Nowaekt and Sharma 
Brunnstein (1968). They identify two counteracting forces on the rudder 
in the slipstream : a thrust resulting from virtual angles of attack in- 
duced by the rotation of the slipstream, and a frictional drag due to 
the increased axial velocity in the slipstream. Depending on the re- 
lative magnitudes of these two forces, the net effect might be a de- 
crease or increase in the thrust deduction as compared to the no- 
rudder case. 
We admit that our hull form has rather poor wavemaking 
properties so that the results may not be representative of ordinary 
ships. As explained in Section 3.1, an unusually high waterplane coef- 
ficient was necessary to produce appreciable thrust deduction effects 
without sacrificing thinness (L/B = 10), which seemed to be a prere- 
quisite for the application of wavemaking theory. 
Professor Weinblum caught us on a vulnerable formulation 
in Section 4 of our paper. Of course, it is a matter of opinion whether 
or not a dominant wave component in the wake runs contrary to ''com- 
mon belief'', However, we accept Professor Weinblum's better jud- 
gement on this point. 
To Professor Eggers 
Professor Eggers has hit upon the most intricate point in 
our theoretical analysis : the calculation of thrust deduction taking 
account of the wavemaking of the hull and the propeller. Despite its 
misleading name thrust deduction is actually a force physically act- 
ing on the hull. Therefore, the conceptually most direct approach 
would be to compute it by Lagally's theorem as an integral over the 
source distribution of the hull, see Equation (B63). However, as ex- 
plained in Section B.7 we preferred an indirect but numerically more 
expedient approach involving the wave resistances of the hull and the 
propeller and a fictitious force 6;,;Rwp induced by the hull on the 
propeller sources, see Equation (B65). Our method thus involved in 
some cases the evaluation of relatively small differences of large 
numbers, This made us a bit doubtful of our results, specially be- 
cause the wave component t,, of the calculated thrust deduction frac- 
tion (t, + t.3) changed its sign at about F,, = 0.23, a feature we 
could not intuitively explain, see Figure 30. 
Fortunately, Professor Eggers recently suggested to us an 
alternative and analytically equivalent but numerically even more ex- 
pedient method based on the inverse flow principle. Since the longitu- 
dinal flow induced at the location (x,z) of a hull source by a unit 
propeller source at (x,,R,9) is numerically equal to the longitudi- 
nal flow induced at the location (x, R,®) by a unit hull source at 
1958 
