ship Maneuvering in Deep and Confined Waters 



certain astern r.p.m. which must be attained before fuel may be 

 injected to start engine back. For a discussion of detailed features 

 of diesel maneuvering the reader is referred to a paper by Ritterhoff, 

 [72]. 



The energy-converting efficiency of a turbine wheel has a 

 maximum of some 80 per cent at a certain ratio of blade velocity to 

 nozzle steam velocity, attainable at the design point. Assuming this 

 ratio equal to 0.5, and a parabolic curve of efficiency symmetric 

 to the design point, the following simple formula is obtained for 

 the torque output: 



Q^ = ZkQI (1 



^Mc 



) 



(7.7) 



Here Q^ and n^ refer to torque and shaft speed at design conditions 

 for full steam inlet K = i. The formula furnishes a good approximation 

 also for present multi-staged ship turbines. In practical applica- 

 tions to studies of slow-speed port approach maneuvering it must be 

 realized' that steam production may then be limited to say K = 0.7. 



VIII. MODELLING THE DEEP-WATER HORIZONTAL MANEUVER 



The General Case 



The ship will be regarded^as a rigid body moving under the ^ 

 influence of the gravity force mg and the buoyancy force - p • Vq • g 

 — where Vo is the volume displacement at rest — as well as under 

 that of the external forces, including the control forces applied by 

 use of rudders and thrusters. Before reducing the problem to the 

 normal merchant ship case the more general form of the rigid body 

 dynamics will be included. 



The centres of mass (G) and buoyancy (B) may be off- set 

 from the origin of the moving system (0), and it is then practical 

 to apply Newton's laws in a summation of the acceleration forces 

 on the mass elements (cf, (4. 10) and (4.4)): 



863 



