413 Waves produced by the Rolling of a Ship. 
from exceptional resistance due to bilge keels; it has been remarked, 
for instance, that no reasonable values of head resistance and skin friction 
coefficient account for more than one-third of the actual decrement 
obtained by experiment, and in one case such a calculation gave only 
one-seventeenth of it (Baker, 1914). Nevertheless, no attempt appears 
to have been made to compute the wave resistance to rolling from the 
characteristics of the ship. 
7. We shall now compare wave heights calculated from (16) with 
various cases to which Froude’s energy method has been applied. 
In the case examined in Froude’s first paper already quoted, the data 
are T=8 sec. ; 0)—5-65°. The draught of the ship was not stated, but 
we may assume D=15 ft. With these values, (16) gives h=1-2 inch. 
Froude’s estimate from energy dissipation was a wave height of 1} inch. 
Other writers who have used the same formula assume that that part of the 
resisting couple which is proportional to the angular velocity of rolling 
may be attributed to the loss of energy in surface-waves. Thus 
Sir W. White (1895), for the rolling of H.M.S.‘ Revenge’ without bilge 
keels, deduced a wave height of about 1}inch. In this case T=15-5 sec. ; 
6)=13° ; D=27 ft. ; and these give from (16) a wave height of just over 
1 inch. 
L. Spears (1898), from the rolling of U.S.S. ‘ Oregon,’ deduced a wave 
height of 0-62 inch. Here T=15-2 sec. ; 0)=12°; D=23 ft.; and (16) 
gives a wave height of 0-67 inch. 
It should be remarked that in all these cases Froude’s formula was used ; 
according to the argument given in § 6 and expressed in equation (18), 
these estimates of wave height should be increased by a factor V2. 
A final example is taken from a recent paper by G. S. Baker (1939) 
on the rolling of ships under way. We take the data for model R 8(a), 
for rolling at zero speed ahead, given in Tables 1 and 3 of the paper ; 
in the notation already used 
W=10,150 ton; m=4-4 ft.; T=11-52 sec. ; 
A=680 ft. ; E4004. D=23:2 4. < a=0-022. 
In this case we shall use equation (18) to see what height of waves would 
suffice to account for the whole of the dissipation of energy, neglecting 
for the moment any due to friction or eddy making. With the given 
values we find from (18), A=2A—2-65 inch. Again, using the values 
of D and T in (16), we find h=1-58 inch. 
It should be noted that (16) was derived by regarding the ship as a thin 
plank. The formula could be modified in an empirical manner to take 
into account the displaced volume and the inertia coefficient of the ship ; 
this might be represented by multiplying (16) by a factor whose probable 
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