--- title: "Train services for trapezoidal and quadrilateral curves" subject: "Utilization of Electrical Energy" chapter: 4 key: "semester_7/utilization_of_electrical_energy:trapezoidal-quadrilateral-train-services" source: https://www.bctengineer.com/q/semester_7/utilization_of_electrical_energy/trapezoidal-quadrilateral-train-services site: BCT Engineering --- # Train services for trapezoidal and quadrilateral curves Utilization of Electrical Energy · Chapter 4: Electric Traction - Asked in: 2073 Chaitra, 4 marks - Video: [4.4 Trapezoidal speed time curve, Quadrilateral](https://www.youtube.com/watch?v=IrxVddeDToQ) — EE - 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/trapezoidal-quadrilateral-train-services - Whole chapter: https://www.bctengineer.com/md/semester_7/utilization_of_electrical_energy/chapter-4 ## Question What types of train service correspond to trapezoidal and quadrilateral speed time curves? ## Short answer A trapezoidal speed-time curve (acceleration, free run, braking) represents main-line long-distance service with long constant-speed runs. A quadrilateral curve (acceleration, coasting, braking) corresponds to urban and suburban services where stops are frequent and coasting replaces sustained free running. ## Answer A **trapezoidal** speed-time curve (acceleration, free run, braking) represents **main-line (long-distance) service**, while a **quadrilateral** curve (acceleration, coasting, braking) represents **urban and suburban service**. #### Trapezoidal curve: main-line service - Stations are far apart (often more than 10 km), so the train runs most of the time at constant (crest) speed. - The acceleration and braking periods are short compared with the free-run period. - So the actual curve is closely approximated by three straight lines: constant acceleration, constant speed and constant retardation. Together with the time axis these form a trapezium. - It is used for main-line and long-distance express trains. #### Quadrilateral curve: urban and suburban service - Stops are close together (about 1 km for urban and 1–8 km for suburban), so the train never runs long at constant speed. - After the initial constant acceleration, the speed rises slowly along the motor curve; then power is switched off, the train **coasts**, and finally it brakes. - In the simplified curve, the speed-curve running is merged into the acceleration line, so there are three straight lines: acceleration, coasting and braking. Together with the time axis these form a quadrilateral. - Used for city and suburban trains, metro and tram services, where high acceleration and braking matter more than top speed. ```text Speed Speed | ________ | /\ | / \ | / ``--._ | / \ | / \ |/ \ | / \ +--------------\-- t +/-------------\-- t Trapezoidal (main line) Quadrilateral (urban) ``` | Curve | Service | Main feature | |---|---|---| | Trapezoidal | Main line | Long free run at crest speed | | Quadrilateral | Urban / suburban | Coasting, no long free run | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which service corresponds to a trapezoidal curve? A. Urban B. Main-line long-distance C. Suburban D. Tram Answer: B. Stations far apart mean a long free run at crest speed. (Key point: Trapezoidal service) 2. Why does urban/suburban service give a quadrilateral curve? A. Close stops leave no long constant-speed run; it has acceleration, speed-curve running, coasting and braking B. Trains run at constant speed C. There is no braking D. Stops are over 10 km apart Answer: A. Four sides arise: acceleration, speed-curve, coasting, braking. (Key point: Quadrilateral service) 3. What matters most in urban/suburban service? A. High acceleration and braking more than top speed B. Top speed only C. Long free run D. No braking Answer: A. Short distances mean acceleration and braking dominate schedule speed. (Key point: Priority) ## Related in Utilization of Electrical Energy - [Speed-time curves for services; notching, coasting etc.](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Aspeed-time-curves-services-periods) — Utilization of Electrical Energy, chapter 4 - [Quadrilateral speed-time curve on down gradient](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Aquadrilateral-curve-down-gradient-energy) — Utilization of Electrical Energy, chapter 4 - [Speed-time curves: urban, sub-urban, main line](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Aspeed-time-curves-urban-mainline) — Utilization of Electrical Energy, chapter 4 - [Schedule speed for a 2 km run (trapezoidal)](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Aschedule-speed-trapezoidal-2km-run) — Utilization of Electrical Energy, chapter 4, asked 3× - [Schedule speed for a 1.5 km run (trapezoidal)](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Aschedule-speed-trapezoidal-1-5km-run) — Utilization of Electrical Energy, chapter 4, asked 3× - [Schedule speed for a 2.5 km run (trapezoidal)](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Aschedule-speed-trapezoidal-2-5km-run) — Utilization of Electrical Energy, chapter 4, asked 3× ## Related in other subjects - [Compound gear train speed numerical](https://www.bctengineer.com/question.md?key=semester_6%2Ftheory_of_mechanism_and_machine_i%3Acompound-gear-train-speed-numerical) — Theory of Mechanism and Machine I, chapter 6 - [Time and space mean speed from 14 travel times](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Atime-space-mean-speed-14-vehicles) — Transportation Engineering II, chapter 1 - [Time and space mean speed from 20 spot speeds](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Aspot-speed-20-observations-travel-time) — Transportation Engineering II, chapter 1 - [Time/space mean speed and density from spot speeds](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Aspot-speed-20-values-time-space) — Transportation Engineering II, chapter 1