Cruising and Hovering Response of a Tail-Stabilized Submersible 



Zg -''G^e > (15) 



in the case where w = B (neutral buoyancy), the main operating condition of the 

 submersible. The expressions for e^ and s^ are obtained from Eqs. (1) under 

 the conditions that wj = 0, e^ is small, w = B, and Mg = (1/2)25. This gives 



Wx, 



(M;-iz;)fA^u,^-w. 



and 



-z;w''G 



[(M;-|z;)f A^u/-w. 



Use of Eq. (16) in Eq. (15) results in 



Z', 



(16) 



(17) 



Wxq^ 



(M;-|z;)f a^u.^-wzg 



> 



(18) 



as a necessary condition for dynamic stability. For a body with tail fins, the 



coefficients z^, z^, m^, and M^ can be represented by the relations (Ref. 6) 



z' = z' + z' 



W W 



Mw - ^w "^ T ^w 



^^=^^h4^%^ m;:.m;^.1z; 



(19a) 

 (19b) 



Since the quantity 



M ', - 77 Z ' - M„ 



w w. 



Z' > , 



2 *h 



(20) 



Eq. (18) shows that 



zo > 



(21) 



is a necessary condition for dynamic stability of the neutrally buoyant submers- 

 ible. 



The other basis for defining acceptable cruising conditions is that 1 8^1 < S^^ 

 or, from Eq. (17) 



z;W''G 



m; - ^ z;) f A-eu.^ - wz^ 



z; 



< s . 



(22) 



285 



