Free Surface Effects tn Hull Propeller Interactton 
Then the free-wave spectrum of the model is given by 
G(u) =——— 
z {C"(s,y,)eos(uy,) - S*(s,y,)sin(uy,) | 
; * 
F(u) =——— {c*(s,y )sin(uy_)+S (s,y_)cos(uy )} (B71) 
re) fe) fe) ) 
2s -l 
2 i , g y 
where u = sl s -l in accordance with (B18). By applying this pro- 
cedure separately to the model hull with and without propeller one can 
obtain the spectrum G-r(u), F.p(u) of the total system hull and propel- 
ler and the spectrum Gy,(u), Fy ,(u) of the bare hull respectively. The 
spectrum of the propeller alone Gp(u) , F p(u) then follows from the 
principle of linear superposition. 
lO 
Us 
cer er 
II I 
hy OD 
a — 
eos Oy 
1 1 
yO 
ae 
Ss 
(B72) 
For the ease of comparison with theory the propeller spectrum may 
be transformed to a new coordinate system Oxyz which has its ori- 
gin in the propeller plane. If x = X-Xp ; yoy, Bee then 
a) = 9G u)cos(sx,,) + F,(u)sin(sx 
p! p) 
(B73) 
F(a) = F,(u)cos(sx,) - G u) sin(sx 
p!| p) 
The associated wavemaking resistances of bare hull (Ry ), bare 
propeller (Ry p) and total system hull-propeller ee are obtain- 
ed from the respective spectra by use of the general formula : 
= \ Mae 
Ry == if fei PG tape dia (B74) 
8 r > 
0 1+ Vl+4u 
It is assumed here that the wave pattern has transverse symmetry. 
1905 
