Hong Life CalculatorsUnderstanding the rolling resistance calculator — concept and principle
This calculator finds the rolling resistance force of a vehicle from its mass, the rolling resistance coefficient and the road gradient, and then the power needed at a given speed and the energy per kilometre and per 100 km. Cyclists, EV owners and vehicle engineers use it to understand where energy goes.
How it is calculated
Normal force N = m g cos θ, with θ = arctan(gradient)
F_rr = C_rr × N
Power P = F_rr × v; energy per km = F_rr × 1,000 m
- g = 9.80665 m/s²; speed in km/h is converted to m/s; 1 kWh = 3.6 MJ.
The principle
A rolling tyre flattens where it meets the road and springs back as it rolls on. Rubber does not return all the energy used to flex it, and the lost energy acts like a small braking force. That force is roughly proportional to the load on the tyre, so it is written as a coefficient times the normal force. Because the force barely depends on speed, the power to overcome it grows in proportion to speed, while aerodynamic drag grows much faster.
Worked example
Default inputs: 1,500 kg, C_rr = 0.010, gradient 0%, 90 km/h.
- N = 1,500 × 9.80665 = 14,710 N; slope angle 0°.
- F_rr = 0.010 × 14,710 = 147.1 N = 15 kgf.
- Power at 25 m/s = 147.1 × 25 = 3.68 kW.
- Energy per km = 147.1 × 1,000 J = 40.9 Wh/km, or 4.09 kWh per 100 km.
| Vehicle mass incl. load (kg) | Rolling resistance force (N) |
|---|---|
| 375 | 36.8 |
| 750 | 73.5 |
| 1,125 | 110.3 |
| 1,500 | 147.1 |
| 1,875 | 183.9 |
| 2,250 | 220.6 |
| 3,000 | 294.2 |
How to read the result
Hermans gives C_rr ≈ 0.01 as a standard value for car tyres and about 0.005 for bicycle tyres. Lower tyre pressure increases C_rr noticeably. At highway speeds air drag usually exceeds rolling resistance for cars, so rolling resistance matters most at low speeds and for heavy vehicles.
Common mistakes
- Adding the gradient's climbing force into rolling resistance; it is a separate force.
- Using the mass in kg as a force without multiplying by g.
- Assuming C_rr stays constant with tyre pressure and temperature.
Frequently asked questions
What is a typical C_rr for a car tyre?
About 0.01; bicycle tyres around 0.005.
Does speed change rolling resistance?
Only slightly; the power needed rises in proportion to speed.
Why do underinflated tyres waste energy?
They flex more, losing more energy each revolution.
Is climbing included?
No. The climbing force m g sin θ is separate.
Sources: L. J. F. Hermans, "Drag 'n' Roll", Europhysics News 35(4) (2004)