An ideally banked curve can provide the needed inward force through the road’s normal force without relying on friction.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, consistent units, and the stated model assumptions
Source
OpenStax, College Physics 2e, §6.3 (Paul Peter Urone and Roger Hinrichs)OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.
An ideally banked curve can provide the needed inward force through the road’s normal force without relying on friction. The bank angle matches one design speed for a given radius.
| Symbol | Meaning | Units |
|---|---|---|
| Bank angle above horizontal | ||
| Vehicle speed | ||
| Radius | ||
| Acceleration Due to Gravity |
Find the frictionless design angle.
Compare ideal bank angles at different speeds.
Find the ideal bank angle for speed 20 m/s, path radius 100 m, and g = 9.80 m/s². Express the angle in radians.
OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.
Assumptions
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