ITTC Recommended Procedures and Guidelines

Transcription

1 ITT Recommended Page of 8 00 Table of ontents PURPOSE OF PROEDURE... EXAMPLE FOR RESISTANE TEST. Test Design.... Measurement Systems and Procedure.... Uncertainty Analysis ias Limit Hull Geometry (Model Length and Wetted Surface Area) Speed Temperature/Density/ Viscosity Skin Frictional oefficient Form Factor Total ias Limit- Total oefficient Total ias Limit- Residuary oefficient..... Precision Limit..... Total Uncertainties...5 REFERENES.7 Edited by Approved Specialist ommittee of rd ITT: Procedures for, Propulsion and Propeller Open Water Tests Date Date 00 rd ITT 00

2 ITT Recommended Page of 8 00 PURPOSE OF PROEDURE The purpose of the procedure is to provide an example for the uncertainty analysis of a model scale towing tank resistance test following the ITT Procedures Rev 00, Uncertainty Analysis in EFD, Uncertainty Assessment Methodology and Rev 00, Uncertainty Analysis in EFD, Guidelines for Towing Tank Tests. according to the equipment used and procedures followed in each respective facility.. Test Design y measuring the resistance (R x ), speed (V) and water temperature (tº), and by measuring or using reference values for the wetted surface (S) and density (ρ) the total resistance coefficient ( T ) can be calculated for a nominal temperature of 5 degrees, according to: EXAMPLE FOR RESISTANE TEST 5 deg Tm 5 deg Tm T T + ( F F )( + k) (-) This procedure provides an example showing an uncertainty assessment for a model scale towing tank resistance test. The bias and precision limits and total uncertainties for single and multiple runs have been estimated for the total resistance coefficient T, and residuary resistance coefficient R in model scale at one Froude number. In order to achieve reliable precision limits, it is recommended that 5 sets of tests with speed measurements in each set are performed giving in total 5 test points. In this example the recommended sequence was followed. Extrapolation to full scale has not been considered in this example. Although it might lead to significant sources of error and uncertainty, it is not essential for the present purpose of demonstrating the methodology. When performing an uncertainty analysis for a real case, the details need to be adapted where Tm Tm Rx 0.5ρV T S (-) The residuary resistance coefficient can further be calculated as + R Tm T Tm 5 deg 5deg ( + k) F T ( k) F (-) In Eq. (-) the conversion of the resistance coefficients from the measured model temperature (index Tm) to a nominal temperature of 5 degrees is made by the ITT-978 prediction method. F in Eq. (-) is calculated according to the ITT-957 frictional correlation line F (log -) 0Re (-4)

3 ITT Recommended Page of 8 00 where Re is the Reynolds Number for the respective temperatures.. Measurement Systems and Procedure Figure. shows a block diagram for the resistance test including the individual measurement systems, measurement of individual variables, data reduction and experimental results. In Section.. the bias limits contributing to the total uncertainty will be estimated for the individual measurement systems: hull geometry, speed, resistance and temperature/density/viscosity. The elementary bias limits are for each measurement system estimated for the categories: calibration, data acquisition, data reduction and conceptual bias. EXPERIMENTAL ERROR SOURES HULL GEOMETRY SPEED RESISTANE TEMPERATURE, DENSITY, VISOSITY Individual measurement systems X, Y, Z, S, L V, V R x, Rx T 0, ρ, ν T 0, ρ, ν Measurement of individual variables T 5deg T Tm + ( F 5deg - F Tm )(+k) T Tm R x Tm / (0.5ρV S) R T - (+k) F Data reduction equations T 5deg, R, T Tm, R P T 5deg (M), P R (M), P T 5deg (S), P R (S) U T (M), U R (M), U T (S), U R (S) Experimental results Figure. lock diagram of test procedure.

4 ITT Recommended Page 4 of 8 00 Using the data reduction Eqs. (-) and (- ) the bias limits are then reduced to T Tm, and R respectively. As the adjustments in model temperature from the measured temperature to 5 degrees are very small the bias limits associated with the Eq. (-) conversion have not been considered. The precision limits for the total resistance coefficient at a nominal temperature of 5 degrees P 5deg T, and residuary resistance coefficient P R are estimated by an end-to-end method for multiple tests (M) and a single run (S). Table. Ship particulars. Definitions Symbol Value (unit) Length between perp. L PP (m) Length on waterline L WL 6.66 (m) Length overall submerged L OS 6.8 (m) readth.00 (m) Draught even keel T 0.00 (m) Wetted surface incl. rudder S (m ) Area water plane A WP 4.86 (m ) Displacement. (m ) lock coefficient /LPPT (-) Water plane coefficient WP A WP /L PP (-) Wetted surface coefficient S S/ ( L PP ).695 (-) Table. onstants. Definitions Symbol Value (unit) Gravity g 9.80 (m/s ) Density, model basin ρ 000 (kg/m ) Water temperature (resistance test average) tº 5 (degrees) In Tables. and. the ship particulars and constants used in the example are tabulated.. Uncertainty Analysis The uncertainty for the total resistance coefficient is given by the root sum square of the uncertainties of the total bias and precision limits ( U ) ( ) + ( P ) T T T ( U ) ( ) + ( P ) R R R (-5) (-6) The bias limit associated with the temperature conversion of the measured data, Eq. (-), will not be considered in the present example and therefore (-7) 5deg Tm T T The bias limit for T can therefore be calculated as: ( ) T T Rx S Rx T S T + V T + ρ ρ V The bias limit for Eq. (-) is + (-8)

5 ITT Recommended Page 5 of 8 00 ( ) R + R F F R T T + k R k (-9) The precision limits will be determined for 5deg T and for R by an end-to-end method where all the precision errors for speed, resistance and temperature/density/viscosity are included. The precision limits for a single run (S) and for the mean value of multiple test (M) are determined. Regardless as to whether the precision limit is to be determined for single or multiple runs the standard deviation must be determined from multiple tests in order to include random errors such as model misalignment, heel, trim etc. If it is not possible to perform repeat tests the experimenter must estimate a value for the precision error using the best information available at that time. The precision limit for multiple tests is calculated according to K SDev P ( M ) (-0) M where M number of runs for which the precision limit is to be established, SDev is the standard deviation established by multiple runs and K according to the methodology. The precision limit for a single run can be calculated according to P ( S) K SDev (-).. ias Limit Under each group of bias errors (geometry, speed, resistance and temperature/density/viscosity) the elementary error sources have been divided into the following categories: calibration; data acquisition; data reduction; and conceptual bias. The categories not applicable for each respective section have been left out.... Hull Geometry (Model Length and Wetted Surface Area) The model is manufactured to be geometrical similar to the drawings or mathematical model describing the hull form. Even though great effort is given to the task of building a model no model manufacturing process is perfect and therefore each model has an error in form and wetted surface. The influence of an error in hull form affects not only the wetted surface but also the measured values by an error in resistance. For example, two hull forms, with the same wetted surface and displacement, give different resistance when towed in water if the geometry is not identical. This error in hull form geometry is very difficult to estimate, and will not be considered here. Only the bias errors in model length and wetted surface area due to model manufacture error are taken into account. Model length Data acquisition: The bias limit in model length (on the waterline) due to manufacturing error in the model geometry can be adopted from the model accu-

6 ITT Recommended Page 6 of 8 00 racy of ± mm in all co-ordinates as given in ITT Procedure Rev Ship Models. Hence the bias limit in model length will be L mm. Wetted surface Data acquisition: In this example, the error in wetted surface due to manufacturing error in model geometry is estimated using an ad hoc method. y assuming the model error to be ± mm in all coordinates, as given in ITT Procedure Rev, Ship Models, the length will increase by mm, beam by mm and draught by mm. If the dimensions are changed while keeping the block coefficient constant, the displacement becomes ( ) kg which is an increase of kg. Assuming the wetted surface coefficient to be constant, the wetted surface for the larger model becomes S.696 ( L PP )7.6 m, which corresponds to an increase of S -S0.0 m or 0.9% of the nominal wetted surface S. The model is loaded on displacement and therefore an error in hull form with, for example, too large a model are somewhat compensated by the smaller model draught. The increased displacement of 6.7 kg gives, with a water plane area of A WP 4.86 m, a decreased draught of.8 mm. With a total waterline length of L WL.7 meters the smaller draught decreases the wetted surface by m. Totally, the bias limit in wetted surface due to the assumed error in hull form will be S m. alibration: The model weight (including equipment) is measured with a balance and the model is loaded to the nominal weight displacement. The balance used when measuring the model weight is calibrated to ±.0 kg. The errors in model and ballast weights are seen in Table.. Table. Error in displacement. Item Weights Individual weights Weights Group weights Ship model 60 kg ±.0 kg ±.00 kg allast weights x00 kg ±.0 kg (.0) ±.7 kg x50 kg ± 0.75 kg (0.75) ±.06 kg 6x0 kg ± 0.05 kg 6(0.05) ± 0. kg x kg ± kg (0.005) ± kg Total weight displ. kg ±.67 kg The total uncertainty in weight is given by the root sum square of the accuracy of the group of weights,.67 kg. An increase in model weight of kg gives, with ρ000 and a water plane area of 4.86 m, an additional draught of / mm. With a waterline length of.7 m this

7 ITT Recommended Page 7 of 8 00 results in an increased wetted surface of m per kg. V cπd 8000Δ t (-) For the deviation in displacement of ±.67 kg, the error in weight displacement equals.67/ 0.85%, the error in draught equals mm and the error in wetted surface equals S m. Finally the error in wetted surface is obtained by the root sum square of the two bias components as S )0.007 m corresponding to 0.0 % of the nominal wetted surface area of 7.6 m.... Speed The carriage speed measurement system consists of individual measurement systems for pulse count (c), wheel diameter (D) and bit DA and AD card time base (Δt). The speed is determined by tracking the rotations of one of the wheels with an optical encoder. The encoder is perforated around its circumference with 8000 equally spaced and sized windows. As the wheel rotates, the windows are counted with a pulse counter. The speed circuit has a 00 ms time base which enables an update of the pulse every 0 th of a second. A -bit DA conversion in the pulse count limits the maximum number of pulses in 00 ms to The output of the speed circuit is 0-0 V so that 4096 counted in 00 ms corresponds to 0 V output. The output from the encoder is calculated with the equation where c is the number of counted pulses in Δt00 ms and D is the diameter of the carriage wheel (0.8 m). The bias limit from blockage effects has not been considered. Pulse count (c) alibration: The optical encoder is factory calibrated with a rated accuracy of ± pulse on every update. This value is a bias limit and represents the minimum resolution of the -bit AD data acquisition card. Therefore, the bias limit associated with the calibration error will be c pulse (0V/ V). Data acquisition: In the given data acquisition cycle, the speed data is converted to the P by two -bit conversions. The resolution is resol0 V/ V / bit. The AD boards are accurate to.5 bits or pulses, which was determined by calibrating the boards against a precision voltage source. Therefore, the bias associated with the two conversions is c c.5 pulses ( V). Data reduction: The final bias occurs when converting the analogue voltage to a frequency that represents the pulse count over 0 time bases or one second. This is enabled if correlating the given frequency to a corresponding voltage output. The bias limit results from approximating a

8 ITT Recommended Page 8 of 8 00 calibration (set of data) with a linear regression curve fit. The statistic is called standard error estimate (SEE) and is written from oleman and Steele (999) as SEE N i ( Y -(ax + b) ) i i N (-) It is proposed by oleman and Steele (999) that a ±(SEE) band about the regression curve will contain approximately 95% of the data points and this band is a confidence interval on the curve fit. The curve fit bias limit is calculated to be.5 Hz corresponding to c4 0.5 pulse ( V). be The total bias limit for pulse count will then c ( c + c + c + c 4 ) ( ).58 pulse( v ) (-4) Wheel diameter (D) One of the driving wheels of the carriage is used for the speed measurement. The wheel is measured with constant time intervals to ensure the right calibration constant is used. alibration: The wheel diameter is measured with a high quality Vernier calliper at three locations at the periphery of the wheel which are averaged for a final value of D. The wheel diameter is considered accurate to within D0.005 m. Time base (Δt) The time base of the speed circuitry is related to the clock speed of its oscillator module. alibration: The oscillator module is factory calibrated and its rated accuracy is seconds on -5 every update giving Δt.05 0 seconds. The data reduction equation is derived from Eq. (-) and can be written V V c c V + D D V + Δ t Δt (-5) Using the nominal values of c8.4, D0.8 m and Δt0. s for the mean speed of V.70 m/s the partial derivatives can be calculated as V πd (-6) c 8000Δt V cπ (-7) D 8000Δt V cπ D (-8) Δt 8000 Δt The total bias limit can then be calculated according to Eq. (-5) as V ( ) + ( 5 ( ) ) (-9)

9 ITT Recommended Page 9 of 8 00 The total bias limit for the speed is V m/s corresponding to 0.% of the nominal speed of.70 m/s. The bias limit for the speed could alternatively be determined end-to-end, by calibrating against a known distance and a measured transit time.... The horizontal x-force is to be measured for the model when towed through the water. alibration: The resistance transducer is calibrated with weights. The weights are the standard for the load cell calibration and are a source of error, which depends on the quality of the standard. The weights have a certificate that certifies their calibration to a certain class. The tolerance for the individual weights used is certified to be ± 0.005%. The calibration is performed from 0 to 8 kg with an increment of 0.5 kg. The bias error arising from the tolerance of the calibration weights, Rx, is calculated as the accuracy of the weights, times the resistance measured according to Eq. (-0). Rx accuracy of weights Rx N (-0) Data acquisition: The data from the calibration tabulated in Table.4 shows the mass/volt relation. From these values the SEE can be calculated with Eq. (-) to SEE0.085 resulting in a bias for the curve fit to be Rx0.706 N. The third error is manifest in the load cell misalignment, i.e., difference in orientation between calibration and test condition. This bias limit is estimated to be ±0.5 degrees and will effect the measured resistance as Rx R - x ( cos 0. 5 Rx) 479. ( cos 0. 5 o ) N (-) data is acquired by an AD converter, which normally has an error of bit out of AD accuracy of bits. AD conversion bias error in voltage shall be given by AD converter error in bit multiplied by AD range (-0 volts to 0 volts) divided by AD accuracy. This voltage can be translated into Newton by using the slope value of calibration. 0 Rx N Table.4 transducer calibration. Output (Volt) Mass (kg) Force (N) R6.089-Volt.58 (-)

10 ITT Recommended Page 0 of 8 00 Data reduction: The transducer is fitted in the middle of a special rod, which connects the model to the carriage and tows the model. During the resistance tests the running trim and sinkage of the model result in an inclination of the towing force compared to the calibration which is expressed as a bias limit Rx5. The mean running trim fore and aft are measured to be ΔTf4. mm and ΔTa8.4 mm. If the towing force is applied in Lpp/ the sinkage + trim in the towing point ΔTtp can be calculated as ΔTtp(ΔTf+ΔTa)/6.8 mm. The rod used for towing the model is 500 mm long and therefore the inclination of the towing force will be arcsin(6.8/500)0.7 degrees compared to the calm water level. The bias limit can then be computed as Rx5 R x - o ( cos 0. 7 R ) 479. ( cos 0. 7 o x ) N (-) This error can be corrected for during the measurements if the angle in the rod is measured. If the transducer is mounted directly to the carriage and is constructed to take loads only in the x-direction this error will be eliminated. The total bias limit in resistance is obtained by the root sum square of the four bias components considered R x ( ) 0.84 N corresponding to 0.4 % of the mean resistance of 4.79 N....4 Temperature/Density/Viscosity Temperature alibration: The thermometer is calibrated by the manufacturer with a guaranteed accuracy of ±0.0 degrees within the interval -5 to +50 degrees. The bias error limit associated with temperature measurement is tº0. degrees corresponding to % of the nominal temperature of 5 degrees. Density alibration: The density-temperature relationship (table) according to the ITT Procedure Rev 00 Density and Viscosity of Water for g9.8 can be expressed as: ρ tº tº tº (-4) ρ (-5) t t t Using Eq. (-5) with tº5 degrees and tº0. degrees the bias ρ can be calculated according to: ρ t ρ t kg/m (-6) Data reduction: The error introduced when converting the temperature to a density (table lookup) can be

11 will ITT Recommended Page of 8 00 calculated as two times the SEE of the curve fit to the density/temperature values for the whole temperature range. omparing the tabulated values with the calculated values (Eq. -4) the bias error ρ can be calculated as ρ kg/m. onceptual: The nominal density according to the ITT- 78 method is ρ 000. Using this method introduces a bias limit as the difference between ρ (5 degrees) and ρ 000 such as ρ kg/m corresponding to % of the density. The bias for ρ can then be calculated according to: + + ρ kg/m ( ) ( ) ( ) ρ ρ ρ ( ) (-7) The bias limit for density is thus ρ0.660 kg/m corresponding to % of ρ 000. If using the density value determined by the temperature, the bias limit ρ be eliminated. Viscosity alibration: The viscosity-temperature relationship for fresh water adopted by ITT Procedure ; Rev 0, Density and Viscosity of Water can be calculated as ν (( ( t.0) 0.06) 6 ( t.0) +.50)0 t t + ( )0 Partial derivative of Eq. (-8) is ν 6 (0.07t )0 t (-8) (-9) Using Eq. (-9) with tº5 degrees and tº0. degrees the bias ν can be calculated according to: ν ν t 0.00 t m (-0) Data reduction: For a nominal temperature of 5.0 degrees this formula results in ν m /s. Meanwhile the fresh water kinematic viscosity according to the table in ITT Procedure , Rev 00, for 5.0 degrees is equal to ν m /s. Using this method introduces a bias error due to the difference between ν(5.0) m /s and ν m -0 /s such as ν m /s. With these results the total bias limit can be calculated as ( ) ( ) ν ν ν + (-) The bias limit associated with fresh water viscosity due to temperature measurement and viscosity calculation method is thus ν m²/s corresponding to 0.79 % of the kinematic viscosity. /s

12 ITT Recommended Page of Skin Frictional oefficient The skin frictional resistance coefficient is calculated through the ITT-957 skin friction line F VL (log0 ) ν (-) ias errors in skin friction calculation may be traced back to errors in model length, speed and viscosity. ias limit associated with F can be a found as ( ) F F F V + L F + ν ν V L (-) partial derivatives of Eq. (-) by model speed, model length and viscosity are F V VL (log ) V ln0 ν (-4) F L VL Lln0 (log ) ν (-5) F ν VL ν ln0 (log ) ν (-6) y substituting V0.006 m/s, L m, ν m /s, bias limits associated with corre- F in model scale is F sponding to 0.4 % of the nominal value of F Form Factor The recommended method for the experimental evaluation of the form-factor is that proposed by Prohaska. If the wave-resistance component in a low speed region (say 0. < Fr 4 <0.) is assumed to be a function of Fr, the 4 straight-line plot of T/ F versus Fr / F will intersect the ordinate (Fr 0) at (+k), enabling the form factor to be determined. hence T + k at low Froude numbers (-7) F ( ) In the case of a bulbous bow near the water surface these assumptions may not be valid and care should be taken in the interpretation of the results. The bias limit (+k) can be determined from the data reduction Eq. (-7). The determination of the precision limit requires about 5 set of tests for several speeds. As there was no example data available, the uncertainty in

13 ITT Recommended Page of 8 00 form factor has for the time being and for indicative purposes been assumed to be 0.0, equal to 0% of k or.66% of +k....7 Total ias Limit- Total oefficient In order to calculate the total bias and precision limits the partial derivatives have to be calculated using input values of Rx4.79 N, g9.8 m/s, ρ000 kg/m, S7.60 m and V.70 m/s. T S R x 0.5ρV S T R x V 0.5ρS V T Rx 0.5ρV S 5 T Rx.79 0 ρ 0.5V S ρ 6 (-8) (-9) (-40) (-4) The total bias limit can then be calculated according to Eq. (-8) as T corresponding to 0.65% of the total resistance coefficient T Total ias Limit- Residuary oefficient Residuary resistance can be obtained from Eq. (-) as R T ( + k) F (-4) The bias limit of residuary resistance coefficient can be calculated according to R R R T + k T k R F F ( ) + partial derivatives of Eq.(-4): R T R F k R ( + k). F by using Eq. (-4): R (-4) (-44) (-45) (-46) 5 (. 0 ) + ( ) 6 ( ) 5 + (-47) The total bias limit associated with residuary resistance coefficient is corresponding to.7 % of the nominal value of R Precision Limit

14 ITT Recommended Page 4 of 8 00 In order to establish the precision limits, the standard deviation for a number of tests, with the model removed and reinstalled between each set of measurements, must be determined. In this example 5 sets of testing (A-E) with speed measurements in each set have been performed giving totally 5 test points. This is the best way to include random errors in the set-up such as model misalignment, trim, heel etc. As resistance is highly dependent on viscosity, the resistance values measured have to be corrected to the same temperature. For a single towing tank the resistance values can preferably be corrected to the mean temperature of the tests in order not to make too large a correction. If the results are to be compared to results from other facilities all the resistance values must be corrected to the same temperature. In the present case the total resistance coefficient for the measured resistance and speed are corrected to the temperature of 5 degrees centigrade, according to the ITT-78 method, by the following: Series /run Table.5 Standard deviation of T and R. Measured values Nominal speed /temp Eq.(-) T Eq.(-) R 000 Rx (N) V (m/s) Temp (deg) T A A A D D D E E E MEAN SDev The residual resistance R, which is considered temperature independent, is calculated by - ( + k) Tm Tm R T F (-48)

15 ITT Recommended Page 5 of 8 00 where index T m measured temperature (compare also Eq. (-)). T for 5 degrees is then calculated from: 5deg 5deg + (+ k) T R F (-49) y combining equation Eq. (-48) and Eq. (-49) T can be calculated as in Eq. (-). In the above table the total resistance coefficient is calculated for each run, using the measured resistance and speed. This corrects the measured resistance to the nominal speed by the assumption that the resistance is proportional to V. For small deviations in speed this assumption is considered accurate. 5deg The mean value over 5 runs for T (corrected to nominal speed and temperature) is calculated as.79 0 T as shown in table.5. With Eq. (-), using the nominal values for speed, density and wetted surface, the corrected, mean resistance can be recalculated to Rx 4.79N. The precision limit for the mean value of 5 runs is calculated as P T K SDev M T (-50) according to Eq. (-0) and corresponding to 0.6% of T. For a single run the precision limit is calculated as P K SDev T T (-5) according to Eq. (-) and corresponding to. % of T. The residual resistance coefficient can also be calculated as shown in table.5. The precision limit for the mean value of 5 runs is calculated as P R K SDev M R (-5) according to Eq. (-0) and corresponding to 4.87% of R. For a single run the precision limit is calculated as P K SDev R R (-5) according to Eq. (-) and corresponding to 8.88 % of R... Total Uncertainties ombining the precision limits for multiple and single tests with the bias limits the total uncertainty can be calculated according to Eq. (-5) and Eq. (-6). The total uncertainty for T for the mean value of 5 runs will then be ( U ) ( ) + ( ) ) T P T T ( )

16 ITT Recommended Page 6 of 8 00 which is corresponding to 0.67% of T. (-54) total uncertainty are decreasing with increasing number of repetitions. orrespondingly the total uncertainty for a single run can be calculated as ( U ) ( ) + ( ) ) T P T T ( ) which is.8% of T. (-55) % OF T TOTAL UNERTAINTY IAS LIMIT PREISION LIMIT The total uncertainty for R for the mean value of 5 runs can similarly be calculated as ( U ) ( ) + ( ) ) R P R R ( ) (-56) which is corresponding to.09% of R. orrespondingly the total uncertainty for a single run can be calculated as ( U ) ( ) + ( ) ) R P R R ( ) which is 6.9% of R. (-57) As can be seen from the values above the uncertainty will decrease if it is calculated for the mean value of 5 tests compared to the single run value. This is also displayed in Figure. where the bias is constant regardless of the number of tests while the precision and NUMER OF TESTS Figure. ias, precision and total uncertainty. Expressed in relative numbers the bias for T represents only 7% percent of the total uncertainty for a single run but as much as 85% of the total uncertainty for the mean value of 5 tests. The bias for R represents 74% of the total uncertainty for a single run and 98% of the total uncertainty for the mean value of 5 tests. y comparing the bias and precision limits and the uncertainties, the relative contribution of each term can be calculated. This makes it possible to determine where an upgrade in the measurement system has the largest effect. The bias and precision limits and the uncertainties for the total resistance coefficient are summarised in Table.6 where the relative contribution of each term is calculated. This makes it possible to determine where an upgrade in the measurement system has the largest effect. If considering the total resistance

17 ITT Recommended Page 7 of 8 00 coefficient in this example, the most effective would therefore be to improve the speed and resistance measurement systems as they respectively contribute too 47% and 50% of the total bias limit. The uncertainty in speed consists of 98% of the uncertainty in pulse count c. This uncertainty consists of over 80% of the bias limits c and c. The bias limit in resistance consists of almost 00% of the uncertainty in acquisition, R x and R x4. It is therefore most important to:. Upgrade the resistance measurement system by changing the resistance transducer to a transducer with better linearity (Reduction of error Rx ).. Upgrade the data acquisition cycle in the speed measurement system (Reduction of error c and c ). Table.6 Error contributions to total uncertainty. Term Value Percentage values Model geometry (m ) S (m ).666E % of S S (m ) 6.89E % of S S (m ) 7.9E % of S Model speed (m/s).70 c (bit) % of c c (bit) % of c c (bit) % of c c4 (bit) % of c c (bit) % of c8 D (m).50e % of D0.8 Δt (s).05e % of Δt 0. s θ V cc (m/s).59e % of V θ V DD (m/s) 5.4E % of V θ V ΔtΔt (m/s) -.746E % of V V (m/s).570e-0 0. % of V Model resistance (N) 4.79 Rx (N).090E-0 0. % of Rx Rx (N).706E % of Rx Rx (N).978E % of Rx Rx4 (N) -6.4E-0.47 % of Rx Rx5 (N).96E % of Rx Rx (N).84E- 0.4 % of Rx Model Density (kg/m ) Temperature (deg) T (deg) % of 5 deg ρ (kg/m) E % of ρ ρ (kg/m) 7.00E-0. % of ρ ρ (kg/m) 6.55E % of ρ ρ (kg/m) 6.605E % of ρ Total oefficient.79e-0 θ T SS -.588E-06.7 % of T θ T VV -.589E % of T θ T RxRx.646E % of T θ T ρρ -.504E-06.6 % of T T.9E % of T P T (S).89E-05. % of T P T (M) 9.886E % of T U T (S) 4.48E-05.8 % of T U T (M).50E % of T Residual Resist. oefficient.00e-04 θ R TT.9E % of R θ R kk E % of R θ R FF -5.09E % of R R 6.48E-05.7 % of R P R (S).8E % of R P R (M) 9.895E % of R U R (S) 7.49E % of R U R (M) 6.5E % of R r where θ i r i REFERENES () oleman, H.W. and Steele, W.G., 999, Experimentation and Uncertainty Analysis for Engineers, nd Edition, John Wiley & Sons, Inc., New York, NY. () ITT, 999a, Uncertainty Analysis in EFD, Uncertainty Assessment Methodology, nd International Towing Tank onfer-

18 ITT Recommended Page 8 of 8 00 ence, Seoul/Shanghai, ITT Recommended, Procedure , Rev 00 () ITT, 999b, Uncertainty Analysis in EFD, Guidelines for Towing Tank Tests, nd International Towing Tank onference, Seoul/Shanghai, ITT Recommended, Procedure , Rev 00 (4) ITT, 999c, Density and Viscosity of Water, nd International Towing Tank onference, Seoul/Shanghai, ITT Recommended, Procedure , Rev 00 (5) ITT, 999d, Example for Test, nd International Towing Tank onference, Seoul/Shanghai, ITT Recommended Procedures and Guidelines, Procedure , Rev.00 (6) TT, 00, Ship Models, rd International Towing Tank onference, Venice, ITT Recommended Procedures and Guidelines, Procedure , Rev.