Non-Linear Shtp Wave Theory 
1 
Ohl an B Gpu o,f ert t (s) 1 7 (s) 
Wan es Maron” ea sae | z-ih-s BS Ridin eat all eae 
ey = 
(78) 
Ww; may be found by analytical continuation across y=0. After 
some manipulations (Dagan, 1972b) the solution is found to be 
p : f Zz 
M23): = a - wi += 2/E ; 
F 
: O,u Wag aed ye 
ae is (A )e e 1 dy (79) 
-00 
which is analogous to (71). The profile of the free waves N = € ND == 
is derived from (79) as 
2 2 
0 bs 
N, =Im Ave Blea Im[ 2p ws athe 
£20" 9) Be ix/F° 
oie fy /F dd] e ~ix/F (x + oo) (80) 
6 
- 
In (79) and (80), f Sous (v)d» and S§S is the cut |x| <Tf, 
fa h+ 0 inthe » plane. Along S wr =a a7 and 
fo = = + ¢' 4 + it. Hence, we can write for A the following 
expression 
: ; ii 1,u 2 
Ae Une eis /F encie (f’ + % Er 
- 14th 
itea sinh od it cosh aS) dy (81) 
F F 
The wave resistance coefficient Cy is given by 
2- ihe Doip2 2 
G1 Sis Jat | / 8F (82) 
(iv) €=0(1), F* =0(i), ¢/F2 =0(1) (thin body, small 
This limit 
length Froude number, large thickness Froude number). 
can be obtained in two ways : by expanding W, of (i) for F*—0 or 
E721 
