Practical Ship Hydrodynamics

Ship seakeeping 121
between near field and far field. In principle methods with overlapping
regions also appear possible.
4.4.2 Strip method
This section presents the most important formulae for a linear frequencydomain
strip method for slender ships in elementary waves. The formulae will
be given without derivation. For a more extensive coverage of the theoretical
background, the reader is referred to Newman (1978).
Two coordinate systems are used:
ž The ship-fixed system x, y, z, with axes pointing from amidships forward,
to starboard and downwards. In this system, the ship’s centre of gravity is
time independent xg, yg, zg.
ž The inertial system , , . This system follows the steady forward motion of
the ship with speed V and coincides in the time average with the ship-fixed
system.
The main purpose of the strip method is to compute the ship’s rigid-body
motions, i.e. the three translations of the origin of ship-fixed system in the ,
, direction and the three rotations around these axes. We denote, (Fig. 4.15):
u1 surge u4 roll
u2 sway u5 pitch
u3 heave u6 yaw
u 4
u 2
u 6
Figure 4.15 Six degrees of freedom for motions
u 3
u 5
The motions are combined in a six-component vector Eu. The forces and
moments acting on the ship are similarly combined in a six-component vector
EF. Eu and EF are harmonic functions of time t oscillating with encounter
frequency ωe:
EF D Re⊲ O EFe iωet ⊳Eu D Re⊲ O Eue iωet ⊳
u 1