TRN-32

Jam density from spacing

kj = 1000 / sj. sj is bumper-to-bumper spacing in metres, kj in veh/km.

Reading speed

TrafficJam density

Governing equation

k_j=1000/s_j

$s_j \in \left[4.5, 12\right]$

where

s_j: Jam spacing (m)
k_j: Jam density (veh/km)

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

k_j=1000/s_j

$s_j \in \left[4.5, 12\right]$

$s_j = 4.5$ $k_j = 222.2$

Along the curve

②

Domain of the variable — blue

s_j_{\min} = 4.5,\quad s_j_{\max} = 12

$s_j \in \left[4.5, 12\right]$

$s_j = 4.5$ $s_j = 4.5$

Along the curve

③

Response curve — green

k_j=1000/s_j

$s_j \in \left[4.5, 12\right]$

$s_j = 4.5$ $k_j = 222.2$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}k_j}{\mathrm{d}s_j}

$s_j \in \left[4.5, 12\right]$

$s_j = 4.547$ $k_j^{\prime} = -48.37$

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-32 — Jam density from spacing) is the form associated with Jam density. Working symbols: $s_j$ $\rightarrow$ $k_j$ . A parked queue occupies about 6–8 m per car. kj ≈ 125–170 veh/km/lane is the usual range.

Purpose

Purpose: compute

k_j

from

s_j

in Transport via

k_j=1000/s_j

kj = 1000 / sj. sj is bumper-to-bumper spacing in metres, kj in veh/km. Use it when a real transport question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

s_j = 7.000\,\mathrm{m}

, the governing relation

k_j=1000/s_j

yields

k_j = 142.9\,\mathrm{veh/km}

. Parked cars, a spacing, a jam density. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Jam spacing s_j7 m

Outputs

Jam density k_j142.9 veh/km

Reading speed

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Narration of this film

Parked cars, a spacing, a jam density.

A parked queue occupies about 6–8 m per car. kj ≈ 125–170 veh/km/lane is the usual range.

Reading speed

Watch on YouTube