THE WAVE RESISTANCE OF A CYLINDER 
STARTED FROM REST 
By T. H. HAVELOCK (King’s College, Newcastle-on-Tyne) 
[Received 13 August 1948] 
SUMMARY 
A method of obtaining expressions for wave resistance in accelerated motion is 
given, but the particular problem examined is the motion due to a circular cylinder 
submerged at a given depth below the free surface, the cylinder being suddenly 
started from rest and made to move with uniform velocity. The surface elevation 
at any time is discussed, and expressions obtained for the finite wave resistance 
at any time after the start. Numerical calculations have been made for three 
different speeds, and curves are given showing how the resistance rises initially 
and oscillates about the steady value for each speed. 
1. Introduction 
CALCULATIONS of wave resistance have hitherto been made only for a body 
moving with constant velocity, the problem being treated directly as one 
of a steady state when referred to axes moving with the body. The case 
of non-uniform motion is of interest in itself, and also has possible applica- 
tions. For instance, in measuring the resistance of ship models, the question 
arises how long it is before the effect of the starting conditions becomes 
inappreciable. As a matter of fact, measured resistance curves always 
show oscillations about the steady value for a given speed, but these are 
no doubt mainly due to the natural period of the measuring apparatus; 
however, it would be of interest to have some examination of the approach 
to the steady resistance after the initial stage of accelerated motion. 
Expressions for wave resistance in accelerated motion have been given 
by Sretensky (1), who obtained them by transforming the hydrodynamical 
equations to a form suitable for axes moving with acceleration, but the 
formulae are too complicated for numerical calculations in general; 
Sretensky has, it is understood, made some calculations more recently for 
a particular law of acceleration, but the results are not available. 
In some early work (2), instead of assuming the steady state as estab- 
lished, I used an alternative method for uniform motion. This may be 
described as finding the disturbance due to an infinitesimal step in the 
motion of the body and then integrating. It was pointed out at the time 
that the method could be applied to motion with variable velocity. It is 
shown now that this method leads directly to expressions equivalent to 
those obtained otherwise by Sretensky. However, the present note deals 
mainly with one particular problem, namely, a circular cylinder submerged 
(Quart. Journ. Mech. and Applied Math., Vol. II, Pt. 3 (1949)] 
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