Free Surface Effects tn Hull Propeller Interactton 
(x,z) in reverse motion, our basic Equation (B63) can be written as 
Rp 1/2 - 
ee: ale a ax [ R do {o(R,0) @ (x sD) 
Rey - 1/2 ; * ; 
where the arrow is supposed to indicate reverse motion of the hull. 
This formula is no more complex than our Equation (B64) for the fic- 
titious force 6,,R P and yet elegantly obviates any need for cal- 
culating differences of wave resistances. Moreover, by virtue of the 
fore and aft symmetry of our hull form we have 
—H 7 H 
(x yRO) = -o. (-x,,R, 8) 
so that the required inverse flow in the propeller plane is simply the 
"bow wake" already computed by us for other purposes, Therefore, 
taking the circumferentially averaged propeller source strengths 
from Figure 29 and the circumferentially averaged bow wakes from 
Figure 6 we were easily able to recalculate our nondimensional thrust 
deduction 5pRy,, and thence by Equation (B66) the thrust deduction 
fraction (tp + t,,) for the three cases y, = 4.0, 7.0 and 12.5. The 
results turned out to be identical with our original calculations, thus 
providing a useful crosscheck and enhancing our confidence in the 
numerical analysis, 
To Dr. Johnsson 
Our detailed discussion of relative rotative efficiency in 
reply to Professor Telfer will hopefully satisfy Dr. Johnsson, The 
reason we used wake wheels rather than Pitot tubes was simply that 
they happened to be available. Moreover, they provided an easy means 
of measuring both stern and bow wake. Our calibrations (revolutions 
versus speed) were sometimes highly nonlinear, specially for the 
larger diameters, but always perfectly consistent and repeatable. 
fo-Dr. Dyne 
Dr. Dyne's critical discussion is very welcome, specially 
in view of his own recent contributions to the subject referred to also 
by Professor Weinblum, 
Although we have not been able to fully verify the details of 
Dr. Dyne's analysis, we basically agree with him that the Hough and 
Ordway (1965) analysis applies strictly to lightly loaded propellers 
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