Calculators · Vehicle
Cornering, turning radius and Ackermann steering calculator
Every corner asks the tyres for sideways grip. How much depends on speed and the tightness of the bend, and the limit depends on the road surface. These calculators give the lateral acceleration in a corner, the highest speed the tyres can hold on a given radius, a vehicle’s turning radius from its wheelbase and steering lock, and the Ackermann steering angles that let both front wheels follow their own circle.
Lateral acceleration in a corner
Calculates the sideways acceleration — cornering g-force — at a given speed and corner radius. Everyday driving rarely exceeds 0.3 g; road cars on dry asphalt typically reach their grip limit around 0.8–1.0 g.
a = v² / r
Maximum cornering speed
The fastest a vehicle can take a flat corner before the tyres lose grip, from the corner radius and the friction coefficient. It ignores banking, weight transfer and tyre load sensitivity, so the true limit is usually a little lower.
v_max = √(μ × g × r)
Turning radius from wheelbase and steering lock
Estimates the radius traced by the outer front wheel at full steering lock, from the wheelbase and the maximum steering angle. Kerb-to-kerb turning circles quoted by manufacturers are slightly larger because they include tyre width.
R = wheelbase / sin(δ)
Ackermann steering angles
In a turn the inner front wheel follows a tighter circle than the outer one, so it must steer more. Ackermann geometry gives the outer-wheel angle that matches a given inner angle, so neither tyre scrubs sideways at low speed.
cot(δ_outer) = cot(δ_inner) + track / wheelbase
Worked example: a 50 m bend
- At 60 km/h (16.7 m/s) on a 50 m radius, lateral acceleration is 16.7² / 50 = 5.6 m/s², or 0.57 g.
- With dry-road grip of μ = 0.8 the limit on that bend is √(0.8 × 9.81 × 50) = 19.8 m/s, about 71 km/h.
- A 2.7 m wheelbase with 35° of lock gives a turning radius of about 4.7 m — a 9.4 m turning circle.
- With a 1.55 m track, a 35° inner wheel angle needs about 26.5° on the outer wheel.
Maximum speed on a level curve
| Radius | Dry (μ 0.8) | Wet (μ 0.5) | Snow (μ 0.2) |
|---|---|---|---|
| 20 m | about 45 km/h | about 36 km/h | about 23 km/h |
| 50 m | about 71 km/h | about 56 km/h | about 36 km/h |
| 100 m | about 101 km/h | about 80 km/h | about 50 km/h |
| 250 m | about 159 km/h | about 126 km/h | about 80 km/h |
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About these results
Results are theoretical estimates from standard engineering formulas. Real-world figures depend on conditions these formulas do not capture. Always follow the manufacturer's specifications for maintenance, loading and safety decisions.
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