Air Gap Power in Induction Motor

The motor converts electrical energy into the mechanical rotational energy. The input voltage is fed to the stator of an induction motor. The stator coil opposes the applied voltage and this opposition limits the starting current of the motor. The flux is generated in the stator and the flux travels through the air gap and gets linked to the rotor conductors. The air gap power is equal to the rotor input power. 
The input power drawn by the induction motor is expressed by the following formula.
P=√3* VL*IL* cosΦ ———-(1)
VL-Line voltage, IL- Line current, cosΦ- Power Factor
The electric power drawn is converted into the magnetic power. The air gap between the stator and the rotor is unwanted but necessary for motor operation. Without having an air gap, the rotation of the rotor is not possible. However, the losses in the motor can be minimized by keeping the air gap length as minimum as practically possible. The following losses occurs in the motor at no load.
Core Losses or No Load Losses
The loss comprises the eddy current and hysteresis loss. The loss is more or less constant so it is called the fixed losses.
Stator I2R loss :
The loss occurs due to heat loss in the resistance of the stator because of the current flowing through the stator coils.
Thus the total losses in the stator at no load is given by;
PstL=Ps(h+e)+Ps ————–(2)
PstL – Total losses in the stator at no load
Ps(h+e)- Core losses-Eddy current and hysteresis loss
Ps- Copper loss in the stator
The air gap power(Pg) can be calculated as;
=Total Input power – Losses in the stator
Pg=√3VL x IL cosΦ-[(Ps(h+e)+Ps)] ——(3)
The air gap power (Pg) is transferred to the input to the rotor.
The air gap Power= Rotor Input Power
The air gap power gets converted into the kinetic rotational power. The following losses occur in the rotor.
1. Rotor copper loss
2. Rotor core loss- Negligible
3. Friction, windage and stray losses
The air gap power(Pg) can also be calculated by following formula.
Pg  = The mechanical power output(Pm) + Rotor Ohmic loss + Friction and Windage loss

Calculation of Air Gap Power

The equivalent rotor circuit of an induction motor is shown below.
equivalent circuit of induction motor rotor
The X2 and E2 is the rotor reactance per phase and EMF /Phase induced in the rotor circuit. R2/s is the rotor winding resistance.
The rotor input power  = Air Gap Power
gross power of induction motor- formula derivation
The rotor copper loss = sPg
Mechanical power output(Pm)= (1-s)Pg
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