Cruising and Hovering Response of a Tail-Stabilized Subnnersible 



time tj are minimized when z^ =0.065 ft. The submersible with < z^, < 0.065 

 ft also responds rapidly but its marginal stability causes larger depth excursions 

 than in the optimum case. All three measures of performance increase from 

 the values at Zq = 0.065 ft to infinite values at z^ = 0.137 ft. It can be shown 

 analytically (1) that the submersible with z\ = -1.50 and h fixed at o = 0.175 

 radians attains a steady, downward, straight course condition with It'T < 0.80 

 radians for z^ > 0.137 ft. It is for this reason that the execute angle of f j = 

 -0.80 radian is never attained in the cruising maneuver computations when 

 Zq > 0.137 ft. Hence z^ = 0.137 ft is a limiting value for the standard maneuver 

 conditions. 



However, values of z^ which are excessive for cruising operations might 

 be desirable for hovering maneuvers. Therefore, the variation of the limiting 

 values of z^ with both d ^ and Z5S was investigated (1) using the otherwise 

 standard conditions given previously. Figure 10 shows this variation with 6 ^, 

 and indicates that the limiting value of z^ decreases with increasing \By\, ap- 

 proximately like -0.1/sin e ^. If a value of z^ < 0.09 ft is chosen for cruising 

 operations, all pitch angles will be attainable for the submersible with standard 

 conditions. 



Figure 11 shows how this limiting value of Zq can be increased by increas- 

 ing the maximum elevator force coefficient \2.\\ - s^. It is a plot of the limiting 

 value of Zq vs iZjl • s^ for 6^ = -0.80 radian and otherwise standard conditions. 

 The limit value of Zq increases linearly with \z'^\ • &^, and has a value of about 

 0.30 ft when \zlh \ = 0.60. If Iz^s j = 0.60, it can be shown (1) that all values of 

 e^ are attainable when z^ < 0.209 ft. 



Therefore, it has been shown that for a given value of Z^ • s^, there exists 

 a tail appendage force rate coefficient z^^ and a metacentric height z^ which 

 yields optimum cruising overshoot maneuver response. However, the optimum 



0.2 



0.4 



0.6 0.6 ».0 



-Gi , RAD"A,MS 



».2 



1.6 



Fig. 10 - Linnit values of vertical CG position above which 

 execute pitch angle cannot be attained for otherwise standard 

 cruising pitch maneuver conditions 



297 



