A Vortex Theory for the Maneuvering Ship 



Let Cv •, c, and c„ be the characteristic coefficients of the plane fitted 



B Lp nig *• 



to the body. 



The absolute set of forces due to the plane, referred to the axis attached to 

 the body, is 



Y3 = , 



(S)^, 



1 + 2 (^1 + 2 1^1 ^ r^\ c (1 + ...) , 



1 



.-oUM 1 + 2 



-B - - 2 ^'"B^ 1^ ^ ^ \u/., " " vu j., -b[ ^Lg/^;, 



+ 2 



Lq 



T>b = ^P-bLU^ {1+ 2(^)^^.2(^)^^^b}[-CbC.^. ='bCl,-c.^ .■5;]. 

 ^B=ip-BLU^{l^2(^)^,.2(tH)^^CB}[.BC.J. 



But a set of diving plane is generally made of two parts, symmetrical with 

 respect to the (;z,x)-plane. Consequently, Sg and Jl^ are null. The non-null 

 components of the set of forces are 



1 2 



^B - ~ 2 '^'^B^ '^Xj 



^B = - 2 ^^bU Cl^ ]P 



1^ 2iuj^, . 2^^;^, ^3 





(J) -(^)„fB]^E^o.w.'>|-- 



Zr . 



^'B^ ^'---bLU^ \[-i 



.-X3+ (.-BCL3--n,3 



+ [^^B^L - C„ 





1^ 2iu)^, - Miry./^B 



y (3) 



[^: 



B'-L^ 



,u/., Vu/.- 



I] ^ok fok^t') 



A^, 



863 



