Linearized Potential Flow Theory for ACVs in a Seaway 



hull 



[*< 



+ Q") sec 3 d6 (6-30) 



where 



•c + 1Q o= II 



2 

 exp (-k z' sec 6 + ik x' sec0) dx'dz 

 o o 



which is the familiar Michell integral for the steady state wave resist- 

 ance of a single hull. The constant 2 is usually given as 4 in Michell' s 

 formula, but we have taken h to be the total width of the hull and 

 not the semi -width. 



We will now consider the wave resistance of the air cushion 



1 



R 



cushion 



l[[\7 p o p o - Vp o*oioo (x ' y ' o) 



J J L X XX . 



% 



dxdy 



where the potential is given by (6-21). This is an integral equation 

 and attempts are being made to solve this, but we can obtain a sim- 

 ple integral representation for the potential of the form 



0100 4wpg JJ 



(*.n) 



*ninn = AT7^/| J| G (x, y, z; £ , t, , o) d SdT? 



if we make the following assumptions. 



(i) The pressure in the cushion is diffused in such a manner 

 that it becomes zero at the front and rear boundaries where the 

 plenum air escape with air entrainment from the atmosphere and the 

 generation of trapped vortices will probably ensure that this is so in 

 practice. If this assumption is valid, the "jumps" in the potential and 

 in the longitudinal velocity of the water particles will vanish and the 

 line integral in (6-21) may be ignored. 



(ii) Although a discontinuity in the potential may be assumed 

 not to exist at the front and rear boundaries, a discontinuity will cer- 

 tainly be present across the vertical barriers imposed by the side 

 hulls as there is no air escape across these boundaries to alleviate 

 a discontinuity of the pressure. However, if the depth of immersion 

 of the side hulls is small and of the same order, say, as that of the 

 hull width, the surface integral over S will be of ( 8 ) higher 



o 



153 



