1910. ] The Wave-making Resistance of Shaps. 207 
obtained by Froude’s method from tank experiments on a model of the ship ; 
no details of the calculation are given. Although the estimate above is only 
approximate, another possible factor should be noted; this is the influence of 
the finite depth of the tank. It has been stated that, from recorded experi- 
mental data, this effect becomes appreciable when the length of the waves 
exceeds twice the depth; this means approximately when c>1-9h/L, 4 being 
the depth of water and L the length of the model. This appears to agree 
with the curves of fig. 11 of my previous paper, which were obtained from 
theoretical considerations. The effect of shallow water is an excessive 
increase in the resistance for a considerable range, but if the speed is made 
high enough the resistance may become even less than in deep water at the 
same speed. It seems possible that the tank experiments quoted above come 
within the range of excess of transverse wave-making resistance. It is stated 
that, assuming a propulsive coefficient of 60 per cent., the value of 946 means 
a corresponding indicated horse-power of 1576; it may be noted that the 
estimate of 880 corresponds to the same indicated horse-power with an efficiency 
of about 56 per cent. In this connection the following remark may be quoted 
from a recent discussion: “Is it possible that this is one contributing cause 
to the large propulsive coefficients obtained by torpedo craft compared with 
those obtained in full-sized vessels, viz., that the tank effective horse-power of 
torpedo craft models is over-rated, because of excessive transverse wave- 
making resistance in the ‘shoal water’ of the tank ” ?* 
6. It must be noted that all the preceding calculations refer to rather full- 
ended models, that is, with a cylindrical coefficient of about 0°68 and 
upwards. It was upon such a type that the original experiments of Froude 
were performed, and it seems that the characteristic interference effects occur 
specially in such vessels ; the latter are associated with the idea of two fairly 
distinct systems of pressure disturbance at bow and stern respectively. Now 
if the ends are made finer it is reasonable to imagine the two systems 
coalescing into what could be more accurately interpreted as one pressure 
system. This would be more diffused over the length of the ship, so the 
equivalent index m should be larger; further, since for constant displace- 
ment finer ends mean larger beam and draft, the limiting coefficient 6 should 
be larger. Consequently, for decreasing cylindrical coefficient, at constant 
displacement, the curves of residuary resistance should be intersecting curves, 
lower at low speeds and then ultimately higher. This is illustrated in the 
curves in fig. 4, which have been superposed to show the point in question. 
The curves are taken from a series of 1000-lb. models by D. W. Taylor, of 
* E. Wilding, ‘Trans. Inst. Nav. Arch.,’ 1909, vol. 51, p. 160. 
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