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THE BELL SYSTEM TECHNICAL JOUKXAL, JANUARY 1954 



giving corresponding values of In 1 '(1 — v), which may be used in 

 specific cases to determine the correction corresponding to the term 

 in Ge . 



In most cases of slow operation, the operate time is of little im- 

 portance, and Gr is chosen to make NI greater than (A'V)o in all cases: 

 i.e., after allowing for possiljle variations in (.V/)(, resulting from varia- 

 tions in the load and in the magnetic characteristics. These variations 

 result in a variation in v, and the corresponding variation in time is shown 

 by the curve of Fig. 5. If, however, it is desired to minimize the operate 

 time for a given power input, Gc should be chosen to give the value of 

 V (0.715) corresponding to the minimum of the curve. As this minimum 

 is broad, variations in v, corresponding to those in (.V/)o , produce little 

 change in tne operate time. 



4 Two Stage Approximatiox 



Unless the rate of flux de\'elopment is ^•ery slow, as assumed in the 

 single stage approximation, the pull attained in the early travel is in 

 excess of the load, and the kinetic energy T is a considerable part of 

 the total work output V -\- T. As a first approximation to this case, the 

 operate time can be computed as though operation occiu'red in two suc- 

 cessive stages: (1) a stage of flux development with the armature at rest 

 in the unoperated position (x = Xi), and (2) a stage of motion, in which 



1.5 



0.5 



0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



V 



Fig. 5 — Relations for estimating time of flux development. 



