Calculation
FR = fr·m·g·cos α
Rolling resistance is approximately speed-independent and proportional to wheel load normal to the road.
Dubbel Kraftfahrzeugtechnik Q 2.1.1: FRo = f·m·g (f ≈ 0,008 … 0,017); hier mit cos α für geneigte Fahrbahn
Vehicle rolling resistance force
Rolling resistance is approximately speed-independent and proportional to wheel load normal to the road.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Rolling resistance force FR — Force opposing motion due to tyre deformation and road contact.
- Rolling resistance coefficient fr — Tyre- and road-dependent coefficient; passenger cars on asphalt typically 0.010 to 0.015.
- Vehicle mass m — Total vehicle mass including payload.
- Gravitational acceleration g — Local gravitational acceleration, about 9.81 m/s² near sea level.
- Road grade angle α — Road inclination angle; 0° is a level road.
Example
fr=0.012, m=1,500 kg, g=9.81 m/s² and α=0° give FR≈176.6 N.
Assumptions and limits
Constant fr over speed and tyre temperature; the dependence of fr on tyre pressure, road surface and speed, as well as cornering, are excluded.
Understand Vehicle rolling resistance force
This calculator determines a vehicle's rolling resistance force, the driving resistance usually dominant at lower speed, from tyre coefficient, mass and road grade.
What does this quantity describe?
Rolling resistance follows from FR=fr·m·g·cos α, where fr summarises tyre and road properties and cos α reduces wheel load on an inclined road.
Formula and variables
FR = fr·m·g·cos α
FR = fr·m·g·cos α
| Symbol / input | Meaning |
|---|---|
| Rolling resistance force FR | Force opposing motion due to tyre deformation and road contact. |
| Rolling resistance coefficient fr | Tyre- and road-dependent coefficient; passenger cars on asphalt typically 0.010 to 0.015. |
| Vehicle mass m | Total vehicle mass including payload. |
| Gravitational acceleration g | Local gravitational acceleration, about 9.81 m/s² near sea level. |
| Road grade angle α | Road inclination angle; 0° is a level road. |
Choose the inputs correctly
fr is the rolling resistance coefficient, m vehicle mass, g gravitational acceleration and α road grade angle.
How to use the calculator
Take fr from a tyre datasheet or experience values; use α=0° on level ground so cos α=1.
Worked example
fr=0.012, m=1,500 kg, g=9.81 m/s² and α=0° give FR≈176.6 N.
Understand the result and units
Rolling resistance often exceeds drag at low speed; at highway speed this ratio reverses.
fr is dimensionless, m a mass, g an acceleration and α an angle. FR is output as a force.
Typical applications
Estimating driving resistance for range and consumption calculations, and comparing tyre types.
Assumptions, limits and common mistakes
Constant fr over speed, tyre temperature and pressure; cornering, slip and road condition (wet, snow) are excluded.
Common mistake: Do not confuse fr with the static friction coefficient of braking physics; rolling resistance is a distinct, much smaller quantity.
Frequently asked questions
What is “Vehicle rolling resistance force” used for?
Estimating driving resistance for range and consumption calculations, and comparing tyre types.
Where do the input values come from?
fr is the rolling resistance coefficient, m vehicle mass, g gravitational acceleration and α road grade angle.
What does the result not cover?
Constant fr over speed, tyre temperature and pressure; cornering, slip and road condition (wet, snow) are excluded.