ROTHERT'S METHOD 



'57 



effect, a demagnetizing one, while a leading current gives a mag- 

 netizing effect ( 47). Hence Rothert, regarding the actual or effective 

 ampere-turns (to which the terminal p.d. is regarded as due) as the 

 vectorial resultant of the field ampere-turns and the armature ampere- 

 turns, compounds these two vectorially, making the angle between 

 the resultant and the armature ampere-turns 90 for zero phase 

 difference, and 90 + d> for a phase difference of ^ degrees, the + sign 

 being taken for a lagging current and the sign for a leading one. 



In this construction, / should, strictly speaking, be taken as the 

 angle of phase difference between the current and the e.m.f. But 

 since this angle is not known, we may, as an approximation, assume 

 it to be equal to the angle of phase difference between the current 

 and the p.d. The actual diagram is then constructed as follows. 

 Lay off OK (Fig. 116) to represent the direction of the resultant or 



FIG. 116. Rothert'a Ampere-turn Method of determining Drop. 



effective ampere-turns, and draw OA, making an angle 90 -f with 

 OE, cos </> being the given power factor of the load (the current is 

 assumed to lag; for a leading current, the angle AOR would be 

 acute, and equal to 90 ^). Find from the short-circuit curve the 

 value of the armature ampere-turns corresponding to the given load 

 current, and lay off a length OA in the diagram to represent these 

 ampere-turns. With A as centre, and radius AR equal to the given 

 field ampere-turns, describe an arc cutting OR at R. Then OR is 

 taken to correspond to the resultant ampere-turns. Now refer to 

 the open-circuit curve, and find the e.m.f. corresponding to these 

 resultant ampere-turns ; this e.m.f. is taken to be equal to the required 

 terminal p.d. corresponding to the given load current, power factor, 

 and excitation. 



Rothert's method is only capable, like Behn-Eschenburg's, of 

 giving approximately correct results so long as the field is well below 

 saturation. Beyond a certain value of the exciting current, it yields 

 values of the p.d. which are far too high. In this respect, it is an 



