72 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



the latter reflects the inside coil dimensions, which varj^ with the required 

 core section a. The variation of the latter with Ui discussed above has a 

 minor effect on the power sensitivity, partially offsetting the effect of 

 the term/(wi), so that V/{Nlf is nearly independent of Wi in the range 

 1 ^ Wi ^ 2. 



Ignoring these secondary variations, equation (40) shows that the 

 steady state power required to operate a given load varies directly as the 

 closed gap reluctance (Ro , and inversely as S/m , where *S is the coil 

 volume and m the mean length of turn. Fig. 29 shows the relationship 

 between the work that can be done, and the steady state power that 

 must be supplied to the coil at this time. Since, in ordinary practice, use 

 cannot be made of the entire area under the force-deflection curve, the 

 "constant-load work," V c is often used in comparing magnet designs. 

 The maximum value for this term, as determined for a number of 

 Western Electric relays, is shown in the figure. According to equation 

 (40) the ratio of Fc to / 7^ should here have the value 



Vc _ ttGc 

 PR ~ 2(R^' 



since for constant-load output /(i(i) = 7r/2, when the optimum work con- 

 dition has been chosen. 



Work Capacity 



In applications where maximum sensitivity is not required, higher 

 output may be obtained by operating the electromagnet through much 

 of its travel in the non-linear region. The controlling factor is the flux 

 developed at the point of closest approach of the load and pull curves, 

 so the attainable output is controlled by the pull curve for constant 

 flux, as given by equation (30). In what follows the flux will be taken 

 as the saturation flux (p" , corresponding to the upper limit of attainable 

 output. The same relations may be used, however, to estimate the out- 

 put attainable with any value of flux approaching <p" in magnitude. For 

 (p = (p", (30) may be written in the form: 



L = ^ (41) 



n (c. + uY- ' ^ ^ 



where u = x/{A(S{o), d == ((Ro + (51l)/(Ro , and F^ is given by: 



Equation (41) is of the same form as equation (31), with u replaced 



