158 THE MAGNETIC CIRCUIT [ART. 50 



Assuming that r is usually small as compared to x, describe a simple 

 method for calculating the short-circuit curve, using only the reactance 

 of the machine and the demagnetizing ampere-turns of the armature. 

 In practice, the influence of the neglected factors is accounted for in short- 

 circuit calculations by taking sin (J> in formula (79) as equal to between 

 0.95 and 0.98 instead of unity. 



Prob. 17. Plot the no-load phase characteristic of the machine 

 >*pprifit>(l in problem 14, when it is used as a motor. The iron loss and 

 t'rirtlon amount to 8.5 kw. 



Ans. Field amperes 14.9 23.4 32.6 



Armature amperes 30 2.13 30 



Prob. 18. The machine specified in problem 14 is to be used as a 

 motor, at a constant input of 150 kw. Plot its phase characteristics, 

 i.e., the curves of the armature current and of power-factor against the 

 field current as abscissae. 



Ans. Field amperes 32 . 6 24 . 3 16 . 65 



Armature amperes . . 47 . 00 37 . 65 47 . 00 

 Power-factor 0.80 1 .00 0.80 



Prob. 19. Write complete instructions for the predetermination of 

 the regulation of alternators and of the phase characteristics of synchro- 

 nous motors, by Blondel's method. The instructions must give only 

 the successive steps in the calculations, .without any theory or explana- 

 tions. Write directions and formulae on the left-hand side of the sheet, 

 and a numerical illustration on the right-hand side opposite it. 



Prob. 20. Calculate the overload capacities of the foregoing motor 

 at field currents of 25 amp. and 35 amp., by the two methods described 

 in the articles refered to near the end of Art. 47. 



Prob. 21. Show that for a machine with non-salient poles Blondel's 

 and Potier's diagrams are identical. 



50. The Calculation of the Value of the Coefficient of Direct 

 Reaction in Eq. (79) - 1 The average value 0.83 of the ratio of the 

 effective armature m.m.f. over a pole-face to the maximum m.m.f . 

 at the center of the pole is given in Art. 48 without proof. The 

 following computations show the reasonable theoretical limits of 

 this ratio. If the armature m.m.f. (direct reaction) at the center 

 of the N pole (Fig. 39) is M, its value at some other point along 

 the air-gap is M cos x, where x is measured in electrical radians. 

 Let the permeance of the active layer of the machine per electrical 

 radian be (P at the center of the pole, and let this permeance vary 

 along the periphery of the armature according to a law f(x), so 

 that at a point determined by the abscissa x the permeance per 



1 This and the next article can be omitted, if desired, without impairing 

 the continuity of treatment. 



