Horizontal and vertical curves

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CHAPTER 11

HORIZONTAL AND VERTICAL CURVES

As you know from your study of chapter 3, the center line of a road consists of series of straight lines interconnected by curves that are used to change the alignment, direction, or slope of the road. Those curves that change the alignment or direction are known as horizontal curves, and those that change the slope are vertical curves.

As an EA you may have to assist in the design of these curves. Generally, however, your main concern is to compute for the missing curve elements and parts as problems occur in the field in the actual curve layout. You will find that a thorough knowledge of the properties and behavior of horizontal and vertical curves as used in highway work will eliminate delays and unnecessary labor. Careful study of this chapter will alert you to common problems in horizontal and vertical curve layouts. To enhance your knowledge and proficiency, however, you should supplement your study of this chapter by reading other books containing this subject matter. You can usually find books such as Construction Surveying, FM 5-233, and Surveying Theory and Practice, by Davis, Foote, Anderson, and Mikhail, in the technical library of a public works or battalion engineering division.

HORIZONTAL CURVES

When a highway changes horizontal direction, making the point where it changes direction a point of intersection between two straight lines is not feasible. The change in direction would be too abrupt for the safety of modem, high-speed vehicles. It is therefore necessary to interpose a curve between the straight lines. The straight lines of a road are called tangents because the lines are tangent to the curves used to change direction.

In practically all modem highways, the curves are circular curves; that is, curves that form circular arcs. The smaller the radius of a circular curve, the sharper the curve. For modern, high-speed highways, the curves must be flat, rather than sharp. That means they must be large-radius curves.

In highway work, the curves needed for the location or improvement of small secondary roads may be worked out in the field. Usually, however, the horizontal curves are computed after the route has been selected, the field surveys have been done, and the survey base line and necessary topographic features have been plotted. In urban work, the curves of streets are designed as an integral part of the preliminary and final layouts, which are usually done on a topographic map. In highway work, the road itself is the end result and the purpose of the design. But in urban work, the streets and their curves are of secondary importance; the best use of the building sites is of primary importance.

The principal consideration in the design of a curve is the selection of the length of the radius or the degree of curvature (explained later). This selection is based on such considerations as the design speed of the highway and the sight distance as limited by head-lights or obstructions (fig. 11-1). Some typical radii you may encounter are 12,000 feet or longer on an interstate highway, 1,000 feet on a major thorough-fare in a city, 500 feet on an industrial access road, and 150 feet on a minor residential street.

Figure 11-1.—Lines of sight.

TYPES OF HORIZONTAL CURVES

There are four types of horizontal curves. They are described as follows:

1. SIMPLE. The simple curve is an arc of a circle (view A, fig. 11-2). The radius of the circle determines the sharpness or flatness of the curve.

2. COMPOUND. Frequently, the terrain will require the use of the compound curve. This curve normally consists of two simple curves joined together and curving in the same direction (view B, fig. 11-2).

3. REVERSE. A reverse curve consists of two simple curves joined together, but curving in opposite direction. For safety reasons, the use of this curve should be avoided when possible (view C, fig. 11-2).

4. SPIRAL. The spiral is a curve that has a varying radius. It is used on railroads and most modem highways. Its purpose is to provide a transition from the tangent to a simple curve or between simple curves in a compound curve (view D, fig. 11-2)