COMPUTATION OF SHALLOW WATER SHIP MOTIONS 
R.F. Beck and E.O. Tuck 
Untverstty of Adelatde 
Adelatde, Australta 
ABSTRACT 
In previous papers by Tuck (Journal of Ship Research, 
1970) and Tuck and Taylor (8th Symposium on Naval 
Hydrodynamics, 1970), a framework was set up for 
a complete theory of ship motions in shallow water, 
in all 6 degrees of freedom. The present paper con- 
tinues this work by presenting actual computed mo- 
tions for a full form hull, both restrained andunre- 
strained, in long waves of various headings. 
i ANT RODUGTION 
In this paper we present computed results and/or discussion 
of motions in all six degrees of freedom of a Series 60, block coef- 
ficient 0.80 ship, at zero speed of advance in shallow water. These 
motions are supposed to be induced by incident plane sinusoidal 
waves of various headings. 
The shallow water theory of Tuck (1970) (see also Tuck and 
Taylor, 1970,and Beck and Tuck, 1971) is used to provide the coeffi- 
cients in the equations of motion. This theory requires that the wave- 
length be much greater than the depth of the water, which restricts 
attention to long waves and low frequencies. Such long waves are im- 
portant for large ships, since they have the greatest potential for mo- 
tions excitation, even though the low frequency assumption rules out 
resonance in heave, pitch or roll. 
In Section 2 we discuss some general analytical features of the 
equations of motion of a ship in shallow water, and consider the re- 
lative importance for each mode of motion in turn of various types of 
inertial, hydrostatic, and hydrodynamic forces. The force balances 
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