Str^m-Tejsen and Chislett 



Accepting that a phase angle between the forward and aft scotch-yokes given 

 by Eq. (9) results in pure angular motion of the model relative to the water, the 

 expressions for the model's angular velocity and angular acceleration are ob- 

 tained by differentiating Eq. (7) with respect to time: 



a . / <^\ 

 angular displacement, = ~T sin — cos I ojt + — ] (7) 



angular velocity, r = - —r sin -x sin Ic^t + -^ \ \}-^) 



aoj^ (p I (p\ /1 1 \ 



angular acceleration, r = - ~~r- sin -z cos Iwt + -z j K^*-) 



It is seen that angular velocity and angular acceleration are out of phase 

 with each other. 



Similarly, when the scotch-yokes are in-phase (0 = 0), the model centre line 

 is always parallel to that of the tank and carriage, and the model experiences 

 pure swaying motions. In terms of body-axis parameters, lateral displacement, 

 velocity, and acceleration are then given by: 



sway displacement, y = a sin cot (12) 



sway velocity, v = aoj cos cot (13) 



sway acceleration, v = - aco^ sin cot . (14) 



To summarize, hydrodynamically pure yawing or swaying motions can be 

 generated by setting the phase angle between forward and aft scotch-yokes to an 

 appropriate value. In both cases, the velocity and acceleration are 90 degrees 

 out of phase with each other. 



A constant drift angle or rudder angle can easily be superimposed on the 

 pure yaw motion as shown in Fig. 4. Nonzero drift angle is obtained by changing 

 the lengths of the arms shown symbolically in Fig. 6 as SjF and S2A. This has 

 the effect of adding a sizable constant component /3 to the small cyclic value of 

 ^P resulting from yawing motion. The phase-angle is then found from Eq. (9) by 

 substituting d cos yS for d, and similarly d is replaced by d cos ,3 in Eqs. (7), 

 (10), and (11). 



DESCRIPTION OF THE HyA PLANAR-MOTION MECHANISM 



Mechanical Structure 



The HyA planar-motion mechanism is in many ways similar to instruments 

 previously reported (6,7,9,10). Hence the following description is limited to a 

 general outline of the main structural arrangement and of some novel features. 



The HyA towing tank facility measures 240 x 12 x 6 metres in length, width, 

 and depth respectively (8), enabling resistance and propulsion experiments to be 



328 



