TRN-10

Stopping sight distance

SSD = v t + v² / (2 g (f±G)). Perception–reaction plus braking.

Reading speed

TrafficAASHTO SSD

Governing equation

SSD=vt+\dfrac{v^2}{2g(f+G)}

$v \in \left[5, 45\right]$

where

v: Speed (m/s)
t: Reaction time (s)
f: Friction (—)
G: Grade (—)
SSD: Sight 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

SSD=vt+\dfrac{v^2}{2g(f+G)}

$v \in \left[5, 45\right]$

$v = 5$ $SSD = 16.14$

Along the curve

②

Domain of the variable — blue

v_{\min} = 5,\quad v_{\max} = 45

$v \in \left[5, 45\right]$

$v = 5$ $v = 5$

Along the curve

③

Response curve — green

SSD=vt+\dfrac{v^2}{2g(f+G)}

$v \in \left[5, 45\right]$

$v = 5$ $SSD = 16.14$

Along the curve

④

Rate of change — amber

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

$v \in \left[5, 45\right]$

$v = 5.252$ $SSD^{\prime} = 4.03$

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-10 — Stopping sight distance) is the form associated with AASHTO SSD. Working symbols: $v$ , $t$ , $f$ , $G$ $\rightarrow$ $SSD$ . t ≈ 2.5 s AASHTO. f is the longitudinal friction available.

Purpose

Purpose: compute

SSD

from

v

t

f

G

in Transport via

SSD=vt+\dfrac{v^2}{2g(f+G)}

SSD = v t + v² / (2 g (f±G)). Perception–reaction plus braking. 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}

t = 2.500\,\mathrm{s}

f = 0.350\,\mathrm{—}

G = 0.000\,\mathrm{—}

, the governing relation

SSD=vt+\dfrac{v^2}{2g(f+G)}

yields

SSD = 153.5\,\mathrm{m}

. A driver, a brake, a fading speed. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Speed v25 m/sReaction time t2.5 sFriction f0.35 —Grade G0 —

Outputs

Sight distance SSD153.5 m

Reading speed

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Narration of this film

A driver, a brake, a fading speed.

t ≈ 2.5 s AASHTO. f is the longitudinal friction available.

Reading speed

Watch on YouTube