Speed Time Curve of Electrical Traction System

What is a Speed-Time Curve?

Speed-time curves are the most convenient means of studying the movement of trains and their energy consumption. A speed-time curve is defined as the graph plotted between the speed and time, by taking speed (in km/hour) on the Y-axis and time (in seconds or minutes) on X-axis. The speed-time curve provides complete information of the motion of the train.

The speed-time curve gives the speed of the train at various time instants after the start of the run directly. The slope of the curve at any point gives the acceleration at the corresponding instant or speed.

The area covered by the speed-time curve, time axis and the ordinates through the instants between which the time is taken, represents the distance covered in the corresponding time.

Parts of a Speed-Time Curve

A typical speed-time curve (refer the figure) mainly consists of the following −

  • Initial Acceleration
  • Constant Speed Run or Free Run
  • Coasting
  • Retardation

Initial Acceleration

The acceleration consists of two parts −

  • Constant Acceleration or Acceleration during Notching Up – During the notching up period (0 to t0), the current to the motor is maintained approximately constant and the voltage across the motor is gradually increased by cutting out the starting resistance. Therefore, the tractive effort is constant and hence the acceleration remains constant during this period.

  • Speed Curve Running or Acceleration on Speed Curve – During the speed curve running (𝑡1 to 𝑡2), the voltage across the motor remains constant and the current starts decreasing with the increase in the speed according to the characteristics of the motor and finally the current taken by the motor becomes constant. During this period, though the train accelerates but the acceleration decreases with the increase in speed and finally becomes zero at the speed at which the tractive effort developed by the motor becomes exactly equal to the resistance to motion of the train.

Constant Speed Run or Free Run

At the end of speed curve running, i.e., at 𝑡2, the train attains the maximum speed. During this period, the train runs with constant speed attained at the time instant t2 and constant power is drawn by the motor.


At the end of constant speed run or free running period, i.e., at 𝑡3, the power supply is cut off and the train is allowed to run under its own momentum. The speed of the train starts decreasing on account of resistance to the motion of train. The rate of decrease of speed during the coasting period is termed as coasting retardation.

Retardation or Braking Period

At the end of coasting period, i.e., at 𝑡4, the brakes are applied to bring the train to rest. During this period, the speed decreases rapidly and finally reaches to zero.

Updated on: 19-May-2022

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