THE FORWARD SPEED DIFFRACTION PROBLEM

This paper examines the theory and computational methods behind predic ting the linear unsteady motion of a ship with steady forward speed in waves. The focus is on the wave exciting force impulse-response funct ion as computed via the transient free-surface Green function. The lin ear equation of motion for a ship in waves was first written in a rati onal form. using the concept of the impulse-response function, by Cumm ins (1962). Some years later King et al (1988) added the corresponding wave exciting force in its appropriate convolution form. We extend th is work by clarifying the definition of the impulsive incident wave in following seas. and show it to be easily computable. Continuing trunc ated calculations towards infinite time becomes especially important i n following waves, and the method suggested by Bingham et al (1994) is employed here. A novel filtering scheme is also introduced to prevent short wave contamination of the solution. These developments allow ca lculations in following waves to be presented for the first time using this approach. The integral equation formulation of the linear seakee ping problem is reviewed in some detail. and the relevant equations de rived. Transient Haskind relations for bodies with forward speed are a lso derived although, like their frequency-domain counterparts, these are only approximate. Computed, first-order exciting forces and respon se-amplitude operators for real ship geometries, in head and following seas, are presented that demonstrate the usefulness of the transient approach for the diffraction problem.