Computing Hearing and Pitching Motions 511 
Resistance 
Since the deformation of the longitudinal wave has been determined one could try to 
compute the mean force generated by the wave in direction of the negative x-axis, i.e., the 
resistance WV. However, it is necessary to simplify the distribution of the pressure for this 
purpose. 
(52) G6" 2, Uy - pUp- 20-92 
For the free moving ship body (see sketch) the contour of the surface of the wave is 
given by (51) relative to a line fixed in space and by (52) relative to a zero-line moving 
with the ship. An element of the ship body of length dx, bounded by two sections, displaces 
the volume: 
V = [BT6 + B(Ge*”* - 2,0, - yU, - z, - Yx)] dx. (53) 
The simplifications now are introduced, when computing the resistance, that the magni- 
tude of the buoyancy force equals SV and that its direction is perpendicular to the contour 
of the surface of the wave. These assumptions lead to the following formula for the force 
in the direction of the negative x-axis: 
pe 5 J [BT 6+ B(Ge*”*- 2,U,,- WU, ~ z,-x)] d(Ge*”*- z,U,-yU,). (54) 
Only the time mean value of this force is of interest, viz., 
y= — P dt: (55) 
The first member in (54), viz., BBT does not contribute to this mean value. The re- 
mainder may be written as the following sum: 
W= HtoW, 
We ee sface, = We) pAGGers cos z Uy - rm) 
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