318 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 57.7 



TABLE 57.0— Residuary-Resistance Prediction for ABC Ship From Gertler's Cr Contours 



The characteristics and proportions listed correspond to those of the fifth approximation in Table 66. e of Sec. 66.11. 

 The Cr contours are given in TMB Report 806, "A Reanalysis of the Original Test Data for the Taylor Standard 

 Series," by M. Gertler, March 1954. One particular pair of contours required here is reproduced in Fig. 56.D. 

 The calculation is made for one speed only, 20.5 kt (the designed speed), at a T, value of 0.908. 



Length on waterline, L = 510 ft 

 Displacement volume, V = 574,000 ft' 

 Wetted surface, S = 44,759 ft^ 

 Beam, S = 73 ft 

 20.5 kt =0= 34.62 ft per sec 



Draft, H = 26 ft 



V/(0.10Ly = 4.327 



B/H = 2.808 



Cp = 0.62 



0.5p = (0.5) (1.9905) slugs per ft' = 0.9953 slugs per fts 



- 2.25 



2.808 - 2.25 



= 0.743 



0.743(0.033) = 0.025 



0.75 0.75 



Rr = Cr{0.5)pSV^ = 1.270(10-')(0.9953)(44,759)(34.62)'= 67,630 lb. 

 This is to be compared with the 65,829 lb derived in Table 57.b. 



tables in TMB Report 806 is 1,000 times smaller 

 than the 0-diml fatness ratio V/{0.10Ly, so that 

 the Gertler graphs are entered with the numerical 

 value of this fatness ratio by neglecting the multi- 

 plier 10~^ marked on the graphs. 



The fact that the residuary resistance as calcu- 

 lated by the Gertler Cr method is 2.7 per cent 

 higher than that calculated from Taylor's Rr/^ 

 contours indicates that for certain combinations 

 of proportions there are real differences between 

 the original and the reworked TSS data. These 

 differences have been explored by the Preliminary 

 Design staff of the Bureau of Ships of the U. S. 

 Navy Department for a considerable number of 

 ship types, without revealing any systematic 

 difference pattern. The magnitude of the differ- 

 ences, while not negligible, is small enough to 

 permit a naval architect to use either method in 

 the preliminary-design stage. 



57.7 Teller's Method of Predicting Ship Re- 

 sistance. A method of extrapolating model test 

 data to predict ship resistance was proposed and 

 described by E. V. Telfer several decades ago 

 [INA, 1927, Vol. 69, pp. 174-210; NECI, 1928- 

 1929, Vol. 45, pp. 115-184]. Basically this scheme 

 is simply a graphic one for effecting the extrap- 



olation from model to ship data by the well- 

 known Froude method [SNAME, 1932, p. 87], 

 especially when the extrapolation is to be done, 

 not from the test data on one but from the com- 

 bined data on several geosim models of different 

 scale ratios. Test data are available on a number 

 of geosim families, each comprising three to six 

 or more models. While the specific residuary 

 resistance coefficients for selected T, or F„ values 

 are held constant, the specific friction resistance 

 coefficients are modified in accordance with some 

 accepted friction formulation such as the ATTC 

 1947 meanline. This is equivalent to drawing one 

 line of a graph parallel to another line having a 

 given position and slope. 



Examples of Telfer extrapolations of this kind 

 are found in: 



(1) Telfer, E. V., "The Frictional Resistance of Ships," 



MENA, Oct 1922, pp. 387-390 



(2) Telfer, E. V., "Notes on the Presentation of Ship 



Model Experiment Data," NECI, 1922-1923, Vol. 

 XXXIX, pp. 221-299. Appendix 3 gives notes on 

 the determination of the friction resistance by 

 analysis of tests on ship-formed models of different 

 length. 



(3) Telfer, E. V., "Ship Resistance Similarity," INA, 



1927, Vol. LXIX, pp. 174-190, 196-210, and Pis. 



