INTRODUCTION 



There is a need to develop an analytical method to co&pute the forces and 



moments acting on a submersible when it is beneath the tree surface or near a 



wall. The methodologies presently available to compute these hydrodynaalc 



forces and raoraents are Halted in application. Pond * computed the nioaenta 



developed on a Rankine ovoid by using the method of axial distribution of 



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 sources and sinks. McCreight improved the csethod used by Pond by distributing 



the dipolea and cosaputed the vertical force. Their results are in good agreement 



with the experimental data. However, the methods used by Pond and McCreight are 



valid only for zero pitch angle. 



The present method computes the vertical and longitudinal forces and pitch 



moment acting on a submersible with and without control planes when the 



submersible eoves beneath the free surface or near a wall. This method Is more 



accurate taathesatically than that of Pond . Furthermore, the effect of pitch 



nngle is incorporated in the computation. For the computation of fcrces and 



saoEent acting on the bare hull, the so-called panel method is applied. The body 



surface is discretlzed with teany quadrilateral planes, and sources and sinks are 



distributed on these surface elements. Tnis method can be applied to a 



submerged body of arbitrary shape. To conpute the forces and raoment of the 



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 control planes, the set hod developed by Giesing and Smith is used. 



Two-dimensional sources and sinks are distributed around the sections of a 



control plane, and a vortex located in the middle of each section is introduced 



to compute lift fotce. The inlet velocity to the control planes is computed at 



the tips of the sections of the control plane to include the interaction effort 



between the bare hull and control planes. 



'References are given on page 45. 



