202 ALTERNATING CURRENTS 



that point on the torque circle where it is intersected by the line 

 drawn from B to the extremity of the primary current vector (ZT in 

 Fig. 129). If we wish to measure the torque in Ib.-feet i.e. in 

 terms of the pull which the motor would exert at the circumference 

 of a pulley one foot in radius then we may fix the scale of torque 

 very simply, as follows. Assuming, for the moment, that there are 

 no losses at all in the stator, we must have the power transmitted to 

 the rotor equal to that supplied to the stator. Now the former is, in 



p T 

 terms of the torque T,* equal to ^ . =^7. . 746 watts, p being 



2ir X frequency and P = number of pairs of poles ; while the latter 

 is, for a three-phase motor, VJ cos 0\/3 (I being primary current 

 and cos 6 = power factor). Thus 



P 



or 



550 



= 746 'p 

 = M cos (3) 



550 P 

 k being the constant 5^ . . V iV /3. Now when, as we have 



momentarily assumed, there are no losses in the stator, the points 0', 

 O, and A in our diagram become coincident, and the maximum torque 

 T m is represented by AB. We may thus write 



c being the required constant of proportionality, so that 



_2Tm 



~AB 



The value of T may be determined by means of (3) ; in this, le 

 has a known value, and I and cos may be found by describing a 

 circle on AB as diameter, from its centre drawing a horizontal radius, 

 and joining its extremity to B. The point in which this line inter- 

 sects the current circle determines I and cos in equation (3). 



The slip might be found as in Fig. 129, but if we wish to consider 

 large values of the slip, the line OS there shown would correspond 

 to an inconveniently large scale for the slip. It is, therefore, more 

 convenient to choose a point B, in OB nearer B, and to draw PiS 

 parallel to BK. Since P s corresponds to the short-circuit current 

 when the slip is unity (or 100 per cent.), the point of intersection S of 



* In Ib.-feet. f AB being measured on the scale of current*. 



