Library / Mechanical / MEC-41
Mechanical
Braking distance
Stopping distance on a surface with coefficient of friction μ.
- Ref
- MEC-41
- Rev
- v1
- Field
- Mechanical
- Result
- d [m]
v is the speed when the brakes are applied, μ the coefficient of friction between the tyres and the surface, and g the gravitational field strength. Braking at the limit of grip gives a deceleration μg, and the distance follows from v² = 2ad. The reaction distance before the brakes bite is not included.
Stopping distance on a surface with coefficient of friction μ. It grows with the square of speed.
Calculator
- Deceleration μg6.867 m/s²
- Time to stop v/(μg)2.912 s
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 20 m/s (72 km/h) on dry road (μ = 0.7) the car stops in 29 m, but on a wet road (μ = 0.3) it needs 68 m. Add the reaction distance, of about 14 m for a 0.7 s reaction at this speed.
- Doubling the speed to 40 m/s makes the braking distance four times as long, about 116 m, while the time to stop only doubles.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| v Speed | 1 to 100 m/s | 0.07281 | 728.1 | 728 | +10% | +21 % |
| μ Coefficient of friction | 0.05 to 1.2 | 16.99 | 407.7 | 390.8 | +10% | −9.09 % |
| g Gravitational field strength | 1 to 30 m/s² | 9.524 | 285.7 | 276.2 | +10% | −9.09 % |
Sweep of Coefficient of friction
| Coefficient of friction | Braking distance (m) |
|---|---|
| 0.05 | 407.7 |
| 0.1937 | 105.2 |
| 0.3375 | 60.41 |
| 0.4812 | 42.36 |
| 0.625 | 32.62 |
| 0.7688 | 26.52 |
| 0.9125 | 22.34 |
| 1.056 | 19.3 |
| 1.2 | 16.99 |
Sweep one variable
Variables and how each one contributes
Braking distance
What the equation gives you. Everything else feeds it.
Speed
The speed at the start of braking. Squared: doubling the speed quadruples the stopping distance. A 10 % rise in v raises d by 21 %.
Coefficient of friction
The coefficient of friction between the tyres and the surface. Inverse: halving the grip doubles the distance. It ranges from about 0.8 on dry tarmac to 0.1 on ice, so it is the most important input.
Gravitational field strength
The gravitational field strength (9.81 m/s² on Earth). Inverse: weaker gravity (less weight on the tyres) means less friction force and a longer stop.
Worked example with the values above
- Deceleration: μg = 0.7 × 9.81 = 6.867 m/s².
- Square the speed: v² = (20)² = 400 m²/s².
- d = 400 / (2 × 6.867) = 29.12 m.
Assumptions and limits
- Constant friction coefficient and the full braking force at the limit of grip, with the wheels not locked or the ABS working at its best.
- A level road and negligible air resistance.
Common mistakes
- Entering the speed in km/h instead of m/s.
- Forgetting the reaction distance, which is the driver’s speed multiplied by the reaction time.
Statistics and uncertainty
d ∝ v²/μ, so a 1 % error in speed gives 2 % in distance. The coefficient of friction is the weak input: it varies by ±20 % or more with surface, wear, temperature and load transfer, so a calculated distance should be given a safety margin.
Where it is used
- Vehicle stopping distances on wet, dry or loose surfaces.
- Setting safe following distances in a convoy.
Maths you need
- Constant acceleration: v² = u² + 2as
- Friction: F = μN