TRN-07

Friction braking distance

d = v² /(2 μ g) on a level road.

Reading speed

BrakingAASHTOUNECE R13

Governing equation

d=\dfrac{v^2}{2\mu g}

$v \in \left[10, 160\right]$

where

v: Speed (km/h)
\mu: Friction coefficient (—)
d: Braking distance (m)

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

d=\dfrac{v^2}{2\mu g}

$v \in \left[10, 160\right]$

$v = 10$ $d = 0.562$

Along the curve

②

Domain of the variable — blue

v_{\min} = 10,\quad v_{\max} = 160

$v \in \left[10, 160\right]$

$v = 10$ $v = 10$

Along the curve

③

Response curve — green

d=\dfrac{v^2}{2\mu g}

$v \in \left[10, 160\right]$

$v = 10$ $d = 0.562$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}d}{\mathrm{d}v}

$v \in \left[10, 160\right]$

$v = 10.94$ $d^{\prime} = 0.123$

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-07 — Friction braking distance) is the form associated with AASHTO · UNECE R13. Working symbols: $v$ , $\mu$ $\rightarrow$ $d$ . Work–energy or constant-deceleration kinematics with a = μ g yields the classic braking length.

Purpose

Purpose: compute

d

from

v

\mu

in Transport via

d=\dfrac{v^2}{2\mu g}

d = v² /(2 μ g) on a level road. 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 = 90.000\,\mathrm{km/h}

\mu = 0.700\,\mathrm{—}

, the governing relation

d=\dfrac{v^2}{2\mu g}

yields

d = 45.507\,\mathrm{m}

. Level, locked or ABS-equivalent μ, no aerodynamic drag. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Speed v90 km/hFriction coefficient \mu0.7 —

Outputs

Braking distance d45.507 m

Reading speed

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Narration of this film

Level, locked or ABS-equivalent μ, no aerodynamic drag.

Work–energy or constant-deceleration kinematics with a = μ g yields the classic braking length.

Reading speed

Watch on YouTube