The stopping distance is the reaction distance plus the braking distance. The reaction distance grows linearly with speed, but the braking distance grows with the square — which is why it quadruples when the speed doubles.
Introduction
The stopping distance is the total distance from the moment you see a hazard until the bus comes to a stop. It consists of two parts: the reaction distance (while you manage to react) and the braking distance (while the bus slows down).
The formulas
The reaction distance grows linearly with speed, but the braking distance depends on the speed squared. So: if you double the speed, the braking distance quadruples. That is the core of why small increases in speed produce large stopping distances.
Examples
With a reaction time of 1.0 s and a deceleration of 6 m/s² (dry asphalt): at 50 km/h (13.9 m/s), s_R ≈ 13.9 m and s_B ≈ 16.1 m, i.e. about 30 m. At 80 km/h (22.2 m/s), s_R ≈ 22.2 m and s_B ≈ 41.2 m, i.e. about 63 m. The braking distance alone more than doubles, because the speed only increases ~1.6 times (1.6² ≈ 2.6).
Road grip determines deceleration
Decelerationen a hænger direkte sammen med friktionskoefficienten µ mellem dæk og vej: a = µ · g, hvor g ≈ 9,82 m/s². På tør asfalt er µ høj, på is er den lav — og fordi bremselængden er omvendt proportional med a, mere end fordobles bremselængden, når µ halveres. En tung bus kan sjældent udnytte hele det tørre vejgreb, fordi bremsesystemet og hensynet til stående passagerer begrænser decelerationen; regn derfor i praksis med lavere a end den rene friktion tillader.
| Lead | Typical µ | Deceleration a ≈ µ·g |
|---|---|---|
| Dry asphalt | 0,7-0,8 | approx. 7-8 m/s² (bus: often 5-6) |
| Wet asphalt | 0,4-0,6 | ca. 4-6 m/s² |
| Sne | 0,2-0,3 | ca. 2-3 m/s² |
| Is | 0,1-0,15 | ca. 1-1,5 m/s² |
Stopping distance at different speeds
Med reaktionstid 1,0 s og deceleration a = 6 m/s² (tør) hhv. a = 3,5 m/s² (våd) fås standselængderne nedenfor. Læg mærke til, hvordan afstanden vokser langt hurtigere end farten — fordi bremselængden går med kvadratet.
| Speed | Reaction distance | Braking distance, dry | Braking distance, wet |
|---|---|---|---|
| 30 km/t | ca. 8 m | ca. 14 m | ca. 18 m |
| 50 km/t | ca. 14 m | ca. 30 m | ca. 41 m |
| 70 km/t | ca. 19 m | ca. 51 m | ca. 73 m |
| 80 km/t | ca. 22 m | ca. 63 m | ca. 93 m |
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