70 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



(Vc) and linear load (Fl) characteristics, the highest values of useful work 

 were shown to be T{Nlf/(26\()), and Tr{NI)~/6{o , respectively. 



These relations establish the important design requirement that the 

 point of closest approach of the load and pull curves should be at iii = 1, 

 or where the gap reluctance ih/A ecjuals the closed gap reluctance (Ro . 

 To the extent permitted by space requirements and manufacturing con- 

 siderations, this may be met by a proper choice of lever arm ratio or of 

 pole face area. In the latter case (Ro is not a wholly independent parame- 

 ter but includes a term varying with A, so that allowance must be made 

 for the change in (Ro in changing A. The curves of Fig. 27 show that 

 Vc/Wmax. and ]\/]Fmax dccrcase slowly for values of Ui between 1 and 2. 

 The ampere turn sensitivity is therefore close to its maximum value if 

 «i lies in this range. 



These relations are particularly useful in preliminary design estimates, 

 as they permit the ampere turn requirement to be estimated for a known 

 load merely from estimates of (Ro and .4. For this purpose it is only 

 necessary to determine F/TFmax by the procedure outlined above. With 

 V known, this determines ir„,ax , which equals ASioFo. Thus f o can be 

 evaluated, and NI determined from equation (32). 



Core Cross-Section 



These relations are formally applicable only in the range of linear mag- 

 netization. For the estimates to be valid, however, it is only necessary 

 that this condition be satisfied at the point of closest approach of load 

 and pull curves, as an approach to saturation at smaller gaps will redu( e 

 the pull in a region where, in most cases, it is well in excess of the load 

 curve. 



For linear magnetization to obtain at the point of closest approach 

 (u = Ui), the core flux should not materially exceed <;p', or aB', where B' 

 is the density for maximum permeability and a is the core cross-section. 

 The flux is equal to 47r.V//(R((/i), and the reciuired \'alue of a is therefore 

 given by: 



AirNI , 



a = p, . . • (39) 



5(R(wi) 



Here the values of AU and ui applying are those determined as de- 

 scribed above, and (R(i<i) is given by equation (24) for x = Hi.4(Ro . To 

 determine the core section a needed therefore requires an estimate of 

 (R/, , as well as of (Ro and .4 . 



If the expression for NI given by (38) is substituted in (39), it is 

 apparent that a varies as the square root of V(^i)/f(u\) and inversely as 



