Strumpf 



the time tj when the depth Zqj of 20 ft again is attained, and the run is stopped. 

 A run also is stopped if |z^| > 100 ft, \e\ > 1.57 rad, or t > 200 sec. In a com- 

 pleted hovering heave maneuver, there is a time in the interval (tj, tj) where 

 z^ - 0. It is noted that the control moment M^ and the longitudinal propeller 

 speed n^ have the equilibrium values M^^ = x^CZ^ - z^,^) and n^ for all time 

 (o, tj) in a hovering heave maneuver. Hence, any net unbalanced pitch moments 

 or longitudinal forces are due entirely to transient inertial and hydrodynamic 

 effects. Some of the measures of performance are Z^ , z^ , tj, i9j, x^ , ^_^, 



"On,' ^°m' ^"^ ^2- 



Figure 13 shows the effect of Z^^ on six measures of performance in the 

 hovering maneuver for otherwise standard conditions with u^ = (i.e., u^ = 0). 

 Although the vessel is marginally stable for all Z^^ when u^ = 0, the asymmetry 

 of the submersible due to the presence of the tail appendage is manifested in the 

 increasingly large heave-to-surge and heave-to-pitch coupling effects that are 

 obtained as \l'.^J\ is increased. For example, when Z^^ = -1.5, the vessel at- 

 tains a pitch angle of almost -33 deg and moves forward a distance of 80 ft be- 

 fore the heave maneuver is completed. This occurs without applying any unbal- 

 anced pitch moments M^ or longitudinal forces x^ to the system. The source of 

 this behavior is the nosedown hydrodynamic pitch moment due to the tail append- 

 age (-CgwU) which acts when a pure downward force Z^ is applied to the vessel. 

 The tail-stabilized submersible also is characterized by its slow response and 

 large depth overshoot in hovering heave maneuvers with u^ = 0. 



Figure 14 demonstrates the strongly adverse effects that positive longitudi- 

 nal current velocities u^ have on the hovering heave maneuver response of the 

 tail-stabilized submersible for otherwise standard conditions. These results 

 confirm the trends predicted by the analysis of dynamic stability. For a positive 



x„^ 



sec. 



lOO r 

 80 

 eo I- 



MO 



O.XtO*, RAO. 



-20 



z -«-»o 



e~»»0 , RAD. 



■fcO 



o.e 



2.0 



Fig. 13 - Effect of tail fin force rate coefficient 

 on hovering heave overshoot maneuver for oth- 

 erwise standard run conditions 



300 



