TRN-06

Traffic fundamental relation

q = k v, the definition of traffic flow.

Reading speed

Traffic flowLighthill–WhithamHCM

Governing equation

q = k\,\bar v

where

k: Density (veh/km)
\bar v: Space-mean speed (km/h)
q: Flow (veh/h)

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-06 — Traffic fundamental relation) is the form associated with Lighthill–Whitham · HCM. Working symbols: $k$ , $\bar v$ $\rightarrow$ $q$ . Flow is the product of spatial density and space-mean speed. It is the identity behind every fundamental diagram.

Purpose

Purpose: compute

q

from

k

\bar v

in Transport via

q = k\,\bar v

q = k v, the definition of traffic flow. Use it when a real transport question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

k = 25.000\,\mathrm{veh/km}

\bar v = 70.000\,\mathrm{km/h}

, the governing relation

q = k\,\bar v

yields

q = 1750.000\,\mathrm{veh/h}

. Single stream, consistent units veh/km and km/h. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Density k25 veh/kmSpace-mean speed \bar v70 km/h

Outputs

Flow q1750.000 veh/h

Reading speed

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Narration of this film

Single stream, consistent units veh/km and km/h.

Flow is the product of spatial density and space-mean speed. It is the identity behind every fundamental diagram.

Reading speed

Watch on YouTube