Car - Traction Force
Adhesion and tractive effort
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 |
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 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.
mass of car (kg)
traction coefficient
no. of traction wheels
final velocity (km/h)