Once you have specified the hull geometry, the hull mass distribution, the roll damping and the environment conditions, you may proceed with the analysis.

There are various options to control the exact formulation and solution of the strip theory problem. At present it is possible to specify the following options:

Transom terms

According to the underlying strip theory formulation, corrections should be applied to vessels with transom sterns. These corrections have the effect of increasing the heave and pitch damping and thus reducing the maximum response of the vessel. The transom terms also depend on the vessel speed and are greater at high forward speed.

It is possible that the inclusion of transom terms may over predict the damping, particularly for vessels with large transoms at high speeds. It is suggested that for this type of vessel, results be compared for calculations with and without transom terms and that the user use their judgement as to which results are the most plausible.

Added resistance

Three alternative methods are provided for the calculation of added resistance. The different methods will give different results and again the user must use their judgement as to which are the most likely. Added resistance calculations are second order with respect to wave amplitude and are based on the calculated motions. This means that if motions are calculated with an accuracy of approximately 10–15%, the accuracy of the added resistance calculation will be no better than 20–30% (Salvesen 1978).

The method by Salvesen is purported to be more accurate than those of Gerritsma and Beukelman for a wider range of hull shapes; whilst Gerritsma and Beukelman have found their method to be satisfactory for fast cargo ship hull forms (Salvesen 1978).

The Salvesen method is based on calculating the second-order longitudinal wave force acting on the vessel. Theoretically, this method may also be applied to oblique waves.

The two methods by Gerritsma and Beukelman are very similar and are based on estimating the energy radiated by the vessel including the effect of the relative vertical velocity between the vessel and wave. Method I uses encounter frequency in the wave term whereas Method II uses wave frequency. Method II is mathematically rigorous, however, in some cases, Method I has been found to give better results. Strictly speaking, both of these methods apply to head seas only.

The interested user is directed to the original papers: Gerritsma and Beukelman (1967, 1972) and Salvesen (1978) for full details of the methods.

The methods are only applicable to head seas and are calculated only from the heave and pitch motions.

The added resistance calculated is due only to the motion of the vessel in the waves. It does not account for speed loss due to wind; reduction of propeller efficiency or voluntary speed loss in order to reduce motions.

Wave force

Two alternative methods for calculating the wave excitation may be used in Seakeeper:

Head seas approximation: here a simplifying assumption that the vessel is operating in head seas is used, this speeds up the calculations to some degree. This method is exactly valid in head seas and can be applied with reasonable accuracy up to approximately 20° either side of head seas; i.e. 160° < m < 200°

The arbitrary wave heading method does not make this assumption but is somewhat more computationally intensive. This method should be used for off-head seas calculations.

After the hull has been measured, or at the beginning of the seakeeping analysis, if the hull has not been previously measured, the conformal mappings which are used to approximate the vessel's sections should be computed.

Note:

If you are unfamiliar with the principles and limitations of conformal mapping, or you have an unusual design, then it is a good idea to check the mapped section thoroughly before continuing with the rest of the analysis.

Also see: Measure Hull and Higher order conformal mappings on page 12.

The mapped sections are used to compute the section hydrodynamic properties. For unusual hull forms, it is advisable to check that the mapped sections are an adequate representation of the hull before proceeding with the more time consuming response and seakeeping calculations. Typical mappings are shown below:

Note that, in general, due to the limitations of the conformal mapping technique, the mapped sections will not be an exact match to the actual hull sections. However, these mapped sections are only used to estimate the hydrodynamic properties of the hull and, in most cases, these will be calculated with sufficient accuracy for the strip theory analysis.

The main limitations of the conformal mapping method are:

§   The mappings always cross the axes at 90°.

§   The sections are continuous (chines will be rounded off).

§   There are limitations in the range of section breadth to draught ratio and sectional area coefficients that can be accurately mapped.

Also see Limitations and Guidelines and in particular Asymmetrical sections on page 41.

Once you are satisfied with the mapped sections, you may proceed with calculating the vessel's response; select Solve Seakeeping Analysis from the Analysis menu.