# Car - Traction Force

The tractive force between a car wheel and the surface can be expressed as

* F = μ _{ t } W *

* = μ _{ t } m a _{ g } (1) *

* where *

* F = traction effort or force acting on the wheel from the surface (N, lb _{ f } ) *

* μ _{ t } = traction - or friction - coefficient between the wheel and the surface *

* W = weight or vertical force between wheel and surface (N, lb _{ f } ) ) *

* m = mass on the wheel (kg, slugs ) *

* a _{ g } = acceleration of gravity (9.81 m/s^{2}, 32.17405 ft/s^{2}) *

### Traction Coefficients for normal Car Tires

Surface | Traction Coefficient - μ _{ t } - |
---|---|

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

* F _{ one_wheel } = 0.5 ((2000 kg) (9.81 m/s^{2}) / 4) *

* = 2453 N *

The traction force from both rear wheels

* F _{ both_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

* a _{ car } = F / m *

* = (4904 N) / (2000 kg) *

* = 2.45 m/s ^{2}*

* = (2.45 m/s ^{2}) / (9.81 m/s^{2}) *

* = 0.25 g *

* where *

* a _{ car } = acceleration of car (m/s^{2}) *

The minimum time to ** accelerate from 0 km/h to 100 km/h ** can be calculated as

* dt = dv / a _{ car } *

* = ((100 km/h) - (0 km/h)) (1000 m/km) (1/3600 h/s) / (2.4 m/s ^{2}) *

* = 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.

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