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Speed-time curves for services; notching, coasting etc.

Short answer

Urban curves have no free run; suburban have short free run and long coast; main line have long free run. Notching period: constant acceleration while cutting out starting resistance. Accelerating period: from start to crest speed (includes notching and falling acceleration). Free run: constant speed. Coasting: power-off glide. Retardation: braking to a stop.

Draw the speed-time curves for urban and suburban and main line service. Also explain the following terms: (i) Notching period (ii) Accelerating period (iii) Free run period (iv) Coasting period (v) Retardation period.

A speed-time curve shows how the speed of a train varies with time between two stops; its slope gives acceleration and its area gives distance travelled.

Speed-time curves for different services

(a) Urban: stops ~1 km, no free run
 V |   /\__
   |  /    ``--.
   | /          \
   |/            \
   +--------------\--- t

(b) Suburban: stops 1-8 km, short free run, long coast
 V |   /--.___
   |  /       ``--.
   | /             \
   |/               \
   +-----------------\--- t

(c) Main line: stops > 10 km, long free run
 V |   ______________
   |  /              \
   | /                \
   |/                  \
   +--------------------\--- t
  • Urban: high acceleration (1.5–4 km/h/s) and braking (3–4 km/h/s), no free-running period, short coasting.
  • Suburban: similar to urban but with a short free run and a longer coasting period.
  • Main line: long free run at high speed; acceleration and braking periods are small in comparison.

Terms (refer to a complete curve)

 V |       B     C
   |      .------.
   |     /        ``--. D
   |    / A            \
   |   /                \
   |  /                  \
   | /                    \
   +-----------------------\E--- t
   O  t1   t2    t3     t4  t5
  1. Notching period (O–A): the train starts and speed rises at nearly constant acceleration while the starting resistance is cut out step by step (notch by notch) and the motor current is kept nearly constant.
  2. Accelerating period (O–B): the total time from start to the end of acceleration; it includes the notching period (constant acceleration) and the speed-curve running period (A–B), where the motor runs on its natural characteristic and acceleration falls as speed rises.
  3. Free run period (B–C): the motor stays connected and the train runs at constant (crest) speed; the motor output just balances the train resistance.
  4. Coasting period (C–D): power is switched off; the train moves on its own kinetic energy and speed falls slowly due to friction and air resistance. Coasting saves energy.
  5. Retardation (braking) period (D–E): brakes are applied and the train comes to rest at the next stop.

✓ Answer checked by Claude Opus 5.5 (high effort)

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