Linearized Potential Flow Theory for ACVs in a Seaway 



uncoupled if x . = . 



When we set the parameter 8 denoting the thickness of the 

 side hulls equal to zero and also the water plane area A equal to ze- 

 ro we get the results for an amphibious ACV which are discussed in 

 great detail in Section 9 of Reference 1. 



Having calculated the oscillatory displacements and thereby 

 the accelerations in the threee modes we can estimate the ride com- 

 fort in waves by combining these accelerations in the appropriate 

 forms at various locations in the ACV. 



The higher order displacements can also be derived by consi- 

 dering the higher order forces and moment. 



The response functions in surge pitch and heave can be com- 

 puted for a specific ACV configuration and motion predictions in an 

 irregular seaway can be made by the use of spectral analysis within 

 the limits of the theory of linear superposition. 



IX . DISCUSSION AND CONCLUSIONS 



The assumptions underlying this theoretical investigation of 

 the motions of an ACV in a seaway and some of the results obtained 

 here have been discussed in the Introduction and Summary. Attention 

 is confined in this study to coplanar motion in the longitudinal plane 

 with freedom in surge, pitch and heave only. Results for the amphi- 

 bious ACV free from water contact can be obtained from the general 

 results by setting the hull parameter 6=0 and omitting the surface 

 integral over the longitudinal plane of the hull and the line integral 

 over the waterline occurring in the integral representation for the 

 potential due to the air cushion. These results can then be applied 

 equally well for beamwise motion in the lateral direction as the 

 beam/length ration is generally of the order of unity and the distur- 

 bance of the water due to longitudinal, drifting or purely lateral mo- 

 tion will be of the same order. Obviously, this does not apply to an 

 ACV with immersed side hulls. 



The primary results are contained in the horizontal and ver- 

 tical forces and for the pitching moment derived at the end of Sec- 

 tion 5. As may be expected, the lowest order forces and moment 

 are purely of inertial and hydrostatic nature. The hydrodynamic 

 pressure of the water does enter in the higher order and it is possi- 

 ble to calculate the added mass and damping of water, the mean in- 

 creased resistance due to forced oscillation in calm water and due 



165 



