Doctors 



I. INTRODUCTION 

 I, 1. Background 



Havelock (1909, 1914 and 1926) was the first to study the 

 theoretical problem of the wave resistance of a pressure distribu- 

 tion. His interest lay in a desire to represent the disturbance from 

 a ship. As a result, the pressure distributions that he chose to ana- 

 lyze were very smooth and were not typical of the pressure under- 

 neath an air-cushion vehicle (ACV). However, later on, Havelock 

 (1932) derived the general expression for a pressure distribution 

 travelling at a constant speed of advance. In this paper, he also 

 showed that, under the assumption of a small disturbance, the action 

 of the pressure was equivalent to a source distribution on the undis- 

 turbed free surface. The relation was : 



c JLP (1) 



P g dx 



where o and p are the source intensity and pressure at the same 

 point, c is the velocity in the x direction, p is the density of the 

 fluid and g is the acceleration due to gravity. 



Lunde (1951a) extended the theoretical treatment to include 

 the case of an arbitrary distribution moving over finite depth. Nume- 

 rical calculations which are directly applicable to the ACV have been 

 carried out by other workers. For example, Newman and Poole 

 (1962) considered the two cases of a constant pressure acting over a 

 rectangular area, and over an elliptical area. The most striking 

 feature of their results is the very strong interaction between the 

 bow and stern wave systems. The resistance curves displayed a se- 

 ries of humps and hollows - particularly for the rectangular distri- 

 bution (where the interaction would be greater). A hump is produced 

 when the bow and stern wave systems are in phase and combine to 

 give a trailing wave of a maximum height. A hollow occurs when the 

 two wave systems are out of phase by half a wavelength so that the 

 combined amplitude is a minimum. 



The interference effects are found to be stronger for large 

 beam to length ratios, as would be expected from this argument, 

 since the wave motion becomes more nearly two-dimensional. The 

 humps are found to occur at Froude numbers given approximately by 



= 1 / \(2n - 1)tt for n = 1, 2, 



3, 



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