Using RAO and Drift coefficients can enable for using simplified systems to account for larger and more complex models. Consider the figure below, the model to the left is the aquacultural concept AquaTraz. This is a comprehensive model and consist of many elements and component groups. As we know, large and complex models will contribute increasing analysis time. Instead, this system could be simplified to a model of just a few elements and apply response amplitudes and drift coefficients. This is illustrated in the left part of the figure below.

Principles of Response Amplitude Operators and Drift coefficients

Displacement and load

RAO are statistics used for determining the probable behaviour of an object at sea. It is widely used in ship design to determine how the ship will behave under influence of current, wind and waves.

AquaSim provides the opportunity to apply response amplitudes on displacement and loads. When a displacement RAO is applied, the ship will translate and rotate (1st order motion) according to amplitudes defined in a table. When a load RAO is applied, the ship will experience forces and moments according to amplitudes defined in a table. The displacement and loads can be induced either as a function of incoming waves or in time.

Drift coefficient

This is a type of response amplitude that account for slowly-drift excitations loads (2nd order motion). Slow-drift excitation loads are forces due to non-linear interaction effects between waves and the ship motions. When a drift RAO is applied, the ship will experience drift forces according to drift coefficients defined in a table.

For an irregular sea state, the drift force is in AquaSim calculated according to this formula:

$${ F_i^{SV}=2 \Bigg( \sum_{j=1}^N A_j (T_{jj}^{ic} )^{1/2} cos(ω_j t+ϵ_j)\Bigg)^2 [N]}$$

where \( F^{SV} \) is the drift force, \( A_j \) is the wave amplitude of the j-th sinusoidal wave and \( \sqrt T \) is the drift coefficient. It is \( \sqrt T \) that is input to the table in AquaSim. For regular waves, the above equation can be simplified to:

$${ F^{SV} = A^2 (\sqrt T)^2 \text{ [N] }}$$

AquaSim models

Following this tutorial is three AquaSim models:

1. RAO-displacement.amodel: demonstration of displacement RAO.
2. RAO-load.amodel: demonstration of load RAO.
3. DRIFT-load.amodel: demonstration of drift coefficients.