46 SYNCHRONOUS MOTORS 



It is therefore sufficient to divide the segment AN in the proportion 

 of \i -|| to obtain the power-lines shown in Fig. 27. 



If, for example, we take the series of values,' 

 p 



-=^ = 0.10, 0.20, 0.30, 0.40, 0.50, O.60, 0.70, 0.8o, O.QO, 1. 00, 



we will find 



-=0.949, 0.894, 0.837, -774, 0.707, 0.632, 0.548, 0.447, 0.316. 



In practice, these lines should be graduated in kilowatts, in the 

 usual way. 



It is often unnecessary to draw the lines for the high powers, since 

 the power P is much greater than that which the armature can with- 

 stand without dangerous heating, in continuous operation. 



Since cos f is very small (usually <o.io), in ordinary practical 

 cases, the center N of the circles will often be outside the diagram, but 

 it will be always easy to draw the circles by points, from their equation 

 in rectangular co-ordinates. 



Moreover, in that case, the circles are of very large radius, and are 

 quite sufficiently determined by two tangents. Now for each circle, 

 such as GFG', the directions of the two tangents at F and G' are known, 

 because they are, respectively, perpendicular to A\N and ON. Again, 

 the position of the points F and G' corresponding to a power P-z, is 

 given by the obvious equation : 



2 COS f f 2 COS 



It is very easy, therefore, to construct these two tangents and then 

 to draw approximately the circular arc which they determine. 



It will be noted that the " P^ " power-values, in Fig. 27, are positive 

 above the point A\, and negative below it. This shows that the alter- 

 nator will operate as a motor in a certain portion of the plane, contained 

 inside the power-circle ^2=0, and that it will operate as a generator 

 beyond that circle. In the cross-hatched space comprised between the 

 lines 7*2 =^0 and P\=o it cannot operate either in one way or in the 

 other, because the current which would then pass through the machine 

 would cause a loss of energy in the armature greater than the available. 

 power. 



