I’m Daniel Findley with the Institute for Transportation Research and Education (ITRE) at NC State University.
I’m going to introduce the topic of horizontal and vertical alignment in this video.
The layout of a highway is comprised of two components:
a horizontal component which is viewed from above
and the vertical component which is viewed from the side.
The horizontal alignment dictates the left or right turning required to remain on the roadway,
while the vertical alignment exerts forces on the vehicle as the grade along the roadway changes.
In the horizontal perspective, a roadway is primarily comprised of tangent, or straight, sections which are smoothly connected by curves.
The horizontal curves that are used to provide drivers with the transition from one tangent to the next tangent are typically simple curves which are an arc of circle.
These curves have a single radius value which represents the sharpness or flatness of the curve.
A tangent roadway section has an infinite radius, since it is a straight line and a horizontal curve has a single, finite radius.
Therefore, a spiral transition is used in some instances to help make the shift from a tangent to a curve a little smoother.
Geometric relationships and equations can be used to find important information for each curve.
This information includes the radius, the length of the curve, the change in direction of the two tangents, and other factors depending on your needs.
Several points of interest along the curve include the location where the tangents intersect, which is known as the Point of Intersection.
The location where the vehicle leaves the tangent section and begins to drive along the curve, is known as the point of curvature.
The location where curve ends and the vehicle returns back to the tangent is known as the Point of Tangency.
In the vertical perspective, a roadway is also comprised of tangents which are smoothly connected by curves.
For vertical alignment, the tangents represent grades which can either be flat, uphill, or downhill.
The typical vertical curve is a symmetric, parabolic curve whose shape is defined by the parabolic equation.
The information required to fully define a vertical curve is the elevation of the beginning of the curve, the grades of the two tangents that are connected, and the length of the curve.
The naming convention of vertical alignment is similar to horizontal alignment.
Several points of interest along the curve include that the location where the tangents intersect, which is known as the Point of Vertical Intersection.
The location where the vehicle leaves the tangent grade and begin to drive along the curve, is known as the point of vertical curvature.
The point where the curve ends and the vehicle returns back to the tangent grade is known as the Point of Vertical Tangency.
Let’s take a look at a few pictures and discuss the vertical and horizontal elements in each picture.
Let’s consider this short section of a residential street with one vertical curve and one horizontal curve.
There is a slight horizontal curve to the left between the triangle and the star.
The triangle in the foreground of the picture has an elevation of 414 feet, the circle at the midpoint of the roadway has an elevation of 390 feet, and the star at the end of the section has an elevation of 409 feet.
These elevations demonstrate the presence of a sag vertical curve between the beginning and end of the section which has a downhill grade as the driver leaves from the triangle, a flat grade near the circle, and an uphill grade when approaching the star.
Now let’s take a look at the horizontal and vertical components separately.
The overhead aerial view of the roadway is shown on the left and the simplified roadway alignment is shown on the right with the points corresponding to the locations we discussed in the street level view.
Each end of the roadway is a tangent and they are connected with a horizontal curve.
The vertical alignment is shown in profile view, from the perspective of someone standing along the side of the roadway and perpendicular to the roadway.
As illustrated with the street level picture, the triangle has an elevation of 414 feet, the circle has an elevation of 390 feet, and the star has an elevation of 409 feet.
This profile view shows a sag vertical curve between the beginning and end of the section which has a downhill grade as the driver leaves from the triangle, a flat grade near the circle, and an uphill grade when approaching the star.
This example shows three perspectives: a street level view in the top portion of the screen, the horizontal alignment in the bottom left, and the vertical alignment in the bottom right.
We see an example of a roadway with no complex horizontal alignment, this section is completely straight in the horizontal plane.
However, we see a curve in the vertical plane.
As the vehicles moves along this section of roadway, the driver will not be required to make any turns to the left or right, but the vehicle will move vertically along the section by traveling downhill at the beginning and uphill at the end.
Similar to the previous example, this example shows the same three perspectives.
We see an example of a roadway with very complex horizontal alignment, but relatively simple alignment in the vertical plane.
A driver on the section of roadway will travel downhill at a relatively constant grade in the vertical perspective,
while experiencing a series of horizontal curves which will require significant left and right steering to remain on the roadway.
Thank you for your interest in this topic.
Examples of complex and simple alignments in the vertical and horizontal perspectives exist all around us and I hope this presentation will help you understand the basics of these elements.