Cruising and Hovering Response of a Tail-Stabilized Submersible 



vessel reaches the prescribed execute pitch angle e^ = -0.80 radian. At time 

 tj, the elevator is deflected at the rate -o^ until it reaches the angle -b^ and 

 held there until the time t2 when the depth velocity z is zero. The run is 



stopped when t 

 or t > 100 sec. 

 z , 6_, and t, 



tj. The run also is stopped at any time when 

 Some of the measures of performance are 



> 1.57 rad 



Figure 7 shows how the maximum depth z^^ and the time t^ vary with Z^ 

 for the previously given values of the other parameters. There exists a value 

 z' ~ -1.3 for minimum z and nearly minimum t ,. The submersible with 



"a om •' -i 



0.86 < \z^J < 1.3 may also respond rapidly but because of its marginal stabil- 

 ity, requires larger depths than in the optimum case to complete the maneuver. 

 A submersible with |z^^| < 0.86 cannot complete the maneuver because the 

 pitch angle 6 exceeds the limit of 1.57 radians. For example, when z^ = -0.70, 

 exceeds 1.57 radians after only 26.0 seconds and while the depth velocity is 

 still increasing. This confirms the result of the previous stability analysis. 

 Lastly, when \z^J > 1.3, the vessel has an excessive amount of hydrodynamic 

 stability and requires greater depth and longer time to complete the maneuver 

 than in the optimum case. Since an automatic control with elevator deflected in 

 proportion to an error in t^ would (in effect) add hydrodynamic stability to the 

 system, it would be preferable to choose a tail fin with 0.86 < |z^ | < 1.3 than 

 one with |z' | > 1.3. 



O.S 

 FIN F 



t.O 1.5 2.0 



ORCe RATE. COEFFICIENT, -Zur 



Fig. 7 - Effect of Z^^ on maximum depth and 

 time to complete cruising speed limit maneuver 



295 



