--- title: "Speed-time curves: urban, sub-urban, main line" subject: "Utilization of Electrical Energy" chapter: 4 key: "semester_7/utilization_of_electrical_energy:speed-time-curves-urban-mainline" source: https://www.bctengineer.com/q/semester_7/utilization_of_electrical_energy/speed-time-curves-urban-mainline site: BCT Engineering --- # Speed-time curves: urban, sub-urban, main line Utilization of Electrical Energy · Chapter 4: Electric Traction - Asked in: 2069 Chaitra - Video: [Speed Time Curve Analysis for Sub Urban & Urban Service |Electric Traction & Control|](https://www.youtube.com/watch?v=m9wNFqSdUuQ) — Anish Vora - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/utilization_of_electrical_energy/speed-time-curves-urban-mainline - Whole chapter: https://www.bctengineer.com/md/semester_7/utilization_of_electrical_energy/chapter-4 ## Question Define speed time curve for traction system. Discuss speed time curve of urban service, sub-urban service and main line service. ## Short answer Speed-time curve graphs speed vs time; slope = acceleration, area = distance. Urban (~1 km stops): high acceleration/braking, no free run, quadrilateral shape. Suburban (1-8 km): short free run, long coasting, quadrilateral. Mainline (>10 km): low acceleration/braking, long free run, short coasting, trapezoidal shape. Schedule speed depends on stop spacing and acceleration/braking rates. ## Answer A **speed-time curve** of a traction system is the graph of train speed against time for a run between two stations. Its slope is acceleration, the area under it is distance travelled, and it is used to find schedule speed, energy use and motor rating. #### 1. Urban (city) service - Stops are about 1 km apart; trains must start and stop often. - High acceleration (1.5–4 km/h/s) and braking (3–4 km/h/s) are needed to keep a reasonable schedule speed. - There is **no free-run** period; acceleration is followed by a short coasting and braking. - Curve shape is approximately quadrilateral. ```text V | /\ | / ``-._ | / \ |/ \ +------------\--- t accel coast brake ``` #### 2. Suburban service - Stops 1–8 km apart; acceleration and braking similar to urban service. - A short free-run period may appear after acceleration, followed by a long coasting period. ```text V | /---.___ | / ``--. | / \ |/ \ +------------------\--- t accel free coast brake ``` #### 3. Main-line service - Stops are more than 10 km apart, so the train runs mostly at crest speed. - Acceleration and braking are low (0.6–0.8 and about 1.5 km/h/s) and occupy a small part of the time. - Long free run, short coasting before braking; curve approximately trapezoidal. ```text V | ____________________ | / ``-. | / \ |/ \ +-----------------------------\--- t accel free run coast brake ``` | Feature | Urban | Suburban | Main line | |---|---|---|---| | Stop spacing | ~1 km | 1–8 km | > 10 km | | Acceleration | High | High | Low | | Free run | Nil | Short | Long | | Coasting | Short | Long | Short | | Approximate shape | Quadrilateral | Quadrilateral | Trapezoidal | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. On a speed-time curve, the area under the curve represents: A. Acceleration B. Distance travelled C. Energy consumed directly D. Schedule speed Answer: B. Slope gives acceleration and the area under the curve gives distance between stations. (Key point: Meaning of speed-time curve) 2. Which feature describes the urban service speed-time curve? A. Long free run at crest speed B. No free run; acceleration, short coasting, then braking C. Trapezoidal shape with low acceleration D. Stops more than 10 km apart Answer: B. Stops are about 1 km apart, so there is no free run; high acceleration and braking give an approximately quadrilateral curve. (Key point: Urban service) 3. Why is the main-line curve approximately trapezoidal? A. Stops are very close B. Stops are >10 km apart so the train mostly runs at crest speed with low acceleration/braking C. Coasting is very long D. It uses very high acceleration Answer: B. Long free run at crest speed forms the flat top, with small accel and braking portions. (Key point: Main line service) 4. How does the suburban curve differ from the urban one? A. It has no coasting B. Acceleration is much lower C. It has a short free run and a long coasting period D. Stop spacing is below 1 km Answer: C. Stops are 1-8 km apart, so a short free run may appear and coasting is long. 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