TRN-27

Highway lane capacity

c = c0 N fw fHV fp. HCM multilane snapshot, c0 ≈ 2200 pc/h/ln.

Reading speed

TrafficHCM

Governing equation

c=c_0 N f_w f_{HV} f_p

$N \in \left[1, 6\right]$

where

c_0: Ideal capacity (pc/h/ln)
N: Lanes (—)
f_w: Width factor (—)
f_{HV}: Heavy-vehicle factor (—)
f_p: Driver factor (—)
c: Capacity (veh/h)

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

c=c_0 N f_w f_{HV} f_p

$N \in \left[1, 6\right]$

$N = 1$ $c = 1900.8$

Along the curve

②

Domain of the variable — blue

N_{\min} = 1,\quad N_{\max} = 6

$N \in \left[1, 6\right]$

$N = 1$ $N = 1$

Along the curve

③

Response curve — green

c=c_0 N f_w f_{HV} f_p

$N \in \left[1, 6\right]$

$N = 1$ $c = 1900.8$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}c}{\mathrm{d}N}

$N \in \left[1, 6\right]$

$N = 1.031$ $c^{\prime} = 1900.8$

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-27 — Highway lane capacity) is the form associated with HCM. Working symbols: $c_0$ , $N$ , $f_w$ , $f_{HV}$ , $f_p$ $\rightarrow$ $c$ . Ideal capacity is derated for lane width, heavy vehicles and driver population. fHV = 1/(1+PT(ET−1)).

Purpose

Purpose: compute

c

from

c_0

N

f_w

f_{HV}

f_p

in Transport via

c=c_0 N f_w f_{HV} f_p

c = c0 N fw fHV fp. HCM multilane snapshot, c0 ≈ 2200 pc/h/ln. Use it when a real transport question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

c_0 = 2200.000\,\mathrm{pc/h/ln}

N = 3.000\,\mathrm{—}

f_w = 0.960\,\mathrm{—}

f_{HV} = 0.900\,\mathrm{—}

f_p = 1.000\,\mathrm{—}

, the governing relation

c=c_0 N f_w f_{HV} f_p

yields

c = 5702\,\mathrm{veh/h}

. N lanes, three adjustment factors, a capacity. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Ideal capacity c_02200 pc/h/lnLanes N3 —Width factor f_w0.96 —Heavy-vehicle factor f_{HV}0.9 —Driver factor f_p1 —

Outputs

Capacity c5702 veh/h

Reading speed

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Narration of this film

N lanes, three adjustment factors, a capacity.

Ideal capacity is derated for lane width, heavy vehicles and driver population. fHV = 1/(1+PT(ET−1)).

Reading speed

Watch on YouTube