Torque Reduction Factor

In a DC Motor, at any given moment of time, a number of the armature conductors will not be under the pole faces, their contributions to the development of the torque will be zero. To take this effect into account, the torque given

$$\tau =K\varphi I_a$$

is multiplied by a torque reduction factor, $k$, which depends on the structure of the machine. Therefore:

$$\tau =kK\varphi I_a,K=\frac{ZP}{2\pi a}$$

As an example, if, on average, 95% of the conductors are always under the pole faces, then $k=0.95$.