56 THE APPROXIMATE CALCULATION OF WAVE RESISTANCE AT HIGH SPEED 
The midship section are is 0-4671 sq. ft., and the depths of the centroids 
of the upper and lower portions are 0-113 ft. and 0-334 ft. respectively. For the 
horizontal distances, in ft. we obtain 
x (upper) : 6-11, — 4-89, 3-09, 2-71, 4-763, 6:11 
x (lower) : — 4:6, — 3-53, 2-42, 5-355 
Comparing with the scheme for Model A, we see that there is a greater 
degree of dissymmetry between the positive and negative distributions ; this 
makes the calculations more troublesome, as we cannot neglect the cosine 
terms altogether. Grouping the terms in pairs as before, we neglect the cosine 
terms for the lower row of sources as unimportant, and we obtain 
T= e 113? { .314 sin (2-9 q) + -38 sin (4-826 q) + -515 sin (6-11 q)} 
+ e— 334? {.4 sin (2:975 q) + -391 sin (4:978 q)}, 
J=e, 113p {:164 cos (2:9 gq) — -027 cos (4-826 q) 
= 37/7 GoS@Ul™ so « so 9 6 » WD 
The resistances have been calculated from (17) and (4) ; it was found that 
in this case the cosine terms add about six per cent. to the final values. The 
calculated and experimental curves are shown in Fig. 4 ; the calculated values 
are in general rather higher than might have been anticipated. For both these 
models, the calculated values at the lower speeds could probably be improved 
by a more suitable subdivision and more detailed computation. 
General Remarks 
11. A few notes may be added on matters left over for further investigation. 
Beam. In addition to subdivision in length and depth, we might also take 
longitudinal sections ; for instance, suppose we take a section through the 
median vertical plane. Then instead of a distribution of sources in one plane, 
we have a space distribution which could be specified and located by the 
same methods ; and expressions for the wave resistance could be obtained from 
the general formule. The effect might be examined theoretically in some simple 
case ; but if is only likely to be of importance at low speeds where several 
other factors also affect the results. 
Viscous Effects. One effect of viscosity is that the frictional belt round 
the ship makes the run and stern less effective in wave-making. This can be 
represented, somewhat empirically, by a reduction factor for the after part of the 
ship. This reduction factor, if obtained from comparison between calculated 
and measured resistances, will include other effects of viscosity than that just 
mentioned ; in fact, it will also probably include in some cases effects for 
non-viscous.flow which have been left out of account meantime—for instance, 
what might be called a screening effect of the bow for models with broad beam. 
However that may be, any empirical factor could be used in the present scheme 
by making the necessary reduction in the numerical magnitudes of the negative 
sources for the after part ; this would mean including the cosine series in the 
formule ; otherwise the calculations would be the same. At sufficiently 
low speeds, if we assume that—for one reason or another—the stern contri- 
butes little to the wave-making, then the same number of sections as were 
necessary for the whole length of the ship might, if concentrated over the effective 
length of the bow, give a sufficiently fine subdivision for approximate calculation. 
Location of Sections. Probably the best method of locating the transverse 
sections would be one which was to some extent related to the type of model ; 
there are some indications to that effect in the present work. For convenience 
in a first survey the sections have been taken at fixed stations, both thé strengths 
of the sources and their positions varying from model to model. Another 
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