CHAP. XII] INDUCTANCE OF WINDINGS 235 



this high density causes a glowing at the edge of the brushes, 

 making the commutation still less satisfactory. 



The average reactance e.m.f. in the coils of a full-pitch lap 

 winding. For an empirical criterion of the quality of commutation 

 Mr. Hobart takes the average reactance voltage induced in the coil. 

 This is a reasonable criterion, because the ratio of the maximum 

 voltage occurring when the brush leaves a segment to the average 

 voltage, will be more or less the same in machines of usual 

 design constants. Of course, the average reactance voltage 

 is only a relative criterion, to be used with great discretion, 

 and applied only for comparison with machines which proved 

 in actual operation to commutate satisfactorily. 



Let the inductance of an armature coil between two adjacent 

 commutator segments be L^. The subscript eq (meaning equiva- 

 lent) is added to indicate that the value of L includes not only the 

 true inductance of the coil itself, but also the average inductive 

 action of the coils which are undergoing commutation simultane- 

 ously with it. Let the frequency of the current in the coil under- 

 going commutation be / cycles per second. Then the current is 

 reversed in a time J/. The flux changes during this time 

 from -i-Leqli to L^/I. Hence, according to the fundamental 

 eq. (26) Art. 24, the average reactance voltage, which is taken 

 as the criterion of commutation, is 



(156) 



In order to obtain a satisfactory commutation, the voltage 

 <* must not exceed a certain value, determined from actual 

 irnco with machines in regular operation. Mr. Hobart 

 recommends values for e ave not to exceed 3 to 4 volts, provided 

 that one* does not depend upon the fringe flux of the main poles 

 to facilitate commutation. 



The inductance A,,/. \vluYh enters in the foregoing formula, 

 is calculated according to the general formula (150), as follows: 

 Assume first that there is no common flux or mutual induction 

 between the coil under consideration and the other coils which 

 are simultaneously short-circuited. Then, if </ is the number 

 of turns per commutator segment, (in I iir. 57 tf 1) we must put 

 Cpp-=<i. This will irivr the inductance of one side of the coil, 

 say C. To obtain the inductance of both sides, C and D, the 

 result must be multiplied by 2, or L^-2L PP . 



