TRN-36

Passenger-car equivalent flow

qpce = qcar + ET qtruck + ER qRV. Heavy vehicles counted as ET cars.

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TrafficHCM PCE

Governing equation

q_{pce}=q_{car}+E_T q_{tr}+E_R q_{RV}

$q_{tr} \in \left[0, 800\right]$

where

q_{car}: Cars (veh/h)
q_{tr}: Trucks (veh/h)
q_{RV}: RVs (veh/h)
E_T: Truck PCE (—)
E_R: RV PCE (—)
q_{pce}: PCE flow (pc/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

q_{pce}=q_{car}+E_T q_{tr}+E_R q_{RV}

$q_{tr} \in \left[0, 800\right]$

$q_{tr} = 0$ $q_{pce} = 1240$

Along the curve

②

Domain of the variable — blue

q_{tr}_{\min} = 0,\quad q_{tr}_{\max} = 800

$q_{tr} \in \left[0, 800\right]$

$q_{tr} = 0$ $q_{tr} = 0$

Along the curve

③

Response curve — green

q_{pce}=q_{car}+E_T q_{tr}+E_R q_{RV}

$q_{tr} \in \left[0, 800\right]$

$q_{tr} = 0$ $q_{pce} = 1240$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}q_{pce}}{\mathrm{d}q_{tr}}

$q_{tr} \in \left[0, 800\right]$

$q_{tr} = 5.031$ $q_{pce}^{\prime} = 2.5$

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-36 — Passenger-car equivalent flow) is the form associated with HCM PCE. Working symbols: $q_{car}$ , $q_{tr}$ , $q_{RV}$ , $E_T$ , $E_R$ $\rightarrow$ $q_{pce}$ . HCM passenger-car equivalents grow on grades and in the terrain. ET ≈ 1.5 level, 4+ on a long climb.

Purpose

Purpose: compute

q_{pce}

from

q_{car}

q_{tr}

q_{RV}

E_T

E_R

in Transport via

q_{pce}=q_{car}+E_T q_{tr}+E_R q_{RV}

qpce = qcar + ET qtruck + ER qRV. Heavy vehicles counted as ET cars. Use it when a real transport question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

q_{car} = 1200.000\,\mathrm{veh/h}

q_{tr} = 150.000\,\mathrm{veh/h}

q_{RV} = 20.000\,\mathrm{veh/h}

E_T = 2.500\,\mathrm{—}

E_R = 2.000\,\mathrm{—}

, the governing relation

q_{pce}=q_{car}+E_T q_{tr}+E_R q_{RV}

yields

q_{pce} = 1615\,\mathrm{pc/h}

. A mixed stream, two equivalency factors, a PCE flow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Cars q_{car}1200 veh/hTrucks q_{tr}150 veh/hRVs q_{RV}20 veh/hTruck PCE E_T2.5 —RV PCE E_R2 —

Outputs

PCE flow q_{pce}1615 pc/h

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Narration of this film

A mixed stream, two equivalency factors, a PCE flow.

HCM passenger-car equivalents grow on grades and in the terrain. ET ≈ 1.5 level, 4+ on a long climb.

Reading speed

Watch on YouTube