VOLTAGE REGULATION OF THE ALTERNATOR. 119 



windings would be of little practical value, and the following dis- 

 cussion is limited therefore to a few simple special cases. 



Uniform distribution of flux under pole faces. Suppose that 

 the flux ^> is evenly distributed under the pole faces, as shown in 

 Fig. 1 07, the fringe of flux beyond the pole tips being ignored 

 for the sake of simplicity. Let w be the width of the pole faces 

 in degrees, and let s be the distance between the tips of adjacent 

 poles, in degrees. Then w may be taken as the number of 

 units of time that a given armature conductor is under a pole 

 face, s as the number of units of time that the conductor is be- 

 tween two pole tips, and w + s as the number of units of time 

 in a half-cycle. Under these conditions let us consider two dif- 

 ferent armature windings, namely : (a) A concentrated winding ; 

 and (b) a particular distributed winding. 



(a) Concentrated armature winding. In this case the average 

 value (during half-a-cycle) of the electromotive force of the alter- 

 nator is equal to pQZn abvolts as stated above, and to find the 

 effective value, we must find the value of the ratio : * effective 

 value divided by average value. With this object in view let & 

 be the actual value of the electromotive force of the alternator 

 during the w units of time that the armature conductors are 

 under the pole faces. Then, since the actual electromotive is 

 zero during the s units of time that the windings are between 

 the pole tips on the assumption that there is no flux beyond the 

 pole tips, it is evident that the average electromotive force of the 

 alternator during half-a-cycle is Sw/(w + s), and that the effec- 

 tive electromotive force of the alternator is 8 i/w/(w -f s), so 

 that the ratio, effective value divided by average value, is equal 

 to V(w -f s)/w. Therefore the effective value of the electro- 

 motive force of the alternator is equal to pQZn V\(^-\-s)\w\ 

 abvolts. 



(b) Distributed armature winding. Let us consider an arma- 

 ture winding in which the armature conductors are grouped in 



* This ratio depends upon the shape of the electromotive force curve, and it is 

 called the form factor of the electromotive force curve. 



