Ship Waves 423 
5. The wave resistance of a ship model in a frictionless liquid is the 
same whether it is moving bow first or stern first, even when the model 
is not symmetrical fore and aft. If, however, we introduce a reducing 
factor to represent the effect of fluid friction, it is clear that we shall 
obtain a difference between the two cases, and it is also easy to foresee 
the general character of the result. Suppose that the bow is finer than 
the stern, and assume that the reducing factor is the same whether going 
ahead or astern. Then it is obvious that the resistance will be less when 
going bow first than when going stern first; and further, that interference 
effects between bow and stern waves will be relatively more marked in the 
former case than in the latter. 
03 0-35 0-4 0:45 0-5 
e/ V (gl) 
Fic. 2 
We shall now work out a particular case, a model of great draught 
with parabolic ends and with some parallel middle body. The lines of 
the horizontal section are given by 
p=B0=ED, O<hei 
=p: ee 0 
=-2+m, —1<h<-¥ (21) 
In this model the change of gradient at the stern is twice that at the 
bow. 
In order to simplify the calculations, we shall assume that the reducing 
factor is constant and equal to unity over the front half of the model, 
and has a constant value fs over the rear-half; there will be only a small 
difference between the results so obtained and those with a more natural 
form of reducing factor, because in any case the middle portion of this 
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