5 DIRECT CURRENT MOTORS. [Exp. 



APPENDIX I. 



INTERPRETATION OF METHOD; AND SEPARATION OF LOSSES. 



1 6. Interpretation* of Figure 2. For constant flux density (con- 

 stant field excitation in a shunt machine), the losses due to hystere- 

 sis, friction and windage are proportional to speed ( 10, n) and 

 may be expressed as AS, where A is some constant and 5" is speed. 

 Eddy current loss being proportional to the square of the speed may 

 be expressed as BS Z , in which B is some constant. The total rota- 

 tion loss is accordingly the sum 



which is the equation of the W curve in Fig. 2. Dividing by S, 

 we have the torque to overcome rotation losses 



which is the equation of the straight linef ac in Fig. 2. (See 3b, 

 Exp. 2-A.) Extending this line back to zero speed at a and draw- 

 ing the horizontal ab, we have be the torque to overcome eddy cur- 

 rent loss (proportional to speed) and db the torque to overcome hys- 

 teresis, friction and windage (independent of speed). These state- 

 ments and the statements made in the following paragraphs, hold 

 true throughout the range of speeds for which W 9 -r- 5" is a straight 

 line, which is much more than the working range of the machine. 

 17. Determination of Watts Eddy Current Loss. For any speed, 



*(i6a). The principle of the graphical method which is here used 

 was brought out by R. H. Housman and by G. Kapp, independently, in 

 1891 (London Electrician, Vol. XXVI. , pp. 699 and 700) ; each made use 

 of a straight line relation for plotting data obtained by running a motor 

 at constant excitation and varying armature voltage. The details, as here 

 given, have been modified by the writer with a view to making the method 

 simpler and more useful. The original papers are excellent, but their 

 method has been made unnecessarily cumbersome by writers who have 

 followed them. Earlier, Mordey had used equations similar to those of 

 16 for analytical separation of losses. 



f ( i6b). Since, at constant excitation, armature voltage (or more 

 strictly counter-electromotive force) is proportional to speed, the U 7 o 

 curve can be drawn with E' as abscissae instead of speed. We then 

 divide by E' (instead of 5") and get the straight line ac, the ordinates of 

 which (Wo-i-E') are amperes. 



