Free Surface Effects tn Hull Propeller Interactton 
where I, is the modified Bessel function of zero order [see Gradsh- 
teyn and Ryzhik (1965) , formula 3.9372 ] . This last integral can be 
easily evaluated for any numerically defined function o (R) 
B.4. Wavemaking Resistance 
The individual wavemaking resistances of the bare hull 
and the free running propeller Rwp are found directly by substituting 
the appropriate free-wave spectra (B23) and (B27) into the general 
formula (B21) 
; 1 (16d 2ov 
RwWH ="8 f {— Fm, sh) F'2)(n, <, Ts(?)) | du 
Rp 
1 l+v 2 Vv 
= ag ifs [ 16” { = | exe sz) f Ro(R)Io (sR) aR Tay de 
0 Ry 
(B29) 
To calculate the wavemaking resistance Rwyr of the total 
system hull with propeller one can use the principle of linear super- 
position of free-wave spectra , that is 
Gr (u) Gy (u) + Gp (u) 
Fr (u) + Fp (u) (B30) 
Fey (u) 
provided both spectra are expressed in the same coordinate system . 
The general formula (B21) can then be applied to the total spectrum 
2 2 
Eq(a) = yor (u) + Fp “(u)} 
Evidently , in general 
Rwr # RwH + Ryp (B31) 
1893 
