1. Geometric Design of Highways Highway Alignment is a three-dimensional problem –Design & Construction would be difficult in 3-D so highway alignment is split into two 2-D problems

2. Austin, TX

3. Near Cincinnati, OH

4. Components of Highway Design Plan View Profile View Horizontal Alignment Vertical Alignment

5. Horizontal Alignment Today’s Class: Components of the horizontal alignment Properties of a simple circular curve

6. Horizontal Alignment Today’s Class: Components of the horizontal alignment Properties of a simple circular curve

7. Horizontal Alignment TangentsCurves

9. Tangents & Curves Tangent Curve Tangent to Circular Curve Tangent to Spiral Curve to Circular Curve

10. Layout of a Simple Horizontal Curve R = Radius of Circular Curve BC = Beginning of Curve (or PC = Point of Curvature) EC = End of Curve (or PT = Point of Tangency) PI = Point of Intersection T = Tangent Length (T = PI – BC = EC - PI) L = Length of Curvature (L = EC – BC) M = Middle Ordinate E= External Distance C = Chord Length Δ = Deflection Angle

11. Circular Curve Components

12. Properties of Circular Curves Degree of Curvature Traditionally, the “steepness” of the curvature is defined by either the radius (R) or the degree of curvature (D) Degree of curvature = angle subtended by an arc of length 100 feet R = 5730 / D (Degree of curvature is not used with metric units because D is defined in terms of feet.)

13. Properties of Circular Curves Length of Curve For a given external angle (Δ), the length of curve (L) is directly related to the radius (R) L = (RΔπ) / 180 = RΔ / 57.3 In other words, the longer the curve, the larger the radius of curvature R = Radius of Circular Curve L = Length of Curvature Δ = Deflection Angle

14. Properties of Circular Curves Other Formulas… Tangent: T = R tan(Δ/2) Chord: C = 2R sin(Δ/2) Mid Ordinate: M = R – R cos(Δ/2) External Distance: E = R sec(Δ/2) - R

15. Circular Curve Geometry