In the geometric design of motorways, railways,
pipelines, etc., the design and setting out of curves
is an important aspect of the engineer’s work. The initial
design is usually based on a series of straight sections whose positions
are defined largely by the topography of the area. The intersections of
pairs of straights are then connected by
horizontal curves.
In the vertical design, intersecting gradients are connected by
curves in the vertical plane.
Circular curves are used to join intersecting straight
lines (or tangents). Circular curves are assumed to be concave.
Horizontal circular curves are used to transition the change in
alignment at angle points in the tangent (straight) portions of
alignments. An angle point is called a point of intersection or PI
station; and, the change in alignment is defined by a deflection angle,
Δ.
Types of Circular Curves are:
- Simple Curve
- Compound Curves
- Broken Back Curves
- Reverse Curves
A. Radius of a circular curve

The Radius is the distance from the center of the curve to any point on the circular curve.
B. Direction of a circular curve
The Direction of a Circular Curve is defined as the
direction the curve tends, as stationing along the curve increases. Can
be expressed as: Left, Right, North, East, South, West, free text
C. Central angle of a circular curve
The Central Angle of a Circular Curve is the angle at
the center of radius of a circular arc included between the radii,
passing through the beginning and ending of the arc.
D. Long Chord Length
The Long Chord Length is the straight line distance connecting the beginning of the curve and the end of the curve.
E. Degree of Curvature
The Degree of Curve is defined as the angle subtended
by an arc whose length is 100 ft. A Radian is the angle subtended by an
arc whose length equals the length of the Radius, or
57° 17’ 44.8” , or 57.295779513°.
i. Curvature can be
expressed in two ways, By:
- Stating the length of the chord of
the curve
- Stating the
radius of curvature
F. Laying out Circular Curves
-
Select tangents, and general curves making sure you meet minimum radius criteria
-
Select specific curve radii/spiral and calculate
important points (see lab) using formula or table (those needed for
design, plans, and lab requirements)
-
Station alignment (as curves are encountered)
-
Determine super and runoff for curves and put in table (see next lecture for def.)
-
Add information to plans
G. Sight Distance of a circular curve
Sight line is a chord of the circular curve. Sight
Distance is curve length measured along centerline of inside lane.
Sight distance can be the controlling aspect of horizontal curve design
where obstructions are present near the inside of the curve. To
determine the actual sight distance that you have provided, you need to
consider that the driver can only see the portion of the roadway ahead
that is not hidden by the obstruction. In addition, at the instant the
driver is in a position to see a hazard in the roadway ahead, there
should be a length of roadway between the vehicle and the hazard that
is greater than or equal to the stopping sight distance
Curves should be designed with their radius greater than R
min. If R
min cannot provided enough lateral clearance to an obstruction.