Paritian

Physics

Banked Curve Speed Calculator

Design speed of a banked curve with no friction, the maximum speed with grip, and the flat-road limit.

Results

Speed 46.30 km/h
Speed 119.24 km/h
Speed 103.32 km/h
Banking angle 8.000 °

What this tool does

The first result is the speed at which a car rounds the curve needing no sideways grip at all — that is the speed roads are banked for, so ice makes no difference to it. The second adds the grip the tyres can supply on top. Typical dry asphalt gives about 0.7; wet drops to 0.4 and ice to under 0.1, which is where the first number earns its keep.

Formula

v = √(r g tan θ) (banked curve, no friction)

Variables

SymbolMeaningUnit
rRadiusm
anBanking angle°
muFriction coefficient
VSpeedkm/h
VMSpeedkm/h
VFSpeedkm/h
ANBanking angle°

Worked example

  • Radius120 m
  • Banking angle8 °
  • Friction coefficient0.7
  • Speed46.30 km/h
  • Speed119.24 km/h
  • Speed103.32 km/h
  • Banking angle8.000 °

Limitations

  • The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
  • The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
  • For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.