ittc – recommended 7.5-02 -02-02 procedures …ittc – recommended procedures and guidelines...

ITTC – Recommended Procedures and Guidelines

7.5-02 -02-02

of 16 Testing and Extrapolation Methods,

General Guidelines for Uncertainty Analysis in

Resistance Towing Tank Tests

Effective Date 2008

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Table of Contents

Updated / Edited by Approved

Specialist Committee on Uncertainty Analysis of 25th ITTC

25th ITTC 2008

Date 2008 Date 09/2008

1. PURPOSE OF PROCEDURE .............. 2

2. UNCERTAINTY ASSESSMENT PROCEDURE ........................................ 2

2.1 Measurement objectives .................... 2

2.2 Data reduction equations .................. 2

2.3 Measurement system description. .... 3 2.3.1 Geometry. ..................................... 3 2.3.2 Installation. ................................... 3 2.3.3 Calibration. ................................... 3 2.3.4 Direct measurement. ..................... 4 2.3.5 Data reduction. ............................. 4

2.4 Uncertainty analysis for total resistance ............................................ 5

2.4.1 Model geometry verification ........ 5 2.4.2 Model weight/displacement and

static trim/draught verification ..... 5 2.4.3 Model installation ......................... 7 2.4.4 Calibration .................................... 7 2.4.5 Total resistance measurement ...... 8

2.4.6 Tow speed measurement .............. 9 2.4.7 Running sinkage/trim

measurement ................................ 9 2.4.8 Dominant uncertainty

components…………………….10

2.5 Data reduction and uncertainty analysis for resistance coefficient ... 10

2.5.1 Total resistance coefficient......... 10 2.5.2 Froude number and Reynolds

number ........................................ 10 2.5.3 Frictional resistance coefficient . 10 2.5.4 Form factor ................................. 11 2.5.5 Residuary resistance coefficient . 12

2.6 Report of uncertainties ................... 13

3. RECOMMENDATIONS .................... 13

4. LIST OF SYMBOLS ........................... 14

5. REFERENCES .................................... 15


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General Guidelines for Uncertainty Analysis in Resistance Towing Tank Tests

1. PURPOSE OF PROCEDURE

The purpose of the procedure is to provide guidelines for implementation of uncertainty analysis in model scale towing tank resistance tests that follow the ITTC Procedure 7.5-02-02-01, “Resistance Test” (2002b). Uncertainties related to extrapolation and full scale prediction are not taken into consideration. This general guideline does not discuss some specific details, such as turbulence stimulation, drag of append-ages, blockage and wall effect of tank, scaling effect on form factor, etc.

2. UNCERTAINTY ASSESSMENT PROCEDURE

2.1 Measurement objectives

The objectives of measurement in resistance towing tank tests are to obtain the relationship between residuary resistance coefficient CR and Froude number Fr of a ship model and, if re-quired, the form factor k. The direct measure-ment of the tests is the total resistance (RRT) as well as the running attitudes of a ship model at each speed.

2.2 Data reduction equations

The data reduction equations are the mathematical models through which the propa-gation of various uncertainty components into an experimental result is analysed. Usually, the following equations are applied for data reduc-tion in a resistance test.

Froude Number

gL/VFr = (1)

Reynolds Number

(2) /VLRe = ν

where V is the speed, L the representative length, normally LWL for Fr and LOS for Re, and ν is water kinematic viscosity. The water properties should be calculated from ITTC (1999a).

Total Resistance Coefficient

)/(2 2TT SVRC ρ=

( )210F 20750 −= Relog/.C

FTR CCC −

(3)

where S is the wetted surface area that is nor-mally calculated from the body plan to the still waterline and ρ is the water density.

Frictional Resistance Coefficient; ITTC (1957) model-ship correlation line

(4)

Residuary Resistance Coefficient by two-dimensional method, e.g., the David Taylor Model Basin (DTMB) method (Forgach, 2001),

= (5a)

or by three-dimensional method (ITTC, 1999b),

)k(CCC +⋅= − 1FTR (5b)


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where the form factor k is introduced and ob-tained through regression analysis of data at low Froude numbers (Fr < 0.2, if no separation is present) by the straight line plot of (CT/CF) versus Frn/CF by Prohaska’s method (1966) in van Manen and van Oossanen (1988) and ITTC (2002b),

)(1 FFT C/FrbkC/C n+=−

64

(6)

where b is the slope from linear regression analysis, k the intercept, and n the power ex-ponent of Froude number, where ≤≤ n .

2.3 Measurement system description.

From uncertainty analysis, the whole test system for resistance test, in a general sense, may be grouped under five blocks of No. ① to No. ⑤, as shown in Figure 1. Each block is re-lated to one group of uncertainty sources, as stated in the following paragraphs. In a nar-rower sense, the measurement system just in-cludes three blocks of No. ② to No. ④.

2.3.1 Geometry.

No. ① block lists the uncertainty sources related to model geometry, including the errors from manufacturing and deformation during test. Determination of the real wetted surface of a hull model underway is very difficult, even if no error from manufacturing occurs, because of the effect of waves and running attitudes. The nominal wetted surface area of a hull model at rest is usually adopted and theoretically ob-tained from the body plan by a given calcula-tion method. The error resulted from this calcu-lation method itself is not included into uncer-tainty analysis in this procedure.

The relation between the uncertainties of resistance and geometry is very complicated. The frictional resistance is generally assumed to be proportional to the wetted surface of hull model. The residuary resistance is influenced by the shape of waterline surface, while the form factor is more related to the form of hull than the surface area of hull.

In general, no analytical formula exists for the expression of the propagation of geometry uncertainty into the resistance. However, errors of geometry may originate from the uncertainty of size/scaling of a hull model, when the ship model is either enlarged or shrunk in scale.

2.3.2 Installation.

No. ② block outlines the uncertainty sources related to the model installation /alignment and weight and draught verification. Any misalignment of ship model and resistance dynamometer to the direction of motion of the towing carriage, any misalignment of tow force to the line of propeller shaft, etc., will bring un-certainty into the measurements of ship resis-tance, running sinkage, and trim. The errors of model draught verification and model weight/displacement verification will directly produce an error in the wetted area surface of the model.

2.3.3 Calibration.

No.③ block shows the uncertainty sources related to the calibration of the measurement instruments/systems which is always to be con-ducted by the concerned laboratory itself. Cali-bration uncertainty estimates are described in ITTC (2008b). Other uncertainties related to the measurement devices/systems can be ob-


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tained directly from the specifications given by producers/manufacturers or other calibration laboratories. The calibration results should be traceable to a National Metrology Institute (NMI).

2.3.4 Direct measurement.

No. ④ block indicates the uncertainty sources related to the time history of sampling data or human readings. For the data acquisi-

tion system (DAS), the sampling rate, the length of data sample, and the frequency of low-pass filter may affect the values of meas-urement. The effect of the DAS on uncertainty of measurement is preferably included in the calibration by a through system or end-to-end calibration. That is, the instruments are cali-brated on the data acquisition system for the test.

Figure 1: Schematic diagram of whole test system

2.3.5 Data reduction.

No. ⑤ block outlines the uncertainty sources related to the data reduction process, including the resistance curve fitting. The di-

mensions of towing tank are large enough to avoid wall and blockage effects for most com-mercial model tests. Otherwise, correction of blockage should be included into data reduction. In this procedure, no detail is proposed for the uncertainty of correction.


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2.4 Uncertainty analysis for total resis-tance

2.4.1 Model geometry verification

The wetted surface area is the most impor-tant geometric parameter in data reduction of a resistance test. If the model manufacturing tol-erances are controlled within the ranges rec-ommended by the ITTC (2002a), no special at-tention should be paid to the uncertainty related to hull geometry. As stated previously, the rela-tion between the manufacturing errors and the wetted surface area of hull model is very com-plicated. However, the detailed information about hull geometry verification will be useful for those experienced engineers or those labo-ratories with a relatively large database for es-timation of the uncertainties concerned.

The length of a hull model is another geo-metric parameter adopted in the expressions of Reynolds number and Froude number. In un-certainty analysis, such a length parameter is defined as a characteristic length and more re-lated to the real size of hull than to the real value of a specific length. The size of a model is usually estimated by its displacement volume, i.e., the characteristic length L can be taken as

3 ∇∝L

)3()()( ∇

(7)

or the relative uncertainty of the length can be approximated as

∇= /uL/Lu

)(tΔ

(8)

where ∇ is the moulded displacement volume of the hull model. Its uncertainty should be es-timated empirically, or from a reliable database

by the laboratory concerned if no detailed geo-metric data are available.

The potential trend in the hull model geome-try verification is measurement by some ad-vanced technical devices, such as a laser scan-ner described in Smith and Harvey (2007) and Hand, et al. (2003). A laser scanner can deter-mine the real 3D spatial coordinates of points on the hull model surface in much detail and with high efficiency and accuracy. Such tech-nology provides a practical tool for measure-ment of the real wetted surface area of a hull model at rest, although for the time being such devices have not been equipped most towing tanks. No method for laser data uncertainty analysis has been developed that is generally accepted (Arias, et al., 2007). Additionally, if detailed measurements can confirm whether the hull model is larger or smaller, correction should be made before ballasting and trimming.

Finally, the deformation of hull model un-der static loadings by ballasting and tank water may introduce uncertainty in the real hull ge-ometry. The difference between the circum-stantial temperature of the model check loca-tion and the temperature of water of the towing tank may also be taken into consideration if ap-plicable.

2.4.2 Model weight/displacement and static trim/draught verification

The designated weight/displacement mass (kg), Δ, of hull model is calculated theoretically by the nominal displacement volume times the mass density of water of the towing tank,

=∇⋅ρ ⋅∇≡ ρ (9)

where ∇ is the displacement volume, which is


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A/T ∇= δδ

( )( )

theoretically calculated for a specific static draught and trim from the body plan by a given method, and t the temperature of tank water during testing. If the real density of water is different from that calculated, the real dis-placement volume or the draught of hull would be changed spontaneously to keep the weight of the ballasted hull unchanged. From equation (9),

ρδρδ // −=∇∇ (10)

Therefore, the variation of draught T and wet-ted surface area S can be approximated respec-tively by

W (11)

[ ] ( )∇⋅−=⋅=

δκδκδ

WWL

WL

ALTLS

2>κ

(12)

where AW is the area of hull water-plane, (κLWL) the expanded length of hull waterline, and

. And then, uncertainties of the wetted area from the water density can be estimated by

)/)()(()( WWL ρρκ uALSu ∇⋅=

ε

εε

ε

ε

ρ/Δ=∇

δΔ/Δ/ =∇∇δ

(13)

When the hull model is ballasted to the nominal weight and trimmed to the nominal loading condition, various factors related to the hull model, such as errors of draught, trim and displacement volume, interact with each other, even when no error in the ballasting occurs. Establishment of a rational relationship be-tween the uncertainty of wetted surface area of the hull model and each of these factors is very difficult.

As an example, a two-dimensional box with length L and draft T is shown in Figure 2. The wetted surface area and displacement of the

box are LT. If the box is uniformly enlarged or expanded, from the circumstantial temperature increase, by while its displacement keeps unchanged. The draught of the box will be re-duced to T/(1+ ) and the length enlarged to L(1+ ) while the wetted area will remain un-changed.

Figure 2: Sketch of 2D box submerged with

fixed weight/displacement volume

If the dimensions of box remain unchanged and the weight is reduced by , the draught and the wetted area of the box will be reduced by , too. The real wetted area is closely re-lated to the real displacement volume. Then, equation (9) can be rewritten as

(14)

Then, the variation of displacement due to the ballasting error is as follows:

(15)

Similarly, the uncertainty of wetted area can be estimated with Equation (12),


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Δ/ΔuALSu )()()( WWL ⋅ (16) ⋅= ∇κ

From equations (14) and (16), the combined uncertainty of wetted area due to model ballast-ing is as follows,

22WWL ))(())(()()( ρρκ /uΔ/ΔuALSu +∇⋅=

)1( wa

(17)

2.4.3 Model installation

The effect of installation on resistance measurement is quite complicated. The align-ment of resistance dynamometer can be consid-ered analytically in uncertainty analysis of re-sistance through trigonometry. Uncertainties from the other factors of installation can only be estimated by reliable database or benchmark test results.

2.4.4 Calibration

As stated above, calibration should be per-formed by the end-to-end method so that details of uncertainty analysis of signal conditioning and data acquisition systems are not necessary. The calibration uncertainties of the water tem-perature thermometer, the balance for model weight measurement, and the devices for run-ning attitude measurement can be obtained through the uncertainties determined by cali-bration.

The calibration uncertainties of the resis-tance dynamometer and sinkage/trim measure-ment devices should be determined by calibra-tion processes before the model test. Such a calibration process should be regarded as a whole test independent of the resistance test, so that the uncertainty analysis of calibration will be separately performed and reported in accor-

dance with ISO (1995) and the newly edited draft of ITTC (2008b). The results of uncer-tainty analysis can be applied directly in the re-sistance test.

Usually, the total resistance of ship model is measured with a variable reluctance block gage or strain-gage balance, i.e., a resistance dyna-mometer. Typically, the electronic balance is calibrated on a calibration stand with masses where the force is related to mass by the equa-tion

ρρ /mgF − (18) =

where m is the mass of weight on the calibra-tion stand, g is the local acceleration of gravity, ρa is the air density, and ρw is the density of the weight. The last term in Equation (18) is a buoyancy correction term. Local gravity may differ from standard gravity by as much as 0.1%.

Force is changed with the removal or addi-tion of mass. The total mass of n weights on the calibration stand for the applied force is

∑=

=n

iimm

1 (19)

A calibration stand may include levers for in-creasing the applied force, in which case the force multiplier should be included in Equation (18).

A weight set is usually calibrated against the same reference standard. In this case, the uncertainty in the total mass is correlated, and the total uncertainty in mass is the sum the un-certainties of the weights given by


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∑=

=n

iim uu

1 (20)

where is the standard uncertainty of the i-th weight .

iu

im

With the assumption that the contributions in the uncertainty in the air and weight densi-ties are small compared to the other terms, the combined relative uncertainty in the applied force from equation (18) is

221 )()()( g/um/uF/Fu gm += (21)

If the calibration stands includes a force multi-plier, the uncertainty in the lever arm lengths should be included in Equation (21).

The force balance should be calibrated with the same data acquisition system used in the test. Nominally, the calibration curve should be linear. Linear regression analysis will then pro-duce the slope and intercept for the conversion of digital volts to force units during the test. The standard uncertainty in the curve fit is de-noted as

)2()(2 −== n/SSSEEFu R (22)

also contributes to the combined uncertainty in calibration and total resistance measurement, where SEE is the standard deviation for the lin-ear regression analysis, SSR the sum of the square of the residuals and n the number of data points. Details of the recommended calibration uncertainty estimates are described in ITTC (2008b).

R

The combined standard uncertainty in cali-bration from the reference force and the curve

fit can be estimated from equations (21) and (22) as

(23) )()()( 22

21 FuFuFu +=

Equation (23) is, then, a Type B when it is ap-plied in a test. In addition, the alignment of re-sistance dynamometer in calibration should also be considered by trigonometric analysis. The calibration uncertainty estimates for tow speed measurement device are also recom-mended in the ITTC (2008b).

2.4.5 Total resistance measurement

Although the resistance test is steady, the resistance signal recorded by data-acquisition-system (DAS) will vary with time due to the turbulent boundary layer flow and wake of hull model, test-rig vibration, electro-magnetic in-terference, drift of measuring system, fluctua-tion of power supply, electronic noise, and other unknown interference. The measurement of the resistance by DAS at each speed is ob-tained by averaging the time history of the re-sistance signal in an interval of time, Δt = n/fs,

∑=

=n

iiRn/(R

1T )1 (24)

where fs is the sampling rate, n the number of the samples, RRi the i-th data of the sample. The uncertainty in Equation (24) is computed by the Type A uncertainty method described in the general guideline on uncertainty ITTC (2008a). The uncertainty is then the standard deviation of the mean of RTR given by

n/suu RR TTA == (25)

where sRT is the standard deviation computed from RRi.


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The combined standard uncertainty of total resistance can be estimated from the Type A and Type B uncertainties by

2B

2AT

uuuR +=

)( tp/DnV Δ

(26)

where uA is from Equation (25) and uB from Equation (23).

The uncertainty in the direct measurement of total resistance typically includes three ele-ments:

• Uncertainty in the applied force measure-ment during calibration,

• Uncertainty in the curve fitting from the calibration data,

• Type A uncertainty in the resistance during collection of the test data.

The first two items are a Type B uncertainty with regard to the measurands. For a steady state operation, the uncertainty in the curve fit will usually be the dominant element in the un-certainty estimate. In some cases, repeat meas-urements on the order of 10 may be necessary for establishment of a better uncertainty esti-mate. An example of the importance of repeat measurements is described by Forgach (2002).

2.4.6 Tow speed measurement

The tow speed is one of the most important parameters in data reduction for resistance measurement. For many carriages, the velocity is determined by the rotation of a metal wheel, which has an optical encoder attached or other pulse generating device such as a metal and magnetic pick-up. The carriage velocity is then given by

(27) = π

where n is the number of pulses, D the diameter of the wheel, p the number of pulses per revo-lution for an optical encoder or other pulse generating device, and Δt the time interval for the pulse count. From Equation (27), the rela-tive uncertainty in velocity is

222 )()()( t/un/uD/uV/u tnDV Δ++= Δ (28)

The diameter D can be measured very accu-rately with a laser scanning coordinate system. A computer data acquisition card (DAC) nor-mally has a counter port and very accurate tim-ing. The timing on the DAC and its uncertainty should be certified by an NMI. The uncertainty in the pulse count may be estimated from a uni-form pdf as described in ITTC (2008b). Repeat measurements of the carriage speed, at least 10 at a single speed, may be necessary for more accurate estimate in carriage speed uncertainty as described by Forgach (2002).

2.4.7 Running sinkage/trim measurement

The sinkage and trim during resistance test running will be closely related to the real wet-ted surface of the hull model and be influenced some with the friction of the guide and the mis-alignment of the hull model installation. As a result, interaction between the running sink-age/trim and the tow force/resistance of the hull model occurs, although no analytical formula is available for a description of this interaction. The running sinkage/trim measurement data to-gether with their corresponding uncertainty analysis will be useful for intra- and inter- labo-ratory comparison analysis.


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2.4.8 Dominant uncertainty components

If a laboratory conducts the uncertainty analysis for one kind of hull model test, all un-certainty components/sources should be listed. The relationship to the measurand, the total re-sistance in this case, should be established. Each uncertainty component should be evalu-ated and finally combined and expanded uncer-tainties should be computed. The uncertainty analysis described above should be included with the processing of the data during data col-lection or as part of the post-processing analy-sis. The final analysis should include all of the elements of the uncertainty estimates with their relative importance. Usually not more than two significant figures are kept in the final com-bined uncertainty of any measurement result.

For simplification in the estimation of un-certainty, identification of those dominant un-certainty components is important. The remain-ing minor components that make no contribu-tion to the significant value of combined uncer-tainty may be neglected in the uncertainty esti-mate. The criterion is that, if they are negligible, the minor components do not change the sig-nificant figures of the final combined uncer-tainty of measurement. For an example, when a minor uncertainty component (Ui) and a domi-nant component (U0) is combined, the contri-bution of Ui will be negligible in combination when 03

1 Ui <

22T

222T

)()(

)2(])[()(

T

T

S/uR/u

V/u/t/uC/u

SR

VtC

++

+∂∂⋅= ρρ

U .

2.5 Data reduction and uncertainty analy-sis for resistance coefficient

2.5.1 Total resistance coefficient

From Equation (3), the combined relative uncertainty for the total resistance coefficient is

(29)

where the uncertainty in water density equation is assumed small in comparison to the contribu-tion from water temperature, t. In general, the water temperature, velocity, and total resistance may be acquired with a data acquisition system (DAS); consequently, the uncertainty estimate will include estimates from both Type A and Type B methodologies. The uncertainty in the wetted surface area is estimated before the test and is estimated by the Type B method. Fric-tional/viscous resistance is proportional to the wetted surface rather than total resistance.

2.5.2 Froude number and Reynolds number

From Equation (1), the combined relative uncertainty for Froude number is

( ) ( ) ( ) ( )2222 5050 gu.Lu.VuFru gLVFr ++=(30)

From Equation (2), the combined relative uncertainty for Reynolds number is

( ) ( ) ( )( )2

222

)( νν tu

LuVuReu

t

LVRe

∂∂⋅

++= (31)

where the uncertainty in water viscosity equa-tion is assumed small in comparison to the con-tribution from water temperature, t °C.

2.5.3 Frictional resistance coefficient

From Equation (4), the relative uncertainty for skin frictional resistance coefficient is

)2())(2( 1010F−= Relog/ReuelogC/u ReFC (32)


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bxky

2.5.4 Form factor

Equation (6) can be re-written as

∑∑∑

∑

===

=

−=

−−=

N

ii

N

ii

N

iii

N

iiixy

yxnyx

yyxxs

111

1

)/1(

))((

1FT −

+=

F

FT 1

C/Frx

C/Cyn=

−=

(33)

where

The slope b and intercept k of fitting curve can be determined by linear regression analysis as described in the ITTC (2008b). As in calibra-tion, the number of data sets, (xi, yi), at low Froude number should total 10 at approxi-mately equal increments in Froude number.

The standard uncertainty of form factor k, also the intercept, can be estimated by linear regression analysis as describe in ITTC (2008b).

The value of the slope is

xxxy s/sb = (34a)

and the intercept

xbyk −= (34b)

The uncertainty in the intercept is then

∑=

==N

ixxikka sxNSEEsu

1

2 /)/1( (34c)

where

(34d)

and the other parameters are defined in ITTC (2008b).

In addition to the uncertainty in the inter-cept from linear regression analysis, k also has an uncertainty associated with the uncertainty in the measured values of CT and CF. From equation (33) at x = 0,

= C/Ck (35)

Then the uncertainty in the measured value of k at the smallest measured value of Fr is

2F

22F )()1()(

FTC/ukC/uu CCkb ++= (36)

The total combined uncertainty in k comes from equations (34c) and (36)

22kbkak uuu += (37)

An example of test data from CSSRC (China Ship Scientific Research Center) towing tank is listed in Table 1, in which outliers are removed after initial linear regression analysis.

In Figure 3, the curve fit (solid red straight line) is given as well as the ±95% prediction limit (red dash lines) and ±95 % confidence limit (solid blue curved lines). The resulting curve-fit expression is

( ))0097015740()02601920( ..x..y ±+ = ± ⋅

where the coverage factor k = 2. The intercept


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is k = 0.1574 with the standard uncertainty of ±0.00485, the slope b = 0.192 with the standard uncertainty of ±0.0132, SEE = 0.0105, and the correlation coefficient r = 0.977. In summary for this example, the value of the form factor is 0.1574 with an expanded uncertainty of ±0.0097 (±6.2 %).

The estimate for k is from the uncertainty in the intercept of the curve fit. An additional un-certainty in k from the measured values of CT and CF in Equation (36) should be included.

Nominal Froude No. Fr4/CF CT/CF - 1

0.10 0.0293 0.1597

0.10 0.0293 0.1660

0.11 0.0436 0.1724

0.13 0.0877 0.1665

0.15 0.1596 0.1988

0.16 0.2054 0.2033

0.16 0.2041 0.1811

0.18 0.3359 0.2298

0.20 0.5216 0.2408

0.20 0.5183 0.2489

0.21 0.6504 0.2878

0.21 0.6408 0.2925

Table 1: Example of resistance test data at low Froude numbers for form factor analysis

Fr4/CF

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

CT/

CF -

1Slope: 0.1924k: 0.1574SEE: 0.0105r: 0.977

Linear Fit+/-95% Prediction Limit+/-95% Confidence Limit

Model Data

Figure 3: Curve fit for form factor

2.5.5 Residuary resistance coefficient

From Equation (5a) in which the form fac-tor is not introduced, the combined standard uncertainty for the residuary resistance coeffi-cient is

22 )()(FTR CCC uuu += (39a)

From Equation (5b) by ITTC (1999b), the combined standard uncertainty for the residuary resistance coefficient is

2222 )()1(FFTR kCCCC uCukuu +++= (39b)

Finally, the residuary resistance coefficients are converted from the state of the tank water tem-perature/density to the nominal temperature of 15°C and the nominal density, in which no more uncertainty source is introduced.


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2.6 Report of uncertainties

Report of uncertainty analysis in the resis-tance test document can be given as a table in which the following information and data are summarized:

(1) All the dominant uncertainty sources and components related to the measurements (total resistance, resistance coefficients, form factor, etc.);

(2) The type of evaluation method for each un-certainty component;

(3) The expressions of sensitivity coefficients for each component to the desired meas-urands (total resistance, resistance coeffi-cients and form factor);

(4) The combined standard uncertainty of the desired measurands;

(5) The expanded uncertainty at the 95 % con-fidence limit, usually with the cover-age factor k = 2, for the desired measurands;

(6) The measurement results of running sink-age and trim and their uncertainties;

(7) The information on hull model geometry verification or the uncertainty of hull model displacement;

(8) Documentation of calibration results with their uncertainties and statement of trace-ability to an NMI.

Additionally, data should be presented graphically whenever possible. Calibration data should be plotted as residual plots as described in ITTC (2008b). Coefficients with a functional

relationship, such as Prohaska plot for deter-mining the form factor, should be plotted with a curve fit to the data and with error bars and the uncertainty in the curve fit. If the error bars are smaller than the symbols, the data should be plotted as residuals relative to the curve fit.

3. RECOMMENDATIONS

(1) Uncertainty depends on the entire towing tank testing process, and any changes in the process can significantly affect the uncer-tainty of the test results.

(2) Uncertainty assessment methodology should be applied in all phases of the tow-ing tank testing process including design, planning, calibration, execution and post-test analyses. Uncertainty analysis should be included in the data processing codes.

(3) Simplified analysis by prior knowledge, such as a database, tempered with engineer-ing judgement is suggested. Dominant error sources should be identified, and effort fo-cused on those sources for possible reduc-tion in uncertainty.

(4) Through system or end-to-end calibrations should be performed with the same DAS and software for the test. A database of the calibrations should be maintained so that new calibrations can be compared to previ-ous ones.

(5) A laboratory should have a benchmark test with uncertainty estimates that is repeated periodically. A benchmark test will insure that the equipment, procedures, and uncer-tainty estimates are adequate.


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(6) A reference test condition in a test series should be repeated about 10 times in se-quence as a better measure of uncertainty and check on uncertainty estimates. Also, reproducibility of test results for a represen-tative test condition should be checked in a long duration test of more than one day with a test at the beginning, middle, and end of the test series.

(7) Together with uncertainty report, the fol-lowing statements should be included in the test documentation:

a. Towing tank test process, measure-ment systems, and data streams in block diagrams.

b. Equipment and procedures used.

Forgach (2002) is a detailed report on a re-sistance test including uncertainty analysis. However, the uncertainty estimates are based upon earlier ITTC uncertainty analysis proce-dures, but it does include the results in tabular form so that the data may be reanalysed per ISO (1995) and ITTC (2008a). Longo and Stern (2005) is another example of a detailed assessment on uncertainty analysis in resistance testing; however, it is also based on the previ-ous ITTC uncertainty procedures.

Another paper on resistance testing is by Fong and Karafiath (2005). A significant result is that form factor is a function of model scale and it decreases with increasing scale.

The ITTC “Example for a Resistance Test” ITTC Procedure 7.5-02-02-02 (2002c) also contains data that may be updated for consis-tency with the present procedure. The uncer-tainty analysis based on the above data will

give a practical guide for identification of the dominant uncertainty components.

4. LIST OF SYMBOLS AW Water-plane area of ship model m2

b Slope of the fitting curve for form factor 1

CF Coefficient of the frictional resistance 1

CR Coefficient of the residuary resistance 1

CT Coefficient of the total resistance 1

D Diameter of wheel of towing carriage m

F Force applied for calibration of balance N

Fr Froude number 1

fs Sampling rate Hz

g Acceleration of gravity m/s2

k Form factor; coverage factor 1

L Length of ship model m

LWL Waterline length of ship model m

m Mass of weight kg

n Number of samples; number of pulses; power exponent of Froude number 1

p Number of pulses per revolution 1

Re Reynolds number 1

RRT Total Resistance of ship model N

S Wetted surface area of ship model m2

s Experimental standard deviation

SEE Standard error of estimate

SSR Sum of square of the residuals R

t Temperature of tank water °C

T Draught of ship model m


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2>

u Standard uncertainty

uA Standard uncertainty of Type A

uB Standard uncertainty of Type B

V Speed of ship model m/s

Δ Displacement mass of ship model kg

Δt Interval of time s

κLWL Expanded length of waterline, κ m

ν Water kinematic viscosity m2/s

ρa Density of the air kg/m3

ρw Density of weight kg/m3

Displacement volume of ship model m3 ∇

5. REFERENCES

Arias, P., Armesto, J., Lorenzo, H. and Ordóñez, C., 2007, “3D Terrestrial Laser Technology in Sport Craft 3D Modelling”, International Journal of Simulation Model-ling, Vol. 6, No. 2, pp. 65-72.

Fong, D. S. T. and Karafiath, G., 2007, “The Effect of Model Size on Form Factor and Predicted resistance”, Twenty-Eighth American Towing tank Conference, Au-gust 9-10, 2007, Michigan.

Forgach, K. M., 2001, “Comparison of ITTC-78 and DTMB Standard Ship Performance Prediction Methods”, Technical Report NSWCCD-50-TR-2001/033, Naval Sur-face Warfare Center Carderock Division, West Bethesda, Maryland, USA.

Forgach, K. M., 2002, “Measurement Uncer-tainty Analysis of Ship Model Resistance

and Self Propulsion Tests”, Technical Re-port NSWCCD-50-TR-2002/064, Naval Surface Warfare Center Carderock Divi-sion, West Bethesda, Maryland, USA.

Hand, S., Ober, D., Bond, B. and Devine, E., 2003, “Dimensional Measurement of a Composite Ship Hull Using Coherent La-ser Radar Yielding Sun-Millimeter Re-sults”, SNAME 2003 Ship Production Symposium.

ISO, 1995, “Guide to the Expression of Uncer-tainty in Measurement”, International Or-ganization for Standardization, Genève, Switzerland.

ITTC, 1957, Proceedings of the 8th ITTC, Ma-drid, Spain, Canal de Experiencisas Hidrodinamicas, El Pardo, Madrid.

ITTC, 1999a, “Density and Viscosity of Water”, ITTC Recommended Procedures and Guidelines, Procedure 7.5-02-01-03, Revi-sion 00.

ITTC, 1999b, “1978 Performance Prediction Method”, ITTC Recommended Procedures and Guidelines, Procedure 7.5-02-03-01.4, Revision 00.

ITTC, 2002a, “Model Manufacture Ship Mod-els”, ITTC Recommended Procedures and Guidelines, Procedure 7.5-01-01-01, Revi-sion 01.

ITTC, 2002b, “Resistance Test”, ITTC Rec-ommended Procedures and Guidelines, Procedure 7.5-02-02-01, Revision 01.

ITTC, 2002c, “Uncertainty Analysis, Example for Resistance Test”, ITTC Recommended


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Procedures and Guidelines, Procedure 7.5-02-02-02, Revision 01.

ITTC, 2008a, “Guide to the Expression of Un-certainty in Experimental Hydro-dynamics”, ITTC Recommended Proce-dures and Guidelines, Procedure 7.5-02-01-01, Revision 01.

ITTC, 2008b, “Uncertainty Analysis: Instru-ment Calibration”, ITTC Procedure 7.5-01-03-01.

Longo, J. and Stern, F., 2005, “Uncertainty As-sessment for Towing Tank Tests With Ex-ample for Surface Combatant DTMB Model 5415”, Journal of Ship Research, Vol. 49, No. 1, pp. 55–68.

Prohaska, C. W., 1966, “A Simple Method for the Evaluation of Form Factor and Low Wave Speed Resistance”, Proceedings,

11th ITTC.

Smith, P. and Harvey, B., 2007, “Boat Hull Modelling Using Terrestrial Laser Scan-ners”, ○,c2007 P Smith and B R Harvey, Web ‘published’ paper, School of Survey-ing and Spatial Information Systems, The University of New South Wales; also, http://www.gmat.unsw.du.au/ cur-rentstud-ents /ug/projects/SmithP/.

van Manen, J. D., and van Oossanen, P., 1988, “Resistance”, Chapter V, Volume II Resis-tance, Propulsion, and Vibration in Princi-ples of Naval Architecture, Edward V. Lewis, editor, The Society of Naval Archi-tects and Marine Engineers, Jersey City, New Jersey.

http://www.gmat.unsw.du.au/%20currentstud-ents%20/ug/projects/SmithP/

http://www.gmat.unsw.du.au/%20currentstud-ents%20/ug/projects/SmithP/

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