Wave Resistance: Some Cases of Unsymmetrical Forms. 237 
5. For comparison we require a solid of revolution of which the front end 
is a sharp point of finite angle while the rear end is cut away to a point of zero 
angle ; there will, of course, be a point of inflection in the curve of the rear 
portion. 
This is obtained by taking the source distribution to be 
f(h) = ah (21 — h) (314 bP; — 31< a <2. (11) 
The equivalent doublet distribution over the same range is 
(hk) = — 4 a (20 — hy (31 -+ hy. (12) 
The outline of the model was found by the graphical methods described in 
§ 2; the work is not reproduced here as it was only carried out with sufficient 
accuracy to verify that the curve was of the required type. A similar curve Is 
shown later in fig. 1. The model has now a length 51, and it is not symmetrical 
fore and aft of the maximum cross-section. 
From (4) we find the wave resistance 
ar | 2. 
R = }8zg!pa%e-® | (I2 + J2) sec® ger Calersee# dg, (13) 
0 
where 
21 
Ter | (21 — h)2 (31 + A)% eishlecosd dh, (14) 
31 
Evaluating (14) and substituting in (13), the terms can be collected in the 
same form as in (10); if we write, with 2b as the maximum breadth of the 
model, 
a@—abe/l25I, p—dgl/ce, B= 2f/5I, (15) 
we obtain ultimately 
272 em/2 .- 3 
R = 220zgeb la: Ab Ua | | eos & + us cos? ¢ + $32 oss d+ ge00 cos’ ¢ 
Pp 0 Pp p 19 
1 9 128 1200 . 
= @ ( cos” 6 — —— cost fd + cos® ) sin ( sec d) 
P $ iy ¢ > ¢ psec ¢ 
—6 (FF cos® fd — 328 cos! éd + tape cos’ 4) cos (p sec #)| Enh odd. 
19 12 
(16) 
We may now compare (10) and (16) as regards the matter under discussion. 
We imagine the resistance graphed as a function of the velocity, and we com- 
pare the relative magnitude of the oscillations superposed upon the mean 
curve. The terms in (10) and (16) which give rise to these oscillations are the 
244 
