THE FORCES ON A SUBMERGED BODY MOVING UNDER WAVES 
this arises because when account is taken of the speed, 
the pressure distribution on the solid is altered and is 
no longer symmetrical fore and aft. 
The general character of the results in (11) can be 
shown best by diagrams, and for this purpose we take 
the case of a fairly long spheroid for which we assume 
the approximate values e = 1, kj = 0, k2 = k’ 1. Figs. 
4, 5, and 6 show curves of the coefficients of heaving 
force, pitching moment, and yawing moment for the 
0-8 
O4 
1e) 60 8090100 120 140 160 180 
Fic. 4.—HEAVING FORCE COEFFICIENT FOR A/L = 0-5, 1:0, 1-5; 
AT ZERO SPEED, -——— AT SPEED f = 0:5 
waves at any angle to the direction of advance. In each 
case the results are shown for three different ratios 
of A/L. The continuous curves are for zero speed; and, 
in order to bring out the difference, the dotted curves 
are for a speed of advance given by the Froude number 
jf =0-5. Thecurves give some indication of the manner 
in which these quantities depend upon the ratio A/L, 
upon the speed and direction of attack, and upon 
whether the waves are from ahead or from astern. 
“Oi 8090100 120 140 160 180 
° 20 40° 60 
Fic. 5.—PITCHING MOMENT COEFFICIENT FOR A/L = 0:5, 1:0, 2-0; 
AT ZERO SPEED, -——— AT SPEED f = 0-5 
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5° 
-0-4 1 
° 20 40 60 
8090 100 120 
140 160 180 
Fic. 6.—YAWING MOMENT COEFFICIENT FOR A/L = 0:5, 1:0, 2:0; 
AT ZERO SPEED, -——— AT SPEED f = 0:5 
