Sohveihev 3 Bentkowsky and Kerr 



buoyancy at the initial operating depth of the problem. 

 Thus 



Wn = Wn + \ Wn dt n= 1,2,3,4,5 



Wn = ^no **■ ^-^^^ ■*■ ) ^n ^* n=6,7 



The term 2j^\i which is used in the vehicle equations matrix is 

 given by 



Location of the center of gravity is given by 



"" w, +2w,i 



„ ,X2W^_tiaW3 

 y G v« 



Wo+Zy^ti 



Z^n(W„ - W„ J 



Wo +ZWti 







Zft=Zfi + ?:^ ; n= 1,2,3,4,5 



Dynamic Forces 



The hydrodynamic forces arise because of the motion of the 

 body with respect to the water and are defined in terms of hydro- 

 dynamic force coefficients. The hydrodynamic force and moment 

 coefficients used in this report are not the standard non-dimensional 

 coefficients used in most studies. It has been found that a set of 

 dimensional coefficients provides a much easier nomenclature. The 

 force and moment coefficients are represented by subscripted capital 

 letters of the form Xgbc.o The letter denotes the direction of the 

 force (X for forces along the x-body axis, Y along the y-body axis, 

 and Z along the z-body axis) or the axis about which the moment 

 results (L , M and N for moment coefficients describing the mo- 

 ments about the x, y, and z body axes respectively). 



The subscripts vary in number and form and denote the 

 variable quantities that the coefficient must be multiplied by to 

 obtain a force or moment on the body. For example, Xuiui is the 

 dimensional axial drag coefficient since when multiplied by u |u| 

 the square of the axial velocity, u. It results In an axial force 



1122 



