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Rail Gradient Resistance Calculator

Work out rail gradient resistance instantly with clear inputs, formula shown and shareable results.

About Rail Gradient Resistance Calculator

Train resistance is the sum of gradient resistance (mass times g times gradient), rolling resistance (a few newtons per tonne) and aerodynamic resistance growing with the square of speed. On any gradient above about 0.5% the gradient term dominates, which is why railway alignments are kept so flat.

Formula

Train resistance

R = m x g x grade + m x rolling coefficient + air term; power = R x v

Worked example

With the default values below, Rail Gradient Resistance Calculator returns Total resistance of 146.81. Change any input above and every figure here is recalculated in your browser.

Inputs used

Train mass
1,200 t
Gradient
1.2 %
Speed
60 km/h
Rolling resistance coefficient
2.5 N/t

Results

Total resistance
146.81 kN
Gradient resistance
141.22 kN
Rolling resistance
5.59 kN
Power to hold speed
2,446.80 kW

Step by step

  1. 1Values used
  2. 2Train resistance
  3. 3Total resistance= 146.81 kN
  4. 4Gradient resistance= 141.22 kN
  5. 5Rolling resistance= 5.59 kN
  6. 6Power to hold speed= 2,446.80 kW

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
  • Rail results are planning estimates only. Verify against the infrastructure manager's rule book, approved braking curves and applicable railway safety regulations.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Rail results are planning estimates only. Verify against the infrastructure manager's rule book, approved braking curves and applicable railway safety regulations.

Frequently Asked Questions

Why is rolling resistance so low?

Steel wheel on steel rail gives a rolling coefficient of roughly 0.002, around a tenth that of a truck tyre on asphalt, which is the fundamental efficiency advantage of rail.

What does 1% gradient cost?

About 98 N per tonne, roughly forty times the rolling resistance, so a 1,200 t train needs an extra 118 kN of tractive effort.

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