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

7. ELEMENTS OF A 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

8. ELEMENTS OF A HORIZONTAL CURVE
POC = POINT OF CURVE. The point of curve is any
point along the curve.
LC = LONG CHORD. The long chord is the
straight-line distance from the
PC= to the PT. Other types of chords
are designated as follows:
C=The full-chord distance
between adjacent stations
(full, half, quarter, or onetenth
stations) along a curve.

9. ELEMENTS OF A HORIZONTAL CURVE
C1 = The subchord distance between the PC
and the first station on the curve.
C2 = The subchord distance between the last
station on the curve and the PT.

10. 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 or meter

11. Degree of Curvature (arc definition)
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 or meter

12. Degree of Curvature (chord definition)
This definition states that the degree of curve is the central angle formed by two radii drawn from the center of the circle to the ends of a chord 100 feet (or 100 meters) long.
Notice that in both the arc definition and the chord
definition, the radius of curvature is inversely
proportional to the degree of curvature.

13. Length of Curve
For a given external angle (Δ), the length of curve (L) is directly related to the radius (R)

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
Sec: secant
exact opposite of cos

15. Circular Curve Geometry

16. EX:1

20. EX:2

23. EX:3