70 THE MAGNETIC CIRCUIT [ART. 29 



are occupied, the value of k 8 is the same as for a two-phase wind- 

 ing with three slots per pole per phase. 



Prob. 20. Check some of the values of k a given in the table above. 



Prob. 21. The armature core of a single-phase alternator is built of 

 stampings having three slots per pole; two slots per pole are utilized. 

 What is the value of fc,? Ans. 0.866. 



Prob. 22. A single-phase machine has S uniformly distributed slots per 

 pole, of which only /S" are used for the winding. What is the value of fc s ? 

 Ans. Use S' in eq. (33) instead of S; preserve S in eq. (34). 



Prob. 23. A six-pole, 6600 v., Y-connected, 50-cycle turbo-alternator is 

 to be built, using an armature with 90 slots. The estimated flux per pole 

 is about 6 megalines. How many conductors are required per slot? 



Ans. 20. 



Prob. 24. What is the value of k 8 when the winding is distributed uni- 

 formly on the surface of a smooth-body armature, each phase covering ft 

 electrical degrees? Solution : Referring to Fig. 18, k a is in this case equal 

 to the ratio of the chord E' to the arc of the circle which it subtends. The 

 central angle is ft, and we have k 8 = (sin^/9) / (%ftn/ 180) . In a three-phase 

 machine /?=60 degrees, and therefore k a = 0.955. This is the value given 

 in the last column of the table above. 



Prob. 25. Deduce the expression for k s given in the preceding problem 

 directly from formula (33). Solution: Substituting So. = ft-, S = 00 and 

 a =0, an indeterminate expression, O.oo, is obtained. But when the 

 angle a approaches zero its sine is nearly equal to the arc, so that the 

 denominator of the right-hand side of eq. (33) approaches the value 

 S.a = %ft, where ft is in radians. Changing ft to degrees, the required 

 formula is obtained. 



29. The Winding- pitch Factor k w . Let the distance between 

 the two opposite sides of a coil (Fig. 16) be 180 f degrees, where 

 7- is the angle by which tfye winding-pitch is shortened. The volt- 

 ages induced in the two sides of the coil are out of phase with 

 each other by the angle 7-, so that if the voltage induced in each 

 side is e, the total voltage is equal to 2e Gosjf (Fig. 17). Fig. 17 

 will apply to this case if we read ? for the angle a. Hence, we 

 have that 



k w = cos \v (35) 



In practice, the winding-pitch is measured in per cent, or as a frac- 

 tion of the pole pitch T. For instance, if there are nine slots per 

 pole and the coil lies in slots 1 and 8, the winding-pitch is 7/9, or 

 77.8 per cent. If the coil were placed in slots 1 and 10 we would 

 have a full-pitch, or a 100 per cent pitch winding. Let in gen- 



