**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:

- Be able to calculate a vertical curves rate of change;
- Know why vertical curves are used in grade transitions rather than other kinds of curves;
- Learn the common acronyms used in the description of the components of vertical curves;
- See the differences between crest and sag vertical curves;
- Understand the difference between the priorities in design criteria for vertical curves on railroads and highways;
- Learn two different methods of calculating the elevations along a symmetric, equal tangent, vertical curve;
- Walk through several vertical curve calculations in detail;
- Be well versed in the application of an asymmetric vertical curve;
- Be able to calculate the elevations of stations along an asymmetric vertical curve;
- Work out a practical problem in using an asymmetric vertical curve to solve a field problem;
- Know how to calculate the point of zero slope on a vertical curve; and
- Learn some of
the most common calculation errors made in the preparation of vertical curves.

**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**

**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.

**Quiz**

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

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.