How this calculator works
An ideal bank tilts the support force inward to provide centripetal acceleration. The same geometry describes a level coordinated aircraft turn, whose load factor rises as bank increases. Road friction permits a range of speeds. The minimum is zero when friction can hold the vehicle stationary on the slope. These limits omit rollover, suspension, aerodynamics and changing grip.
Formula
tan(theta) = v²/(rg); r = v²/(g tan(theta)); n = 1/cos(theta). Road vmax² = rg(tan(theta)+mu)/(1-mu tan(theta)); vmin² = rg max(0,(tan(theta)-mu)/(1+mu tan(theta))).
Worked example
At 10 m/s, radius 10 m and g = 10 m/s², the ideal bank is 45 degrees. With the same speed and bank the turn radius is 10 m.
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Frequently asked questions
Is bank angle a road safety recommendation?
No. It is an ideal steady-turn calculation and cannot establish a safe driving speed.
Which angle should I enter?
Measure the road surface or aircraft wings from horizontal, with the bank leaning into the turn.
Why is there no finite maximum in some cases?
The simplified point-mass friction model stops imposing an upper speed when its denominator is zero or negative. Real vehicles still have limits.