TRN-28

Minimum curve radius

R = v² / (g (e + f)). Side friction plus superelevation balance the lateral acceleration.

Reading speed

Geometric designAASHTO Rmin

Governing equation

R=\dfrac{v^2}{g(e+f)}

where

v: Speed (m/s)
e: Superelevation (—)
f: Side friction (—)
R: Minimum radius (m)

Lecture brief

Historical brief

Highway and traffic theory crystallized with Greenshields’ 1935 speed–density line, then AASHTO stopping sight and equivalent axles. The lab is that operational arithmetic of flow, braking and pavement load. This sheet (TRN-28 — Minimum curve radius) is the form associated with AASHTO Rmin. Working symbols: $v$ , $e$ , $f$ $\rightarrow$ $R$ . Resolve weight on a banked pavement. e is the cross-slope, f the lateral friction used (less than available).

Purpose

Purpose: compute

R

from

v

e

f

in Transport via

R=\dfrac{v^2}{g(e+f)}

R = v² / (g (e + f)). Side friction plus superelevation balance the lateral acceleration. Use it when a real transport question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

v = 25.000\,\mathrm{m/s}

e = 0.060\,\mathrm{—}

f = 0.120\,\mathrm{—}

, the governing relation

R=\dfrac{v^2}{g(e+f)}

yields

R = 353.9\,\mathrm{m}

. A car, a banked curve, a minimum R. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Speed v25 m/sSuperelevation e0.06 —Side friction f0.12 —

Outputs

Minimum radius R353.9 m

Reading speed

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Narration of this film

A car, a banked curve, a minimum R.

Resolve weight on a banked pavement. e is the cross-slope, f the lateral friction used (less than available).

Reading speed

Watch on YouTube