ELECTRIC TRACTION - PART - 03 - POWER OUTPUT FROM DRIVING AXLES

Ft = tractive force and V is the train velocity

Power output = Ft x V watts, 
where velocity V is metre per second.

Power output = Ft x (1000/3600) x V in watts
                    = Ft x V / 3600 in kW.

Where velocity V is in km per hour.

If η is the efficiency of transmission gear, then power output of motors is Ft = [Ft X V]/η in watts.
where velocity V is in metre per second.

Ft = [Ft x V] / [3600 x η] in kW.
where velocity V is in km per hour.

PROBLEM - 01

A 200 ton motor coach driven by 4 motors takes 20 seconds to attain a speed of 42 km per hour, starting from rest on an ascending  gradient of 1 in 80. The gear ratio is 3.5, gear efficiency 92%, wheel diametre 92 cm, train resistance 40 N/t and rotational inertia 10 percent of the dead weight.

Find the torque developed by each motor.

PROBLEM - 02

A 200 ton motor coach having 4 motors, each developing a torque of 8000 N-m during acceleration, starts from rest. if up-gradient is 30 in 1000, gear ratio 3.5, gear transmission efficiency 90 percent, wheel diametre 90 cm, train resistance 50 N/t, rotational inertia 10% of the dead weight, calculate the time taken by the coach to attain a speed of 80 km per hour.

If the supply voltage is 3000 V and motor efficiency 80%, calculate the current taken during the accelerating period.

PROBLEM - 03

A train weighting 500 tons is moving down a gradient of 20 in 1000. The speed of train is to be maintained at 50 km per hour through the use of regenerative braking. If the tractive resistance 40 N/ton, and the efficiency of conversion is 75%. Calculate the power fed to the line.