288 PRINCIPLES OF ELECTRICAL DESIGN 



conductors. The average value of the voltage lost per phase 

 winding is therefore 



2<t>,,pN 



& (average) == }Q8 ^ QQ (I 8 n 8 p) 



or, since Np = 120/ 



E ave r aa e = 4 



Assuming the sinusoidal wave shape, it is necessary to multiply 

 by ,- to obtain the r.m.s. value. Thus 



e888 

 V2XW* 



The slot flux in the neutral zone will be a maximum on zero 

 power factor when the current i a producing it is approximately 

 equal to the maximum value of the armature current, or to \/2I a . 

 Inserting this value of i 8 in formula (104) and substituting in 

 formula (105) we get 



E. = 27T/ X OATrT 8 *n a plJ a (j^ + P 2 + PS) X 10~ 8 (106) 



This quantity is usually referred to as the reactive voltage drop 

 per phase due to the slot inductance. It appears as the vector 

 E' E g in Fig. 114. 



If it were permissible to assume the alternating quantities 

 and the flux distribution in the air gap to be sinusoidal, the con- 

 struction of Fig. 114 might be repeated for conditions other than 

 zero power factor. These assumptions involve the idea of a 

 slot leakage flux diminishing with increasing power factor, the 

 actual change with varying angle of lag being in accordance with 

 the sine law. This does not take into account tooth saturation 

 and distortion of the current wave; but as a practical and ap- 

 proximate method it is permissible. The vector diagram for any 

 power-factor angle 6 is then as shown in Fig. 115. Here \p is 

 the angle of lag between the current and the e.m.f. actually 

 developed in the armature conductors; and cos ^ is the " internal " 

 power factor. The angle \f/ f shows the lag of the current behind 

 the "apparent" developed voltage, OE' g , and it will be seen that 

 the combined effect of end flux and slot flux is to reduce this 

 voltage by an amount approximately equal to PE' g sin \f/ f . 



98. Method of Determining Position of Armature M.m.f. 

 Turning again to Fig. 108 (page 277), we are still unable to de- 

 termine the angle 0, or the displacement (/3 + 90) of the 



