MAGNETIC DEblGX OF RELAYS 



69 



The ratio Vl/Wu,ixx ^^ shown plotted aj>;aiiist the point of taiigency Ui 

 in Fig. 27. Its maximum vakie is at Ui = 1, when V/, = ir,„ax/2. For 

 this optimum condition, Uo = 2, so that the total travel, x-z , equals 

 '_M(Ro , while the point of tangency, Xi , is at half that travel. For this 

 linear load case, under the optimum condition, the maximum work that 

 can be usefully applied is, then, W = irmnx/2. 



Actual load curves seldom conform to either of the simple cas(\s of Fig. 

 2(i, and more commonly have the irregular chai'acter illusti'ated in Fig. 1 . 

 Most of them, however, show a point of closest approach to the pull 

 curve either at the junction of two segments, as in Fig. 28(a), or at a 

 point of tangency to a linear segment, as in Fig. 28(b). In the former 

 case, the coordinates of the junction point may be taken as Fi and Xi , 

 as indicated, and the relations for a constant load for which Vc = FiXi 

 applied. In the other case, the tangent segment may be extended, as 

 indicated, to intersect the axes at Fo and x^ , and the relations for a linear 

 load for which Vl = F^x^ 2 applied. 



Quite generally, therefore, the work I'^ done against the load cur\'e is 

 proportional to TF^ax , and the proportionality constant is some function 

 of ?/i = Xi/(A(Ro), where Xi is the point of closest approach of the load 

 and pull curves. Writing /(i/i)/(27r) for the ratio V/Wmax , it follows from 

 equation (3-1:) that the ampere turn sensitivity, V/{NI)' is given by: 



V 



{Niy 



(Ro 



(38) 



where f(ui) is a maximum for Ui = 1, and is similar to the curves of 

 Fig. 27. For the particular load conditions represented by constant load 



ARMATURE GAP, X 



Fig. 28 — Determination of pull curve to match load. 



