TRN-30

Crest vertical-curve offset

y = A x² / (200 L), A = |g2 − g1| in percent. Midpoint offset E = A L / 800.

Reading speed

Geometric designAASHTO vertical curve

Governing equation

y=\dfrac{A x^2}{200 L},\quad E=\dfrac{AL}{800}

where

g_1: Entry grade (%)
g_2: Exit grade (%)
L: Curve length (m)
x: Station from PVC (m)
y: Offset (m)
E: Midpoint offset (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-30 — Crest vertical-curve offset) is the form associated with AASHTO vertical curve. Working symbols: $g_1$ , $g_2$ , $L$ , $x$ $\rightarrow$ $y$ , $E$ . A parabolic vertical curve equalises centripetal comfort and sight. K = L/A is the design parameter.

Purpose

Purpose: compute

y

E

from

g_1

g_2

L

x

in Transport via

y=\dfrac{A x^2}{200 L},\quad E=\dfrac{AL}{800}

y = A x² / (200 L), A = |g2 − g1| in percent. Midpoint offset E = A L / 800. Use it when a real transport question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

g_1 = 2.000\,\mathrm{%}

g_2 = -3.000\,\mathrm{%}

L = 120.000\,\mathrm{m}

x = 60.000\,\mathrm{m}

, the governing relation

y=\dfrac{A x^2}{200 L},\quad E=\dfrac{AL}{800}

yields

y = 0.750\,\mathrm{m}

E = 0.750\,\mathrm{m}

. Two grades, a parabola, an offset y. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Entry grade g_12 %Exit grade g_2-3 %Curve length L120 mStation from PVC x60 m

Outputs

Offset y0.750 m
Midpoint offset E0.750 m

Reading speed

Watch on YouTube

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Narration of this film

Two grades, a parabola, an offset y.

A parabolic vertical curve equalises centripetal comfort and sight. K = L/A is the design parameter.

Reading speed

Watch on YouTube