CRUISING AND HOVERING RESPONSE OF 

 A TAIL-STABILIZED SUBMERSIBLE 



A. Strumpf 



Davidson Laboratory 



Stevens Institute of Technology 



Hoboken, New Jersey 



ABSTRACT 



Equations of motion are used as a basis for analyzing the inherent dy- 

 namic stability and limit maneuver response of a tail-stabilized sub- 

 mersible in cruising and hovering vertical plane motions. It is shown 

 that this type of vessel can perform adequately in cruising, but is sub- 

 ject to highly coupled, unstable hovering motion, especially in stern-to- 

 bow ocean currents. The stability of a submersible with both bow and 

 stern stabilizers, having fore-aft symmetry, also is treated. This lat- 

 ter type of design has inherent hovering stability, and its symnnetry 

 would have a salutory effect on the coupled motions of the vessel. 



NOMENCLATURE 



The basic nomenclature is adapted from SNAME Technical and Research 

 Bulletin No. 1-5. Three different right-handed rectangular coordinate frames 

 are used: 



1. Body axes (x,y, z) with origin at the center of buoyancy (CB) 



2. An inertial frame (xo.yg.Zo) fixed in the earth 



3. Fluid axes (x^yp Zf ) which move with a constant velocity U^ relative to 



(xo.yo.Zg) 



A sketch of the axes systems and the positive directions of the various angles, 

 velocities, and forces is shown. 



Hydrodynamic forces in the x, y, and z directions are designated by X, Y, Z 

 and moments by K, M, and N. Velocity components u, v, and w of the CB are 

 measured relative to the fluid axes in directions of the x, y, and z axes, re- 

 spectively. Angular velocity components of body axes are designated by p, q, 

 and r. Velocity components upv^.w^ of the fluid current relative to earth are 

 measured in the directions of the x^.y^z^ axes, respectively, which are always 

 parallel to the x^.y^.z,, axes. 



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