Nowaekt and Sharma 
A useful check on the numerical accuracy of the calculated 
values of w,(R,@) is obtained by using them to determine the wave- 
making resistance of the propeller by virtue of Lagally's theorem [see 
Equation (11) of Eggers , Sharma and Ward (1967) }: 
Rp 7/2 
forltawt arf R a(R) f ws (R,@)d@ dR 
R -7/2 (B62) 
Analytically , of course , this is identical to the more direct formula 
(B29) based on the free-wave spectrum . Numerically , we found that 
the differences were negigibly small for a reasonable step size AO< 7/6. 
B.7. Thrust Deduction 
We wish to calculate the force of thrust deduction , i.e. the 
augmentation of hull resistance due to propeller action . Let us call 
it S>RwH . Conceptually , the most direct approach would be to use 
Lagally's theorem., i.e; 
6 R = 92) au >P (x, 0,2) 
Pp WH = a2 mf dz {0 (2) Viz » 0, \ aaa, 
This would seem to necessitate the explicit calculation of the longitu- 
dinal perturbation flow eP induced by the propeller on the center-plane 
of the hull y = 0O , which is not quite easy due to the singular double 
integral in formula (B58) . However , we will circumvent this diffi- 
culty by an indirect approach . Let us denote by 6yRwp the augmen- 
tation of propeller resistance due to hull action . Then again by 
Lagally's theorem 
w/2 
Rp - 
buRwp = Zan aR f R dO (o(R,0)ex (x, R, 8) 
Ry - 1/2 (B64) 
where yl now is the axial perturbation flow induced by the hull in 
the propeller plane , i.e. the wake as already defined by (B53) 
On the other hand , by virtue of previous definitions we have 
Rwt = RwH + Rwp + 6pRwH + 6yHRwp 
Hence, 
(B65) 
1902 
