uncertainty in the analysis of speed and powering trials

ARTICLE IN PRESS

Ocean Engineering 35 (2008) 1183– 1193

Contents lists available at ScienceDirect

Ocean Engineering

0029-80

doi:10.1

� Tel.:

E-m

journal homepage: www.elsevier.com/locate/oceaneng

Uncertainty in the analysis of speed and powering trials

M. Insel �

Department of Naval Architecture, Istanbul Technical University, ITU, Gemi Insaati ve Deniz Bil. Fak., 34469 Maslak, Istanbul, Turkey

a r t i c l e i n f o

Article history:

Received 3 March 2008

Accepted 13 April 2008Available online 1 May 2008

Keywords:

Speed trials

Uncertainty

Full-scale powering

18/$ - see front matter & 2008 Elsevier Ltd. A

016/j.oceaneng.2008.04.009

+90 212 2856512; fax: +90 212 2856508.

ail address: [email protected]

a b s t r a c t

Full-scale speed trials of a ship have been questioned for the uncertainty of speed and power

measurements especially when the sea conditions differ from the ideal calm water conditions. Such

uncertainty has been investigated by utilizing ITTC standard speed/powering trial analysis procedure

through Monte Carlo simulations. A case study was conducted for a set of sea trials with 12 sister ships

for which sea trial data were available for a range of displacement, water depth, water temperature,

wind speed and wave height values. Precision errors were observed as the most influential error source

for the whole speed range, even though their effects were more substantial at low speeds. Beaufort scale

was observed as the most important elementary error source indicating the need for the best weather

conditions for the most reliable sea trail predictions.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Prediction of full-scale power requirement of a ship is anessential part of ship design process. Extrapolation of scaledmodel tests is currently the most reliable method available for thepurpose. However, verification/validation studies are requiredeven with model tests to ensure the accuracy of the results.Hence, uncertainty analysis in ship model testing is currentlywidely utilized to asses the quality of test data by followingInternational Towing Tank Conference (ITTC) recommendations.The prediction of ship power is also effected by a number ofuncertainty components due to the extrapolation process. Theresults of predictions are compared with ship trials, whichrepresent uncertainties due to uncontrollable environmentalconditions in addition to the measurement errors. This paper isintended to investigate uncertainty in the full-scale ship speedtrials to be used in the validation studies through a case study.

Speed trials are conducted at the end of ship constructionusually at a limited time scale. It is rarely possible to conduct thetrials at contract conditions. Therefore, measured ship speed andshaft power must be corrected for the differences between trialconditions and the contract conditions. Hence, ship trials haveuncertainties mainly due to two sources:

�
Trial measurements: torque, shaft rate of revolution, shipspeed measurement uncertainties. � Trial analysis: uncertainties due to corrections applied to trial
measurements.

ll rights reserved.

The uncertainty assessment in shaft torque and speed measure-ments during sea trial for a single run was outlined by 23rd ITTC,The Specialist Committee on Speed and Powering Trials (ITTC,2002). Current study extends this work to include uncertaintyfrom other full-scale measurements such as wind, waves, seawater temperature, etc.

An attempt to understand the magnitudes of these errorswas made through analysis for a set of speed/powering trialswith a series of 12 twin-screw sister vessels. Each trial consists of5 pairs of runs in opposite directions and was conducted indifferent environmental conditions. Hence, whole set of trialresults include errors due to hull form production, seatrial measurements, and corrections for the environmentalconditions.

Each run in a trial was analysed and corrected according to theprocedure outlined in ITTC Standard Procedure (ITTC, 2005).Monte Carlo methods were utilized for uncertainty estimations, asdata reduction equations are complicated and highly correlated.Sensitivity to error sources was derived and conclusions on theeffect of error sources are presented.

2. Uncertainty in engineering measurements and analysis

Error is defined as difference between experimentally deter-mined value and the true value. An estimate of the error is definedas uncertainty, which is made at some confidence level, such as95%. This means that the true value of the quantity is expected tobe within 7U interval about the experimentally determined value95 times out of 100.

www.sciencedirect.com/science/journal/oe

www.elsevier.com/locate/oceaneng

dx.doi.org/10.1016/j.oceaneng.2008.04.009

mailto:[email protected]

ARTICLE IN PRESS

M. Insel / Ocean Engineering 35 (2008) 1183–11931184

Total error can be divided into two parts: precision errors(random), which contribute to the scatter of the data andbias errors (systematic), which shift all readings to a new mean.A precision limit (P) is defined as an estimator of the precisionerrors (e). A 95% confidence estimate of P is interpreted tomean that the 7P interval about a single reading of Xi,which should cover the population mean 95 times out of 100.The bias limit (B) is defined as an estimator of bias errors (b).A 95% confidence estimate is interpreted as the experimenterbeing 95% confident that true value of bias error would be within7B.

Total uncertainty in a measurement can be expressed as rootmean squares of precision and bias errors as

U2¼ P2

þ B2 (1)

The precision limit is estimated from the scatter in themeasured values by

P ¼ KS (2)

where K is the coverage factor and is equal to 2 for 95% confidenceinterval and large sample size (NX10) and S is the standarddeviation of the sample of N readings (ITTC, 1999).

The bias limit can only be estimated by careful investigation ofbasic measurement errors and their propagation into final result.

X1 X2

r=r{X1 ,X 2….XJ}

1 2

rBr=2s

-2s 2s

B1A

B1B

B1C B2A

B2B

B2C B3A

B

-2s 2s

-2s 2s -2s 2s

-2s 2

-2s

-2s 2s -2s 2s-2s 2s

rPr=2

rUr

2=Br2+Pr

2

Fig. 1. Uncertainty assessment metho

3. Monte Carlo method for the determination of uncertainty

Monte Carlo methods can be applied into uncertainty estima-tion in complicated and correlated measurement systems. Atevery speed, the basic measurement error sources are given as astatistical distribution. Usual calculation method is applied bychoosing a random sample from the error sources satisfyingGaussian distribution, and large number of times calculation isrepeated , such as 50,000. The distribution of result over thesimulations indicates the uncertainty in total result.

The methodology steps (Fig. 1) are:

(a)

X3

3

3B

s

s

dolo

Determine elemental bias/precision error sources and theirbias/precision limits.

(b)
Create Gaussian (or other) error distributions of bias/precisionerrors by assuming a standard deviation equal to half of bias/precision error limit (for 95% confidence).
(c)
Create a calculation model by using data reduction equations.If an elemental bias/precision error source is shared amongtwo or more variables, the same random value of elementalbias/precision error value is used in those variables.
(d)
Setup simulations consisting of N number of simulations, inwhich elemental bias/precision error values are assignedrandomly complying with Gaussian error distributions.
(e)
Calculate the result and its distribution. i.e. calculate meanand standard deviation of result from N simulations.
ELEMENTAL ERROR SOURCES

MEASUREMENT OF INDIVIDUAL VARIABLES

INDIVIDUAL MEASUREMENT SYSTEMS

DATA REDUCTION EQUATION SOURCES

B3C

2s

-2s 2s

REPEATTESTS

-2s 2s

gy by Monte Carlo method.

ARTICLE IN PRESS

M. Insel / Ocean Engineering 35 (2008) 1183–1193 1185

(f)
Determine the bias limit by taking twice the standarddeviation.
(g)
Perform repeat tests (minimum 10) and find standarddeviation.
(h)
Take twice the standard deviation to find the precision limit(for 95% confidence).
(i)
Root-sum-square bias and precision errors to find the totaluncertainty limit.
4. Full-scale speed/power trial analysis method

Speed/power analysis recommended by 24th ITTC (ITTC, 2005)was utilized in the current work. This procedure follows amethodology similar to the one recommended by InternationalStandardization Organization (ISO) ISO 15016 (2002). The analysisspeed/power trial data are based on thrust identity and theknowledge of the thrust deduction factor, the wake fraction, therelative rotative efficiency and the propeller open water char-acteristics of the full-scale propeller are required. Fig. 2 describesthe analysis method.

Ideally, the wind resistance coefficients of the ship should beobtained from model tests. In most cases, model tests are notavailable and reliable statistical values can be used.

Concerning environmental influences on the performanceof sea trials, speed runs should only be performed against andwith the waves. The correction methods existing so far accountfor the influences of waves only for these two conditions; in thecase when waves do not come from the bow or the stern, thecorrection methods are not sufficiently reliable and the effects ofsteering and drift on the ship’s performance might be under-estimated.

Sheltered areas provide the comfort of protection from waves,but normally in these areas shallow water effects have to beconsidered. When choosing a trials site, the advantage of anaccepted and simple correction for shallow water effects has to beconsidered against doubtful corrections for the effects of waves,steering and drift.

Reliable methods to estimate the influence of currents, steeringand drift effects do not yet exist. Hence, no corrections wereutilized in the current work. Methods to correct for roughnesseffects on propellers and for roughness and fouling on a ship’s hullare of doubtful accuracy to date.

Fig. 2. Speed/power analysis method (ITTC, 2005).

5. Uncertainty in basic measurements

Bias errors in a single run originate from measurementsand corrections for the environmental conditions. A number ofbasic measurements are conducted during the trials for bothanalysis and corrections. The bias error limits in each measure-ment should be determined by using the basic principles. Anexample case is presented as follows to explain the basicmeasurement errors.

5.1. Ship conditions

5.1.1. Ship length and breadth

Ship dimensions are affected by the production errors. In thecurrent work, 710 cm in the ship length and 72 cm in the shipbreadth error were assumed.

5.1.2. Draught

In order to define the ship loading, fore and aft draughtsshould be measured. The draught marks at the perpendi-culars are read by eye before departing the trials. Depending

on the sea conditions, a reading error of 72 cm can beassumed.

T ¼TA þ TF

2(3)

5.1.3. Displacement

Block coefficient error was accepted as 0.001. Hence, the errorin the displacement can be calculated through displacementequation:

D ¼ rgCBLBT (4)

ARTICLE IN PRESS


5.2. Environmental conditions

5.2.1. Water temperature, density

Water temperature and salt content are also required if theyare different from contract conditions. Water temperature ismeasured with a thermometer and best accuracy in trialconditions can be assumed of 0.5 1C. This error is the combinationof measurement and temperature changes in the trial area. Saltcontent is usually assumed to be constant at trial site; however incase of no measurements, a bias error limit of 0.005 in density dueto salt content uncertainty was assumed in the current work.

5.3. Shaft torque measurement

Shaft torque measurements are generally conducted with afull-bridge strain gauge rosette excited with a battery box andamplified with a purpose built amplifier-decoder and transmittedto stationary receiver through antenna as shown in Fig. 3.

Calibration is performed by placing a shunt resistor (RCAL) intoone of the arms of strain gauge bridge, which simulatescorresponding strain as

�CAL ¼1

4k

R

Rþ RCAL(5)

where k is the strain gauge factor, R is the strain gauge resistancein one arm, RCAL is the shunt calibration resistance and eCAL is thestrain corresponding to shunt resistor.

During measurements, resistance of Wheatstone bridgechanges with shaft strain as such

� ¼1

k

DR

4R(6)

where DR is the strain gauge resistance change in all arms.The torque can be calculated from

Q ¼4GI�

D(7)

where

I ¼pðD4

� d4Þ

32; moment of interia (8)

Q is the shaft toque, D is the shaft outside diameter, d is the shaftinside diameter and G is the shaft material shear modulus.

The uncertainty of this measurement system consists ofelemental error sources based on

�
strain gauge, � calibration of measurement system,
Battery

AD Converter

Fig. 3. Shaft torque and rate of

�

R

rev

installation on a ship,
� calculation of torque.
5.3.1. Strain gauge bridge

Strain gauge rosette consists of four equivalent strain gaugeswith inaccuracies on strain gauge resistance and gauge factor.Typical examples of such errors are:

gauge resistance Rg ¼ 350.070.4%Ogauge factor at 24 1C 2.04570.4%hence, bias errors:gauge resistance BRg ¼70.4�350/100 ¼71.4Ogauge factor at 24 1C BRgf ¼70.4�2.045/100 ¼ 0.00818

5.3.2. Measured value transmitter and receiver

Transmitter and receiver are utilized to condition rotatingstrain gauge signal, convert it to frequency modulation andtransmit to stationary data acquisition system. Typical errors dueto such system are:

sensitivity, output frequency Df ¼ 5 kHz725 Hz (70.5%)effect of ambient temperature on sensitivity 70.1%hence, bias errors:sensivity bias BTR1 ¼ 25 Hzsensivity due to ambient temp BTR2 ¼ 0.1�5000/100 ¼ 5 Hz

5.3.3. Frequency/voltage converter module

A frequency to voltage converter is required to transferfrequency modulation signal-to-voltage to acquire with dataacquisition system. Typical specifications are:

measurement range 75 kHzmeasured value nominal voltage 710 Vlinearity deviation 0.02%residual ripple and disturbing peaks 70.3%effect of temperature on sensitivity 70.1%effect of change in supply voltage 0.01%

5.3.4. Analog digital conversion error

Signal from frequency/voltage converter is fed into an analog/digital converter with 12-bit accuracy and 710 V range. Error in atypical analog digital conversion is 1.5 bits. Hence bias error in

SGAmp

FVConverter

Amplifier

eceiver Sensor

olution measurements.

ARTICLE IN PRESS

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14BF

Win

d S

peed

(m/s

)

y = -0.00532x3 + 0.23797x2 + 0.80594x - 0.01113R2 = 0.99997

Fig. 4. Beaufort scale and wind speed relation.

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12BF

Mea

n W

ave

Hei

ght (

m) y = 0.02556x3 - 0.11520x2 + 0.17985x

R2 = 0.99982

Fig. 5. Beaufort scale and wave height relation.

Table 1Main specification of the ship utilized

Ship length 135 m

Ship breadth 23.4 m

Ship draught 5.85 m

Ship displacement 10�353 t

Number of propellers 2

Propeller diameter 4.05 m

Ship service speed 22 knots

Table 2Environmental conditions for the trials

Trial

set

Water depth/

ship length

Wind

(Beaufort)

Trial disp/

contract disp

Water

temperature

(1C)

Run

time (s)

7 0.145 4 0.935 15.1 294

21 0.301 3 0.966 8.7 477

28 0.186 2.6 0.932 15.1 474

29 0.346 3.5 0.882 5 366

31 0.320 7 0.901 18 557

33 0.246 6 0.876 15.9 600

35 0.190 6.5 0.962 13 600

37 0.331 5 0.963 12.3 601

56 0.323 6 0.884 5 601

63 0.346 0 0.885 4.4 600

87 0.323 4 0.915 11 432

95 0.176 6 0.948 4.5 600


analog digital conversion:

BADC ¼1:5

2048� 10 ¼ 0:0732� V (9)

5.3.5. Calibration uncertainty

A standard resistor is utilized for the calibration of shaft torquemeasurement. This resistor, shunt resistor, is connected instead ofa strain gauge in the full bridge to create a resistance change effectin the measurement chain. Standard calibration resistor in thisexample has error not more than 0.01%. The shaft relative strain eis obtained from Eq. (5).

5.3.6. Installation on a ship

Installation in the ship has elemental error sources due toalignment of strain gauge with shaft axis. Twenty third ITTC (ITTC,2002) has given alignment error as

�a ¼ �cos ð2aÞ (10)

where angle error is assumed to be about 51.

5.3.7. Calculation of torque

Diameter of ship shaft can be determined from certification ofshaft, for the current case, a bias limit of 70.5 mm was utilized forboth outside and inside diameter. The bias error in shear modulusdepends on the material of the shaft. For the current case, 1.15%specified in 23rd ITTC (ITTC, 2002) was utilized.

5.4. Shaft rate of revolution measurements

Shaft speed measurements are made with optical or magneticpulse generator, a sensor and a frequency/voltage converter asshown in Fig. 3. The number of pulses are counted for apredetermined time and divided into number pulses per revolu-tion to find shaft rate of revolution:

n ¼count

N time(11)

where N is the number pulses per revolution.Bias error in pulse count is 1 pulse, there is no uncertainty in N.

As time window gets larger, the bias error associated with shaftrate of revolution drops. However, then the transient changes inthe shaft power are not acquired. For the current work timewindow is taken as 1 s as power is calculated once every second.

5.5. Ship speed measurements

Ship speed is nowadays measured by dGPS systems, and can becalculated with different methods (ITTC, 2002). The mostcommon method for ship speed calculation is to determine therun start position and run end positions, and dividing the distancebetween the two by time elapsed. The uncertainty in timemeasurement is negligible, the typical positional bias error limitis about 3–5 m:

VS ¼S

Dt(12)

where S is the run length and Dt is the time to measure,

S ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDx2 þ Dy2;

qDx ¼ x� x0; Dy ¼ y� y0

Dt ¼ t � t0 (13)

where x, y are end point coordinates; x0, y0 are start pointcoordinates; t is time at the end point and t0 is time at the startpoint.

ARTICLE IN PRESS


5.6. Uncertainty due to environmental corrections

The corrections are applied into measured ship speed and shaftpower. ITTC speed/power trials procedure (ITTC, 2005) hasrecommended a number of methods for the environmentalconditions. Shallow water, displacement, temperature correctionsof ITTC was utilized in the current work. Sea state correction was

0

2000

4000

6000

8000

10000

12000

14000

16000

8 10 12 14 16 18 20 22 24Ship Speed (knots)

Del

iver

ed P

ower

(kW

)

72829333537566387952131

Fig. 6. Result of 12 sets of speed/powering trials.

0

2000

4000

6000

8000

10000

12000

14000

16000

8 10 12 14 16 18 20 22 24Ship Speed (knots)

Del

iver

ed P

ower

(kW

)

72829333537566387952131

Fig. 7. Result of 12 sets of speed/powering trials with bias error limits.

taken from Havelock and Kreitner. Wind correction due toBlenderman (1990) was utilized.

5.6.1. Uncertainty due to shallow water correction

The predictions of power are based on deep water; however,the trials are conducted in restricted sea due to weatherconditions or other requirements. In this case, speed lossdue to shallow water must be made. The shallow water correc-tion method given by Lackenby is utilized. The speed loss isgiven as

DVS

VS¼ 0:1242

AM

H2� 0:05

� �þ 1:0� tanh

gH

V2S

!(14)

y = -0.0042x + 0.2196

0.00.10.20.30.40.50.60.70.80.91.0

5 10 15 20 25Ship speed (knots)

Pow

er/V

3 (k

w/(m

/s)3 )

Fig. 8. Bias errors in trials.

Table 3Number of trial pairs and standard deviation of trial pairs

Ship speed (knots) No of trial pairs St. dev.

15–16 5 0.30887

16–17 4 0.13574

17–18 2 0.44679

18–19 5 0.13802

19–20 3 0.53653

20–21 6 0.31009

21–22 14 0.41375

22–23 10 0.18008

23–24 4 0.29896

0.0

0.1

0.2

0.3

0.4

0.5

0.6

15 17 19 21 23 25Ship Speed (knots)

Pow

er/V

3 -P

reci

sion

Std

ev (k

W/(m

/s)3 )

Fig. 9. Standard deviation distribution (precision error) for 1 knot segments.

ARTICLE IN PRESS


where H is the water depth in m, AM is the midship section areaunder water in m2, DVS is the speed loss due to shallow water inm/s and VS ship speed in m/s.

Water depth bias error was accepted as 72 m. Bias error inmidship section area originates from bias errors in breadth,draught and midship section area coefficient, which is assumed tobe within 0.001. Bias error on ship speed follows the proceduregiven above.

5.6.2. Wind and wave corrections

Wind corrections and wave corrections are based on the windspeed, wind direction, wave height, and wave direction.

6

8

10

12

% P

ower

5.6.2.1. Wind correction.

RAA ¼rA

2V2

WRAXVCAAðcAAÞ (15)

where RAA is the resistance increase due to wind, rA is the airdensity, VWR is the wind speed, AXV is the cross-sectional windagearea; CAA(cAA) is the directional wind resistance coefficient frommodel tests and cAA is the wind angle.

0

2

4

15 16 17 18 19 20 21 22 23 24Ship Speed (knots)

Precision Bias Total

Fig. 11. Percentage error in sea trials.

5.6.2.2. Wave correction.

dR0 ¼ 0:64HV2 CBB2

LgrTRIAL (16)

dR ¼ dR0½0:667þ 0:333 cosðaÞ� (17)

0

2000

4000

6000

8000

10000

12000

14000

16000

8 10 12 14Ship S

Del

iver

ed P

ower

(kW

)

7

28

29

33

35

37

56

63

87

95

21

31

Fig. 10. Total error

where a is the heading angle; dR0 is the wave resistance increasein head seas and HV2 is the wave height.

The current set of data includes Beaufort scale and winddirection values only. Hence, a relation between Beaufort scaleand wind speed and wave height were established by fittingcurves for both variables.

It is proposed by Coleman and Steele (1999) that a 72(SEE) bandabout the regression curve will contain approximately 95% of thedata points and this band is a confidence interval on the curve fit:

SEE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXN

i¼1

ðYi � ðaXi þ bÞÞ2

N � 2

vuut (18)

16 18 20 22 24peed (knots)

in sea trials.

ARTICLE IN PRESS


SEE values of 0.075 m/s for wind speed and 0.0845 m for waveheight was derived from the curve fit. Beaufort scale is normallyestimated by expert opinion; hence, a bias error limit of 1 Beaufortscale was accepted in the current study. The relation betweenBeaufort scale and wind speed, wave height are given in Figs. 4and 5, respectively.

Wind and wave directions are assumed coinciding in the currentwork. Wind direction and wave direction bias error limits wereestimated as 101, course estimation bias error limit is taken as 41.

-64.1%

-80% -60%

Run 2 - Beaufort Scale Estimation Error

Run 2- Port Shaft Rate of Revolutions Count Error


Run 1 - Beaufort Scale Estimation Error

Fig. 12. Sensitivity of corrected shaft power on b

-44.1%

-55% -45% -35

Run 2-Beaufort Scale Estimation Error



Trial Density Error

Relative Rotative Efficency Error

Transmission Efficiency Error


-26.1%

-35% -25%




Trial Density Error

Relative Rotative Efficieny Error

Transmission Efficiency Error

Trial Draught Error

Draught Error


Stb Shaft Strain Gauge Factor Error

Stb Shaft Strain gauge Resistance Error


5.6.3. Displacement correction

ISO 15016 (2002) recommendation for displacement correctionwas utilized

RADIS ¼ 0:65RTDTRIAL

D� 1

� �(19)

where DTRIAL is the displacement at trial conditions and D is thedisplacement for trial prediction.

17.1%

12.5%

1.3%

-40% -20% 0% 20% 40%

asic measurement bias errors for 8.2 knots.

26.5%

18.8%

-3.1%

1.7%

1.0%

% -25% -15% -5% 5% 15% 25% 35%


24.7%

22.0%

-8.9%

4.0%

2.6%

-2.4%

2.1%

-1.5%

-1.2%

1.1%

-15% -5% 5% 15% 25% 35%


ARTICLE IN PRESS


Contract displacement did not include any uncertainty. Mean-while trial displacement bias error is explained above.

5.6.4. Water temperature and salt content

Water temperature correction was the same as ISO 15016(2002)

RAS ¼ RT0 1�rTRIAL

r

� �� RF 1�

CF

CF�TRIAL

� �(20)

Density has elemental errors due to temperature measure-ment, temperature–density fit error, and salt content error.

0

1000

2000

3000

4000

5000

6000

351 391 431Delivered

Freq

uenc

y

Beaufort Scale Bias Limit: 0.5

Speed:


Fig. 15. Uncertainty of corrected shaft power for Be

0

500

1000

1500

2000

2500

3000

3500

4000

4500

2,516 2,612 2,707

Delivered

Freq

uenc

y


Speed:


Fig. 16. Uncertainty of corrected shaft power for Bea

Frictional resistance errors originate from viscosity, length andspeed.

6. Example full-scale speed/power trial uncertainty

In order to demonstrate the errors associated with sea trials, acase study was conducted for a twin-screw ferry by using crystalball Monte Carlo simulations. The details of the ship are given inTable 1. Model resistance, self-propulsion and open water testresults were available for the form. A set of sea trials with 12 sister

471 511 547 Power (kW)

8.2 knots

Beaufort Scale Bias Limit: 1.0 Beaufort Scale Bias Limit: 2.0

aufort scale variations bias errors for 8.2 knots.

2,803 2,899 2,985

Power (kW)

14.1 knots


ufort scale variations bias errors for 14.1 knots.

ARTICLE IN PRESS


ships were also available. Environmental conditions of the currentset were various as given in Table 2. All trial results were correctedaccording to the standard ITTC method (ITTC, 2005). The results ofcorrected trials are given in Fig. 6.

6.1. Total bias error

Uncertainty in each run was analysed separately, Gaussiandistributions were set up for each elemental bias error sources. Ifcorrelated bias errors were applicable, then the same distributionwas used for the whole runs of the trial. For example, sametemperature measurement bias error was applied into all runs in atrial.

0

500

1000

1500

2000

2500

3000

3500

9,164 9,349 9,535

Delivered

Freq

uenc

y


Speed: 2



9303

9403

9503

9603

9703

9803

BeaufortS

ca leB

iasLim

i t:0.5(M

163 )

Beaufo rtS

c aleB

iasLi m

i t:1 .0( M

16 3 )

Pow

er (k

W)

Speed: 21.8 k


The results of trials are plotted in Fig. 7 with error bars definedby bias error limits. Both bias errors on speed and power areobserved as substantial amount of tests were performed inshallow water.

Bias error limits in all trials are plotted by dividing third powerof speed in Fig. 8 to reduce the effects of speed. In order to definean average bias error with speed, a linear curve fit was applied tothese bias error limits to represent the whole set of trials.

6.2. Precision errors of trials

Precision errors were defined as the difference between trialresult and curve fit value at that speed. Then these errors were

9,721 9,906 10,07

Power (kW)

1.8 knots



Bea ufortS

ca leB

i asL im

i t: 1.5(M

163)

Bea uf or t S

ca leB

iasL im

it:2 .0( M

1 63 )

90.00%50.00%25.00%10.00%Median

nots


ARTICLE IN PRESS


separated into groups for each 1 knot speed intervals within thespeed range. The precision errors were divided by third power ofspeed, and their standard deviation values were calculated foreach speed group and given in Table 3 and Fig. 9. Average standarddeviation was found to be approximately 0.3. Hence precisionerror at each speed range was accepted equal to twice of meanstandard deviation (i.e. 2�0.3�V3).

A 95% confidence level was plotted in Fig. 10 by taking root-sum-square of bias and precision error limits. Precision and biaserror uncertainties are plotted as percentage of power in Fig. 11.Precision errors are larger than the bias errors for the data set. Asspeed increases, both bias errors and precision errors drop. Biaserrors are less than 5% for all the speed range and about 3% for thedesign speed. Meanwhile, precision errors are about 9% at lowerspeeds and about 7% at the design speed.

The precision errors determined here include the precisionerrors due to production, environmental conditions and measure-ments. The choice of correction methods could affect bias andprecision error limits, but it should not change the totaluncertainty of the trials. Hence, very careful consideration shouldbe given to minimize the environmental effects for smalleruncertainty.

7. Sensivity of full-scale speed/power trial uncertainty

The sensitivity analysis of uncertainty on basic inputs wascarried out. Figs. 12–14 indicate the result of this sensitivityanalysis for speeds of 8.2 knots, 14.1 and 21.8 knots for one trial. Inall speed trials, Beaufort scale uncertainty is the most critical eventhough the weather was Beaufort scale of 4.

The effect of Beaufort scale error was calculated in Figs. 15–17for speeds of 8.2, 14.1 and 21.8 knots, respectively. Increase inuncertainty of weather conditions increases the spread, henceuncertainty of corrected shaft power for all three speeds.However, this effect is more pronounced in lower speeds.

The second important error source was shaft rate of revolu-tions. This error is highly affected by time window utilized tocount the pulses. Increasing the time window shall decrease theshaft rate of revolution error, but this shall also increase timedifference between the readings.

The other important error sources are shaft modulus, trialdensity, and relative rotative efficiency errors. However, these arevery low compared to the Beaufort scale error. Conducting thetrials in very calm seas can reduce the uncertainty considerably,although this is usually not possible. Hence, the measurement ofactual encountered waves is highly recommended using wavebuoys or wave radars for lower uncertainty bands.

The uncertainty of shaft power for 21.8 knots is givenby varying weather condition bias error in Fig. 18. The spread ofshaft power is considerably higher when Beaufort scale error isabove 1. This result implies that use of weather station datafor sea trials is not possible without high uncertainty of shaftpower.

8. Conclusions

There are uncertainties associated with full-scale poweringtrials, the case study approach indicated that a bias limit of 3–5%is observed. The precision limit however will be governed mainlyby the sea trial conditions such as wind, wave and current. Thewide variety of sea trial conditions and utilization of sister shipshas indicated a precision limit of about 7–9% can be achieved. Thisprecision limit includes also seasonal chances as these sea trialswere conducted over years.

Sensitivity analysis on sea trial uncertainty has revealedthat the most influential error source is the utilization of Beaufortscale for the wave and wind effects. In order to reduce the biaserror below 3%, encountered waves should be measured. Themethods such as wave radars, wave buoys are highly recom-mended.

Lastly, Monte Carlo method has proved to be very effective foruncertainty analysis as only a model of usual calculation methodis required for uncertainty analysis.

Acknowledgment

The author would like to express his special thanks to RichardAnzboeck of Vienna Model Basin for providing the sea trial data,and his comments for the study.

References

Blenderman, W., 1990. External forces, wind forces, Schiff & Hafen Heft 2.Coleman, H.W., Steele, W.G., 1999. Experimentation and Uncertainty Analysis for

Engineers, second ed. Wiley, New York.ISO 15016, 2002. Guidelines for the Assessment of Speed and Power Performance

by Analysis of Speed Trial Data.ITTC, 1999. Testing and extrapolation methods, uncertainty analysis in EFD,

uncertainty assessment methodology. In: 22nd International Towing TankConference, Seul-Shanghai, Quality Manual, Procedure 4.9–03-01–01 Rev 0.

ITTC, 2002. The specialist committee on speed and powering trials. Final Reportand Recommendation to the 23rd ITTC, 23rd ITTC Proceedings, vol. II,pp. 341–367.

ITTC, 2005. The specialist committee on powering performance prediction. FinalReport and Recommendation to the 24th ITTC, 24th ITTC Proceedings, vol. II,pp. 601–636.

uncertainty in the analysis of speed and powering trials

Documents