7.5-02-03-01.4

ITTC – Recommended 7.5 – 02 03 – 01.4 Procedures and Guidelines Page 1 of 9

1978 ITTC Performance Prediction Effective Date Revision Method 2011 02

Table of Contents

2.4.2 Scale Effect Corrections for Propeller 1978 ITTC PERFORMANCE Characteristics...... 6 PREDICTION METHOD 2 2.4.3 Full Scale Wake and Operating 1. PURPOSE OF PROCEDURE 2 Condition of Propeller ...... 7 2.4.4 Model-Ship Correlation Factor ...... 8 2. DESCRIPTION OF PROCEDURE 2 3. VALIDATION 9 2.1 Introduction ...... 2 3.1 Uncertainty Analysis...... 9 2.2 Definition of the Variables ...... 2 3.2 Comparison with Full Scale Results .. 9 2.3 Analysis of the Model Test Results ..... 3 2.4 Full Scale Predictions ...... 4 4. REFERENCES 9 2.4.1 Total Resistance of Ship...... 4

Edited by Approved

26th ITTC Propulsion Committee 26th ITTC

Date 02/ 2011 Date 09/2011

ITTC – Recommended 7.5 – 02 03 – 01.4 Procedures and Guidelines Page 2 of 9 Performance, Propulsion 1978 ITTC Performance Prediction Effective Date Revision 2011 02 Method

1978 ITTC Performance Prediction Method

C Frictional resistance coefficient 1. PURPOSE OF PROCEDURE FC at the temperature of the self The procedure gives a general description propulsion test of an analytical method to predict delivered CNP Trial correction for propeller power and rate of revolutions for single and rate of revolution at power twin screw ships from model test results. identity CP Trial correction for delivered power 2. DESCRIPTION OF PROCEDURE CN Trial correction for propeller rate of revolution at speed 2.1 Introduction identity CR Residual resistance coefficient The method requires respective results of CT Total resistance coefficient a resistance test, a self propulsion test and the D Propeller diameter characteristics of the model propeller used FD Skin friction correction in self during the self propulsion test, propulsion test J Propeller advance coefficient The method generally is based on thrust JT Propeller advance coefficient identity which is recommended to be used to achieved by thrust identity predict the performance of a ship. It is sup- JQ Propeller advance coefficient posed that the thrust deduction factor and the achieved by torque identity relative rotative efficiency calculated for the KT Thrust coefficient model remain the same for the full scale ship KTQ Thrust coefficient achieved by whereas on all other coefficients corrections torque identity for scale effects are applied. KQ Torque coefficient KQT Torque coefficient achieved by In some special cases torque identity thrust identity (power identity) may be used, see section k Form factor 2.4.4. kP Propeller blade roughness NP Number of propellers 2.2 Definition of the Variables n Propeller rate of revolution nT Propeller rate of revolution, CA Correlation allowance corrected using correlation fac- CAA Air resistance coefficient tor CApp Appendage resistance coeffi- P Propeller pitch cient PD, PP Delivered Power, propeller CD Drag coefficient power CF Frictional resistance coefficient

ITTC – Recommended 7.5 – 02 03 – 01.4 Procedures and Guidelines Page 3 of 9 Performance, Propulsion 1978 ITTC Performance Prediction Effective Date Revision 2011 02 Method

PDT Delivered Power, corrected using correlation factor 2.3 Analysis of the Model Test Results PE, PR Effective power, resistance power The calculation of the residual resistance Q Torque coefficient CR from the model resistance test RC Resistance corrected for tem- results is found in the procedure for resistance perature differences between test (7.5-02-02-01). resistance- and self propulsion test Thrust TM, and torque QM, measured in the Re Reynolds number self-propulsion tests are expressed in the non- RT Total resistance dimensional forms as in the procedure for S Wetted surface propulsion test (7.5-02-03-01.1). SBK Wetted surface of bilge keels T Propeller thrust T Q K = M and K = M t Thrust deduction factor TM 4 2 QM 5 2 ρM DMnM ρM DMnM V Ship speed VA Propeller advance speed Using thrust identity with KTM as input data, w Taylor wake fraction in general JTM and KQTM are read off from the model pro- wQ Taylor wake fraction, torque peller open water diagram, and the wake frac- identity tion wR Effect of the rudder(s) on the wake fraction JTM DM nM w Taylor wake fraction, thrust wTM = 1− T V identity M Z Number of propeller blades and the relative rotative efficiency β Appendage scale effect factor ΔCF roughness allowance KQTM ΔCFC Individual correction term for ηR = roughness allowance KQM ΔwC Individual correction term for wake are calculated. VM is model speed. ηD Propulsive efficiency or quasi- propulsive coefficient Using torque identity with KQM as input data, JQM and KTQM is read off from the model ηH Hull efficiency propeller open water diagram, and the wake η0 Propeller open water efficiency fraction ηR Relative rotative efficiency ρ Water density in general JQM DM nM wQM = 1− Subscript “M” signifies the model VM Subscript “S” signifies the full scale ship and the relative rotative efficiency

KTQM ηR = KTM

ITTC – Recommended 7.5 – 02 03 – 01.4 Procedures and Guidelines Page 4 of 9 Performance, Propulsion 1978 ITTC Performance Prediction Effective Date Revision 2011 02 Method

are calculated. VM is model speed. The form factor k and the total resistance coefficient for the model CTM are determined The thrust deduction is obtained from as described in the ITTC standard procedure 7.5-02-02-01. T + F − R t = M D C TM The correlation factor for the calculation of the resistance has been separated from the where FD is the towing force actually applied roughness allowance. The roughness allow- in the propulsion test. RC is the resistance ance ΔCF per definition describes the effect of corrected for differences in temperature be- the roughness of the hull on the resistance. tween resistance and self-propulsion tests: The correlation factor CA is supposed to allow for all effects not covered by the prediction (1+ k).C + C method, mainly uncertainties of the tests and R = FMC R R C (1+ k).C + C TM the prediction method itself and the assump- FM R tions made for the prediction method. The separation of ΔCF from CA was proposed by where CFMC is the frictional resistance coeffi- the Performance Prediction Committee of the cient at the temperature of the self-propulsion th test. 19 ITTC. This is essential to allow for the effects of newly developed hull coating sys- tems. 2.4 Full Scale Predictions The 19th ITTC also proposed a modified 2.4.1 Total Resistance of Ship formula for CA that excludes roughness allowance, which is now given in this proce- The total resistance coefficient of a ship dure. without bilge keels is - ∆CF is the roughness allowance = + + ∆ + + + 1 CTS (1 k)CFS CF CA CR CAAS  3   k  −1 ∆ =  S  − ⋅ 3  + CF 0.044   10 Re 0.000125  L  where  WL  

where kS indicates the roughness of - k is the form factor determined from the hull surface. When there is no meas- resistance test, see ITTC standard pro- ured data, the standard value of -6 cedure 7.5-02-02-01. kS=150×10 m can be used.

- CFS is the frictional resistance coefficient - CA is the correlation allowance. of the ship according to the ITTC- CA is determined from comparison of 1957 model-ship correlation line model and full scale trial results. When using the roughness allowance th - CR is the residual resistance coefficient as above, the 19 ITTC recommended calculated from the total and frictional using resistance coefficients of the model in −3 the resistance tests: CA = (5.68 − 0.6log Re) ×10

CR = CTM − (1+ k)CFM

ITTC – Recommended 7.5 – 02 03 – 01.4 Procedures and Guidelines Page 5 of 9 Performance, Propulsion 1978 ITTC Performance Prediction Effective Date Revision 2011 02 Method

to give values of ∆CF+CA that ap- SS + SBK CTS = [(1+ k)CFS + ∆CF + CA ]+ CR + CAAS proximates the values of ∆CF of the SS

original 1978 ITTC method. It is rec- + CAppS ommended that each institution main- tains their own model-full scale corre- There is not only one recommended lation. See section 2.4.4 for a further method of scaling appendage resistance to full discussion on correlation. scale. The following alternative methods are well established: - CAAS is the air resistance coefficient in full scale 1) Scaling using a fixed fraction: ρ ⋅ A AVS C = (1− β ) ⋅C CAAS = CDA AppS AppM ρS ⋅ SS where (1-β) is a constant in the range where, AVS is the projected area of the 0.6-1.0. ship above the water line to the trans- verse plane, SS is the wetted surface 2) Calculating the drag of each append- area of the ship, ρA is the air density, age separately, using local Reynolds and CDA is the air drag coefficient of number and form factor. the ship above the water line. CDA can n be determined by wind tunnel model 2 Si CAppS = ∑(1− wi ) ⋅(1+ ki ) ⋅CFSi ⋅ tests or calculations. Values of CDA are i=1 SS typically in the range 0.5-1.0, where 0.8 can be used as a default value. where index i refers to the number of the individual appendices. wi is the If the ship is fitted with bilge keels of wake fraction at the position of ap- modest size, the total resistance is estimated pendage i. ki is the form factor of ap- as follows: pendage i. CFSi is the frictional resistance coefficient of appendage i, and Si + SS SBK is the wetted surface area of appendage CTS = [(1+ k)CFS + ∆CF + CA ]+ CR + CAAS SS i. Note that the method is not scaling the model appendage drag, but calcu- where SBK is the wetted surface area of the bilge keels. lating the full scale appendage drag. The model appendage drag, if known When the model appendage resistance is from model tests, can be used for the separated from the total model resistance, as determination of e.g. the wake frac- described as an option in the ITTC Standard tions wi. Values of the form factor ki Procedure 7.5-02-02-01, the full scale ap- can be found from published data for pendage resistance needs to be added, and the generic shapes, see for instance Ho- formula for total resistance (with bilge keels) erner (1965) or Kirkman and Klöetsli becomes: (1980).

ITTC – Recommended 7.5 – 02 03 – 01.4 Procedures and Guidelines Page 6 of 9

1978 ITTC Performance Prediction Effective Date Revision Method 2011 02

= − ∆ 2.4.2 Scale Effect Corrections for Propeller KQS KQM KQ Characteristics. where The characteristics of the full-scale propeller P c ⋅ Z are calculated from the model characteristics as ∆KT = −∆CD ⋅0.3⋅ ⋅ follows: D D c ⋅ Z = − ∆ ∆KQ = ∆CD ⋅0.25⋅ KTS KTM KT D

ITTC – Recommended 7.5 – 02 03 – 01.4 Procedures and Guidelines Page 7 of 9 Performance, Propulsion 1978 ITTC Performance Prediction Effective Date Revision 2011 02 Method

The difference in drag coefficient ∆CD is The wake scale effect of twin screw ships with open sterns is usually small, and for such

∆CD = CDM − CDS ships it is common to assume wTS = wTM. where For twin skeg-like stern shapes a wake correction is recommended. A correction like the  t  0.044 5  one used for single screw ships may be used. CDM = 21+ 2  1 − 2  6 3  c (Rec0 ) (Rec0 )  The load of the full-scale propeller is obtained from and

KT SS CTS −2.5 2 = 2 ⋅ 2 tc J 2DS (1− t) ⋅ (1− wTS ) CDS =+2 1 2 1.89 +⋅ 1.62 log ckP where NP is the number of propellers. In the formulae listed above c is the chord With this 2 as input value the full length, t is the maximum thickness, P/D is the KT / J pitch ratio and Rec0 is the local Reynolds num- scale advance coefficient JTS and the torque ber with Kempf’s definition at the open-water coefficient KQTS are read off from the full scale test. They are defined for the representative propeller characteristics and the following blade section, such as at r/R=0.75. kP denotes quantities are calculated. the blade roughness, the standard value of -6 - the rate of revolutions: which is set kP=30×10 m. Rec0 must not be 5 (1− wTS ) ⋅VS lower than 2×10 . nS = (r/s) JTS ⋅ DS

2.4.3 Full Scale Wake and Operating Condi- - the delivered power of each propeller: tion of Propeller K P = 2πρ D5n3 QTS ⋅10−3 (kW) DS S S S η The full-scale wake is calculated by the fol- R lowing formula using the model wake fraction wTM, and the thrust deduction fraction t obtained - the thrust of each propeller: as the analysed results of self-propulsion test:  K  2 4 2 T =  T  ⋅ J ρ D n (N) S  J 2  TS S S S (1+ k)C + ∆C w = (t + w ) + (w − t − w ) FS F TS R TM R + (1 k)CFM - the torque of each propeller:

KQTS 5 2 where wR stands for the effect of rudder on the Q = ⋅ ρ D n (Nm) S η S S S wake fraction. If there is no estimate for wR, the R standard value of 0.04 can be used. - the effective power:

If the estimated wTS is greater than wTM, wTS 1 − P = C ⋅ ρ V 3S ⋅10 3 (kW) should be set as wTM. E TS 2 S S S

ITTC – Recommended 7.5 – 02 03 – 01.4 Procedures and Guidelines Page 8 of 9 Performance, Propulsion 1978 ITTC Performance Prediction Effective Date Revision 2011 02 Method

- the total efficiency: In such a case the finally trial predicted N ⋅ P trial data are calculated as follows: η = P DS D P E K S C + ∆C T = S ⋅ TS FC 2 2 − ⋅ − + ∆ 2 - the hull efficiency: J 2DS (1 t) (1 wTS wC ) 1− t η = H With this K /J² as input value, JTS and KQTS 1− w T TS are read off from the full scale propeller characteristics and the following is calculated:

(1− wTS + ∆wC ) ⋅VS 2.4.4 Model-Ship Correlation Factor nT = (r/s) JTS ⋅ DS The model-ship correlation factor should be K P = 2πρ D5n3 QTS ⋅10−3 (kW) based on systematic comparison between full DT S S T η scale trial results and predictions from model R scale tests. Thus, it is a correction for any systematic errors in model test and powering pre- (3) Prediction of full scale rates of revolutions diction procedures, including any facility bias. and delivered power by use of a CNP correction In the following, several different alternative concepts of correlation factors are presented as For prediction with emphasis on stator fins suggestions. It is left to each member organisa- and rudder effects, it is sometimes recom- tions to derive their own values of the correla- mended to use power identity for the prediction factor(s), taking into account also the actual tion of full scale rates of revolution. value used for CA. At the point of KT-(J)-Identity the condi- (1) Prediction of full scale rates of revolutions tion is reached where the ratio between the and delivered power by use of the CP - CN propeller induced velocity and the entrance correction factors velocity is the same for the model and the full scale ship. Ignoring the small scale effect ΔKT Using CP and CN the finally predicted trial on the thrust coefficient KT it follows that J- data will be calculated from identity correspond to KT- and CT-identity. As n = C ⋅ n (r/s) a consequence it follows that for this condition T N S the axial flow field in the vicinity of the pro- for the rates of revolutions and peller is on average correctly simulated in the model experiment. Also the axial flow of the P = C ⋅ P (kW) DT P DS propeller slip stream is on average correctly for the delivered power. simulated. Due to the scale effects on the propeller blade friction, which affect primarily the torque, the point of KQ-identity (power iden- (2) Prediction of full scale rates of revolutions tity) represents a slightly less heavily loaded and delivered power by use of ∆CFC - ∆wC propeller than at J-, KT- and CT-identity. At the corrections power identity the average rotation in the slip- stream corresponds to that of the actual ship and this condition is regarded as important if

ITTC – Recommended 7.5 – 02 03 – 01.4 Procedures and Guidelines Page 9 of 9 Performance, Propulsion 1978 ITTC Performance Prediction Effective Date Revision 2011 02 Method

tests on stator fins and/or rudders are to be done 3.2 Comparison with Full Scale Results correctly. The data that led to 1978 ITTC perform- In this case, the shaft rate of revolutions is ance prediction method can be found in the predicted on the basis of power identity as fol- following ITTC proceedings: lows: (1) Proposed Performance Prediction Factors  K  1000⋅C ⋅ P  Q  = P DS for Single Screw Ocean Going Ships  3  πρ 2 3 − 3 (13th 1972 pp.155-180) Empirical Power  J T 2 SDSVS (1 wTS ) Prediction Factor ( 1+X ) K  K  Q0 =  Q  ⋅η 3  3  RM (2) Propeller Dynamics Comparative Tests J  J  th T (13 1972 pp.445-446 )

(1− wTS ) ⋅VS nS = (3) Comparative Calculations with the ITTC J ⋅ D TS S Trial Prediction Test Programme th nCn= ⋅ (14 1975 Vol.3 pp.548-553) TSNP (4) Factors Affecting Model Ship Correlation th (17 1984 Vol.1 pp274-291)

4. REFERENCES 3. VALIDATION (1) Hoerner, S.F. (1965) “Fluid-Dynamic 3.1 Uncertainty Analysis Drag”. Published by the author.

Not yet available (2) Kirkman, K.L., Klöetsli, J.W. (1980) “Scaling Problems of model appendages”, 19th American Towing Tank Conference, Ann Arbor, Michigan