Forces on an A.C.V. Executing an Unsteady Motion 



V. FORCES ON A YAWING ACV 



V. 1. The Potential 



We now consider the special case of an ACV travelling for 

 a long time in the longitudinal or x direction. The craft is either 

 fixed in a steady yaw position, or it starts a yawing motion after 

 initial transients have died away. We may therefore use Eq. (21) for 

 the potential, and drop the second term which will approach zero as 



t — + OO 



V. 2. The Forces 



The wave resistance is defined by Eq. (24), and the side for. 

 ce by 



S(t) = // P S ( { ,y,t) j- d£ dy (45) 



S 

 Thus the side force is the positive force to port (the y direction) 

 required to hold the craft on a straight course. 



The analysis for the two forces now continues, as in the 

 case for rectilinear unyawed motion in horizontally unrestricted wa- 

 ter. The forces are : 

 t 

 R 



S 4^7g-/ dT Jj P(*,y,t)dsjjp(x" f y',r)dS' j dw'jdu(^) 



OS S' -oo -°o 



• sin {7 (t - t)\ • expji(w(x -x' + s(t) - s(t ) + u(y - y')) \ . 



7 



And after some simplification : 



R__ 

 S " 2 



"0 "o -oo 



-2— / dr/ dw / du ( W )» 7 • sin| 7 (t - T )(* 



I I J u < 46 > 



[0 -oo 

 (QP'-PQ'). cosjw(s(t) - s(t))} +(PP i +QQ')* sin{w(s(t) - s( t))\ 



in which 



P = P (w, u, t) , 

 Q = Q (w,u, t) , 

 P' = P (w,u,t) 



53 



