Horizontal Curves

Custom Search

Survey

Intermediate Engineering

Road profile

Horizontal Curves

The road center line consists of straight lines and curves. The straight lines are called tangents, and the curves are called horizontal curves. These curves are used to change the horizontal direction of the road. All information necessary to draw a curve should be furnished by the engineer or taken from the surveyors notebook. The necessary information is known as curve data. Below is the data for curve No. 1 in figure 3-3 and an explanation of the terms.

D = 5600'

D = 2300'

R = 240.11'

T= 132.53'

L= 243.48'

1. The symbol A (Delta), or the symbol I, represents the intersecting angle, which is the deflection angle made by the tangents where they intersect.

2. D is the degree of curvature, or degree of curve. It is the angle subtended by a 100-foot arc or chord (to be discussed in chapter 11 of this TRAMAN).

3. R is the radius of the curve, or arc. The radius is always perpendicular to the curve tangents at the point of curvature (PC) and the point of tangency (PT).

4. T is the tangent distance, which is measured from the PI to the PC and the PT. The PC is the beginning of the curve, and the PT is the end of the curve.

5. L is the length of the curve measured in feet along the curve from the PC to the PT.

A horizontal curve is generally selected to fit the terrain. Therefore, some of the curve data will be known. The following formulas show definite relationships between elements and allow the unknown quantities to be computed:

1. To find the radius (R), or degree of curvature (D), use the following formula:

2. To find the tangent distance (T), compute as follows:

3. To find the length of curve (L), use the following formula:

The PC and PT are designated on the plan by a partial radius drawn at each point and a small circle on the center line. The station numbers of PC and PT are noted as shown in figure 3-3. The length of the curve (L) is added to the PC station to obtain the station of the PT. The curve data is noted on the inside of the curve it pertains to and is usually between the partial radii. Since most horizontal curves have superelevation (that is, the outside edge of the traveled way is higher than the inside edge), there must be a transition distance in which the shape of the road surface changes from a normal crown to a superelevated curve. The transition length is generally 150 feet and starts 75 feet before the PC is reached. The same is true in leaving curves. The transition begins 75 feet before the PT and ends 75 feet beyond. The beginning and end of the superelevation are noted on the plan.

Control Points

A control point maybe a PT, PC, PI, or a point on tangent (POT). Since these control points may be destroyed during construction, you must reference them to other points. In the field, a common practice that you should use is to drive iron pins or other reference stakes at right angles to the control point on each side of the center line, and then measure and record the distance from the pins to the control point. If room allows, these reference points should be drawn on the road plan opposite the control points, as shown in figure 3-3. If not, you should show the control points and References on a separate sheet, called a reference sheet.