BIPOLAR DIAGRAM 149 



salient pole l machine the reluctance of the magnetic circuit through 

 the armature is least in the direction of F and very much larger at 

 right angles thereto; the flux will therefore tend to lie inside of R, 

 i.e., on the side towards F: second, F is taken as the total M.M.F. 

 of the field coils per complete magnetic circuit; but a part of F is con- 

 sumed by the reluctance of the field cores and yoke, and is thus not 

 available to compound with A in the armature space. The errors due 

 to these two assumptions partly neutralize each other as far as the 

 direction of $ is concerned, since the second throws it too far out 

 and the first tends to bring it back. 



But even this diagram with its approximations is too complex 

 to be of service in getting a clear bird's-eye view of synchronous 

 motor operation, although it is an excellent starting point for further 

 approximations, and will prove very useful for reference purposes. 



The two familiar approximations are obtained as follows: 



DIAGRAM TRANSFORMATIONS 



In any dynamo-electric machine there are in general two M.M.F.'s, 

 those of the field and armature. In computing the E.M.F. of such 

 a machine, it is possible either to consider the resultant of these two 

 M.M.F.'s and the corresponding flux, or to consider the fluxes which 

 would be produced by the two M.M.F.'s if acting separately, and to 

 find the resultant of these two fluxes. The results of the two methods 

 of procedure are identical only when the reluctances of the magnetic 

 circuits in which the several M.M.F.'s act are equal. This condition, 

 though never present except in a very roughly approximate degree, 

 is nevertheless a very convenient one to assume for purposes of 

 approximate analysis. With this assumption, the various fluxes in 

 any case will be proportional to their several M.M.F.'s and in the 

 same direction or space phase; moreover, at constant speed of rota- 

 tion the E.M.F.'s generated in the armature by cutting through 

 these fluxes will be proportional thereto and in space and time quadra- 

 ture therewith. 



It will be legitimate, therefore, under the above-mentioned 

 assumption, to substitute for any M.M.F. its corresponding flux or 

 E.M.F., or to substitute for any E.M.F. its corresponding flux or 



1 The most accurate diagram for the salient pole machine is Professor Blondel's 

 Two-reaction Diagram employed in Chapter III; but this does not lend itself 

 readily to a simple visualization of the problem in hand, or to simple calculations. 



