Non-Linear Shtp Wave Theory 
and Gee are represented as functions of the Froude number for 
a body of length submergence ratio 2L' /h' = 20. In fig. 4b the 
same curves are represented for the case 2L' /h' = 10. It is em- 
phasized that the scales of the various quantities are different in 
figs. 3b and 4b. 
II .5 - Discussion of Results and Conclusions. 
Fig. 2 permits to draw a few conclusions on the effect of the 
bow shape on the nonlinear wave resistance. First, it is seen that 
the free surface correction Gas is larger than the body correction 
ens by a factor of three at sufficiently large F = U' / (gh')' 
When F decreases this ratio begins to increase ina very steep 
manner. Hence, any conclusion regarding nonlinear effects which 
is based on the body correction solely is completely misleading, 
particularly at small Froude numbers. The total nonlinear correc- 
tion Cy is a small part of Coy at large F . Again, the nonli- 
near correction becomes unboundedly large as F—0O. In fact, from 
(30) we have Coo /Cp,~- 16/F* as F-s0o and Bao Cn = 
ens / Gay ad ih F* as F-0. The influence on the nonlinear 
wave resistance of making the bow fine is manifest in the medium 
range of F values, when the bow length and the wave length are of 
the same order of magnitude. In that range, for a fine bow Cy2/Cp, 
is almost constant over a large stretch of Froude numbers and is 
smaller than Cho / Coy of a blunt bow. At small and very large 
F the behavior is similar to that of an isolated sources. Finally the 
second order effect is always negative, i.e. it diminishes the wave 
ee eie ane. Moreover, if ¢€ is not sufficiently small Cy =€ Cp, + 
e“ Cy> (figs. 3 and 4) may become negative, which is obviously an 
absurdity. 
Figs. 3 and 4 display clearly the interference effects. The 
nonlinear effect is very large for the large length submergence ratio 
of fig. 3 (2L' / h' = 20) and becomes significantly smaller for 
2L' /h'=10 (fig. 4). Obviously, these large ratios have been select- 
ed in order to emphasize the nonlinear effect. To render it relative- 
ly small, the body has to be execeedingly thin or not so blunt. Again 
the body correction Cy, is generally smaller than roe , especial- 
ly at small F. The nonlinear term Cp> tends to sharpen the peaks 
of the resistance cuve and to widen its hollows. The nonlinear effect 
becomes very large in comparison to the first order wave resistance 
for small F . Again, we may arrive at negative wave resistance 
near the zeros of Cp, if ¢ is not sufficiently small. 
One of the stricking results of our computations, which has 
1707 
