Prediction of Steering and Manoeuvring of Ships 



thus enabling all of the terms in the above nonlinear mathematical model, Eqs. 

 (5), to be measured. 



PLANAR-MOTION MECHANISM - PRINCIPLES 

 OF MOTION GENERATION 



The difficulty of generating a yaw velocity in a conventional tank is due to 

 the fact that if a constant angular velocity is maintained for more than a short 

 length of time, while traveling at the necessary speed, a collision with one of 

 the side walls will result. Use of a planar-motion mechanism overcomes this 

 problem by forcing the model to travel with alternately port and starboard yaw 

 velocities. This results in an S-shaped path which in rough terms may be con- 

 sidered as being built up of segments of the circular path traveled by a model 

 under a rotating arm (Fig. 5). To be more precise, a planar-motion mechanism 

 generates a sinusoidal trajectory and the angular velocity is thus constantly 

 varying, but the rotating arm comparison is nonetheless valid, because the 

 variation is so slow that quasi-steady conditions are obtained. 



Fig. 5 - Comparison of pure 

 yawing motion generated with 

 a planar-motion mechanism 

 and a rotating arm 



TOWING TANK 



ROTATING ARM 



A continuously varying yaw velocity is necessarily accompanied by a con- 

 tinuously varying yaw acceleration to which the same quasi-steady conditions 

 apply. 



Reference to Fig. 5 shows that if the model is to move with a "pure yaw" 

 motion, i.e., with zero drift angle, then it must at all times move along the tan- 

 gent to its path. In terms of the body-axis system fixed in the model (Fig. 1), 

 this means that the side velocity v must be zero, or the total velocity vector u 

 of the origin of the axis system must lie along the model centre line. It can 

 be seen that for a model moving down the tank with carriage speed u,^ this is 

 achieved by moving the model perpendicularly to the carriage centre line with a 

 relative velocity Up. The magnitude of this velocity is given by 



325 



