Vehicle Dynamics Associated with Submarine Rescue 



^ulul^l^l = Fx drag* Similarly, Muiu|w|u| Is the pitching moment 

 used by the normal velocity, w. The use of absolute values In these 

 coefficients provide for the proper signs on the force and moments, 

 and because of most of the near fore-aft symmetry of the DSRV 

 less the shroud, the coefficients are Independent of the direction of 

 various velocity components. The direction of the normal force 

 Zwlul"w|u| Is dependent only on the direction of the normal velocity 

 regardless of whether the vehicle Is going forward (u > 0) or back- 

 ward (u < 0). Since the sign of Zv^iui Is negative the normal force 

 due to normal velocity Is always In the opposite direction of the 

 normal velocity. A brief description of the development of the 

 representation of hydrodynamlc forces on the body follows. First 

 consider the forces on the axlsymmetrlc bare body of the DSRV and 

 then add forces resulting from asymmetries, such as the transfer 

 skirt and splitter plate. The representation of lift, acceleration 

 and axial drag forces on an axlsymmetrlc bare body Is relatively 

 well known and can be obtained from slender body theory, Ref, 2, 

 other potential flow analysis, Ref. 3, or test data and is of the form 



EXT lift, acceleration, axial drag 



Y;v+Y^r +YHu|r|u| +Yvmv|u| 

 _Z^w + Zqq + Zqiui q|u| + Zy,|u|w|u| 



These lift, accelerating and axial drag forces are those normally 

 used to simulate the dynamics of submarines and provide a very 

 adequate representation of the forces and moments at low angles-of- 

 attack (a < 15°). At high angles -of-attack, however, they become 

 Inadequate, For example Zyy|u|w|u| , the only force resulting from 

 normal velocity, w, goes to as u goes to 0, while a vehicle 

 normal to the flow experiences a significant normal force. This 

 normal force Is due primarily to flow separation and Is, excluding 

 Reynolds number effects proportional to the normal velocity squared 

 w^. Wind tunnel and water tunnel tests on the Polaris, Poseidon, 

 DEEP QUEST, and other vehicles have shown that a reasonably 

 good representation of the forces and moments due to normal 

 velocity can be obtained by using the two terms Zy^y w j u | + Zy^|^w|w| 

 where Zy^iy^i Is ineasured force at u = {(p - 90°) divided by the 

 normal velocity squared and Z^^i^i Is the slope of the force versus 

 angle of attack curve. Pitching (yawing) of the vessel will cause a 

 variation In normal velocity along the vessel and therefore a variation 

 in this normal drag over the body. It remains then to develop a 

 method to account for the distribution of this local normal drag 

 caused by pitching and yawing. The use of a strip theory method 

 provides that the normal force due to normal drag can be expressed 

 as Zfjormol drag= J ^wlwl'^'lw'l dx where Z^,^, Is the local value of 

 the normcil force coefficient and w' Is the local normal velocity and 

 can be expressed as w' = w + qX where X is the distance between 



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