TRN-04

Equilibrium rail cant

e = G v² /(g R) for a balanced curve.

Reading speed

Rail geometryEN 13803AREMA

Governing equation

e=\dfrac{G v^2}{g R}

$R \in \left[150, 5000\right]$

where

G: Track gauge (m)
v: Speed (km/h)
R: Curve radius (m)
e: Equilibrium cant (mm)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

e=\dfrac{G v^2}{g R}

$R \in \left[150, 5000\right]$

$R = 150$ $e = 481.6$

Along the curve

②

Domain of the variable — blue

R_{\min} = 150,\quad R_{\max} = 5000

$R \in \left[150, 5000\right]$

$R = 150$ $R = 150$

Along the curve

③

Response curve — green

e=\dfrac{G v^2}{g R}

$R \in \left[150, 5000\right]$

$R = 150$ $e = 481.6$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}e}{\mathrm{d}R}

$R \in \left[150, 5000\right]$

$R = 180.5$ $e^{\prime} = -2.282$

Along the curve

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-04 — Equilibrium rail cant) is the form associated with EN 13803 · AREMA. Working symbols: $G$ , $v$ , $R$ $\rightarrow$ $e$ . Lateral acceleration v²/R is cancelled by a superelevation e that tilts the resultant through the track centre.

Purpose

Purpose: compute

e

from

G

v

R

in Transport via

e=\dfrac{G v^2}{g R}

e = G v² /(g R) for a balanced curve. Use it when a real transport question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

G = 1.435\,\mathrm{m}

v = 80.000\,\mathrm{km/h}

R = 600.000\,\mathrm{m}

, the governing relation

e=\dfrac{G v^2}{g R}

yields

e = 120.394\,\mathrm{mm}

. No deficiency, standard gauge G in m, speed in km/h. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Track gauge G1.435 mSpeed v80 km/hCurve radius R600 m

Outputs

Equilibrium cant e120.394 mm

Reading speed

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Narration of this film

No deficiency, standard gauge G in m, speed in km/h.

Lateral acceleration v²/R is cancelled by a superelevation e that tilts the resultant through the track centre.

Reading speed

Watch on YouTube