ESTIMATION AXD COXTIv'OL OF ( )1'I;h ATH TIMIO OF HKLAYS 149 



to relative actuation time of the several contacts on one relay, the small- 

 est armature travel is ordinarily provided. When a definite seciuence is 

 needed for circuit reasons, the actuating means is arranged to guarantee 

 operation of certain contacts before the oth(M-s. This necessitates the pro- 

 vision of a greater armature motion. 



The principles used in preparing these other types of charts are identi- 

 cal to those used for the two types which are developed specifically in 

 this article. 



Local Circuit Load Controlled Operation 



Power Given 



The best winding for a load controlled relay is not here given explicitly 

 by a formula, but rather is found indirectly by developing a method for 

 determining the operate time for any winding. Then by assuming a range 

 of these, the best one can be selected by interpolation of these derived 

 data. In Part I, the waiting line for a linear system was shown as equa- 

 tion (9) to be: 



47r 1 



h = — (Go + G, + Gs) In r— , (3) 



(Ms l — lo/l 



with lo/I substituted for v. Without motion time, saturation, eddy cur- 

 rents, or non-linear effects, Part I of this article also shows that the best 

 winding is that for which the turns are selected so that NIo/NI — 0.715. 

 Taking the other variables explicitly into account complicates the 

 determination and is at best only approximate. Instead they are included 

 through this interpolation approach. In a previous article a better 

 representation for the core eddy current constant was shown to be: 



G'e = GeC^^^'''^'^^^^^ = effective core eddy current constant. 



Substituting this and explicitly indicating a correction term for the small 

 motion time, the form best suited for the present discussion becomes: 



^0 = (1 + k/t,)L,{Gc + Gs + G'e) In -J— . (4) 



1 - q 



Except for the correction term for the motion time, t^/ti , this is still 

 a linear equation with all factors known. Omitting the motion time 

 correction, it can be solved either by numerical substitution or by a 

 nomogram, once a value for Li has been chosen. A conservative value 

 is the a\'erage one turn inductance, for the late contact critical load point 

 where x = .T3 . A more accurate value is determined through use of both 



