Vertical Curves

Jan Van Sickle, P.L.S.

Course Outline

Surveyors and engineers have traditionally used the term vertical curve to describe the use of parabolic curves in design work. They are used for transitions from one straight grade to another in designing crowns for pavements, routes such as highways and railways, as well as dam spillways, landscape design and of course roller coasters. Preparing the calculations necessary to use vertical curves are based on a few principles, once those are clearly in mind vertical curves are a breeze. This online course teaches some of the calculations involved in creating and analyzing vertical curves. It is direct in its descriptions of the why and how of these parabolic curves.

This course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of the course materials.

Learning Objective

At the conclusion of this course, the student will:

Intended Audience

This course is intended for land surveyors and civil and transportation engineers.

Benefit to Attendees

Attendee of this course will be able to calculated vertical curves with skill and confidence.

Course Introduction

Most often vertical curves are used to improve the comfort, safety and appearance of routes. They are just as crucial to good work as horizontal curves.
However, unlike a circular curve a vertical curve does not have a constant radius at all points along the curve. Nevertheless it does have a quality that is very useful indeed. That quality is its consistent rate of change in slope as one travels along a vertical curve. However, achieving that quality can be a bit of a mystery until a few principles are clearly in mind, after working with vertical curves is quite straightforward.

Course Content

The link to the course content is as follows:

Vertical Curves (PDF file 114 KB)

You need to open or download the above document to study this course.

Course Summary

A smooth transition between constant grades is necessary because if it were not ameliorated the change would be too abrupt. In fact, it is only when the algebraic difference of the intersecting grades is less than one-half of 1 percent that vertical curves become unnecessary. If the grade change were allowed to all take place in one spot it would make for a bumpy ride, but with vertical curves in place its smooth.


Once you finish studying the above course content, you need to take a quiz to obtain the PDH credits.

Take a Quiz

DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.