Horizontal Curves
Simple Curves
Terms
• PC = Point of curvature. It is the beginning of
curve.
• PT = Point of tangency. It is the end of curve.
• PI = Point of intersection of the tangents. Also
called vertex
• T = Length of tangent from PC to PI and
from PI to PT. It is known as subtangent.
• R = Radius of simple curve, or simply radius.
• C = Length of chord from PC to PT.
• L = Length of curve from PC to PT.
Terms
• E = External distance, the nearest distance
from PI to the curve.
• M = Middle ordinate, the distance from midpoint
of curve to midpoint of chord.
• Δ= Deflection angle (also called angle of
intersection and central angle)
• d = Degree of curve. It is the central angle
subtended by a length of curve equal to one
station. In English system, one station is equal to
100 ft and in SI, one station is equal to 20 m.
Formulas Used in Solving Simple
Circular Curves
Horizontal Curves Sample Problems
1. A simple circular horizontal curve has 150m
radius. Its central angle is found to be 32 degrees.
Find all the values of the curve’s parameters.
2. A car with a constant velocity of 76kmph,
traveled along a highway curve. The car entered the
simple curve at exactly 7:00 in the morning and
exited 18 seconds after. The degree of curvature of
the highway curve is found to be 3 degrees.
Compute for all the parameters of the highway
curve.
Horizontal Curves Sample Problems
3. The tangents of a simple curve have bearings
of N50°E and N80°E respectively. The radius of
the curve is 200m.
• Compute for the external distance
• Compute for the middle ordinate
• Compute for the stationing of point A on the
curve having a deflection angle of 6° from PC
which is at 1+200.00.
Horizontal Curves Sample Problems
4. A simple curve of the proposed extension of
Mantabahadra Highway have a direction of tangent AB
which is due north and tangent BC bearing N50°E. Point A
is at the PC whose stationing is 20+130.46. The degree of
curve is 4°.
• Compute the long chord of the curve
• Compute the stationing of point D on the curve along a
line joining the center of the curve which makes an
angle 54° with the tangent line passing through the PC
• What is the length of the line from D to the
intersection of the tangent AB.
Horizontal Curves Sample Problems
5. The tangent distance of a 3° simple curve is
only ½ of its radius.
• Compute the angle of intersection of the
curve
• Compute the length of the curve
• Compute the area of fillet of the curve
Seatwork
1. A simple curve has a radius of 286.48m. Its
distance from PC to PT along the curve is equal to
240m.
• Compute the central angle of the curve use arc
basis. 48°
• Compute the distance from the mid-point of the
long chord to the mid-point of the curve. 24.76m
• Compute the area bounded by the tangents and
the portion outside the central curve in square
meters. 2162.79sq.m
Seatwork
2. A simple curve connects two tangents AB and BC
with bearings N85°30’E and S68°30’E respectively. If
the stationing of the PI is 4+360.2 and the
stationing of PC is 4+288.4:
• Determine the radius. 311m
• Determine the external distance.8.18m
• Determine the middle ordinate.7.97m
• Determine the long chord distance.139.92m
• Determine the length of curve.141.13m
Seatwork
3. The offset distance of the simple curve from
the PT to the tangent line passing through the
PC is equal to 120.20m. The stationing of PC is at
2+540.26. The simple curve has an angle of
intersection of 50°.
• Compute the degree of curvature. 3°24’
• Compute the external distance.34.79m
• Compute the length of the long
chord.284.41m
Assignment
2. A simple curve has a central angle of 40°. The
stationing at the point of curvature is equal to
10+060. The offset distance from the PT to the
tangent line passing through the PC is 80m long.
• Compute the tangent distance of the
curve.124.46m
• Compute the degree of curvature.3.35°
• The deflection angle from the tangent at the PC
to point B on the curve is equal to 8°, what is
would be the stationing of point B.10+155.49m
Assignment
• The radius of a simple curve is twice its
tangent distance, if the degree of curve is 4°.
• What is the angle of intersection of the
curve.53°08’
• Compute the length of the curve.265.65m
• Determine the area enclosed by the
curve.380.54m
Assignment
• The offset distance from PC to PT of a simple
curve is 18m. And the angle of intersection of
the tangents is 24 degrees. If the stationing of
PT is 45+158.32, what is the stationing of the
PI? 45+115.30