Linearized Potential Flow Theory for ACVs in a Seaway 



tion of the lower boundary of the cushion on the undisturbed water 

 surface and over the steady position of the longitudinal planes of the 

 hulls below the load water plane. Some of the expressions also inclu- 

 de a line integral along the load waterline of the hulls. These expres- 

 sions may appear very complicated, but they could be progressively 

 simplified when the air cushion has longitudinal symmetry (as well 

 as lateral symmetry, which is implied throughout this analysis) and 

 when the cushion pressure is taken to be strictly uniform throughout 

 the cushion (as is commonly assumed) or when the pressure is diffu- 

 sed to zero at the boundaries along the front and the rear and parti- 

 cularly for a rectangular cushion. The surface integrals over the 

 hull can be expressed in closed form when the hulls are mathemati- 

 cally defined and, particularly, when they are "polynomial simple 

 ships". However, with the advent of present-day high speed compu- 

 ters the solution from a general table of off- sets need not present 

 any serious problems. 



The steady motion of an ACV in calm water is discussed in 

 Section 6. Expressions have been derived for the sinkage and trim, 

 for the wave resistance in longitudinal motion and for the side force 

 on a drifting amphibious ACV. As may be expected, the expression 

 for the wave resistance combines with exact agreement the well-known 

 Michell integral for the wave resistance of a thin ship and the result 

 for a surface pressure distribution given by Havelock *$) . In addition 

 we have derived for the first time two additional terms denoting res- 

 pectively the interference of the air cushion on the side hulls and that 

 of the side hulls on the air cushion. 



The above expressions involve the steady potential for motion 

 in calm water derived in Appendix V. The potential for the motion of 

 the side hulls is given in the form of an integral representation, but 

 the potential of the air cushion is given by an integral equation in the 

 form of a source distribution on the free surface of water directly 

 below the cushion opening in its steady position and a distribution of 

 line sources and line doublets oriented longitudinally along the boun- 

 daries at the front and the rear of strength equal respectively to the 

 "jump" in the velocity and "jump" in the potential itself across the 

 boundaries. The line distribution may however be ignored in the case 

 of a diffused cushion. We have also, in addition, a distribution of 

 doublets oriented laterally along the longitudinal planes of the two side 

 hulls with strength equal to the "jump" in the potential across the 

 planes. Pending a rigorous solution the resulting integral equation 

 (if possible at all), the surface integral over the longitudinal planes 

 may be ignored if the immersion of the hulls is considered to be small 



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