Library / Automotive and vehicle dynamics / VEH-05
Automotive and vehicle dynamics
Available tractive force (torque or grip limited)
The force the driven wheels can actually push with: the smaller of what the engine and transmission can deliver and what the tyres can grip.
- Ref
- VEH-05
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- Favail [kN]
The first term is the force the engine and transmission can deliver at the contact patch; the second is the greatest force the tyres can transmit by friction, μx times the normal load on the driven wheels. The vehicle can use only the smaller. Excess engine force beyond the grip limit makes the driven wheels spin. Fz,driven should be the actual driven-axle load, including weight transfer and any slope.
The force the driven wheels can actually push with: the smaller of what the engine and transmission can deliver and what the tyres can grip. Below the grip limit the drivetrain governs; above it the wheels spin.
Calculator
- Engine-limited force, ηd G Te / Re10.8 kN
- Grip-limited force, μx Fz,driven8 kN
- Friction coefficient needed to use all the engine force1.08
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At the defaults the engine could deliver 10.8 kN but the tyres can transmit only 8 kN, so the vehicle is traction limited and the extra torque would spin the wheels.
- On a slippery surface (μ = 0.3) the available force drops to 3 kN however much torque there is, which is why traction, not engine power, limits movement on mud, snow and ice.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kN) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Fz,driven Normal load on the driven wheels | 1 to 60 kN | 0.8 | 10.8 | 10 | +10% | +10 % |
| μx Longitudinal tyre–road friction coefficient | 0.1 to 1.5 | 1 | 10.8 | 9.8 | +10% | +10 % |
| Te Engine or motor torque | 50 to 600 N·m | 1.8 | 8 | 6.2 | +10% | 0 % |
| G Total reduction ratio (gearbox × final drive) | 2 to 20 | 1.8 | 8 | 6.2 | +10% | 0 % |
| Re Effective rolling radius | 0.2 to 0.5 m | 6.48 | 8 | 1.52 | +10% | 0 % |
| ηd Drivetrain efficiency | 0.7 to 1 | 8 | 8 | 0 | +10% | 0 % |
Sweep of Engine or motor torque
| Engine or motor torque (N·m) | Available tractive force (kN) |
|---|---|
| 50 | 1.8 |
| 118.8 | 4.275 |
| 187.5 | 6.75 |
| 256.3 | 8 |
| 325 | 8 |
| 393.8 | 8 |
| 462.5 | 8 |
| 531.3 | 8 |
| 600 | 8 |
Sweep one variable
Variables and how each one contributes
Available tractive force
What the equation gives you. Everything else feeds it.
Engine or motor torque
The torque at the engine or motor shaft, in N·m. Raises the engine-limited force in proportion. At the defaults the grip limit is the smaller one, so extra torque changes nothing: it only spins the wheels. It matters only once the torque limit is the smaller. Raising it by 10 % (to 330) moves the result by +0 %, from 8 to 8 kN.
Total reduction ratio (gearbox × final drive)
The overall reduction from engine to wheels (gearbox ratio times final drive). Raises the engine-limited force in proportion, but at the defaults grip governs and the result does not change. It matters only in the higher gears, where the torque limit is the smaller. Raising it by 10 % (to 13.2) moves the result by +0 %, from 8 to 8 kN.
Drivetrain efficiency
The driveline efficiency, between 0 and 1. Raises the engine-limited force in proportion. At the defaults the grip limit governs, so the result is unchanged. Raising it by 10 % (to 0.99) moves the result by +0 %, from 8 to 8 kN.
Effective rolling radius
The effective rolling radius of the driven tyres, in m. Lowers the engine-limited force in inverse proportion, but at the defaults grip is the smaller limit, so the result stays the same. Raising it by 10 % (to 0.33) moves the result by +0 %, from 8 to 8 kN.
Longitudinal tyre–road friction coefficient
The longitudinal friction coefficient between the tyre and the ground: about 0.8 to 1 on dry tarmac, 0.5 on wet, 0.2 on snow and 0.1 on ice. Raises the grip limit in proportion, so while grip governs the result rises in the same proportion. Raising it by 10 % (to 0.88) moves the result by +10 %, from 8 to 8.8 kN.
Normal load on the driven wheels
The normal load on the driven wheels, in kN. For a front- or rear-drive car it is only that axle’s share of the weight, adjusted for weight transfer and slope. Raises the grip limit in proportion, so while grip governs the result rises in the same proportion. Raising it by 10 % (to 11) moves the result by +10 %, from 8 to 8.8 kN.
Worked example with the values above
- Engine and transmission limit: ηd G Te / Re = 0.9 × 12 × 300 / 0.3 = 10,800 N = 10.8 kN.
- Grip limit: μx Fz,driven = 0.8 × 10 kN = 8 kN.
- Favail = the smaller = 8 kN (grip limited).
Assumptions and limits
- A simple adhesion limit with a constant friction coefficient, ignoring that the coefficient varies with slip, speed and surface.
- Fz,driven is the actual normal load on the driven wheels, including weight transfer, slope and any aerodynamic downforce.
Common mistakes
- Using the whole vehicle weight for Fz,driven on a two-wheel-drive vehicle. Only the driven axle load counts.
- Forgetting weight transfer: a rear-drive car gains rear load when accelerating, and a front-drive car loses front load.
Statistics and uncertainty
Only the smaller of the two terms matters, so the uncertainty comes from whichever one governs. The engine-limited force is known to a few per cent. The friction coefficient is the biggest uncertainty: it can differ by 20 % or more between surfaces, tyre temperature and wear, so a grip-limited result should be treated as an estimate and not a precise figure.
Where it is used
- Telling whether a launch or a hill climb is power limited or grip limited.
- Choosing tyres, ballast or a differential type to improve traction.
Maths you need
- Friction: F ≤ μ N
- Drive force: engine torque turned into force at the tyre