Ogilvie 
pcbe hoget e Je = (abe (16) 
For y=0, this simplifies further 
0 
We obtain our simplest form when we make the following changes of 
variables 
xi] 2AiK/a Z(X)ote 3 ee GRE) ee (17) 
oo ae 
ZAK) = [ #€52) (3) (18) 
af # 
Thus, the wave along the side of the wedge can be nondimensionalized 
in such a way that we have a single universal curve, a function of just 
one variable, which purports to describe the wave shape for any speed, 
any draft, and any wedge angle. Of course, we have not yet considered 
the range of validity of these results, but itis clear that they are very 
simple results. 
It is worthwhile to notice the manner in which the length 
scales are made nondimensional : The reference length is (H/K)'? = 
HU2/g)'/2 . This is the geometric mean of two lengths, the draft H 
and characteristic free-surface length U“/g. 
Also, the wedge half-angle enters in a very simple way: The 
non-dimensional wave height, Z , must be multiplied by the ratio, 
1508 
