Train Traction Calculator: Tractive Effort, Speed-Time Run, Schedule Speed and Energy Use

Find what a train needs to run between two stations and how much energy it uses.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the mass, the acceleration and braking rates, the top speed, the distance between the stations, the gradient and the train resistance.

The calculator finds the tractive effort and the power at the wheels, then the time and distance of the acceleration, the run at constant speed and the braking.

It gives the schedule speed, with a stop at the station, and the energy used from the supply, as kWh and as watt-hours per tonne-kilometre.

Formulas used

  • F = m(1 + k)a + mg\sin\theta + F_r
  • P = Fv
  • t_1 = \frac{v}{a},\quad d_1 = \frac{v^2}{2a}
  • V_s = \frac{D}{t + t_{stop}}

Worked example

With the default numbers in the calculator above:

  1. Force to accelerate the train (the rotating parts add to the effective mass): 259.20 kN
  2. Force against the gradient and the train resistance: 0.00 kN and 15.00 kN
  3. Tractive effort while accelerating: 274.20 kN
  4. Power at the wheels at the end of the acceleration: 6093.33 kW at the wheels, 7616.67 kW from the supply
  5. Time and distance: accelerating, at constant speed, braking: Accelerating 27.78 s over 308.64 m; at speed 110.00 s over 2444.44 m; braking 22.22 s over 246.91 m
  6. Running time between the stations: 160.00 s (2.67 min)
  7. Schedule speed (distance over the running time plus the stop): 56.84 km/h
  8. Energy for the run (acceleration and the cruise, braking uses none), at the wheels: 33.69 kWh
  9. Energy from the supply: 42.12 kWh
  10. Specific energy consumption: 46.80 Wh per tonne-km

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is a trapezoidal speed-time curve?

A run of constant acceleration, then constant speed, then constant braking. The curve looks like a trapezoid.

What is schedule speed?

The distance divided by the total time including the stop, which is always lower than the top speed.

Why add an allowance for rotating parts?

The wheels, axles and motors also have to be spun up, which makes the train behave as if it were 8 to 10 percent heavier.

What does regenerative braking do?

It turns the energy of braking back into electricity and returns it to the supply, so the real energy use is lower than this calculation shows.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Partab, Art and Science of Utilisation of Electrical Energy; Open University, traction engineering notes.

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