256 METHODS OF CALCULATION 



q being the number of phases (here 3), R t and R d the reluctances of 

 the transverse and direct circuits respectively. 1 



These reluctances are determined from the drawing of the 

 machine, taking into account the real path of the lines of force and 

 the saturation of the parts through which they pass, particularly the 

 teeth of the armature, the polar horns, the cores, the yokes of the 

 field-magnets, etc. 



If, instead of alternate poles, the machine carries poles of the 

 same name (homopolar inductor), K and K t may again be determined 

 by the preceding methods, drawing only one inductor-pole for two 

 poles of the armature. It results from this that theoretically the 

 reactions would give rise to coefficients 50 per cent less than in the 

 ordinary case. In practice, however, this is far from being the case, 

 because of the very considerable expansion of the flux of the arma- 

 ture in the large spaces existing between the field-magnet poles. 

 The direct flux reaction and particularly the transverse reaction is, 

 therefore, much larger than if they were produced only by the action 

 of the poles; so that finally the reactions are scarcely reduced more 

 than 25 per cent. The stray fields are, moreover, very large in this 

 type of machine, and every expansion of the field-magnet flux beyond 

 the breadth of the pitch produces a hurtful inverse E.M.F. The 

 induction-density in the air-gap should finally be doubled at least, 

 to produce the same useful flux on open circuit. From all the above 

 it follows that homopolar machines are of little advantage and are 

 almost abandoned. 



To completely take into account the practical values of the 

 coefficients, we shall consider again the case of three-phase machines 

 with six coils per field, first concentrated into one pair of slots per 

 coil, and then spread uniformly (or to a large number of slots each) 

 in order to occupy the entire circumference of the armature. 



Figs, ii and 12 represent the curves of magnetic potential 

 obtained in the two hypothetical cases with long bobbins disposed 

 as shown diagrammatically in the figure. The two curves corre- 

 spond to the same hypothesis as above for currents, and Table II 

 represents the separate mean values obtained for K and K t from 

 these curves. 



1 In unsaturated alternators, if one calls e the single air-gap, s the polar surface, 

 and d the coefficient of enlargement of the flux, the equation is approximately 



, i *(i+</) 

 obtained =-= . 



