Drifting Force on a Ship among Waves. 473 
calculations the amplitudes in (16) are those of the forced oscillations of 
heave and pitch ; hence we attempt only a comparison with the results 
of Kent and Cutland for the 490 ft. wave-length, when presumably the 
motions are purely forced vibrations. Another reason for limiting 
comparison to waves of length greater than the ship is that the expressions 
for the buoyancy and pitching moment are probably better approxima- 
tions than for shorter waves. Without attempting any close approxima- 
tion to the form of the ship, we shall simply use the expressions (20) and 
(21) with 
a=140 ft.; 1=60 ft.; d=20 ft.; 
6=27-5 ft.; h=2-5 ft.; A=2n/e=490ft., . . . (22) 
these dimensions giving a ship of about the same displacement, and 
waves of 490 ft. in length and 5 ft. in height. 
With these values (20) and (21) give 
B=345 cos of; P=—83880sin of, . . . . (93) 
in tons, and ft.-tons respectively. 
The numerical factors in (23) are the values of By and P, in (16). The 
amplitudes €, and 0) we shall take from the observed results, assuming 
that these refer to forced vibrations in the period of encounter. The 
remaining factors are the phase differences, and these are more uncertain. 
Tt may be noted that the effect which is under discussion arises from the 
damping and the phase lag produced thereby ; if there is no phase lag 
there is no force. On the simple theory expressed in equations (11) 
and (12) the phase factor, sin or sin B’, has its maximum value of unity 
at resonance and diminishes on either side of this period, the diminution 
being more rapid the less the damping. The importance of the phase 
of the ship’s motion in relation to that of the waves from a practical 
point of view is well known, but there are not many precise measurements 
suitable for the present purpose. The problem was attacked in an early 
paper by Kent (1922), and the recent paper by Kent and Cutland (1941) 
gives further detailed observations. They give a diagram showing 
positions of wave crest and trough along the ship at maximum pitch 
with the bow down, and from this one should be able to deduce the value 
of 8’ for use in (16). However, it must be remembered that the model 
was not a simple symmetrical form, with the axis of pitch at the centre 
of the water-plane section ; in fact, the position of this axis probably 
varied during the motion. It is also clear that the motion is not ade- 
quately covered by the theory of equations (11) and (12). For the 
authors state: “In general, as the ship’s pitching period was not 
isochronous owing to the changing resistance to pitch, successive pitches 
