72 THE MAGNETIC CIRCUIT [ART. 30 



of curves, like the one in Fiir. 19, each curve giving the values of k b 

 for a certain number of slots per pole per phase, against per cent 

 \viiuliiiir pitch as abscissae. 



Prob. 26. In a 4-pole, 72-slot, turbo-alternator the coils lie in slots 1 

 and lo. Wliat is the per cent winding-pitch and by what percentage is 

 the e.in.f. reduced by making the pitch short instead of 100%? 



Ans. 66.7 per cent; 1 k w = 13.4 per cent. 



Prob. 27. What is the flux per pole at no load in a 6600-volt, 25-cycle, 

 .".on r. | i.ni.. Y-connected induction motor which has 90 slots, 36 conduc- 

 tors per slot, and a winding-pitch of about 73 per cent? 



Ans. 7.26 megalines. 



Prob. 28. Show that for a chain winding k w is always equal to unity, 

 in spite of the fact that some of the coils are narrower than the pole pitch. 



Prob. 29. Draw a sketch of a single-layer, fractional-pitch winding, 

 using alternate slots for the overlapping phases. Show what values of k a 

 and k w should be used for such a winding. 



30. Non-sinusoidal Voltages. In the foregoing calculations 

 the supposition is made that the flux density in the air-gap is dis- 

 tributed according to the sine law so that sinusoidal voltages arc 

 induced in each conductor. Under these circumstances the 

 resultant voltage also follows the sine law, no matter what the 

 winding-pitch and the number of slots are. The flux is practically 

 sinusoidal in induction motors because the higher harmonics of 

 the flux are wiped out by the secondary currents induced in the 

 low-resistance rotor. But in synchronous alternators and motors 

 with projecting poles the distribution of the flux in the air-gap is 

 usually different from a pure sine wave. For instance, when the 

 pole shoe is shaped by a cylindrical surface concentric with that of 

 the armature, the air-gap length and consequently the flux density 

 are constant over the larger portion of the pole; therefore, the 

 curve of the field distribution is a flat one. This shape is improved 

 to some extent by chamfering the pole -tips or by shaping the pole 

 shoes to a circle of a smaller radius, so that the length of the air-gap 

 increases gradually toward the pole-tips. 



When a machine revolves at a uniform speed, the e.m.f . induced 

 in a single armature conductor has exactly the shape of the field- 

 distribution curve, because in this case the rate of cutting the flux 

 is proportional to the flux density (see eq. 27 above). There- 

 fore, when a machine has but one slot per pole per phase (which 

 condition is undesirable, but unavoidable in low-speed alternators, 

 or in those designed for extremely high frequencies), the shape of 



