TRN-08

Crest vertical curve length

L = A S² / (200(√h1+√h2)²) when L > S.

Reading speed

Geometric designAASHTO Green Book

Governing equation

L=\dfrac{A S^2}{200(\sqrt{h_1}+\sqrt{h_2})^2}

where

A: Algebraic difference (%)
S: Sight distance (m)
h_1: Eye height (m)
h_2: Object height (m)
L: Curve length (m)

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-08 — Crest vertical curve length) is the form associated with AASHTO Green Book. Working symbols: $A$ , $S$ , $h_1$ , $h_2$ $\rightarrow$ $L$ . AASHTO sets the crest parabola so that stopping sight distance clears the summit between eye and object heights.

Purpose

Purpose: compute

L

from

A

S

h_1

h_2

in Transport via

L=\dfrac{A S^2}{200(\sqrt{h_1}+\sqrt{h_2})^2}

L = A S² / (200(√h1+√h2)²) when L > S. Use it when a real transport question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

A = 4.000\,\mathrm{%}

S = 130.000\,\mathrm{m}

h_1 = 1.080\,\mathrm{m}

h_2 = 0.600\,\mathrm{m}

, the governing relation

L=\dfrac{A S^2}{200(\sqrt{h_1}+\sqrt{h_2})^2}

yields

L = 102.737\,\mathrm{m}

. Long curve case L > S. A = |g2−g1| in percent. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Algebraic difference A4 %Sight distance S130 mEye height h_11.08 mObject height h_20.6 m

Outputs

Curve length L102.737 m

Reading speed

Watch on YouTube

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Narration of this film

Long curve case L > S. A = |g2−g1| in percent.

AASHTO sets the crest parabola so that stopping sight distance clears the summit between eye and object heights.

Reading speed

Watch on YouTube