High Speed Displacement-Type Hulls 579 
of speed. These measurements suggest that the total resistance for typical appendage 
arrangements is more closely estimated by a constant 6 © rather than by a constant pro- 
portion of the naked hull resistance. A tentative value for the resistance coefficient of 
normal stern arrangements, excluding bilge keels, is thus 6 © = 0.20. 
Effect of Changes in Scale 
The average resistance coefficients © in Fig. 7 apply directly only to vessels of 
length L =100 feet; for vessels of other lengths a skin friction correction must be applied. 
The conventional relation for this is 
©y00' - Ox = (M91 - %) O Ov%- 779 
where the subscripts 100’ and L refer to vessels of length 100 feet and L feet respectively, 
“0” is Froude’s friction coefficient, and ©) and © are Froude’s circular wetted-surface 
and speed/length constants respectively. This does not hold for high speed displacement- 
type forms, but a modified relation does give friction corrections with practical accuracy. 
This modified relation is 
© 409" - Ox = MOgq - %) © O17 
where the factor & may be taken as a function of displacement/length ratios A/(0.01L)? 
alone with sufficient accuracy for preliminary design purposes. Values of é and of Froude’s 
“0” are shown in Fig. 16. It should be noted that the wetted surface area of a round-bilge 
displacement-type form does not vary sufficiently with speed to cause appreciable errors in 
using a fixed value of wetted area. For preliminary design purposes it is generally adequate 
to estimate the wetted area S from a simple formula such as the Denny-Munford relation 
S = L(1.7d + BC) 
where Cg is the block coefficient and the other symbols are as previously defined. 
PROPULSION 
Components of Propulsive Efficiency 
Components of propulsive efficiency have been derived from the results of propulsion 
experiments made with eight different models. In these experiments the thrust was measured 
in the direction of the propeller shafting, and corrected to eliminate the effect of the weight 
of the propeller. The resistance was measured as the horizontal force in the direction of 
motion, but no attempt was made to compute the fore and aft component of the thrust. Open 
water experiments with propellers alone were made with the shaft horizontal. 
Values of the thrust deduction fraction t, the wake fraction w based on thrust identity, 
the relative rotative efficiency 7p, and the hull efficiency 7, are given in Figs. 17-20 in 
terms of the speed/length ratio V/\/L. These show that the thrust deduction fraction ¢ 
tends to vary much as the resistance coefficient © , with a maximum near V/V, = 1.5 and 
