TM Wo. 377 



where R is the radius measured from the boom axis to the position of the 

 instrument mounting, and T is the period of rotation. The value of T is 

 measured by the operator using a stop watch. His position near the center 

 of the boom allows him to align a boom guy wire with a telephone pole near 

 the edge of the pond. The rotation is timed only after the system attains 

 constant speed. For slow rotations the time of one-half rotation was measured, 

 and for fast rotations the time of a complete rotation was monitored. 



How closely does this method of rotational towing approximate the 

 characteristics of rectilinear towing in a tank? One effect of rotation 

 would be to increase the load upon the pin bearings caused by the centri- 

 fugal acceleration. This is given by 



\/ T t _ 4TT 2 /? 

 "c - K - — =fT~ (11-15) 



The fastest tangential velocity was about 180 cm sec" . Hence, 



(2 t a, 2<7 cam sec-^-v O.OOZ8<$ 



where g = gravitational acceleration (980 cm sec" 2 ). The effect of this 

 increase in bearing load may be disregarded, since the acceleration inherent 

 in the towing is much less than the gravitational bearing load (weight) of 

 the impellers and shaft in air. 



Rotation also results in a gyroscopic effect produced by the difference 

 in angular momentum between the inboard and outboard side of the impeller, 

 whose axis of rotation lies in the plane tangent to the boom radius. (This 

 is the case for both the u and w meters.) The torque thus produced across 

 the impeller blades is imparted to the impeller axis so as to thrust the 

 leading end of the axis outward. This torque is proportional to the dif- 

 ference in towing radius of the inboard and outboard impeller. The net 

 moment is proportional to (R + r)/(p-r), where r is the radius of the 

 impeller. Since Ryv 1200 cm and r is about 5 cm > "the ratio is about 1.0034. 

 Hence, this small effect can also be disregarded. 



The first series of calibrations, conducted on 11 June 19^4, involved 

 end-on calibration. The range of towing speeds was from 21.9 to 186.5 cm 

 sec-1. A total of 45 calibration runs were made, using the u and w meters 

 individually. Each meter was driven in the forward and backward positions 

 to determine any variations in response. 



A tabulation of the calibration data is given in appendix C. Figure II-9 

 shows the results in terms of the known speed of towing and the resultant 

 frequency of consecutive voltage spikes produced by the impeller rotation. 

 The calibration data for positive and negative directions were essentially 

 indistinguishable ; hence, no effort was made to identify the source of points 

 in figure II-9, The output frequency f is clearly linear with V. . 



27 



