The following section describes some of the limitations inherent in the strip theory method and those which are specific to Seakeeper.

The basic principle behind strip theory is that the hydrodynamic properties of a vessel (that is added mass, damping and stiffness) may be predicted by dividing the vessel into a series of two-dimensional transverse strips, for which these properties may be computed. The global hydrodynamic values for the complete hull are then computed by integrating the two-dimensional values of the strips over the length of the ship. The interested reader is directed to the paper by Salvesen et al. (1970) for a full description of strip theory.

Linear strip theory assumes the vessel’s motions are linear and harmonic, in which case the response of the vessel in both pitch and heave, for a given wave frequency and speed, will be proportional to the wave amplitude.

Lloyd (1989) states that linear strip theory makes the following additional assumptions:

§   The fluid is inviscid – viscous damping is ignored, (In fact the damping factor which the user enters for roll should include viscous roll damping, which is the primary source of damping for roll.)

§   The ship is slender (i.e. the length is much greater than the beam or the draft, and the beam is much less than the wave length).

§   The hull is rigid so that no flexure of the structure occurs.

§   The speed is moderate so there is no appreciable planing lift.

§   The motions are small (or at least linear with wave amplitude).

§   The ship hull sections are wall-sided.

§   The water depth is much greater than the wave length so that deep water wave approximations may be applied.

§   The presence of the hull has no effect on the waves (Froude-Krilov hypothesis.)

In addition, the principle of superposition is used to compute the response of the vessel to irregular waves. Simply, this means that the contributions to the motions of the individual regular waves making up the irregular sea spectrum may be summed to obtain the total response of the vessel to the irregular seas.

Boyd (1995) outlines possible causes of non-linear behaviour, or effects that may cause strip theory to become inaccurate, such as:

§   Emergence or submergence of the bow or stern.

§   Flare (non-wall sidedness) of the hull at the waterplane.

§   Submergence of the bow or stern overhangs in a vessel.

§   Three dimensional flow effects and flow interaction in a longitudinal direction along the hull including dynamic lift at speed.

§   Increasing importance of wave diffraction, wave radiation and the Kelvin wave pattern at speed.

At present, Seakeeper is based upon linear theory, however, in the future, it is intended to include options to account for some of the geometric non-linearities mentioned above.

Whilst not being able to actually represent asymmetrical hulls in the hydrodynamic model, Seakeeper can approximate asymmetric hulls by correctly measuring the sections’ cross-sectional area and waterline beam. This is shown for the asymmetric catamaran demihull below. Here the asymmetrical hull sections are shown in black and the mapped symmetrical sections are shown in red.

See Calculation of Mapped Sections on page 23 for information on mapping sections.

Generally strip theory is applied to vessels operating at low to moderate Froude number. However, experience has shown that reasonable predictions may be made for Froude numbers approaching 0.8, provided that the vessel is quite slender. It should also be remembered that dynamic vertical forces due to forward speed are not included, hence Seakeeper is likely to over-estimate the motions of planing vessels operating in the planing regime.

At present Seakeeper uses strip theory to predict vertical plane motions. The roll motion is simply estimated assuming a damped spring/mass system. The computations have been found to be most reliable from head seas (180deg.) to bow-quartering seas (135, 215deg.). For these calculations, the head seas approximation for the wave excitation force and moment is normally sufficiently accurate. As the wave heading moves more to beam seas, the arbitrary wave heading method should be used to calculate the wave excitation. However, due to the lack of available data, this formulation has not been rigorously tested.

Strip theory calculations for following seas are less accurate, since the motions become much less linear. Calculations made with Seakeeper (or any frequency domain, strip theory program) for these conditions, should be treated with caution and, if possible, validated by other means.

Because of the non-unique mapping of encounter frequency to wave frequency in following waves (i.e. in some cases it is possible to get the same encounter frequency from three different wave frequencies) MSI calculations in following seas are unreliable.