Chain: Added mass

The line type wizard sets up the added mass coefficients $\Ca$ for a chain as follows.

When a line is accelerated in water it requires an impulse in excess of that needed to achieve the same acceleration in air, due to the extra force required to displace the water in the vicinity of the submerged part of the line. This is represented by the added mass term, which is proportional to the volume of displaced fluid $V$ \begin{equation} \text{Added mass} = \Ca\ \rho\ V \end{equation} where $\rho$ is the density of water.

The parts of a line displacing the fluid are said to attract added mass. For asymmetrical bodies the parts attracting added mass will differ in different directions, so we consider the normal and axial directions separately.

For a circular cylinder in flow normal to its axis, the added mass coefficient $\C{an}$ takes the value 1.

The situation for a chain is more complicated as, for flow normal to a link, parts of the link are shielded from the flow but there is also some entrapped water within each edge-on link. An accurate calculation is highly problematic, and seems unlikely to give a value for the normal added mass coefficient very different to 1.0. Hence we assume, for the normal coefficient \begin{equation} \C{an} = 1.0 \end{equation} For the axial added mass coefficient, we refer to Bureau Veritas NR 493, Classification of Mooring Systems for Permanent Offshore Units, section 3, table 2, and take \begin{equation} \C{aa} = 0.5 \end{equation}