CONCLUSIONS AND RECOKMENDATIONS 



The forces end raoraent acting on a submersible moving beneath the free sur- 

 face or near a well with a pitch angle for the bare hull or a control surface 

 deflection have been computed using potential flow theory. There is good 

 agreement between calculation and experiment for the bare hull when the ratio of 

 submergence depth to the diameter is larger than 1 and the pitch angle is zero. 



For the control planes alone, the good agreement between calculation and 



i 

 experiment is achieved when the ratio of submergence depth to chord Is small. 



When this ratio is large, the force due to viscosity is dominant and the present 



method generally computes forces larger than those of experiment. 



From the present study, the following conclusions may be drawn: 



1. The numerical evaluation of the Green function needs to be improved 

 when the ratio of submergence depth to diameter is smaller than 1.0. 

 Near the free surface, the Green function has oscillatory behavior and 

 the exponential function decays slowly. 



2. For nonzero angle of attack, there is a ctoss flow or vortex shedding* 

 The effect of cross flow or vortex shedding should be included in the 

 computation with the help of viscous flow analysis. 



3. When the ratio of submergence depth to the mean chord of a control 

 plane is large, the lift is dominated by the contribution of viscosity. 

 The viscous effect on the lift should be incorporated in the future 

 computation. 



4. To improve the results of potential theory, an empirical or analytical 

 approach should be developed with inclusion of viscous effect. 



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