AIR-GAP FLUX DISTRIBUTION 



297 



The next point to consider is the position of the equivalent 

 sine- wave of maximum ordinate d, relatively to some particular 

 value of the irregular wave. It is obvious that neither the 

 maximum nor the zero value of the two waves must necessarily 

 coincide; but by so placing the equivalent sine-wave relatively to 

 the irregular wave that each quarter wave of the one has the 

 same virtual value as the corresponding quarter wave of the 

 other, the position of the equivalent wave may be approxi- 

 mately determined. This will be better understood by referring 

 to Fig. 121. 



The irregular wave is plotted to polar coordinates, and its 

 area measured with the aid of a planimeter. The line OM is then 

 drawn, dividing this area in two equal parts. This is easily 

 done with the help of the planimeter, the proper position of the 

 dividing line being found when the shaded area of the irregular 



Actual E.M.F. Wave 



Equivalent Sine 

 Wave 



FIG. 122. Curves of Fig. 121 re-plotted to rectangular coordinates. 



wave is exactly equal to the unshaded area. It is upon this line 

 (OM) that the center of the equivalent circle of diameter d (see 

 formula 108) must be placed. If the irregular wave has been 

 correctly plotted relatively to some reference axis, such as the 

 geometrical neutral line, or the pole center, the angle a can be 

 measured. This angle represents the displacement of the 

 maximum value of the equivalent wave beyond the pole center, 

 and when used in connection with the irregular wave, it may be 

 thought of as the average displacement of the distorted e.m.f. 

 behind the position of open-circuit e.m.f., which will be sym- 

 metrically placed about the center line of the pole. This angle a 

 has the same meaning as the angle M OM of Fig. 116; but it has 

 now been determined with greater accuracy than could be 



