Examination of the intact stability and the seakeeping behaviour

2 Theory
2.1 Description of the utilised seakeeping simulation method
For the determination of the seakeeping behavior, E4 includes a simulation method developed
by Söding in connection with the investigation of the capsizing accident of the E.L.M.A Tres
in 1987 [5]. The method has been further developed by Kröger [6] and in the scope of several
research projects at the TUHH which led to the actual seakeeping method E4ROLLS. The
following explanations are based on Krüger [7], Kluwe [8] and the investigation reports of
the three accidents [1][2][3] described in chapter 1.1.
The method is capable of simulating the motion of a ship within the time domain. At this all
six degrees of freedom of a ship are described. Further it is possible to enter regular or irregular,
as well as short or long crested seaways. The method is explained briey in the following chapter.
2.1.1 Linear strip method
In the E4 seakeeping method a linear RAO is determined for each of the six degrees of freedom.
The RAOs are calculated by means of a strip method in the frequency domain. Each set of six
RAOs applies for one vessel's speed. Therefore one set of RAOs has to be calculated for each
speed examined.
Four of the degrees of freedom, namely sway, heave, pitch and yaw are calculated linearly using
the respective RAOs. A link to the nonlinear motions is considered. It is assumed, that the
amplitudes of these four motions stay moderate and that the hydrodynamic inuences outweigh
the nonlinearities. Therefore it is adequate to incorporate them linearly. Due to the linearisation
of the sway and yaw motion, the method is not able to describe broaching in following sea, which
often causes high roll motions and implicates an enhanced danger of capsizing. For the same
reason the method overestimates the ship's motions in beam seas at low speeds. This is related
to an underestimation of the drift motion in beam direction.
2.1.1.1 Calculation model
The lightship weight and the deadweight distribution are represented by a cuboid for each analysed
vessel. The cuboid and the ship have equivalent mass moments of inertia. Its height and
width shown in gure 2.1 are governed by the extension of the light-ship and the loading weight.
The cuboid and the hull form are then used to calculate the RAOs.
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