Linearized Votential Flow Theory for ACVs in a Seaway 



APPENDIX II 



PRESSURE FORCES AND MOMENTS ON THE CUSHION HULL 



The force due to the action of the surface pressure on the 

 cushion hull is form (5-1) 



7/ - 4 



F p = ■•//// i ■ ...l 



where S is the instantaneous position of the IFS and n is the unit 

 normal drawn out of the water surface and into the lower boundary 

 of the cushion. 



The equation of the IFS is given by 



f(x,y) - z = 



so that the outward drawn normal is 



y A y A A 



A s x i + s y i - k 



n = 



[l+tf + fy 2 J 1/2 



and 



dsV-[l + tf + fy 2 ] l/2 dxdy 



where the negative sign has been used on the right-hand side since 

 dS is an element of the cushion hull positive on the upper side of the 

 free surface, whereas in our co-ordinate system the element of area 

 dxdy is positive along the z-direction which is vertically downwards. 



We therefore have 



A A A A v 



ndS = ; -( f.i + f j - k) dxdy 



and ^ is given on the IFS by Bernoulli's equation (1-8) with o = 



P„ (x, y;t) 



r ^[v v vi (V * )2 ] 



+ -s- 



pg 



z =f 



where the potential has the value on z = T, i. e. with the argument 

 (x, y, f ) but may be continued analytically from the surface to the 



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