Practical Ship Hydrodynamics

Figure 6.9 Velocities induced by point dipole
xx D 5 x1x 4
r 2
xy D 5 x1y C 21y Ð ⊲ m/4 r 3 ⊳
r 2
xz D 5 x1z C 21z Ð ⊲ m/4 r 3 ⊳
r 2
yy D 5 y1y 3
r 2
yz D 5 z1y
r 2
xx D 5 x1x 4
r 2
Boundary element methods 227
The expressions for the dipole can be derived formally by differentiation of
the corresponding source expression in x. Therefore usually source subroutines
(also for distributed panels) are used with a corresponding redefinition
of variables in the parameter list of the call. This avoids double programming.
Dipoles like vortices can be used (rather equivalently) to generate lift
in flows.
6.4.2 Thiart element
The ship including the rudder can be considered as a vertical foil of considerable
thickness and extremely short span. For a steady yaw angle, i.e. a
typical manoeuvring application, one would certainly enforce a Kutta condition
at the trailing edge, either employing vortex or dipole elements. For
harmonic motions in waves, i.e. a typical seakeeping problem, one should