THE APPROXIMATE CALCULATION OF WAVE 
RESISTANCE AT HIGH SPEED 
By T. H. HAvELock, F.R.S. 
SYNOPSIS.—The main purpose of the paper is to explore the possibility of 
applying the present theory of wave resistance to models whose lines are not 
given by mathematical equations. A brief survey of the wave theory is given and 
this leads to a sub-division of the ship and the corresponding source distribu- 
tion ; the determination of the latter is based on sectional areas and local pris- 
matic coefficients. For low speeds a large number of divisions is necessary for 
reasonable approximation and the calculations become too laborious, but results 
have been obtained for speeds higher than a Froude number »/(v/gL) of about 0-4. 
These approximations are applied first to experimental models with mathematical 
lines, and the results compared with those calculated from the usual integrals 
and with the measured resistances. Finally the method is applied to two models 
with non-mathematical lines, the necessary data being obtained from the plans 
and the results compared with measured resistances. 
Introduction 
ile IN recent years the comparison of calculated and measured wave 
resistance has been the subject of much research and considerable 
success has been achieved ; but the work has necessarily been limited 
to relatively simple forms of model whose lines can be expressed by 
mathematical equations. The chief desideratum at the present stage would 
seem to be an extension of this comparison to a wider range of types and 
to more normal forms of model ; this would, no doubt, disclose defic- 
iencies in the present theory of wave resistance but would provide a 
basis for further development and improvement. These considerations 
suggest an examination of the application of the present theory to models 
with non-mathematical lines, with a view to seeing whether the diffi- 
culties of the calculations can be avoided by approximations giving 
reasonable accuracy and consistency, even if only over some limited 
range of speed. The present paper is the record of an attempt to make 
such calculations ; whether the particular method prove useful or not, 
it is hoped that the general statement will stimulate interest in the problem 
and lead to further investigation, both experimental and mathematical. 
From one point of view the problem is quite simple. If we assume the 
well-known integral expressions for wave resistance (4, 6), the matter is one 
of approximate integration over the ship’s surface. The main difficulty arises 
from the double computation ; intermediate integrals have to be evaluated 
not only for a sufficient number of stations on the ship but also for a sufficient 
number of values of a parameter so that the final resistance integral may be 
computed. The labour involved has prevented any direct calculation on these 
lines. It is proposed here to examine the problem differently by returning to 
first principles of the theory of wave resistance, beginning with the simplest 
possible expressions and trying to find how far it is necessary to go before we 
get results of sufficient accuracy. 
2. We consider a ship moving steadily through the water, and we neglect 
meantime any effects due to fluid friction. The motion of the water must 
satisfy the laws of fluid dynamics, together with the necessary conditions at the 
surface of the ship and at the free surface of the water. Although the problem 
can be stated thus precisely, and formulated in mathematical terms, it has 
not been possible to obtain an exact solution for even the simplest form of 
floating body ; we have therefore to approximate to a solution by successive 
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