Calculate the maximum cornering speed for a curve radius using typical tire grip, plus banked-turn limits, lateral g and an optional rollover check.

Grip limit v = โˆš(ฮผยทgยทr). Add a vehicle to also check the rollover limit.

Typical peak tire-road friction values; real grip varies with tire, temperature and load.

Rollover check (optional)
Rollover limit uses the static stability factor, track รท (2 ร— CG height); real vehicles tip later or sooner.

Cornering Speed Formula

The following formula is used to calculate the cornering speed for a given set of parameters.

v = โˆš(ฮผ ร— g ร— r)

Variables:

  • v is the cornering speed
  • ฮผ is the tire friction coefficient
  • g is the gravitational acceleration (approximately 9.81 m/sยฒ)
  • r is the corner radius
  • h is the vehicle's center-of-gravity height (optional rollover check)
  • w is the track width (optional rollover check, rollover limit v = โˆš(g ยท r ยท w / (2h)))

To calculate the cornering speed, use the formula above with the tire friction coefficient, gravitational acceleration and corner radius. The result is the grip limit in meters per second. The center-of-gravity height and track width give a separate rollover limit; the lower of the two speeds governs.

What is Cornering Speed?

Cornering speed refers to the maximum speed at which a vehicle can safely navigate a turn or corner without losing traction. This speed is influenced by several factors, including the tire friction coefficient, gravitational acceleration, corner radius, vehicle height, and track width. Understanding and calculating cornering speed is crucial for vehicle dynamics and safety, especially in high-performance and racing scenarios.

How to Calculate Cornering Speed?

The following steps outline how to calculate the cornering speed.

  1. First, determine the tire friction coefficient (ฮผ).
  2. Next, determine the gravitational acceleration (g), which is approximately 9.81 m/sยฒ.
  3. Next, determine the corner radius (r).
  4. Next, for a rollover check, determine the center-of-gravity height (h).
  5. Next, determine the track width (w).
  6. Finally, calculate the cornering speed using v = โˆš(ฮผ * g * r), and compare it with the rollover limit โˆš(g * r * w / (2h)).
  7. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Tire Friction Coefficient (ฮผ) = 0.8

Gravitational Acceleration (g) = 9.81 m/sยฒ

Corner Radius (r) = 50 m

Vehicle Height (h) = 1.5 m

Track Width (w) = 1.8 m