156 ALTERNATING CURRENTS 



be less than 1. The value of the terminal p.d. OA is easily cal- 

 culated from the known values of OC and AC, as follows : 



In the triangle OAC, reproduced for the sake of clearness in 

 Fig. 115, we have 



3 = tan- 1 -^ - 

 r 



AC . 

 sm 7 = sm 



and 



n OC = ~ ? OC 



sm p ' sin p 



These three equations enable us to find OA, and so to determine 



- nn OC - OA 



the percentage drop 100 -- f^ - . 



84. Rothert's Ampere=turn Method 



The method just explained yields very satisfactory results with 

 transformers, but in the case of alternators it is unsatisfactory, and 

 can only be depended on in cases where the alternator field is well 

 below saturation. With a strongly saturated field, it yields excessive 

 values for the drop, so that it is, at all events, a safe method, and 

 has, for this reason, been termed the pessimistic method by Behrend. 

 A different method, involving the vectorial composition of ampere- 

 turns instead of e.m.f.'s, has been proposed by Bothert* For the 

 purpose of applying this method, two curves, the open-circuit and 

 the short-circuit curves or characteristics, are required. The open- 

 circuit curve is the curve connecting the field current (or field 

 ampere-turns) with the e.m.f. or open-circuit p.d., while the short- 

 circuit curve is the curve connecting the field current with the 

 short-circuit current. In the construction, it is immaterial whether 

 we use field current or field ampere-turns, since the latter are pro- 

 portional to the former. The armature ampere-turns corresponding 

 to a given current are taken to denote that value of the field ampere - 

 turns which is necessary in order to produce a short-circuit current 

 equal to the given armature current ; the armature ampere-turns are 

 thus obtainable from the short-circuit curve. 



When the armature current is in phase with the e.m.f., armature 

 reaction consists of a cross-magnetizing or distorting effect pure and 

 simple ; a lagging current gives, in addition to the cross-magnetizing 



* EleJttrotechnisclte Zeitschrift, vol. xx. p. 619 (1899). 



