Strumpf 



^r.-> FT. 



ae 



O.H - 



0.2 - 



o.z 



O.fe 



2%h. 



OB ».0 



. RADIANS 



\.Z 



Fig. 11 - Limit values of Zq for 6^ = -0.8 radian as a 

 function of maximum elevator force coefficient for 

 otherwise standard cruising pitch maneuver conditions 



value of Zq for cruising is small, and it may be desirable to increase Zq for 

 hovering operations. This can be done, without restricting the attainable pitch 

 angles of the submersible in cruising, by increasing the value of the maximum 

 elevator force coefficient \zl\ • S. 



(B) Hovering Limit Maneuvers 



Figure 12 is an example of computed response in a hovering heave over- 

 shoot maneuver (Run 237). The tail-stabilized submersible is well behaved in 

 this example because it is operating in a negative (bow-to-stern) current u^ = 

 -1.69 ft/sec under otherwise standard run conditions of 



Z; = -1.5, S = 0, Mqq = -0.42,* Z^ = 300, Z^ = 100 lb/sec, 

 W = B = 95,500 lb, Xq = z^ = 0.01 ft, Wj = 0, and z^ = 20 ft. 



(47) 



With the vessel initially motionless with zero pitch angle relative to the x^,y^,z^ 

 inertial frame, the bow and stern vertical thrust forces z^ and Z^ are increased 

 from their respective equilibrium values Zb^ = -29.84 lb and Z^^ = 29.84 lb at 

 the maximum rate z^ = 100 lb/sec until the stern vertical thrust force reaches 

 the maximum value z^ = 300 lb and the bow vertical thrust force reaches the 

 value of 240.32 lb. These forces are maintained until time tj when the pre- 

 scribed execute depth z^^ = 20 ft is reached. At time t,, the z^ and z^ forces 

 begin to reverse at the rate -z^ until z^ reaches the maximum negative value 

 of -300 lb and z^ = -240.32 lb. These vertical thrust forces are maintained until 



''^M' was determined analytically (1) using strip theory. The resulting expres- 

 sion is M' 



298 



(1/16) z' + (1/4) z; . 



