A METHOD FOR A MORE PRECISE COMPUTATION OF 
HEAVING AND PITCHING MOTIONS BOTH IN SMOOTH 
WATER AND IN WAVES 
O. Grim 
Hamburg Model Basin (HSVA) 
BACKGROUND 
In the Symposium “On the Behaviour of Ships in a Seaway,” in Wageningen, 1957, a 
paper “Durch Wellen an einem Schiffskorper erregte Krafte” was read by the author, which 
will now be continued. In part II of that paper ideas were deduced which may be considered 
an improvement of the well-known strip method. At that time some simple numerical results 
were given on the basis of this improved strip method although the method was not entirely 
completed. 
In the meantime, some progress.has been made and, in addition, numerical work could 
be done to a much greater extent since an electronic computor is now available. This paper 
gives the results obtained starting from a complete summary of the method which is deemed 
useful since the representation given in 1957 is no longer considered satisfactory. 
The methods which have been applied to the theoretical treatment of the problems of the 
ship waves may be crudely subdivided into two groups, viz., (a) methods of singularities and 
(b) strip methods. The methods mentioned under (a) have as a basis a representation of the 
ship body by periodical singularities [3,4,5]. They enable us in an elegant manner to con- 
sider certain important parameters within an expression for the velocity potential and then to 
examine the influence of these parameters. The weak point of these methods consists in the 
loose connection between the motion and the shape of the ship on the one hand and the dis- 
tribution of the singularities on the other hand. As a consequence the condition on the sur- 
face of the body is hardly sufficiently satisfied. Therefore, these methods can only be ex- 
pected to give qualitative information as to the influence of the main parameters and not 
quantitative results as to the influence of the shape of the ship. 
The methods mentioned under (b), viz., strip methods [6], assume solutions to be known 
for corresponding problems on two-dimensional bodies of which the sections coincide with 
the sections of the ship body. The results for the three-dimensional body will then be ob- 
tained by adding those obtained from the two-dimensional bodies. It must be considered an 
advantage of these methods that one can start from relatively accurate results and that the 
influence of the shape of the sections can be allowed for. The well-known strip method, 
however, has several disadvantages, e.g., that the influence of the three-dimensional flow 
can scarcely be taken into account and that the influence of the speed of the ship cannot be 
established exactly. 
AQQ 
