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Speed-time curve parts; urban and sub-urban

Short answer

A speed-time curve plots train speed vs time; its slope gives acceleration/retardation and area gives distance. Parts: constant acceleration (notching), speed-curve running (acceleration decreases), free running (constant speed), coasting (power off, speed drops), braking. Urban service (~1 km stops) has high acceleration/braking, no free run, quadrilateral shape. Suburban (1-8 km) has short free run and longer coasting.

Describe Speed-time curve for the traction system with suitable example describing all its parts. Describe speed-time curve of urban and sub-urban services.

A speed-time curve is a graph of the speed of a train against time between two stops. Its slope gives acceleration or retardation, and the area under it gives distance travelled. It is used to find schedule speed, energy consumption and motor rating.

Parts of a typical speed-time curve

 V |       B   C
   |      .------.
   |     /        ``--. D
   |    / A            \
   |   /                \
   |  /                  \
   | /                    \
   +------------------------\E--- t
   O  t1   t2   t3     t4    t5
  1. Constant acceleration / notching (O–A): starting resistance is cut out notch by notch; current and torque stay almost constant, so acceleration is constant.
  2. Speed-curve running (A–B): all resistance is out; the motor works on its natural characteristic, so acceleration falls as speed rises.
  3. Free running (B–C): constant (crest) speed; tractive effort equals train resistance.
  4. Coasting (C–D): supply is switched off; the train runs on stored kinetic energy and speed drops slowly. This saves energy.
  5. Braking (D–E): brakes are applied to stop the train at the next station.

Example: in a metro run of about 0.66 km, the train accelerates at 2 km/h/s for 20 s to 40 km/h (about 111 m), coasts for 50 s with its speed falling to about 32 km/h (about 500 m), and brakes at 3 km/h/s for about 11 s (about 47 m).

Urban service

  • Stations are close (about 1 km); high acceleration (1.5–4 km/h/s) and high braking (3–4 km/h/s) are needed to keep a good schedule speed.
  • There is no free-run period; acceleration is followed by coasting, then braking. The curve is approximately quadrilateral.

Suburban service

  • Stations are 1–8 km apart; acceleration 1.5–4 km/h/s, braking 3–4 km/h/s.
  • A short free run may follow acceleration, and the coasting period is longer than in urban service.
 Urban                    Suburban
 V |  /\                  V |  /--.__
   | /  ``-.                | /      ``--.
   |/      \                |/           \
   +--------\-- t           +-------------\-- t
FeatureUrbanSuburban
Distance between stopsabout 1 km1–8 km
Free runNoneShort
CoastingShortLong
Curve shapeQuadrilateralQuadrilateral

✓ Answer checked by Claude Opus 5.5 (high effort)

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