A Vortex Theory for the Maneuvering Ship 



+ ^0 cos cdt , (6-0 >0) , e = g - ^ , C = ^ - -^ cos ( 



L2q d Lq _ 



o^--^ 



Lw „ Lq c^L 



— = , — = '\ — cos 



u2 u ° u 



/ 77 \ L^q d Lc 



The set of forces has the components 



— I cos OJt 



Z - Z + Z cos 



Pi 



,t + Zp^ cos (a>t + J) . 



(< 



X = X + Xp^ COS ot + Xp^ cos y^ + 2 



}ii = 5n + )rL COS a,t + )n^ cos (wt + ^] . 



Pi P2 \ 2/ 



14.2. The Set of Forces in a Steady Motion 



Using results of par. 8, and substituting r for w'U, we get: 



l.ATr2j2WiL 



Z = ^ pAU 



AL 1,2 



Cm- 1) 



Cx-^T^x^- ^X^xJ^-Cl-t) 



V (6) 



(7) 



^0 - a^ - ^ T ^Lg^ 1 - a IB^ ^ - ^ T ""Lp^ i" ' 



1 . 9 1 2W gL r _-, 



^x + ^f ^X3 + ^T^xJ+-n-t) 



— 1 r ow eL _ 



c.-^^c,,?B-^ic,^?,l.>.. 



2W 



> (8) 



■JW r T n 



14.3. The Set of Forces in a Purely Heaving Motion 

 We have to substitute ^ for e, 



885 



