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Cornering Force Calculator

This calculator estimates the lateral cornering force acting on a vehicle during a turn, accounting for road slope, mass, friction, and radius of the curve. It also calculates the maximum safe velocity to prevent skidding. Ideal for civil engineers and transportation safety analysts designing safe roadway curves.

Vehicle Cornering Force and Speed Estimator

Input Fields
μ
g
m/s²
m
kg
r
m
α
°
If enabled, the result will update automatically when you change any value.

Cornering Force and Velocity Formula

Formula
\[\text{Friction Force (t)} = \mu \cdot m \cdot g \cdot \sin(\alpha) \]\[\text{Net Force (f)} = (\mu \cdot m \cdot g \cdot \sin(\alpha)) + (m \cdot g \cdot \cos(\alpha)) \]\[\text{Max Speed (v)} = \sqrt{\frac{f \cdot r}{m}} \cdot 3.6 \]

Where:

  • $$\mu$$ = coefficient of friction
  • $$m$$ = mass of the vehicle (kg)
  • $$g$$ = gravitational acceleration (9.81 m/s²)
  • $$\alpha$$ = road banking angle (in radians)
  • $$r$$ = curve radius (m)
  • $$v$$ = maximum velocity (km/h)


These formulas are used to estimate the lateral force exerted on a vehicle as it corners, which is critical in roadway curve design. The frictional force component reflects grip due to road conditions and incline. Net force combines this with normal force effects from banking. The final equation estimates the highest safe speed before losing traction — essential for highway curve safety and motorsport track design.

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