136 MOMENT ON A SUBMERGED SOLID OF REVOLUTION 
For G, we should work out the next approximation for the velocity 
potential, as in the case of the spheroid; but this does not seem feasible 
for the given solid. Meantime, as already indicated, we shall take (26) as 
giving a sufficient approximation and thus we assume 
a0 
Gy = —4gpb*(1-+-b?/h?) | {1—cos(2k,)h sec 0) eof sec"? sec39 dO. (30) 
0 
Computation of the total moment G can be made from the integrals in 
voice ] 
0:5 
G/rgpbi(1+8/h’) 
1-0 
03 c/v(2gl) 04 
(29) and (30) either by direct quadrature or by asymptotic expansions 
suitable for large values of the parameter 2x )h. To show the nature of the 
results calculations have been made for an ovoid with h = 10b, giving a 
length-beam ratio of about 10-5. Two depths of immersion were taken, and 
the results are shown in the figure with values of G/mgpb4(1-+-b?/h?) graphed 
on a base of Froude number c/,/(2gl). Curve A is for f = 2-5), and curve B 
for f = 5b. Curve A shows the typical oscillations at low speeds due to 
interference between bow and stern waves; these would no doubt be 
damped by viscous effects in an actual liquid. For curve B at greater 
depth these oscillations are too small to be shown on the scale of the 
diagram. 
REFERENCES 
1. T. H. Havetocr, Proc. Roy. Soc. A, 122 (1928), 392. 
2. ibid. A, 138 (1932), 340. 
3. H. Lams, Hydrodynamics, 6th ed. (Cambridge, 1932), p. 141. 
4. E. W. Hosson, Spherical and Ellipsoidal Harmonics (Cambridge, 1931), p. 416. 
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