Torque-Speed Equation for Induction Motor
The curve can be drawn using the following per-phase equivalent circuit:


V1 is the line-to-neutral voltage. The power source is assumed to be wye regardless of the actual configuration. R1 &amp; X1 are the stator resistance and stray reactance. R2 &amp; X2 are the rotor resistance and reactance referred to the stator. The per-unit slip, s is the slip RPM divided by the synchronous RPM. The magnetizing branch, between a and b, is neglected. The effect of the rotor bar shape on X2 and R2 is neglected.

The following equation gives the torque developed in the rotor for assumed values of s. The actual torque available at the shaft would be reduced by the torque lost to friction and windage (aerodynamic drag). q1 is the number of phases. Omega is the stator power frequency.



The images are from Fitzgerald, Kingsley, Umans Electric Machinery 4th ed.