ESTIMATION' AXD CONTKOL OF OPERATE TIME OF RELAYS 173 



Assume first that we want speed on the coil to be designed, say relay 

 No. 1, rather than the known relay in the circuit, say relay No. 2. Then 

 we want the effective power for this relay as high as possible provided 

 that the coil constant is not too far from o{)timum. From Table I it has 

 already been noted that the two effective coil constants are always 

 equal when the structures are identical. Also the sum of the two effective 

 powers is exactly equal to the total power; that is, as the effecti\'e power 

 to the first relay increases by increasing winding turns, that to th(^ other 

 correspondingly decreases. We see that for relay No. 1, the effective 

 })ower increases as .Vi increases, but also that the effective coil constant 

 increases. Thus an optimum turns value can be found, where on one 

 side the low effective power slows up the operate time, and on the other 

 the high coil constant does. Fig. 11 shows these optimum values. The 

 solid curves for relay No. 1 are plots of time ^'ersus the turns ratio 

 N'2/N'i with total power, E^/{Ri + /?2), and the "series coil constant" of 

 relay No. 2, Ni/iRi + Ri), as parameters. The optimum turns values 

 for relay No. 1 show up clearly on this curve, and are seen to vary with 

 both parameters. 



This relation of optimum turns to the two parameters is shown on 

 Fig. 12, where optimum N2/N1 values are plotted against total power 

 with the relay No. 2 series coil constant as the parameter. The added 

 series relaj^ always has the most turns when it is designed for least time. 

 Where speed on relay No. 1 is the only concern, the optimum turns can 

 be chosen directly and easily from Fig. 12. Fig. 11, however is of more 

 general use since it actually gives the times and also shows the time 

 values for the second relay (the dotted curves). Thus the turns can be 

 chosen to approach optimum speed on either relay or to choose a com- 

 promise value. 



Now for relay No. 2 with total power E'/{Ri + Ro), and the second 

 relay series coil constant ^"2/(^1 + ^^2) as parameters, the effective 

 power decreases and the effective G increases when Ni is increased, both 

 increasing the time. In other words, the given relay will always be 

 slowed down by any added series relay winding. 



The minimum Ai value is limited by sufficient ampere-turns to operate 

 the first relay. As shown by the dotted curves of Fig. 11, which are the 

 time versus N2/N1 curves for relay No. 2, the gain in speed is slight as 

 .Yo/Ai is increased beyond about 2. Thus, although a compromise must 

 always be chosen for speed on relay No. 2, the loss in speed for relay 

 No. 2 is not necessarily great if Ao/Ai can be chosen near 2. For the 

 case of equal operate times, in every case equality of turns of course 

 applies. 



