CALCULATION OF E.M.F. 95 



T)olo~ftrc 

 where k is a factor depending on the ratio ' . . , on the number 



of slots per pole per phase, and on the shape of the pole-shoe. 



The earliest attempt to calculate the value of k for various cases 

 is due to Kapp, who, in 1889, determined k for various kinds of 



T) O iC ~ ill 1 ' 



windings and various values of the ratio - v r r , on the assumption 



that the field in the gap is uniform, and ceases abruptly at the edges 

 of the pole-shoe. According to this assumption, the e.m.f. wave 

 induced in each conductor is of the rectangular form shown in Fig. 78. 

 The e.m.f. wave of the entire phase is obtained by superposing the 

 waves corresponding to the various sets of conductors into which the 

 winding of the phase may be divided; each set of conductors con- 

 sisting of those conductors whose e.m.f.'s are coincident in phase. 



The assumption of a rectangular wave-shape for each conductor 

 is, however, unjustifiable, on account of the formation of a magnetic 

 fringe around the polar edges. Owing to the greater spreading of the 

 flux due to the formation of this fringe, the actual e.m.f. is less than 

 that calculated on the rectangular wave assumption. 



More reliable results are obtained by taking into account the 

 effect due to the fringe, as was first done by Mr. C. C. Hawkins in 

 1900.* The following table gives the values of k calculated by Mr. 

 Hawkins, for the case of two slots per pole per phase, the slots being 

 spaced th of the pole-pitch apart : 



pole-arc = Q ^ Q ^ QmtfQ Q . 90 



pole-pitch 



k = 2-48 2-26 210 1'93 



The above values are based on the assumptions of an air-gap 

 length (single) equal to ^th of the pole-pitch, of sharp rectangular 

 polar edges, and of a width of pole-shoe equal to the width of pole 

 or field-core. 



The second of the above assumptions does not in general apply to 

 practical cases, since the edges of the pole-shoe are always more 

 or less rounded. Now if, retaining the same flux per pole and the 

 same length of polar arc, we round off the edges of the pole-shoe, 

 we thereby cause a greater concentration of the flux towards the 

 middle portion of the pole-shoe, and a greater concentration of flux 

 is, as we have seen ( 44), accompanied by a rise of e.m.f. Thus for 

 pole-shoes with rounded corners the value of k will be greater than 

 that given by the above table. 



The latest contribution to this subject is due to A. Miiller,t who 



* Electrical Review, vol. xlvii. p. 055 (1900). 



t Zeitschrift fiir Elelctroti-chnik (Wicn), vol. xxiii. p. 31 (1905). 



