Non-Linear Shtp Wave Theory 
where D =D' / pgLié and D' is the wave drag. 
By using the results for two sources, D, and D.. Mor ‘n 
sources are found after some manipulations (Dagan, 1972a) as 
D, = _-2h/F 3 Se cost. (28) 
jet het 
zZ 
2 z 
metas” ettone ALI. 5d [A* sink... +(BPsB “cosh, erhe 
n ni on 3 ) | 
ne De ail é, [C5 (sin i + sin cee, - 
m= j=1 k=j+1 
b Ss / b: s 
+ (Ea + Ey) (cos “age cos ban + (To +1 Jeos E “ 
s ; 
= ie sint (29) 
Ds and D, are obtained in (29) by the selection of the 
coefficients with the appropriate upper index. All the coefficients 
are given in an analytical closed form in (20) and (24). (29) permit 
the computation of the nonlinear wave resistance of a body of arbi- 
trary thickness distribution at any desired accuracy. The function a 
and £6 (18) may be taken from the ay es Abramowitz and Stegun 
(1964), taking into account that w (‘¢) = 5 [2 9i - E, (-i¢ I" . of 
may be easily calculated by using the cease power series of 
Bal ih). 
I .4 - Application to Bodies of Different Shapes. 
We consider first the simplest conceivable case, i.e. the 
wave resistance of an isolated source. We immediately obtain from 
(28):and (29)! with ‘He= 1, €y=n2 
2 
ah Pb Ae 2h/F 
1 
b Any oe 2 
iD, joer Ey 
1705 
