Sahre-iberj Bentkowsky and Kerr 



p + tan 9(q sin <^ + r cos 

 q cos <^ - r sin <^ 

 _^(r cos (^ + q sin 4) /cos 9 



High Angle of Attack Considerations 



The second major difference between the DSRV simulation 

 and the conventional method Is required because of the high angles 

 of attack experienced during the hovering and docking maneuvers. 

 This high angle of attack problem becomes accentuated by the vehicle 

 which, by using Its thrusters , Is capable of turning without forward 

 way, a maneuver entirely outside the scope of those covered by 

 conventional analysis. These shortcomings of the conventional 

 analysis were overcome by a technique used during development of 

 LMSC'sDEEP QUEST research submersible where the hydrodynamlc 

 forces on the body and appendages (In this case the shroud ring) are 

 considered separately. This allows for adequate representation of 

 stall characteristics of the shroud ring as a function of the local 

 angle of attack at the shroud ring which Is essentially Impossible to 

 account for when a total coefficient for the body- ring combination Is 

 used In the simulation. The coefficients of the body Itself are handled 

 through addition of a normal drag components to the standard small 

 angle of attack representation of forces. These high angle of attack 

 considerations will be discussed further In the following sections. 



The equations of linear motion are derived from the funda- 

 mental equation 



external 



^(^s) 



(1) 



stating that the sum of the external forces acting on a rigid body of 

 mass m, equals the tim e ra te of change of the momentum of the 

 body. The momentum, rnVg, Is a vector quantity and_ Vq Is the 

 inertial velocity of the center of mass. Expressing Vg In termis of 

 the velocities and rates about the vehicle fixed axis system described 

 earlier 



Vr = 



'u + qZG - rYe + Xq 



V + rXQ - pZg + Yq 



Lw + pYg - qXg + Z^ 



1116 



