Results: Roll damping

The roll damping sheet of the results tables gives the following results for each body.

Percentage of critical

For each wave period or frequency, the ratio of total roll damping (radiation damping and external damping) to the critical damping coefficient for roll motion \begin{equation} \frac{B_{44} + D_{44} + E}{ 2 \sqrt{\left(M_{44} + A_{44}\right) \left(K_{44} + \Kext_{44}\right)} } \end{equation} where

$B_{44}$ is the roll-roll element of the radiation damping matrix

$D_{44}$ is the roll-roll element of the body external damping matrix

$E$ is the extra roll damping, if any, needed to meet a user-specified target percentage

$M_{44}$ is the roll-roll element of the body inertia matrix

$A_{44}$ is the roll-roll element of the added mass matrix

$K_{44}$ is the roll-roll element of the hydrostatic stiffness matrix

$\Kext_{44}$ is the roll-roll element of the external stiffness matrix

The above matrices are all transformed to the centre of mass for the purpose of this calculation.

Extra roll damping

The additional roll damping, $E$, which must be included in order to meet a specified target percentage of critical.