Free Surface Effects tn Hull Propeller Interaction 
For x—4 -0 ; 
1 oo 
CO6 3) =ae [iro sin (sxtuy) + G/(u) cos (sxtuy) } du 
(B19) 
Here s and u can be interpreted as the circular wave numbers in- 
duced by a free plane wave (moving with the ship) in the x and y 
direction respectively . Hence F(u) and G(u) are called the sine and 
cosine components of the spectrum and its amplitude is given by 
E (u) = F4 (u) + G2 (u) (B20) 
The phase of the free-wave spectrum depends on the choice of the coor- 
dinate origin but its amplitude does not . The associated wavemaking 
resistance 
Rw suse as (u) du (B21) 
is determined solely by the amplitude spectrum . 
By virtue of formulas (B6) and (B17) the free-wave spectrum 
of the hull becomes 
bo Ma a0 
on wry of Ly fo PHA 
HA Ga/a- 
exp (s*ztisx) 
(B22) 
or after some simplification 
Gy (u) = 0 
1 
F,, (u) 2 pele Fr! ) (m, sf) Fl?) (9, € Seg ) 
Vv 
(B23) 
1891 
