CHAP. VIII] REACTION IN SYNCHRONOUS MACHINES 153 



larger than 0.637. For the ordinary shapes of projecting poles, 

 experiment and calculation (see Art. 50 below) show that this 

 ratio varies between 0.81 and 0.85. Using an average of these 

 limits instead of 2/w in eq. (78) and substituting for M its expres- 

 sion from eq. (64) we obtain the following practical formula for 

 estimating the armature demagnetizing ampere-turns per pole in a 

 synchronous machine with projecting poles: 



(79) 



In this formula i sin $ is the component i d of the armature current, 

 per phase. In actual machines the numerical coefficient in this 

 formula varies between 0.73 and 0.77, depending on the shape of 

 the poles and the ratio of pole-arc to pole-pitch. 



By a similar reasoning, if the ratio of pole-arc to pole-pitch were 

 equal to unity, the equivalent number of exciting ampere-turns on 

 the fictitious poles would be 



M t =(2/n)Mcos<l> ...... (80) 



Since the ratio of pole-arc to pole-pitch on the fictitious poles 

 is less than unity, the numerical coefficient should be larger than 

 2/;r. But, on the other hand, the permeance of the air-gap under 

 the fictitious poles is much higher than the actual permeance of 

 the machine in the gaps between the poles, so that a much smaller 

 number of ampere-turns M t is sufficient to produce the same 

 distorting flux. The combined effect of these two factors is to 

 reduce the coefficient in formula (80) to a value considerably 

 below 2/7T. For the usual shapes of projecting poles, experiment 

 and calculation (See Art. 51 below) show that this ratio varies 

 between 0.30 and 0.36. Using an average of these limits instead 

 of 2/7T in eq. (80), and substituting for M its expression from eq. 

 (64), we obtain the following practical formula for estimating 

 the distorting ampere-turns per pole, in a synchronous machine 

 with projecting poles: 



...... < 



In this formula i cos ^ is the component /, of the armature cur- 

 rent, per phase. In some actually built machines the coefficient 

 in thi.s formula comes out lower than 0.30, but in preliminary cal- 



