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ESSENTIALS 0F TRANSPORTATION ENGINEERING Chapter 7 Highway Design for Safety
Fricker and Whitford 7.11 Chapter 7.
7.1.3 Geometry of Horizontal Curves
The horizontal curves are, by definition, circular curves of radius R. The elements of a horizontal curve are
shown in Figure 7.9 and summarized (with units) in Table 7.2.
Figure 7.9a The elements of a horizontal curve Figure 7.9b
Table 7.2 A summary of horizontal curve elements Symbol Name Units PC Point of curvature, start of horizontal curve PT Point of tangency, end of horizontal curve PI Point of tangent intersection D Degree of curvature degrees per 100 feet of centerline R Radius of curve (measured to centerline) feet L Length of curve (measured along centerline) feet ∆ Central (subtended) angle of curve, PC to PT^ degrees T Tangent length feet M Middle ordinate feet LC Length of long chord, from PC to PT feet E External distance feet
The equations 7.8 through 7.13 that apply to the analysis of the curve are given below.
R
2 R
D =
π
D
L
ESSENTIALS 0F TRANSPORTATION ENGINEERING Chapter 7 Highway Design for Safety
Fricker and Whitford 7.12 Chapter 7.
T Rtan (7.10)
M R 1 cos (7.11)
LC 2 Rsin (7.12)
cos
E R (7.13)
Example 7.
A 7-degree horizontal curve covers an angle of 63 o15’34”. Determine the radius, the length of the curve, and the
distance from the circle to the chord M.
Solution to Example 7.
Rearranging Equation 7.8,with D = 7 degrees, the curve’s radius R can be computed. Equation 7.9 allows
calculation of the curve’s length L, once the curve’s central angle is converted from 63o15’34” to 63.2594 degrees.
The middle ordinate calculation uses Equation 7.11. These computations are shown below.
M 818. 5 *( 1 cos 31. 6297 ) 121. 6 feet
903. 7 feet
L
818. 5 feet
R
× °
If metric units are used, the definition of the degree of the curve must be carefully examined. Because the
definition of the degree of curvature D is the central angle subtended by a 100-foot arc, then a “metric D” would be
the angle subtended by a 30.5-meter arc. The subtended angle ∆ does not change, but the metric values of R, L, and
M become
M 249. 55 *( 1 cos 31. 6297 ) 37. 07 meters
275. 52 meters
L
249. 55 meters
R
o
