Linearized Potential Flow Theory for ACVs in a Seaway 



cannot be ignored by simply setting the parameter representing the 

 width of the hulls equal to zero, for although the wave -making effects 

 of the hulls are thereby eliminated, they nevertheless provide a ver- 

 tical barrier for the fluid flow. However, on the assumption that the 

 immersion of the side hulls is of a small order (say, of the same 

 order as their width) the integral over the longitudinal planes of the 

 hulls can be ignored and if the cushion pressure is also assumed to 

 be diffused in such a manner that it is zero at the front and rear of 

 the cushion where air leakage occurs, it is possible to obtain a simple 

 integral representation for the potential. This procedure enables 

 practical results to be derived pending a rigorous solution of the in- 

 tegral equation. 



The problem is first formulated in the most general terms in 

 Section 2, just to show how impossible it is to obtain a general solu- 

 tion. If the problem is difficult to solve in the case of displacement 

 ships, it will certainly be more so in the case of ACVs, where the 

 laws of cushion aerodynamics relating to ground effect enter with an 

 extremely complicated relationship between the pressure distribution 

 and the relative distance between a point on the hemline of the flexi- 

 ble skirts at the bow and stern and the elevation of the water surface 

 directly below. 



It is therefore clear that the problem has to be linearized in 

 a suitable manner if its solution is to be rendered mathematically 

 tractable . The usual method of solution in problems of this nature 

 is the assumption of a basic slenderness parameter representing geo- 

 metrical restrictions on the body. Thus, for example, in "thin ship" 

 theory, the slenderness parameter is the beam/length ratio which is 

 assumed to tend to zero. Similarly, in "flat ship" theory it is the 

 draught/length ratio and in "slender body" theory both the beam and 

 the draught are assumed to be small compared with the length. These 

 restrictions are necessary for the validity of the linearized theory 

 which assumes that the ship reduces to a thin vertical or horizontal 

 disc or a thin straight line and that it can then have a translatory mo- 

 tion with finite velocity parallel to the plane of the disc or along the 

 longitudinal axis without creating waves of finite amplitude. The squa- 

 res of the perturbation velocities of the water particles can then be 

 neglected and the problem becomes linear. This then is the objective, 

 namely, that the wave making of the vessel in steady motion shall be 

 negligible. In the case of an amphibious ACV, it would appear that 

 the geometrical dimensions are not directly relevant to the problem 

 so long as the craft is not immersed in the water. It is the cushion 

 pressure, i. e. the total weight of the craft divided by the cushion 



105 



