Library / Automotive and vehicle dynamics / VEH-46
Automotive and vehicle dynamics
Steady cornering axle force distribution
Lateral force on the front axle in a level steady corner, from the mass m, lateral acceleration ay and the distances a and b from the centre of gravity to the front and rear axles, with L = a + b.
- Ref
- VEH-46
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- Fyf [N]
In a steady level corner the total lateral force is m·ay, and moments about the rear axle give Fyf·L = m·ay·b, with L = a + b. So the front axle carries the fraction b/L of the lateral force and the rear axle the fraction a/L. The axle nearer the centre of gravity takes the larger share. The force on each axle is then shared between its two tyres, with load transfer making the share uneven.
Lateral force on the front axle in a level steady corner, from the mass m, lateral acceleration ay and the distances a and b from the centre of gravity to the front and rear axles, with L = a + b. The rear axle takes m ay a/L. It ignores steer-angle projection and external yaw moments.
Calculator
- Rear-axle lateral force, m ay a/L2,400 N
- Total lateral force, m ay6,000 N
- Front share of the lateral force, b/L60 %
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.
- The front axle carries 3,600 N of the 6,000 N total, 60 %, and the rear axle takes 2,400 N.
- The shares equal the static weight shares, so tyres of equal capability per unit load run at similar slip angles; that is the neutral-steer condition.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| m Vehicle mass | 100 to 50,000 kg | 240 | 120,000 | 119,800 | +10% | +10 % |
| ay Lateral acceleration | −10 to 10 m/s² | −9,000 | 9,000 | 18,000 | +0.4 m/s² | +10 % |
| b CG to rear axle | 0.2 to 5 m | 857.1 | 4,839 | 3,982 | +10% | +3.77 % |
| a CG to front axle | 0.2 to 5 m | 1,588 | 5,400 | 3,812 | +10% | −3.85 % |
Sweep of Lateral acceleration
| Lateral acceleration (m/s²) | Front-axle lateral force (N) |
|---|---|
| −10 | −9,000 |
| −7.5 | −6,750 |
| −5 | −4,500 |
| −2.5 | −2,250 |
| 0 | 0 |
| 2.5 | 2,250 |
| 5 | 4,500 |
| 7.5 | 6,750 |
| 10 | 9,000 |
Sweep one variable
Variables and how each one contributes
Front-axle lateral force
What the equation gives you. Everything else feeds it.
Vehicle mass
The vehicle mass, in kg. Raises both axle forces in direct proportion. Raising it by 10 % (to 1,650) moves the result by +10 %, from 3,600 to 3,960 N.
Lateral acceleration
The lateral acceleration, in m/s². Raises both axle forces in direct proportion. Raising it by 10 % (to 4.4) moves the result by +10 %, from 3,600 to 3,960 N.
CG to front axle
The distance from the centre of gravity to the front axle, in m. A larger a moves the centre of gravity towards the rear, which lowers the front share b/(a + b) and raises the rear share. Raising it by 10 % (to 1.32) moves the result by −3.85 %, from 3,600 to 3,462 N.
CG to rear axle
The distance from the centre of gravity to the rear axle, in m. A bigger b raises the front-axle share b/(a + b). Raising it by 10 % (to 1.98) moves the result by +3.77 %, from 3,600 to 3,736 N.
Worked example with the values above
- Wheelbase: L = a + b = 1.2 + 1.8 = 3 m.
- Total lateral force: m ay = 1,500 × 4 = 6,000 N.
- Fyf = 6,000 × 1.8 / 3 = 3,600 N.
Assumptions and limits
- A rigid vehicle on a flat road in steady or slowly varying motion, small angles and a linear single-track (bicycle) model where stated.
- Level road, no aerodynamic yaw moment and no roll effects on the axle forces unless the page says so.
Common mistakes
- Mixing up a and b: a is measured to the front axle and b to the rear axle.
- Using the track-averaged force for an axle without checking the total.
- Entering the path radius without its sign, which flips the sideslip sign.
Statistics and uncertainty
Yaw inertia and cornering stiffness are usually known to 10 % to 20 %, and steady sideslip is the small difference of two similar terms, so it is more sensitive to errors than either term alone.
Where it is used
- Splitting cornering force between axles and checking handling balance.
- Yaw-control and torque-vectoring design, and banked test-track layout.
Maths you need
- Newton’s second law: F = ma, for force and for moment
- Single-track model: two tyres lumped as one per axle
- Centripetal acceleration: a = U²/R