Resistance of a Ship among Waves 307 
disturbed water surface and that it is driven forward horizontally at constant 
speed. 
In experiments on models in waves, such as those made by Kent at The 
National Physical Laboratory (Kent 1922), the conditions are different, 
being naturally designed to reproduce to some extent conditions for ships 
at sea. In these experiments the model is free to pitch, and obviously an 
important factor is the relation of the pitching period to the period of 
encounter with the waves. Moreover, the model can move fore and aft 
within certain limits under the influence of the waves. Thus Kent makes the 
statement: “‘ When the model was towed through aregular series of advancing 
waves, it experienced periodic fluctuations in its resistance as it met each 
succeeding wave. Hach fluctuation in resistance was partially absorbed by 
the inertia of the model, but a portion of it was recorded by the resistance 
pen. The fluctuations were of small amplitude when the waves were of short 
length in comparison with the length of the model, but became much larger 
when the wave-length was increased.” The actual results given were for a 
certain mean resistance over the whole experiment in each case. The precise 
relation between this mean resistance and the horizontal forces acting on the 
model at each instant would require a detailed examination of the conditions 
of the experiment and of the recording apparatus. However that may be, 
the present calculations serve to estimate some of these forces and indicate 
how large the fluctuating part of the resistance due to them may be under 
certain conditions. 
A point which arises is the dependence of the amplitude of the fluctuations 
upon the ratio of the wave-length to the length of the model. This is given, 
for the model considered here, by the factor of (25) which involves «l. Taking 
the simpler case of that model with no parallel middle body, that is with 
a = 0), the factor concerned is 
(sin u—u cos u)/u3, (28) 
where uw = 7L/A, with L the total length of the model, and A the wave- 
length. 
An interesting result is that there are certain values of the ratio A/Z for 
which (28) is zero; for these, the additional resultant horizontal force due 
to the waves is zero independently of the position of the model among the 
waves. For this particular model, these values are given by the roots of the 
equation tan u = u; the corresponding values of A/L are 0-7, 0-41, 0-29, .... 
Intermediate values of the ratio give maximum values for the amplitude of 
the fluctuations in resistance. 
437 
