i:h5TIMATIOX AND CONTIKJL OF Ol'EllATE TIMK OF RELAYS 1()7 



th(> jirimc to iiulicato total time, becomes 



^^ ^ y^ 27rn(.T3^ - x,) ^^^^ 



Tliis CHiuatioii was given a.s equation (1) in the early part of this article. 

 P'or the wire spring relay, this expression has a \'alue of 7.5 millisec. 

 Increasing this by 30 per cent for a maximum value, an estimate of 10 

 millisec results, agreeing with the earlier lower estimate of maximum 

 time for load controlled operation. 



Sclcclion of Winding for Mass Controlled Operation 



One more group of factors needs consideration before a winding is 

 selected. These are (1) the range in dc resistance of the windings, (2) 

 the winding temperature as determined by the duty c,ycle, and (3) the 

 range in the battery voltage. The number of turns of the winding is 

 ordinarily not considered as a variable once it is chosen because of the 

 automatic machine method of winding. An examination of Fig. 6 shows 

 that if the turns are too few, a greater time penalty obtains than if 

 there are too many. Also, decreasing the circuit power, increases the 

 best coil constant. These two considerations indicate that the best coil 

 constant should be chosen under worst circuit conditions. For any other 

 condition the operate time will be reduced. Further, the range between 

 worst circuit and average time will be a minimum. 



The procedure for choosing a winding is to determine the dc resistance 

 of a maximum resistance winding at the operating temperature set by 

 minimum battery voltage and the maximum duty cycle. This sets the 

 worst circuit power, and by use of Fig. 6, the best number of turns. In 

 no case is a winding specified with fewer turns than will supply sufficient 

 ampere turns to operate the worst relay with the maximum load. In 

 some cases of low power, this sets the number of turns. For some cases 

 of intermediate power, heating requires the maximum winding surface 

 area, also resulting in excess turns. The average resistance with its 

 variation, all at a standardized temperature at 68°F, completes the 

 design. 



Summary of Single Relay Local Circuit Operation 



An analytical determination of the operate time of a single relay 

 cannot be obtained in closed form because it requires the solution of 

 two simultaneous, non-linear, non-homogenous, differential equations, 

 without adding the complications of representing the magnetic saturation 



