Str^m-Tejsen and Chislett 



interaction between velocity -dependent and acceleration-dependent forces, then 

 the cyclic forces, like the generated velocities and accelerations, will be of sine 

 and cosine form. Each Y gauge thus simultaneously senses a sine -wave force 

 and a cosine -wave force, almost certainly of different amplitude but necessarily 

 of the same frequency, having the form 



gauge force = aj sin cot + a^ cos wt , 



where a^ and a^ are constants in time. 



If such a gauge force is recorded directly on a pen recorder, the record 

 will be a sinusoidal curve of amplitude a^ given by 



a J sin '-^t + 82 cos ojt = a -^ sin {oA + e) , 

 where a^ = 83 cos e and 82 = 83 sin e. 



It is possible to measure 83 and e from a paper record and so obtain 8j 

 and 82, but the authors can say from experience that this is not a practicable 

 solution, if only because of the difficulty of coping with the great quantities of 

 paper records involved. 



In the method chosen for the HyA planar -motion mechanism the force - 

 signal is integrated electrically, with periodic reversals of polarity as illus- 

 trated in Fig. 12. It is seen that if polarity is reversed after half a period, then 

 the sine component is measured and the cosine component eliminated. If polar- 

 ity is reversed after one quarter and three quarters of a period, then the sine 

 component is eliminated and the cosine component measured. Figure 12 also 

 shows that if a constant force component is included to give the more general 

 expression 



gauge force = a^ + aj sin ojt + aj cos ojt , 



then either a^, a^, or a^ may be obtained by suitable polarity reversal. A 

 constant force signal will, for example, result from a constant rudder or drift 

 angle superimposed on pure yaw motion or from imperfect gauge zero- 

 adjustment. 



These simple concepts form the basis used in the HyA planar-motion 

 mechanism system for the measurement of periodic forces. 



Integration Programs 



The integration of the force signals is, in practice, controlled by program- 

 ming circuits contained in a processing unit (Fig. 13) designed for this particular 

 purpose. The same programming circuits simultaneously control two parallel 

 and identical measuring channels, used in conjunction with the forward and aft 

 Y gauges. 



The circuits are built up from flip-flops, pulse shapers, relays, etc., shown 

 in the circuit diagram, Fig. 14. The operations controlled by the programs 



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