CHAP. XII] INDUCTANCE OF WINDINGS 225 



The equivalent permeance <P" of the embedded part in perms 

 per centimeter of the semi-net axial length of the machine, and 

 per centimeter of peripheral length of the air gap, is for 



Open slots Half-open slots Completely closed slots 



11.5 14.5 18. 



The equivalent permeance around the end-connections, and 

 around the parts of the conductors in the air-ducts, decreases 

 with the increasing number of slots per pole per phase, for the 

 same reason that the slot permeance decreased. In induction 

 motors usually at least three slots are used per pole per phase, 

 and under these conditions Mr. H. M. Hobart uses (P/ = 0.8 

 perm per centimeter, with phase-wound rotors, and 0y = 0.6 

 perm per centimeter with squirrel-cage rotors. (P a * may be 

 taken in all cases equal to 0.8 perm per cm. The lengths l e 

 and l a are always understood to refer to the stator winding. 



The foregoing data refer to machines with full-pitch windings 

 in the stator and in the rotor. With a fractional pitch winding 

 the equivalent leakage permeances are somewhat smaller, due to 

 longer phase belts and to the mutual induction of the over- 

 lapping phases. Let the winding-pitch factor (Art. 29) of the 

 primary winding be k wl and that of the secondary winding 

 k w2 - Then the leakage inductance of the machine, calculated 

 for a full-pitch winding (but for J e =l-5W, i g multiplied by 

 &t0i-&t02* This is an empirical correction, which is accurate 

 enough for ordinary practical purposes. In reality, of two 

 machines designed for a given duty, one with a fractional pitch 

 winding and the other not (but otherwise both alike) the first 

 often has a higher inductance than the second. This is because 

 more turns are required with the fractional pitch winding, if the 

 flux densities in the iron and in the air-gap are to be the same 

 in both cases. 1 



With the data given above the calculation of the leakage 

 reactance of a given induction motor is quite simple, and one 

 engaged regularly in the commercial design of induction-motors 

 can obtain sufficiently accurate data for their design or for the 



1 For a theoretical and experimental investigation of the effect of a 

 fractional pitch upon the leakage reactance in iu.lMction machines see 

 < A. Adams, Fractional-pitch Winding* for Induction Motors, Tmn*. Amer. 

 ln*t. Elec. Engrs., Vol. 26 (1907), p. 1488. 



