CHAP. XII] INDUCTANCE OF WINDINGS 231 



we shall assume <P e ' = (P a r , and use the following values, based 

 upon Mr. Hobart's experiments: } 



Number of slots per pole per phase .1 2 3 more than 3 

 (P 9 r = G> a ', in perms per centimeter ..0.8 0.7 0.6 0.5 



With a fractional-pitch winding the inductance is some- 

 what reduced (see the end of the preceding article). As an 

 empirical correction, the inductance calculated for a full-pitch 

 winding may be multiplied by the winding pitch factor k w . 



The leakage reactance of the armature cannot be calculated 

 from a short-circuit test, because the short-circiut current is 

 essentially determined by the direct armature reaction. A 

 difference of 50 or even 100 per cent in the armature reactance 

 would change the short-circuit current by only a few per cent. 

 A much closer approximation is obtained from the so-called 

 air-characteristic. 2 Namely, it has been found by numerous experi- 

 ments that the armature inductance, when the field is revol- 

 ving synchronously, is nearly equal to the armature inductance 

 with the field completely removed, and the armature supplied 

 with alternating currents from an external source. The air- 

 characteristic is the relation between the current and the voltage 

 under these conditions. Eliminating the ohmic drop, the induct- 

 ance of the machine is easily calculated, and the value so found 

 can be used in the prediction of the performance of the machine, 

 Such an air-characteristic is easily taken in the shop or in the 

 power house before the machine is completely assembled. From 

 the three observed curves, namely, the no-load saturation curve, 

 the short-circuit curve, and the air-characierist ic. the perform- 

 ance of a synchronous machine at any load can be predicted 

 to a considerable degree of accuracy. 



Prob. 18. What is tin* induetance per phase of a r.-pole. :t-phaae, 

 turbo-alternator, the armature of which has the following dimensions: 

 Bore, 1.2 m., gross length <>f <-<>re. 1 .'J m., LMI air-duets of I em. each. 

 90 open slots? There are 8 conductors per slot, tin- winding is of the two- 

 layer type, the winding pitch is 11/15. Assume <?,'- 2.5 perms /cm. 



nil. 



Prob. 19. The induetanee of the machine .specified in the preceding 

 problem was determined experimentally (from an air-characteristic), 



1 Journ. Inst. Electr. Eng. (HriiMi). Vol. :U. pp. 192 flf. 

 ' Pichclmaycr, Dynamobau (1908), p. 207. 



