centergravity lab

BIOMECHANICAL ANALYSIS OF PHYSICAL ACTIVITY


Laboratory Experiments: Measurement and Interpretation of the Kinematics of the Center of Gravity of the Human Body

Dr. Eugene W. Brown

Purposes:

These laboratory experiments have several purposes. They include:

1.developing or reviewing the concepts of levers,

2.understanding how to use a reaction board to calculate the center of gravity

of the human body,

3.understanding how to use the segmental method to calculate the center of

gravity of the human body,

4.understanding the use of Walton templates in determining the center of mass

of various segments of the human body,

5.reviewing concepts of mass segment parameters,

6.understanding the concept of the center of gravity,

7.reviewing concepts of projectiles and vectors,

8.developing an understanding of experimental methods in biomechanics,

9.learning how to use a camera for two dimensional videography,

10.understanding the relationship of experimental error to measurements

recorded,

11.preparing subjects for participation in research experiments,

12.setting up experimental procedures in biomechanics,

13.understanding how to calculate field and frame rates, and

14.learning how to report the results of laboratory experiments.

List of Equipment and Supplies

1.acetate grids

2.adult male and female subjects

3.background curtain

4.block to support reaction board

5.calculator

6.camera tripod

7.carpenters square

8.computer and software for down loading video images

9.fiducial markers

10.laser pointer

11.level

12.mass-segment data sheet

13.plumb bob

14.reaction board

15.reference measure (meter stick)

16.subject and trial board and numbers

17.tape

18.tape measure

19.timing light box

20.video camera

21.video tape

22.Walton Template

23.weight scale

24.

25.

26.

27.

Definition of Terms:

1.center of gravity center of mass distribution of an object

2.equilibrium a condition in which the sum of all forces and torques acting on

an object equals zero resulting in a constant linear and angular velocity

3.fiducial two or more marks placed in the field of view of a video or motion

picture camera (usually at the outer edges of the field of view) to be used

to align sequential images to a laboratory coordinate system

4.field rate the number of pictures of video captured in a known period of time

(e.g., 30 fields/second)

5.frame rate - the number of pictures of motion picture film captured in a known

period of time (e.g., 100 frames/second)

6.optic axis of lens line perpendicular to the long axis of a lens

7.perspective error error which occurs when parts of a body or implement lie

outside the principle photographic plane; image of segment closer to the

camera appears larger and segment farther away appears smaller

8.plumb bob weighted string that hangs vertical which is used for spatial

orientation

9.reaction board board that is used as a lever to transmit force to weighted

scale for purposes of determining the center of mass of objects (e.g.,

human body) placed on it

10.reference measure an object of known length (e.g., meter stick) that is

placed in a plane that is perpendicular to the optic axis of the lens of a

camera that is used to assist in determining distance measurements in the

same plane

11.segmental method procedure used to calculate the center of mass of a multi-

segmented system (e.g., human body, horse) that is based on known

segment masses and mass centers of gravity of a similar model (e.g.,

cadaver of a human, cadaver of a horse)

12.timing lights electronic device that uses lights to accurately display time

13.vector a measure that is represented by magnitude and direction (e.g.,

displacement, velocity, acceleration, force, momentum)

14.Walton template a standard measurement device, unique to each segment of

the body, that is used to determine the location of the center of gravity of

each body segment based on known proportions of the center of gravity

from the proximal and distal ends of each segment

14.whole body method a procedure for determining the location of the center of

gravity of a multi-segmented system (e.g., human body, horse) in one

configuration without regard for the position of individual segments

(e.g., reaction board, pendulum)

15.

16.

Review:

1.Projectile

2.Vectors

Reaction Board for the Calculation of Whole Body Center of Gravity

Basically, the reaction board method for the calculation of the center of gravity of the whole body is based on the principle of levers. In a static lever system, the sum of the forces and the sum of the torques are equal to zero. The reaction board system is such a system. If an imaginary fulcrum is placed at the knife edge aligned with the dorsum of the feet, the sum of the positive (counterclockwise) torques and negative (clockwise) torques must equal to zero. In other words:

(Fs)( Lb) = (Wtboard)( 1/2Lb) + (Wtbody)( Lcg)

In this equation, the only variable that is not known is the location of Lcg. Therefore, we can solve for this parameter.

Segmental Method for the Calculation of Center of Gravity of the BodyThis method is based on segmental mass proportions derived from cadaver studies. If we can approximate (1) the proportion of weight (mass) that each segment is of the whole body and (2) the location of the center of gravity of individual segments in a Cartesian axis system, we can approximate the location of the center of gravity in an image of the human body. This image can be a picture, a series of pictures in a film, or a series of pictures in a video sequence. Note that this method results in only an approximation for the location of the center of gravity of the human body because we can not guarantee that the proportions of the live individual are exactly the same as the proportions of the cadavers upon which this method is based. The steps in this process are as follows:

1.Locate the ends of the defined segments according to the link segment boundaries

and place a mark at these points. This will result in marks at the end of the second

toe, ankle, knee, hip knuckle III of the hand, wrist, shoulder, seventh cervical

vertebra, and top of the head. Be careful to perceive the segments as three

dimensional images, even though the picture is seen in two dimensions.

2.Join the segments to form a stick figure consisting of 14 segments. Note that the

trunk segment goes from the seventh cervical vertebra to the midpoint of the line

connecting the two hips

3.Determine the coordinates of the extremes of each of the 14 segments.

4.Use cadaver data on the location of the center of gravity as a proportion of segment

length from the proximal and distal ends of the segments (see Segmental Method

Center of Gravity Table) to determine the location of the center of gravity of each

of the segments in the picture. Note that a special template called the Walton

template can be used for this step.

5.Enter the coordinates of the center of gravity of each segment into the table

provided (see Segmental Method Center of Gravity Table) and multiply these

values by the respective body segment proportion of weight (mass).

6.The sum of these products is the calculated location of the center of gravity of the

body relative to the coordinate system being used.

Segmental Method Center of Gravity Table

Body SegmentCenter of Mass Location from:Proportion of Body WeightX Value of the Center of GravityX - ProductY Value of the Center of GravityY - Product

Prox.

EndDistal End

1. Trunk

.562.438.486

2. Head

and

Neck.567.433.079

3. R.

Thigh.433.567.097

4. R.

Shank.433.567.045

5. R. Foot

.5.5.014

6. L.

Thigh.433.567.097

7. L.

Shank.433.567.045

8. L. Foot

.5.5.014

9. R. Arm

.436.564.027

10. R.

Forearm.43.57.014

11. R.

Hand.506.494.006

12. L.

Arm.436.564.027

13. L.

Forearm.43.57.014

14. L.

Hand

.506.494.006

(=.971(X product(Y product

General Methods and Procedures:

There will be 3 experiments to highlight the position and movement of the center of gravity of the human body. In addition, principles of projectile movement will be reviewed. Students must share the responsibility of carrying out these experiments!!! The general methods and procedures for each of these experiments is as follows:

1.Subject Preparation

a.The subjects should be dressed with minimal clothing (tank top or no

shirt and shorts) to (1)minimize the influence of clothing on the position

of the center of gravity of the body and (2)not obstruct the view of the

body and body landmarks.

b.Before collecting data, each subject should be familiar with the setting

and task requirements.

c.Each subject should not be exposed to any physical harm as a result of

performance and/or physical limitations.

d.For any strenuous activity, subjects should be provided with a warm up

and a few practice trials. They must also be apprised of the tasks they

are being asked to perform. This may reduce the chance of injury.

2.Set Up of Reaction Board

a.See figure in section entitled Reaction Board for the Calculation of

Whole Body Center of Gravity.

b.The board must be supported at both ends (at one end by the platform of

a weight scale and at the other end by a board).

c.One knife edge of the reaction board should be centered on the platform

of the weight scale and the other should be centered on the wooden

support.

d.The surface of the reaction board must be level.

e.The reaction board must support the subjects weight without

appreciably bowing or breaking.

3.Set Up of Video Camera

a.The video camera must be positioned relatively far from the reaction

board to minimize perspective error.

b.Level the camera and orient the optic axis of its lens so that it is

perpendicular to the long axis of the reaction board and plane of

movement.

c.Use the lens to zoom in and focus on the activity plane. Then zoom out

to make the field of view as small as possible to maximize the subject

size. Make sure the entire subject or performance sequence can just be

seen in the field of view.

d.Place a plumb bob, reference measure, fiducials, and timing lights in the

field of view.

e.Use a contrasting curtain in the background to highlight the subjects and

reaction board.

4.Calibration of Field Rate of Video Camera

a.Video tape the timing lights.

b.Determine the time from the timing lights for field one.

c.Count fields from field one to some other field approximately three

seconds later in time.

d.Calculate the field rate.

Field rate = number of fields one

time transpired from field one to last field

5.Data Collection

a.All data should be collected as accurately as possible.

b.As data is being collected, note where inaccuracies occur and potentially

use this information to justify results.

Specific Methods and Procedures:

In addition to the general methods and procedures, the 3 experiments have their own specific methods and procedures that must be followed.

Experiment 1 Whole Body Calculation of the Center of Gravity via Reaction

Board Lying Position

a.Accurately determine the X-value location of the center of mass of the

reaction board; assume the location is total length of homogeneous

board (i.e., measure board in metric units and divide by 2).

b.Determine the weight of the reaction board in metric units by weighing

it on a calibrated scale.

c.Check the alignment of the knife edges (angle iron) on both ends of

the reaction board. Their vertical surface should be aligned with the

ends of the reaction board.

d.Check the height of the wooden block that is used to support the reaction

board. It should be equal in height to the height of the surface of the

scale. Thus, the reaction board, supported by the scale and wooden

block will be level.

e.Weigh each subject in metric units as accurately as possible on a

calibrated scale. Each subject should be wearing only shorts and tank

top.

f.Accurately measure the height of each subject using the metric system.

g.Position one knife edge of the reaction board on center of the scale and

the other on the center of the supporting wooden block.

h.Prior to getting a subjects weight on the reaction board, have him/her

straddle the reaction board and lower his/ her body gently onto the

board.

i.Once a subject is on the reaction board, have him/her assume a

stationary anatomical position with the hands at the sides of his/her body

and the dorsum of the feet perpendicular to the floor and coplanar with

the vertical surface of the knife edge. The head must be oriented in the

Frankfort plane.

j.Accurately weigh each subject on the reaction board in metric units.

k.Each student is responsible for calculating his/her own center of mass

location in metric unit as a distance form the dorsum of the feet. Show

your work.

l.Each student is responsible for calculating his/her own percentage of

total body height that the location of the center of gravity of the body is

from the dorsum of the feet and recording this value on the class record

sheet (see Class Record Sheet). Percents should be recorded in the

appropriate gender category. Show your work.

m.Each student is responsible for calculating the mean and standard

deviation of the percents for the male and female groups. Show your

work.


Board Versus Segmental Method Three Support Positions

a.Place a video camera with the optic axis of its lens horizontal and also

perpendicular to the long axis of the reaction board.

b.Each subject must carefully assume three different support positions on

the reaction board: one with the body weight toward the front edge of

the base of support (anterior), one with the body weight centered over

the base of support (balanced), and one with the body weight toward the

back edge of the base of support (posterior).

c.In the field of view of the video camera, place a (1) contrasting curtain,

(2) plumb bob, (3) calibration measure, and (4) fiducials.

d.Simultaneously capturing the video images and force values from the

scale of the three support positions of each subject. Note that the body

of the subject should just fit into the field of view of the camera.

e.Each student is responsible for their measure, in metric units, of the

distance of the near and far edge of their base to the knife edge (0,0

position) for each of the three support positions.

f.Each student is responsible for following the same methods and

procedures used in Experiment 1 for determining the horizontal position

of their center of gravity relative to the knife edge on the wooden block

(i.e., use the reaction board technique). Show your work.

g.Each student is responsible for applying the segmental method (whole

body method) and cadaver data to their captured video images, to

calculate their horizontal location (X value only) of the center of gravity

of the body for each of their three support positions. Students are

responsible for transforming the units to laboratory (real world) units

relative to the knife edge (zero X value). Show your work.

Experiment 3 Projectile Behavior of the Center of Gravity of the Human Body

a.Select one subject, free of any physically limiting factors, to perform a

standing long jump.

b.Use a starting line for the standing long jumps and position a tape

measure to facilitate the measurement of the distance of the jumps.

Jump distances should be measured in metric units from the tips of the

toes on take off (edge of the starting line) to the tips of the toes on

landing.

c.Provide warm up for the subject and several lead up jumps (less than all-

out practice jumps).

d.During the practice jumps, position the video camera with the optic axis

of its lens horizontal and also perpendicular to the long axis of the

primary plane of movement for the standing long jump. Also, minimize

the field of view so that the entire performance of the standing long

jump (take off to landing) just fits into the field of view. In other words,

maximize the size of the subject in the field of view.

e.In the field of view of the video camera, place a (1) contrasting curtain,

(2) plumb bob, (3) calibration measure, (4) fiducials, and (5) timing light

box.

f.Video tape the timing light box for three or more seconds and calculate

the time interval between frames. Show your work.

g.Apply the segmental method and cadaver data to the captured sequential

video images, to calculate the horizontal and vertical location (X and Y

values) of the center of gravity of the body for each of the selected

fields. Note that these fields must include the images for take off and

landing, first and last two airborne positions, as well as some regular

temporal sequence beginning at take off. Also, select one field that

visually appears to represent the highest vertical position of the body

during the airborne phase of the standing long jump. Show your work.

h.Use the horizontal and vertical position of the center of gravity of the

body for the first and second airborne positions and the calculated time

interval between fields of video to determine the resultant velocity

vector (magnitude and direction) of the center of gravity in laboratory

units. Show your

work.

i.Calculate the magnitudes of the horizontal and vertical velocity vectors

of the center of gravity of the body in laboratory units from the first and

second airborne positions and the known time interval between fields of

video. Show your work.

j.Use the horizontal and vertical position of the center of gravity of the

body for the last two airborne positions and the calculated time interval

between fields of video to determine the resultant velocity vector

(magnitude and direction) of the center of gravity in laboratory units.

Show your work.

k.Calculate the magnitudes of the horizontal and vertical velocity vectors

of the center of gravity of the body in laboratory units from the last two

airborne positions and the known time interval between fields of video.

Show your work.

l. Calculate the horizontal velocity vector in laboratory units for some

interval in the middle of the airborne phase. Show your work.

Results:

The results are the responses to the statements that follow. They are to be written in a scientific format. You should develop figures, graphs, and spreadsheet tables and refer to these in your write-up to make the results easy to read. Also, include and label graphs generated as output. Your format should differ from the normal scientific format in that you must show your work (i.e., how you calculated your results). If there are several iterations of the same calculation process, you only need to show the first to demonstrate your understanding.



1.Compare the percent of total body height that the center of gravity is for the

male and female groups.

2.Are the mean percents in accord with expectations? Explain why or why not.



1.Were the horizontal positions, relative to the knife edge on the wooden block,

of the center of gravity of your body the same for the reaction board and

segmental methods for each of the three positions? Explain why or why not.

2.Which of the two methods do you think is more accurate for determining the

horizontal position of the center of gravity of your body? Explain.


1.Was the take off velocity vector calculated from the first two airborne fields

of video as expected for someone attempting to achieve a maximum standing

long jump? Explain.

2.Was the landing velocity vector calculated from the last two airborne fields


long jump? Explain.

3.What relationship did you find between the velocity vector for take off and

landing? Was or was not this result expected? Explain.

4.What relationship did you find between the horizontal velocity vectors for

take off, landing and the horizontal velocity vector calculated for the

middle of the airborne phase? Was or was not this result expected? Explain.

5.Was the maximum height of the center of gravity as expected on the basis of

the vertical velocity vector at take off? Explain.

Class Record SheetNameStanding Height (cm)Height of Center of Gravity (cm)Height of CG as a % of total Body Height

Females

1.

2.

3.

4.

5.

6.

Mean (sd):

Males

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Mean (sd):



Dr. Eugene W. Brown

Purposes:

These laboratory experiments have several purposes. They include:

1.developing or reviewing the concepts of levers,

2.understanding how to use a reaction board to calculate the center of gravity

of the human body,

3.understanding how to use the segmental method to calculate the center of

gravity of the human body,

4.understanding the use of Walton templates in determining the center of mass

of various segments of the human body,

5.reviewing concepts of mass segment parameters,

6.understanding the concept of the center of gravity,

7.reviewing concepts of projectiles and vectors,

8.developing an understanding of experimental methods in biomechanics,

9.learning how to use a camera for two dimensional videography,

10.understanding the relationship of experimental error to measurements

recorded,

11.preparing subjects for participation in research experiments,

12.setting up experimental procedures in biomechanics,

13.understanding how to calculate field and frame rates, and

14.learning how to report the results of laboratory experiments.

List of Equipment and Supplies

1.acetate grids

2.adult male and female subjects

3.background curtain

4.block to support reaction board

5.calculator

6.camera tripod

7.carpenters square

8.computer and software for down loading video images

9.fiducial markers

10.laser pointer

11.level

12.mass-segment data sheet

13.plumb bob

14.reaction board

15.reference measure (meter stick)

16.subject and trial board and numbers

17.tape

18.tape measure

19.timing light box

20.video camera

21.video tape

22.Walton Template

23.weight scale

24.

25.

26.

27.

Definition of Terms:

1.center of gravity center of mass distribution of an object

2.equilibrium a condition in which the sum of all forces and torques acting on

an object equals zero resulting in a constant linear and angular velocity

3.fiducial two or more marks placed in the field of view of a video or motion

picture camera (usually at the outer edges of the field of view) to be used

to align sequential images to a laboratory coordinate system

4.field rate the number of pictures of video captured in a known period of time

(e.g., 30 fields/second)

5.frame rate - the number of pictures of motion picture film captured in a known

period of time (e.g., 100 frames/second)

6.optic axis of lens line perpendicular to the long axis of a lens

7.perspective error error which occurs when parts of a body or implement lie

outside the principle photographic plane; image of segment closer to the

camera appears larger and segment farther away appears smaller

8.plumb bob weighted string that hangs vertical which is used for spatial

orientation

9.reaction board board that is used as a lever to transmit force to weighted

scale for purposes of determining the center of mass of objects (e.g.,

human body) placed on it

10.reference measure an object of known length (e.g., meter stick) that is

placed in a plane that is perpendicular to the optic axis of the lens of a

camera that is used to assist in determining distance measurements in the

same plane

11.segmental method procedure used to calculate the center of mass of a multi-

segmented system (e.g., human body, horse) that is based on known

segment masses and mass centers of gravity of a similar model (e.g.,

cadaver of a human, cadaver of a horse)

12.timing lights electronic device that uses lights to accurately display time

13.vector a measure that is represented by magnitude and direction (e.g.,

displacement, velocity, acceleration, force, momentum)

14.Walton template a standard measurement device, unique to each segment of

the body, that is used to determine the location of the center of gravity of

each body segment based on known proportions of the center of gravity

from the proximal and distal ends of each segment

14.whole body method a procedure for determining the location of the center of

gravity of a multi-segmented system (e.g., human body, horse) in one

configuration without regard for the position of individual segments

(e.g., reaction board, pendulum)

15.

16.

Review:

1.Projectile

2.Vectors

Reaction Board for the Calculation of Whole Body Center of Gravity

Basically, the reaction board method for the calculation of the center of gravity of the whole body is based on the principle of levers. In a static lever system, the sum of the forces and the sum of the torques are equal to zero. The reaction board system is such a system. If an imaginary fulcrum is placed at the knife edge aligned with the dorsum of the feet, the sum of the positive (counterclockwise) torques and negative (clockwise) torques must equal to zero. In other words:

(Fs)( Lb) = (Wtboard)( 1/2Lb) + (Wtbody)( Lcg)

In this equation, the only variable that is not known is the location of Lcg. Therefore, we can solve for this parameter.

Segmental Method for the Calculation of Center of Gravity of the BodyThis method is based on segmental mass proportions derived from cadaver studies. If we can approximate (1) the proportion of weight (mass) that each segment is of the whole body and (2) the location of the center of gravity of individual segments in a Cartesian axis system, we can approximate the location of the center of gravity in an image of the human body. This image can be a picture, a series of pictures in a film, or a series of pictures in a video sequence. Note that this method results in only an approximation for the location of the center of gravity of the human body because we can not guarantee that the proportions of the live individual are exactly the same as the proportions of the cadavers upon which this method is based. The steps in this process are as follows:

1.Locate the ends of the defined segments according to the link segment boundaries

and place a mark at these points. This will result in marks at the end of the second

toe, ankle, knee, hip knuckle III of the hand, wrist, shoulder, seventh cervical

vertebra, and top of the head. Be careful to perceive the segments as three

dimensional images, even though the picture is seen in two dimensions.

2.Join the segments to form a stick figure consisting of 14 segments. Note that the

trunk segment goes from the seventh cervical vertebra to the midpoint of the line

connecting the two hips

3.Determine the coordinates of the extremes of each of the 14 segments.

4.Use cadaver data on the location of the center of gravity as a proportion of segment

length from the proximal and distal ends of the segments (see Segmental Method

Center of Gravity Table) to determine the location of the center of gravity of each

of the segments in the picture. Note that a special template called the Walton

template can be used for this step.

5.Enter the coordinates of the center of gravity of each segment into the table

provided (see Segmental Method Center of Gravity Table) and multiply these

values by the respective body segment proportion of weight (mass).

6.The sum of these products is the calculated location of the center of gravity of the

body relative to the coordinate system being used.

Segmental Method Center of Gravity Table

Body SegmentCenter of Mass Location from:Proportion of Body WeightX Value of the Center of GravityX - ProductY Value of the Center of GravityY - Product

Prox.

EndDistal End

1. Trunk

.562.438.486

2. Head

and

Neck.567.433.079

3. R.

Thigh.433.567.097

4. R.

Shank.433.567.045

5. R. Foot

.5.5.014

6. L.

Thigh.433.567.097

7. L.

Shank.433.567.045

8. L. Foot

.5.5.014

9. R. Arm

.436.564.027

10. R.

Forearm.43.57.014

11. R.

Hand.506.494.006

12. L.

Arm.436.564.027

13. L.

Forearm.43.57.014

14. L.

Hand

.506.494.006

(=.971(X product(Y product

General Methods and Procedures:

There will be 3 experiments to highlight the position and movement of the center of gravity of the human body. In addition, principles of projectile movement will be reviewed. Students must share the responsibility of carrying out these experiments!!! The general methods and procedures for each of these experiments is as follows:

1.Subject Preparation

a.The subjects should be dressed with minimal clothing (tank top or no

shirt and shorts) to (1)minimize the influence of clothing on the position

of the center of gravity of the body and (2)not obstruct the view of the

body and body landmarks.

b.Before collecting data, each subject should be familiar with the setting

and task requirements.

c.Each subject should not be exposed to any physical harm as a result of

performance and/or physical limitations.

d.For any strenuous activity, subjects should be provided with a warm up

and a few practice trials. They must also be apprised of the tasks they

are being asked to perform. This may reduce the chance of injury.

2.Set Up of Reaction Board

a.See figure in section entitled Reaction Board for the Calculation of

Whole Body Center of Gravity.

b.The board must be supported at both ends (at one end by the platform of

a weight scale and at the other end by a board).

c.One knife edge of the reaction board should be centered on the platform

of the weight scale and the other should be centered on the wooden

support.

d.The surface of the reaction board must be level.

e.The reaction board must support the subjects weight without

appreciably bowing or breaking.

3.Set Up of Video Camera

a.The video camera must be positioned relatively far from the reaction

board to minimize perspective error.

b.Level the camera and orient the optic axis of its lens so that it is

perpendicular to the long axis of the reaction board and plane of

movement.

c.Use the lens to zoom in and focus on the activity plane. Then zoom out

to make the field of view as small as possible to maximize the subject

size. Make sure the entire subject or performance sequence can just be

seen in the field of view.

d.Place a plumb bob, reference measure, fiducials, and timing lights in the

field of view.

e.Use a contrasting curtain in the background to highlight the subjects and

reaction board.

4.Calibration of Field Rate of Video Camera

a.Video tape the timing lights.

b.Determine the time from the timing lights for field one.

c.Count fields from field one to some other field approximately three

seconds later in time.

d.Calculate the field rate.

Field rate = number of fields one

time transpired from field one to last field

5.Data Collection

a.All data should be collected as accurately as possible.

b.As data is being collected, note where inaccuracies occur and potentially

use this information to justify results.

Specific Methods and Procedures:

In addition to the general methods and procedures, the 3 experiments have their own specific methods and procedures that must be followed.



a.Accurately determine the X-value location of the center of mass of the

reaction board; assume the location is total length of homogeneous

board (i.e., measure board in metric units and divide by 2).

b.Determine the weight of the reaction board in metric units by weighing

it on a calibrated scale.

c.Check the alignment of the knife edges (angle iron) on both ends of

the reaction board. Their vertical surface should be aligned with the

ends of the reaction board.

d.Check the height of the wooden block that is used to support the reaction

board. It should be equal in height to the height of the surface of the

scale. Thus, the reaction board, supported by the scale and wooden

block will be level.

e.Weigh each subject in metric units as accurately as possible on a

calibrated scale. Each subject should be wearing only shorts and tank

top.

f.Accurately measure the height of each subject using the metric system.

g.Position one knife edge of the reaction board on center of the scale and

the other on the center of the supporting wooden block.

h.Prior to getting a subjects weight on the reaction board, have him/her

straddle the reaction board and lower his/ her body gently onto the

board.

i.Once a subject is on the reaction board, have him/her assume a

stationary anatomical position with the hands at the sides of his/her body

and the dorsum of the feet perpendicular to the floor and coplanar with

the vertical surface of the knife edge. The head must be oriented in the

Frankfort plane.

j.Accurately weigh each subject on the reaction board in metric units.

k.Each student is responsible for calculating his/her own center of mass

location in metric unit as a distance form the dorsum of the feet. Show

your work.

l.Each student is responsible for calculating his/her own percentage of

total body height that the location of the center of gravity of the body is

from the dorsum of the feet and recording this value on the class record

sheet (see Class Record Sheet). Percents should be recorded in the

appropriate gender category. Show your work.

m.Each student is responsible for calculating the mean and standard

deviation of the percents for the male and female groups. Show your

work.



a.Place a video camera with the optic axis of its lens horizontal and also

perpendicular to the long axis of the reaction board.

b.Each subject must carefully assume three different support positions on

the reaction board: one with the body weight toward the front edge of

the base of support (anterior), one with the body weight centered over

the base of support (balanced), and one with the body weight toward the

back edge of the base of support (posterior).

c.In the field of view of the video camera, place a (1) contrasting curtain,

(2) plumb bob, (3) calibration measure, and (4) fiducials.

d.Simultaneously capturing the video images and force values from the

scale of the three support positions of each subject. Note that the body

of the subject should just fit into the field of view of the camera.

e.Each student is responsible for their measure, in metric units, of the

distance of the near and far edge of their base to the knife edge (0,0

position) for each of the three support positions.

f.Each student is responsible for following the same methods and

procedures used in Experiment 1 for determining the horizontal position

of their center of gravity relative to the knife edge on the wooden block

(i.e., use the reaction board technique). Show your work.

g.Each student is responsible for applying the segmental method (whole

body method) and cadaver data to their captured video images, to

calculate their horizontal location (X value only) of the center of gravity

of the body for each of their three support positions. Students are

responsible for transforming the units to laboratory (real world) units

relative to the knife edge (zero X value). Show your work.


a.Select one subject, free of any physically limiting factors, to perform a

standing long jump.

b.Use a starting line for the standing long jumps and position a tape

measure to facilitate the measurement of the distance of the jumps.

Jump distances should be measured in metric units from the tips of the

toes on take off (edge of the starting line) to the tips of the toes on

landing.

c.Provide warm up for the subject and several lead up jumps (less than all-

out practice jumps).

d.During the practice jumps, position the video camera with the optic axis

of its lens horizontal and also perpendicular to the long axis of the

primary plane of movement for the standing long jump. Also, minimize

the field of view so that the entire performance of the standing long

jump (take off to landing) just fits into the field of view. In other words,

maximize the size of the subject in the field of view.

e.In the field of view of the video camera, place a (1) contrasting curtain,

(2) plumb bob, (3) calibration measure, (4) fiducials, and (5) timing light

box.

f.Video tape the timing light box for three or more seconds and calculate

the time interval between frames. Show your work.

g.Apply the segmental method and cadaver data to the captured sequential

video images, to calculate the horizontal and vertical location (X and Y

values) of the center of gravity of the body for each of the selected

fields. Note that these fields must include the images for take off and

landing, first and last two airborne positions, as well as some regular

temporal sequence beginning at take off. Also, select one field that

visually appears to represent the highest vertical position of the body

during the airborne phase of the standing long jump. Show your work.

h.Use the horizontal and vertical position of the center of gravity of the

body for the first and second airborne positions and the calculated time

interval between fields of video to determine the resultant velocity

vector (magnitude and direction) of the center of gravity in laboratory

units. Show your

work.

i.Calculate the magnitudes of the horizontal and vertical velocity vectors

of the center of gravity of the body in laboratory units from the first and

second airborne positions and the known time interval between fields of

video. Show your work.

j.Use the horizontal and vertical position of the center of gravity of the

body for the last two airborne positions and the calculated time interval

between fields of video to determine the resultant velocity vector

(magnitude and direction) of the center of gravity in laboratory units.

Show your work.

k.Calculate the magnitudes of the horizontal and vertical velocity vectors

of the center of gravity of the body in laboratory units from the last two

airborne positions and the known time interval between fields of video.

Show your work.

m. Calculate the horizontal velocity vector in laboratory units for some

interval in the middle of the airborne phase. Show your work.

Results:

The results are the responses to the statements that follow. They are to be written in a scientific format. You should develop figures, graphs, and spreadsheet tables and refer to these in your write-up to make the results easy to read. Also, include and label graphs generated as output. Your format should differ from the normal scientific format in that you must show your work (i.e., how you calculated your results). If there are several iterations of the same calculation process, you only need to show the first to demonstrate your understanding.



1.Compare the percent of total body height that the center of gravity is for the

male and female groups. (2 points)

2.Are the mean percents in accord with expectations? Explain why or why not.

(2 points)



1.Were the horizontal positions, relative to the knife edge on the wooden block,

of the center of gravity of your body the same for the reaction board and

segmental methods for each of the three positions? Explain why or why not.

(6 points)

2.Which of the two methods do you think is more accurate for determining the

horizontal position of the center of gravity of your body? Explain. (4 points)


1.Was the take off velocity vector calculated from the first two airborne fields


long jump? Explain. (6 points)

2.Was the landing velocity vector calculated from the last two airborne fields


long jump? Explain. (6 points)

3.What relationship did you find between the velocity vector for take off and

landing? Was or was not this result expected? Explain. (2 points)

4.What relationship did you find between the horizontal velocity vectors for

take off, landing and the horizontal velocity vector calculated for the

middle of the airborne phase? Was or was not this result expected? Explain.

(4 points)

5.Was the maximum height of the center of gravity as expected on the basis of

the vertical velocity vector at take off? Explain. (6 points)

Class Record SheetNameWeight

(kg)Standing Height (cm)Fs

(kg)Height of Center of Gravity (cm)Height of CG as a % of total Body Height

Females

1.S.M.

62.3163.19542.27102.1862.6

2.M.D.

64.41168.27542.4198.958.7

3.E.C.

64.86161.2939.6890.3356.0

4.J.A.

56.69158.7537.1994.6559.62

5.

6.

Mean (sd):

Males

1.C.Z.

100.24179.0763.50105.49858.9

2.A.C.

97.52187.32562.14105.6856.4

3.G.H.

87.54178.43556.69105.40159.06

4.J.T.

77.79180.3451.25104.7958.0

5.M.G.

65.43179.70543.99102.5857.0

6.T.K.

79.61180.3451.25102.35756.76

7.B.J.L.

84.36172.7251.7197.6856.56

8.T.E.

97.06177.860.1091.6251.5

9.J.S.

115.21187.9674.84111.2759.1

10.U.V.

80.51184.1552.84105.13657.09

11.J.A.

73.02179.0747.17100.5556.15

12.J.H.

73.48180.3448.98104.7958.11

Mean (sd):



Grade Report

Student: ________________________________

Write-up Area/CommentsPoints ReceivedPoints Possible

Experiment 1 Whole Body Calculation of the Center of Gravity via Reaction Board Lying Position

1.Compare the percent of total body height that the center of

gravity is for the male and female groups.

2

2.Are the mean percents in accord with expectations? Explain

why or why not.

2

Experiment 2 Whole Body Calculation of the Center of Gravity via Reaction Board Versus Segmental Method Three Support Positions

1.Were the horizontal positions, relative to the knife edge on

the wooden block, of the center of gravity of your body the

same for the reaction board and segmental methods for each

of the three positions? Explain why or why not.

6

2.Which of the two methods do you think is more accurate for

determining the horizontal position of the center of gravity

of your body? Explain.

4


1.Was the take off velocity vector calculated from the first

two airborne fields of video as expected for someone

attempting to achieve a maximum standing long jump?

Explain.

6

2.Was the landing velocity vector calculated from the last

two airborne fields of video as expected for someone

attempting to achieve a maximum standing long jump?

Explain.

6

3.What relationship did you find between the velocity vector

for take off and landing? Was or was not this result

expected? Explain.

2

4.What relationship did you find between the horizontal

velocity vectors for take off, landing and the horizontal

velocity vector calculated for the middle of the airborne

phase? Was or was not this result expected? Explain.

4

5.Was the maximum height of the center of gravity as

expected on the basis of the vertical velocity vector at take

off? Explain.

6

Total Points:

38

Grade:

Fs

Wtbody

Wtboard

1/2Lb

Lcg

Lb

Key:

Fs force read at the scale; upward force applied to the board by

the scale

Wtbody weight of the body acting downward at the center of

mass of the body

Wtboard weight of the board acting downward at the center of

the board

Lb length of the board

Lcg distance of the center of gravity of the body to the dorsum

of the feet

Key:

Fs force read at the scale; upward force applied to the board by

the scale

Wtbody weight of the body acting downward at the center of

mass of the body

Wtboard weight of the board acting downward at the center of

the board

Lb length of the board

Lcg distance of the center of gravity of the body to the dorsum

of the feet

1/2Lb

Fs

Wtboard

Wtbody

Lcg

Lb

centergravity lab

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