Roll damping is ususally not linearly depending on the roll amplitude. However, when using potential strip theory calculation, only a linear roll damping coefficient can be used. One solution is thus to solve this iteratively for a given wave amplitude. Another solution is to use an equivalent linear roll damping coefficient calculated at reference amplitude. It is thus important to choose wisely the reference roll amplitude as the obtained response will only be valid at that amplitude. In most cases, the chosen reference amplitude is the roll criteria for operations such that the operational limit can be derived exactly. Finally, systematic linear calculations can also be used in combination with a post processing method depending on the sea condition. This method is presented further on.
Pre-processing
This preliminary part is done outside of RAOViewer using frequency domain tools and empirical roll damping formulations.
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| LaTeX Math Block |
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B_{44}(x_a) = B_L + B_Q \frac{16}{3} \frac{\phi_a}{T} = 2 \left( p+q \phi_a \right) \frac{a_x}{T} |
with:
| linear roll damping coefficient |
| quadratic roll damping coefficient |
| roll amplitude |
| roll period |
| roll decay offset |
| roll decay slope |
| added mass |
| roll amplitude |
Finally, the RAO of motion are computed for all the conditions and all the roll damping values. Each RAO is labeled with the roll amplitude used for the linearisation.
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