Speed - time Curve of Train

In this theory, the speed time curve of the train is discussed. The curve between speed in km per hour ( Y – axis ) and time in second on X – axis is known as speed – time curve of the train.

Importance of speed time curve

• It gives completes information regarding motion of the train.
• It gives information about speed of train at particular time.
• It gives information about acceleration time, free running time and retardation time of the train.
• The area covered by the speed – time curves gives information about distance covered by the train. 

Trapezoidal Speed time Curve

The speed time curve mainly consists of

Constant acceleration ( 0 to t₁ )

• The current is maintained approximately constant and voltage across motor increases step by step during notching period ( 0 to t₁ ) . 
• As the tractive effort remains constant during this period, the acceleration also remains constant.

Acceleration Running period ( t₁ to t₂ )

• The voltage across motor is kept remains constant and current starts to decrease with increase in the speed according to characteristic of DC motor. 
• The current taken by the motor remains constant after some time.

                                     N α ( E_b / I_a )

Free running period ( t₂ to t₃ )

• The train attains maximum speed at the end of time t₂. 
• The train runs with constant speed after time t₂. 
• The motor draws constant power from the supply.

Coasting ( t₃ to t₄ )

• The power supply is cut off and train is allowed to run under its own momentum after free running period ( t₂ to t₃ ). 
• The speed of the train starts to decrease due to resistance of motion of train. 
• The rate of decrease of speed during coasting period is known as coasting retardation.

Retardation ( t₄ to t₅ )

• The brake is applied to train at the end of coasting period ( t₄ ). 
• The speed of train decreases rapidly and finally reduces to zero during retardation period.

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