RESISTANCE OF A SUBMERGED CYLINDER 425 
For the second part of the resistance we include second-order terms: 
from (18) and (28) we have 
Ry = —Tp@*y + 27pa*y(1—a?/4f2)—2mpygtatdB,/ at. (36) 
From (31) and (33), this leads to 
R, = mpa’yp, 
with p = 1—(4+32h6)(a2/f2), 
b= | (—3-+16Bv2)v? Be-88"* dy, (37) 
0 
Numerical computations have been made for the integrals in (35) and 
(37). The quantities A and B depend only upon the acceleration, while 
the instantaneous value of the velocity enters through 8. The integrals 
were calculated for two different accelerations, and for about a dozen 
values of 8 in each case—ranging from + to 40. For small values of B it 
was necessary to go as far as v = 4-0 or further, but subdivisions of 0-1 
for v were usually sufficient. For large values of B the necessary range 
for v was less, but subdivisions of 0-02 had to be taken, especially for the 
larger values of k. For various reasons it was difficult to obtain any high 
degree of accuracy in the final results; but it is considered that the 
calculations are sufficient to show the general character of the effect of 
acceleration upon the resistance. 
8. Some of the results are shown in the curves of resistance. These 
curves show the resistance for a particular value of the ratio of the radius 
of the cylinder to the depth of its centre, namely the value given by 
a*/f? = 0-1. We have chosen to graph the curves on a base of velocity c, 
or yt, the abscissae being c/(gf)?. This was partly so as to bring into the 
diagram the wave resistance curve for uniform velocity; this curve is 
shown as R, in the diagram. 
Taking the resistance R, first, the curve A, shows its value for k2 = 97/2, 
or for y/g = 0-1418; while the curve B, is for k2 = 7/2, or for y/g = 1-276. 
The effect of greater acceleration is shown in the lower maximum wave 
resistance and the higher velocity at which it occurs compared with the 
curve £, for uniform velocity. It should be noted that if we had graphed 
the curves on a time base, the abscissae for curve B, would be reduced 
to one-ninth compared with those for A,. 
We turn now to the resistance R,, which is of greater interest. In 
general, the relative magnitudes of R, and R, depend upon the two ratios 
y/g and a/f. In the diagram, the curve A, shows the resistanee R, for the 
case y/g = 0-1418, and a2/f? = 0-1; the total resistance in that case is 
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