250 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



The above expression gives the equivalent first cost of the power taken 

 by one relay. For each relay operation, or event, however, there may be 

 several relays energized. Then the total cost penalty per event, due to 

 power, is 



Cp = 'i^ dollars, (29) 



n 



where g = number of relays energized, per marker, for the particular 

 function in question even though only one appears in the time sequence. 

 For the power cost to be compared with the cost due to speed, this cost 

 must be spread over the number of relays, w, involved in the function. 

 Then 



C, = ^ (30) 



wH 



This is the equivalent first cost penalty incurred against each relay, due 

 to its power consumption. As R increases, it is seen to decrease. 



However, as R increases, the operate time increases. For speed relays, 

 the time t has been found to be a complicated function of the resistance, 

 varying approximately as R^'^. Thus when R increases, time increases, 

 and the equivalent first cost of this action time increases, as already seen 

 in Section 1.4. 



As power is changed, then, there results two oppositely varying 

 costs — one due to power, and one due to speed. The problem is graphic- 

 ally shown in Fig. 15, where Curve A shows the typical cost variation 

 due to power drain and Curve B shows the variation in cost due to speed. 

 The point where the sum of the two is a minimum is the ideal point to 

 operate, assuming that the coil costs are about equal in each case. 

 Curve C shows how the total cost will vary. Actually, it may be necessary 

 to add the effects of a third variable: the cost of the coil itself as it is 

 redesigned for different power consumption. This can be easily done by 

 the methods shown above, but is ignored in the present treatment for 

 the sake of simplicity. In many actual cases, coil cost has been found to 

 be a much smaller factor than the other variables. 



CHOICE OF OPTIMUM COIL 



In practice the above result may be obtained by a knowledge of how 

 a specific magnet design will vary in operate time as its coil resistance is 

 changed. The values may be substituted in the following equation for 

 total cost: 



