## Thursday, 15 May 2014

### In a nutshell: Cummins

W.E. Cummins (1962), The Impulse Response Function and Ship Motions, Schiffstechnik

This paper derives the equation of motion that is most commonly used to model the dynamics of a body in water, including ships and wave energy converters (WECs). The part of the mathematical argument essential to WECs will be summarised here.

The paper starts off with an interesting bit of history. Up until the 1950s, classical' sea-keeping research only modelled sinusoidal waves and response. The models had the form of second order differential equations. In the 1950s there was growing interest in investigating response to spectra. Initially, they kept the form of the second order differential equations, and expressed the hydrodynamic added mass and damping as frequency dependent parameters. To run such a time domain model, it would be necessary to choose the frequency' at which added mass and damping were to be considered. There was growing disquiet about the rigor of this approach, not to mention the fact that the models did not describe experiments very well. As Cummins muses in this paper "The shoe is squeezed on, with no regard for the shape of the foot". He goes on to derive a better fitting model.