Car - Traction Force
Adhesion and tractive force between car wheel and surface.
The tractive force between a car wheel and the surface can be expressed as
F = μt W
= μt m ag (1)
where
F = traction effort or force acting on the wheel from the surface (N, lbf)
μt = traction - or friction - coefficient between the wheel and the surface
W = weight or vertical force between wheel and surface (N, lbf))
m = mass on the wheel (kg, slugs)
ag = acceleration of gravity (9.81 m/s2, 32.17405 ft/s2)
Traction Coefficients for normal Car Tires
| Surface | Traction Coefficient - μt - |
|---|---|
| Wet Ice | 0.1 |
| Dry Ice/Snow | 0.2 |
| Loose Sand | 0.3 - 0.4 |
| Dry Clay | 0.5 - 0.6 |
| Wet rolled Gravel | 0.3 - 0.5 |
| Dry rolled Gravel | 0.6 - 0.7 |
| Wet Asphalt | 0.6 |
| Wet Concrete | 0.6 |
| Dry Asphalt | 0.9 |
| Dry Concrete | 0.9 |
Note that the static friction varies with the car velocity. Higher velocity -> less friction.
- The static friction of a new tire on dry asphalt is 0.9 at 0 km/h, 0.85 at 50 km/h , 0.8 at 90 km/h and 0.75 at 130 km/h.
The static friction also depends on the tire, if its new or worn (1.6 mm tread dept), in combination with the state of the road surface, if its dry or wet.
- The static friction on dry asphalt at 130 km/h is 0.75 for a new tire and 0.9 for a worn tire.
- The static friction on wet asphalt at 130 km/h is 0.55 for a new tire and 0.2 for a worn tire.
Example - Traction Force on an Accelerating Car
The maximum traction force available from one of the two rear wheels on a rear wheel driven car - with mass 2000 kg equally distributed on all four wheels - on wet asphalt with adhesion coefficient 0.5 - can be calculated as
Fone_wheel = 0.5 ((2000 kg) (9.81 m/s2) / 4)
= 2453 N
The traction force from both rear wheels
Fboth_wheels = 2 (2452 N)
= 4905 N
Note! - that during acceleration the force from the engine creates a moment that tries to rotate the vehicle around the driven wheels. For a rear drive car this is beneficial by increased vertical force and increased traction on the driven wheels. For a front wheel driven car the available traction force will be reduced during acceleration.
The maximum acceleration of the car under these conditions can be calculated with Newton's Second Law as
acar = F / m
= (4904 N) / (2000 kg)
= 2.45 m/s2
= (2.45 m/s2) / (9.81 m/s2)
= 0.25 g
where
acar = acceleration of car (m/s2)
The minimum time to accelerate from 0 km/h to 100 km/h can be calculated as
dt = dv / acar
= ((100 km/h) - (0 km/h)) (1000 m/km) (1/3600 h/s) / (2.4 m/s2)
= 11.3 s
where
dt = time used (s)
dv = change in velocity (m/s)
Accelerating Car Calculator
This calculator can be used to calculate the maximum acceleration and minimum accelation time for a car on different surfaces.
