[Reprinted from the PROCEEDINGS OF THE Royat Society, A, Vol. 136.] 
Ship Waves; their Variation with certain Systematic Changes 
of Form. 
By T. H. Havetocr, F.R.S. 
(Received February 24, 1932.) 
1. The following paper is an examination, by analysis and by curves, of a 
single definite problem in wave profiles. Consider a ship model, of great 
draught, in which at some point in the form, at bow, stern or shoulders, for 
example, there is a sharp corner giving a sudden change of slope of the hori- 
zontal lines of the model. What is the effect on the wave profile of replacing 
this sudden change by a gradual change of slope of the same total amount. 
but distributed uniformly over any given length of the ship’s form? Apart 
from direct applications, the problem is suggested by certain other considera- 
tions. In comparing theoretical and experimental resistance curves, I sug- 
gested some years ago* an indirect effect of the friction belt along the sides 
of the ship in that it may be equivalent to smoothing out the lines of the model, 
especially towards the stern. From an examination of interference effects 
with experimental models, it has been estimated that the effective length of 
the model is roughly 8 per cent. greater than the actual length, and this may 
probably be ascribed to some such frictional effect. The present paper deals 
with wave profiles since measurements of surface elevation are now becoming 
available, though the main results so far are for a simple model with straight 
lines and sharp corners ; such a form simplifies the calculations but no doubt 
introduces other complications in practice, and a small correction for the 
smoothing effect of a friction belt would not be likely to account for the remain- 
ing differences between calculation and observation. It must be noted, 
moreover, that there are other approximations in the theory, apart from the 
neglect of fluid friction, but these need not be discussed here. 
For these reasons no attempt has been made to apply the results of the 
present paper directly to experimental data, but it is hoped that the progressive 
series of curves will be of interest in showing the changes in profile due to 
successive changes of form of a definite kind. 
2. The general analysis will be quoted from a recent paper,f to which refer- 
ence may be made for further detail, and the expressions will then be adapted 
to the particular problem. 
* © Proc. Roy. Soc.,’ A, vol. 110, p. 233 (1926). 
+ ‘ Proc. Roy. Soc.,’ A, vol. 135, p. 1 (1932). 
360 
