tabulated in the Appendix III. The integral R and the functions 7Y\ and 7f[ 

 depend upon the two parameters y - 1 /2F 2 and f/L. The tables have been pre- 

 pared for a range 0.5 < y Q < TO and f/L = 0.125, 0.25, 0.50. Additionally, 

 for In an intermediate depth of immersion ratio f/L = 0.1875 has been intro- 

 duced. From the wave resistance integral it follows immediately that the 

 ratio depth of immersion over length f/L is theoretically preferable to the 

 more commonly used ratio f/D, since f/L appears explicitly as factor of the 

 exponent of the e-function under the integral. With elongated bodies the 

 ratio b/a or D/L influences primarily the constant C = 4C 2 npg b 4 /a only, 

 though in a very decisive way. Although the lower speed limit y = 1 

 (F = 0.224) — up to which the auxiliary integrals have been computed — is 

 rather high, it is thought that for normal hulls with #< 2/3 moving at greater 

 depths than D, the wave resistance becomes unimportant when F <~ 0.224. The 

 low-speed range may, however, be interesting in connection with other research 

 problems. 



In principle the wave-resistance equation, [24], solves the problem 

 for any sets of a within the family following [4i]. Actually since the 

 relative error of the tabulated functions is approximately 0.0001, a loss of 

 accuracy may occur — when the coefficients a reach high absolute values with 

 alternating signs. It is not probable that difficulties of this kind will be 

 important in connection with submarine work; besides, they can be overcome 

 to some extent by plotting suitable simpler resistance curves and by inter- 

 polating. 



4. REPRESENTATION OF RESISTANCE CURVES 



4.1 . THE DIMENSION FACTOR C AND DIMENSIONLESS REPRESENTATIONS 







The dimension factor in Equation [20], C Q = 4C 2 npg b 4 /a, has a 



rather unusual form, but it will be widely used throughout this report 



because of its theoretical merits and the comparative ease with which it can 



be connected with more familiar expressions. We rewrite, in terms of the 



displacement A , 



C = <*7rb 2 2apg^C 2 = A^- C 2 [25] 



^a 2 0a 2 



J_ = r - R <*a 2 or R _ r 2b 2 C 2 

 C o ° A 2b 2 C 2 A ° 0a 2 



