effective index’ to gauge the effectiveness of a rower’s

technique. The one drawback with the ‘impulse of force effective index’ is that

the applied force at the oar handle needs to be measured, which requires

instrumented oars (i.e., using strain gauges), so the measurement system is not

just based on MEMS inertial sensors. This takes away the advantages of

employing MEMS inertial sensors; that they are unobtrusive, inexpensive and

easy to set up and maintain.

8.4 REFERENCE

Umeda, A, Onoe, M, Sakata, K, Fukushima, T, Kanari, K, Iioka, H & Kobayashi, T 2004, 'Calibration of three-axis accelerometers using a three-dimensional vibration generator and three laser interferometers', Sensors and actuators. A, Physical, vol. 114, no. 1, pp. 93-101. Zatsiorsky, VM & Yakunin, N 1991, 'Mechanics and biomechanics of rowing: A review', International Journal of Sport Biomechanics, vol. 7, pp. 229-81.

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