Strip Theory

Theoretical Manual of
Strip Theory Program
“SEAWAY for Windows”
J.M.J. Journée and L.J.M. Adegeest
Report 1370

TU DELFT

September 2003

Ship Hydromechanics Laboratory
Delft University of Technology

AMARCON

Advanced Maritime Consulting
www.amarcon.com

Theoretical Manual of “SEAWAY for Windows”
J.M.J. Journée and L.J.M. Adegeest

2

TUD Report No. 1370
Revision:14-12-2003

Theoretical Manual of “SEAWAY for Windows”
J.M.J. Journée and L.J.M. Adegeest

TUD Report No. 1370
Revision: 14-12-2003

Summary
This report aims to be a guide and help for those people who want to study the theoretical
backgrounds and the algorithms of a ship motions computer code based on the strip theory.
The underlying report describes in detail the theoretical backgroundsand algorithms used by
the first author during the development of his six-degrees-of-freedom ship motions computer
code, called SEAWAY.
The six ship motions of and about the centre of gravity G of the vessel have been defined in
the next figure.

Definition of ship motions
According to Newton’s second law, the equations of motion for six degrees of freedom of an
oscillating ship in waves ina earth-bounded axes system have to be written as follows:

∑ {M
6

j =1

ij

⋅ &&i } = sum of all forces or moments in direction i
x

for: i = 1,...6

Because a linear system has been considered here, the forces and moments in the right hand
side of these equations consist of a superposition of:
• so-called hydromechanic forces and moments, caused by a harmonic oscillation of therigid body in the undisturbed surface of a fluid being previously at rest, and
• so-called exciting wave forces and moments on the restrained body, caused by the
incoming harmonic waves.
With this, the system of a with six degrees of freedom moving ship in waves can considered to
be a linear mass-damper-spring system with frequency-dependent coefficients and linear
exciting forces andmoments:

∑ {(M
6

j =1

ij

&
+ aij ) ⋅ &&i + bij ⋅ x i + cij ⋅ xi } = Fi
x

for: i = 1,...6

3

Theoretical Manual of “SEAWAY for Windows”
J.M.J. Journée and L.J.M. Adegeest

TUD Report No. 1370
Revision: 14-12-2003

In here, x i with indices i = 1,2,3 are the displacements of G (surge, sway and heave) and x i
with indices i = 4,5,6 are the rotations about the axes through G(roll, pitch and yaw). The
indices ij present at motion i the coupling with motion j .
The masses in the equations of motion above consist of solid masses or solid mass moments
of inertia of the ship ( M ij ) and “added” masses or “added” mass moments of inertia caused
by the disturbed water, the hydrodynamic masses or mass moments of inertia (a ij ). An
oscillating ship generates waves itself too; energy will be radiated from the ship. The
&
hydrodynamic damping-terms ( bij ⋅ x i ) account for this. For the heave, roll and pitch motions,
hydrostatic spring-terms ( c ij ⋅ x i ) have to be added. The right hand sides of the equations of
motion consist of exciting wave forces and moments ( Fi ).
In the so-called strip theory, the ship will be divided in 20 tot 30 cross sections, ofwhich the
two-dimensional hydromechanic coefficients and exciting wave loads will be calculated. To
obtain the three-dimensional values, these values will be integrated over the ship length
numerically. Finally, the differential equations will be solved to obtain the motions. These
calculations will be performed in the frequency domain.
It was in 1949 that Ursell published his potentialtheory for determining the hydrodynamic
coefficients of semicircular cross sections, oscillating in deep water in the frequency domain.
Using this, for the first time a rough estimation could be made of the motions of a ship in
regular waves at zero forward speed.
Shortly after that Tasai, Grim, Gerritsma and many other scientists used various already
existing conformal mapping techniques (to...