Braking Distance in Physics
To illustrate the principle of the braking event, tyre tests are carried out as practical experiments using new tyres. The basic assumption is that all cars come to a stop within the same braking distance. In practice, however, systems such as ABS brakes, electronic stability control, as well as differences in vehicle weight and load distribution, all influence the outcome and can alter the braking behaviour significantly.
In Finland, the asphalt surface is rough in spring due to studded tyres, but it becomes smoother over the summer. The braking distances in the tests are reported as average values, and failed braking attempts are excluded from the results. In a panic situation, a braking event refers to the driver applying sudden, maximum braking without any prior preparation.
The calculation of braking distance does not take the driver’s reaction time into account. In addition, friction‑based calculations assume a rigid body, whereas a car with its suspension and tyres does not behave as one in reality. Road‑surface properties also vary, and the surface is not uniform along the entire stretch. There are therefore many variables. Tyre tests are carried out in winter on dry ice and, for summer tyres, on dry asphalt, but real‑world braking conditions may differ significantly from these, even though the tests are performed by professional drivers.
Braking distance is directly proportional to the square of the vehicle’s speed and inversely proportional to the coefficient of friction between the road surface and the tyre.
S = braking distance v = initial speed m/s μ = friction g = 9,82 m/s2
S = v2 / (2 x μ x g)
Friction
Static Kinetic
Wet asphalt 0.6 0,5
Dry asphalt 0,8 0.7
Wet ice 0,1 0,08
Dry ice 0,2 0,15
On a dry road, a car with a weight of 10 kN (equivalent to 1000 kg) travelling at 100 km/h (27.78 m/s) has a calculated braking distance of 49 metres when the coefficient of friction for dry asphalt is taken as 0.8. Tests carried out both with locked wheels and with non‑locking braking show that, on a hard and even surface, the resulting braking distances are practically almost identical.
S = 27.782 /(2 x 0,8 x 9,82) m
S = 49 m
When calculating stopping distance, a friction coefficient of 0.8 corresponds to nominal static friction. The tabulated values describe conditions in which both the tyres and the road surface are in good condition. Friction decreases on wet, icy, slippery, sandy, dirty or oily surfaces. For worn, normally used tyres, a lower value such as 0.7 or 0.6 is typically applied. Depending on conditions, tyres in poor condition may require a friction coefficient as low as 0.5 or even 0.4.
Braking distance at 100 km/h speed is 49 m. How far is the braking distance at 50 km/h?
49/x = (100/50)2
(1002) x = (502) * 49
10 000 x = 122 500
x=122 500/10 000
x= 12.25 m
Check:
S = 13.882 /(2 x 0,8 x 9,82) m
S = 12,26 m
EP-Calculation does not rely on equations but on the relationships between values. The previous text correctly describes its principle: when one value pair is known, the others can be derived from it through proportionality. Calculation is particularly effective in situations where no explicit formula exists. The known value contains, in proportion, the unknown component that is transferred into the quantity being calculated.
26.1.2021*14:30 (990 - 989)
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