Minimum Wave Resistance of Surface Pressure Distribution 



Hb(y) = 0b(^)/sin e , 4>^{d) = Y^ b*2„ ce2^(^.-q) , 



n = 



00 



( 2n) 



(50) 



(51) 



77A\' 



and 



2(-l)" C,„ 



ttD/V- 



V^ (2n) 



Then 



G(y) = agV(27fA) , r* = 2agV(T7A) 



(52) 



(53) 



Although this solution becomes infinite at both ends y = ± l in general, taking 

 as a the value 



a = 0b(O)/t<^b(O)-'^a(O)] . (54) 



this solution becomes zero there, in which case it will be called H^. 



For the numerical computation at high speed, it is more convenient to ex- 

 pand in the series of trigonometric functions as follows: 



4>se) ~- 



CO 



2^ °-2n 



COS 2ne , 4>^{d) 



= 2]/^2n 



cos 2n6 



(55) 



Figures 4, 5, and 6 and Tables 1 and 2 show the results (4). When the ve- 

 locity is very large, that is, when g is very small, the functions become approx- 

 imately 



>(^)^- 



,(^) ^17 



1 - ^ log (8/yg) cos 26 

 Id 



3g' 

 1 + ^ log (8/rg) cos 26 



^c(^) 



- sin2 6 , 



and 



He(y) =-rvi-y^ 



(56a) 



(56b) 



(56c) 



(56d) 



where y means Euler's constant. The wave resistance is, respectively (1,4) 



785 



