Minimum Wave Resistance Problem Solution 
or, in linearized approximation for steady flow, 
Pi- P= SPC WL + pez 
The force in the x direction, exerted on a surface element of the hull is 
dK = - p 2 dxdz 
where dxdz is the projection of the element on the x,z plane. The total resistance is 
+L/2 C4) +L/2 @ 
Bay of( x, z) bes a of 
ne ae | { p  dxdz = 2pc { f So 2 axdz. 
“*L/2 ‘0 -L/2 0 
Substitution of the expression for @ gives for the resistance integral 
+L/2 +L/2 @ © 
c2 OF(x, DECK. nz 
R = ae dx dx. dz dz oe 2) pas 4 
7 1 i Ox Ox, 
-L/2 LL /2 0 0 
2 
a - 2 (2424) a? cos a (x- x,) 
x e cP a ee Vee aie 
K (ea ca 
We introduce dimensionless coordinates 
and the resistance integral takes the form 
p'c2B2T2x2 +1 +1 +1 +1 
ee Gri | bien | eaeas. ce ced) Bes, C,) 
Beate Lv Lp ae eo ge 
0 2 
-A°KT(C+E,) NL 
x e ‘ cos —5~ (€-€,) 
d? dr 
69 
1 VA? - 1 
