1. Road curve

2. Road Curve
In highways, railways, or canals the curve are provided for smooth or gradual change in direction due the nature of terrain, cultural features, or other unavoidable reasons

3. Road Curve
In highway practice, it is recommended to provide curves on straight route to break the monotony in driving on long straight route to avoid accidents.
The vertical curves are used to provide a smooth change in direction taking place in the vertical plane due to change of grade.

4. Horizontal Alignment
Tangents
Curves

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

6. 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

7. Circular Curve Components

8. 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.)

9. 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

10. 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
Sec: secant
exact opposite of cos

11. Circular Curve Geometry

12. EX:1

16. EX:2

19. EX:3