ON A CONSISTENT LINEARIZED THEORY OF THE WAVE-MAKING RESISTANCE OF SHIPS

There are few discussions on the uniqueness in the theory of the wave- making resistance of ships. Moreover, a line integral term, singularit y distribution around a periphery of the waterplane area, appearing in the theory casts a shadow on the uniqueness of the boundary-value pro blem. There is only one well-known consistent theory, that is, the two -dimensional theory of planing on the water surface in which a line in tegral term does not appear explicitly. In this theory, the sinkage an d trim vary with speed and also the wetted length changes to fulfill K utta's condition. However, in a usual displacement ship, having a near ly vertical stem, the wetted length could not vary as in the planing s hip. In the present paper, introducing a new singularity just before t he bow, we try to obtain a consistent linearized theory for a displace ment ship. We solve numerically the boundary value problem, investigat ing the properties of solutions and then calculate the sinkage and tri m when a barge is running freely or is being towed without any externa l force or moment except a towing force. Then, it is found that this f ree-running barge becomes unstable over the speed Fr = 0.61 regardless of the bottom shape. The resistance consists of three components, nam ely, the wave-making, the spray, and the water head resistance. The fo rmer two components are well known and the last one is a component int roduced and named so here temporarily. This component resembles a wave -breaking resistance but we have no direct explanation.