-2X2 THE MAGNETIC CIRCUIT [ART. 68 



and compared to that measured on a similar machine, the gross length 

 of tin- con- of which was 80 cm. and which was provided with \'2 ducts 

 of 1 cm. each. The equivalent leakage permeance of the shorter machine 

 was found to he -SO per cent less than that of the other machine. What 

 arc tli- actual values of (?,' and (P e '(=tfV) for both machines? 



Ans. (P/ = 2.46, 0Y =flY = 0.56 perm /cm. 



Prob. 20. An alternator has 3 slots per phase per pole, and the 

 equivalent permeance is(P/ = 1.8; (P e ' = 0.6. What would be the value 

 of the same constants per slot? Ans. 5.4 and 1.8. 



Prob. 21. A 3-phase alternator has 4 slots per phase per pole. 

 If the coils were connected up for a 2-phase machine without change 

 what would be the ratio of the new L to the old? Ans. 3 : 2. 



68. The Reactance Voltage of Coils undergoing Commuta- 

 tion. Let Fig. 57 represent a part of the armature winding 

 and commutator of a direct-current machine, with two adjacent 

 sets of brushes. During the interval of time when an arma- 

 ture coil, such as CD, is short-circuited by a set of brushes, 

 the current in the coil is reversed from its full value in one 

 direction to an equal value in the opposite direction. The coil 

 is then said to undergo commutation. 



Under unfavorable conditions this reversal of current is 

 accompanied by sparking between one of the edges of the brushes 

 and the commutator. Unless a machine is provided with inter- 

 poles, its output is usually limited by this sparking at the com- 

 mutator. It is of importance, therefore, to have a practical 

 criterion for judging the quality of commutation to be expected 

 of a given machine. Numerous formula and methods have 

 been proposed for the purpose; all rational formula contain, 

 as a factor, the inductance of the coils undergoing commutation, 

 because this inductance determines essentially the law according 

 to which the current is reversed with the time. For this reason, 

 the subject of commutation is treated in this chapter, under the 

 idicral topic of the inductance of windings. The method of 

 calculation of the inductance and the criterion of commutation 

 given below are due to Mr. H. M. Hobart. 1 



A description of the phenomenon of commutation. The phenom- 

 enon of commutation may be briefly described as follows: 

 Let, for the sake of explanation, the armature and the commu- 



1 See Hobart, Elementary Principles of Continuous-Current Dynamo Design 

 (1906), Chap. 4; also Parshall and Hobart, Electric Machine Design (1906), 

 pp. 171-194. 



