286 INDUCTION MOTORS. [Exp. 



APPENDIX I. 



GRAPHICAL CONSTRUCTION FOR OBTAINING POWER FACTOR, 

 SLIP AND EFFICIENCY. 



27. Certain results power factor, slip and efficiency depend upon 

 ratios; these are usually expressed in per cent, and are determined by 

 dividing one quantity by another, as in 23-26. Some prefer to 

 obtain these ratios by using a slide rule; others, by using the graphical 

 construction of Fig. 3 which is in common use, and is particularly 

 convenient when one has many motors to test. The reader, however, 

 should bear in mind that this construction is only a convenience for 

 computing and not an essential for the proper understanding of the 

 circle diagram. 



28. Power Factor. In the direction of OE, lay off an arbitrary 

 scale of 100 parts of any convenient length. From the looth division, 

 draw the quadrant of a circle with the center at 0. 



To obtain the power factor for any primary current OP, extend 

 OP to R; from R draw a horizontal line to the point p, which gives 

 the power factor. The construction is obvious; it may be used in any 

 alternating current problem. 



29. Slip. From the point A, draw AA' parallel to OE. The 

 scale aa r , of 100 equal parts, is drawn parallel to AC at any convenient 

 distance. The point a on AA' is marked zero; the point a' on AP" is 

 marked 100. 



To determine the slip corresponding to any primary current OP, 

 locate the point s where the line AP cuts the slip scale. The per cent, 

 slip* is sa. (If the measured value of the slip at no load is appre- 

 ciable, the scale should be given this value, and not zero, at the point 

 a. Ordinarily this refinement is unnecessary.) 



*(2pa). Proof of Slip. For any point P, the slip is KS -*- PS. The 

 triangles KAS and Aa'a are similar; hence 



KS : AS=^Aa : a' a. (i) 



The triangles APS and sAa are similar; hence 



PS :AS = Aa :sa. (2) 



Dividing (i) by (2), we have the slip 



1 = sa/a'a. 



