306 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 56.7 



V 



(0.101)" 



/ 



:/3^ 





Cb-0.70 



^ A 



Z- 



/ 





-/ 



\/^ 



/ 



"7' 



X 



1 0.35 



Tq-y//r 



^ 



"'' 



// 



/ ^ 



/ 



F„=V/v5l 



Ti 



U 





I6__/. 



rr-r 



0.95 



/ 



/ 



,^ 



/ 



-7^ 



^^ 



O.ao 0.2) 022 0.25 Q24 0.25 Q26 Q27 02a 029 Q30 



Fig. 56.K Cr Data for Fat Ships, Cp = 0.70 



guide in making resistance and power estimates 

 for ships having displacement-length quotients in 

 excess of those of the Taylor Standard Series. 

 The data given are based upon the use of the 

 Froude circular-constant system of notation. 



56.7 Systematic Resistance Data for Parallel- 

 Middlebody Variations. The first systematic 

 model test data on the effect of varied amounts of 

 parallel middlebody inserted between given 

 entrances and runs were those published by W. 

 Froude [INA, 1877, Vol. XVIII, pp. 77-97]. He 

 plotted curves of residuary resistance Rr for 

 constant speed F on a basis of length Lp of 

 parallel middlebody, a procedure which has not 

 been improved upon to this day. The low points 

 in the Rr curves for a succession of speeds, or for 

 a given speed, indicate the Lp values for minimum 

 residuary resistance. These are not necessarily the 

 values for minimum total resistance. 



Data from tests of the 156 combinations of 

 EMB Series 53, tested in 1931 for the U. S. 

 Shipping Board and plotted on the Froude 

 system, are pubhshed in: 



(1) S and P, 1933, pp. 47, 67, 68, and Appendix D, pp. 299 



through 327 



(2) S and P, 1943, p. 50 and pp. 70 through 72; also 



Appendix D, pp. 255 through 271 



(3) Brief extracts from these data are given by K. S. M. 



Davidson in PNA, 1939, Vol. II, pp. 67-69. 



It is to be noted from the body plan of the 

 parent form, given on page 257 of reference (2) 

 above, that the Series 53 models had practically 

 no bulb and were not patterned on the Taylor 

 Standard Series lines. 



The analysis of these parallel middlebody data, 

 not completed for the 1933 and 1943 editions of 

 "The Speed and Power of Ships," still remains to 

 be done. 



56.8 Resistance Data for Very Low Ship 

 Speeds. Published data on ship resistance pre- 

 dicted from model tests rarely include the range 

 all the way down to zero speed, yet it is often 

 convenient to have some idea of the low-speed 

 resistance, or at least to know how it varies with 

 speed in this region. 



The tables of Cp in SNAME Tech. and Res. 

 Bull. 1-2 of March 1952, two small portions of 

 which are reproduced as Tables 45. c and 45. d of 

 Sec. 45.9, extend down to an i2„ of 0.1 million, 

 corresponding to a fore-and-aft space dimension 

 of about 0.73 ft and a speed of 1 kt. The Taylor 

 Standard Series contours [S and P, 1943] stop at 

 a speed-length quotient T^ of 0.30, F„ value of 

 about 0.089. The SNAME RD and ERD sheets 

 carry down to a T^ and an F„ of about the same 

 value. 



A residuary resistance composed entirely of 

 pressure resistance should vary as F" all the_way 

 to F = 0. However, plots of i2„/A on V/Vh for 

 low speeds in the Taylor Standard Series show 

 that it is the exception rather than the rule for the 

 exponent of the curve oi RrOhV to approximate 

 2. This is due partly to the extremely low resist- 

 ances being measured but there appear to be 

 evidences of viscous and other effects not entirely 

 eliminated in the Froude model-testing procedure. 



An approximation to the residuary resistance 

 close to F = is derived from a plot of Rr/A on 

 V/'VL on log-log paper, somewhat similar to 

 that of Fig. 30. B, for say three values of F/ vL = 

 0.40, 0.35, and 0.30. Extending the line in a 

 generally straight direction downward gives an 

 idea of the low value oi Rr on T^ desired. 



56.9 Rate of Variation of Model Residuary 

 Resistance with Speed. For certain lines of anal- 

 ysis it is useful to know the rate at which the 



