Sahreiber , Bentkowsky and Kerr 



keeping in mind the fact that it will be programmed on a digital 

 and/or analog computer and several simplifying assumptions were 

 made to allow for mechanization of the resultant equations. As in 

 any simulation a trade-off must be made between the accuracy of 

 representation of forces and moments, the ability to mechanize 

 certain types of expressions, and the availability of data. 



The presences of the transfer skirt and splitter plate add 

 additional coefficients to the body because of the asymmetries they 

 provide. A complete set of these terms due to asymmetries were 

 developed, their numerical values determined, and their relative 

 importance established, with the reduction in the number of ternns 

 in the simulation as an end goal. It was determined that additional 

 terms of the form Xqv,qw, Xpyrv, Xp^r^, Xqqq^, Xrprp, Ypp, Yp^^pw, 

 Yqpqp, Yy|„|v|w|, Zppp2, Zprpr, ZyyU^, Z^yrv, Z^^r^ , and Zuiuiu|u| 

 would be required for adequate simulation of the dynamics of the 

 DSRV during the hovering maneuvers. 



The addition of forces due to the shroud, Fghroud » propeller, 



Fprop» thrusters , Ffhr > and the interaction forces during mating. 



djst 



, complete the force equations. 



A similar line of development was used for determination of 

 a set of moment equations. Values for most of the coefficients were 

 obtained from model tests conducted at NSRDC (Ref. 4) and Hydro- 

 nautlcs (Ref. 5), and theoretical values were computed for the re- 

 maining coefficients. A complete set of equations of motion used for 

 the DSRV Model for Analysis (Ref. 6) follow along with numerical 

 values of the hydrodynamlc coefficients , Table 2, 



Surge ; 

 m[ u + qw - rv - XQ(q^ + r^) + yG(pq - r) + Zq^P^ "•* ^^3 



= Xi,u + Xqy/iw + Xpvrv + Xuiui uiu| + Xrrr + X^^^q + X^prp 

 - (Wo +2 ^ti - ^) sin e + Xghroud ^ Xp.^p + Xthr + ^6\^\ 



Sway; 

 m[ V + ru - pw - ye(r + p ) + Z6(qr - p) + XQ(qp + r) ] 

 = Y;v + Y^r + Yf,p + YhuI r|u| + Yp^pw + Yppqp 

 + Y^l^iv|wi +Yp|u|p|u| +Yviuiv|u| + 



1126 



