THE APPROXIMATE CALCULATION OF WAVE RESISTANCE AT HIGH SPEED 55 
The midship section area is 0-4306 sq. ft., so the source strengths are the 
numbers in Table 4 multiplied by -4306v/47, with v in ft./sec. For the depths of 
the sources, those in the upper row range between -094 ft. and 1-43 ft., while in 
the lower row they range from -3 ft. to -32 ft. Instead of using all these depths, 
giving separate exponential factors for the terms in the formule, we shall use 
a mean depth for each row. It is obvious from the construction that the mean 
depth in each case is the depth of the centroid of the corresponding half of the 
midship section ; these depths are -107 ft. and -302 ft. respectively. For the 
horizontal positions of the sources we carry out the calculations required 
by (11); with x measured forward from the midship section, we obtain, with 
Xo eimtites 
x (upper) : 6-218, — 4-869, — 2-806, 2:782, 4-804, 6-157 
x (lower) : — 5-16, — 2:635, 2:778, 5°586. 
Since the model is not symmetrical fore and aft, we have to consider both 
sine and cosine series in (5). The expressions for J and J can now be written 
down ; each of them contains ten terms, but we simplify them further for 
approximate computation. We group the terms in pairs for corresponding com- 
partments fore and aft of the midship section. For instance, in the upper 
row we have the pairs. 
-183 sin (2-782 g) + -110 sin (2-806 q) in J, 
and 
-183 cos (2:782 q) — :110 cos (2-806 q) in J, 
where we have written q for (g/v?) cosh u. We replace these by -293 sin (2-794 q) 
and -073 cos (2:794 q) respectively, the difference so made being unimportant. 
Making a similar change for all the pairs of terms, we find that the cosine 
terms are small compared with the sine terms ; further, their contributions to 
the resistance integral are proportional to their squares, and we propose to 
neglect the cosine terms. It has, however, been verified by approximate calcu- 
lation at one or two speeds that the cosine terms would not add more than 
about one per cent. to the resistance. Finally, we are left with 
T=e 107P {.293 sin (2:794 g) + -299 sin (4:83 q) 
+. -624 sin (6-187 q)} 
+e 302P {.271 sin (2:706 g) + -513 sin (5-373 q)} Bg 6 CG) 
where p = (g/v?) cosh? u, g = (g/v*) cosh u. 
With (16) and (4), the wave resistance has been calculated for six speeds 
ranging from f= :352 to f= :749. The results are shown in the dotted curve 
of Fig. 4 as values of R/b?v?, where 25 = beam. The experimental curve has 
been obtained in the usual way, the residuary resistance being the actual measured 
resistance less the skin friction calculated from the wetted surface at rest and 
the appropriate Froude coefficient. The difference between experimental and 
calculated values is much the same as for the previous cases. The falling off in 
calculated value at very high speeds is rather more than usual ; this may be due 
in part to the approximation, but most of it could be accounted for by the 
effect of sinkage and trim. 
Model B. The body plan and other data are shown in Fig. 3. This model 
has the same displacement, length and beam as Model A, but has greater 
draught. 
With the same sections as before, the corresponding source distribution 
is shown in Table 7. 
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