A simple curve is connected by tangents that make an angle of 64°. A point “e” along the curve is 220 m along the back tangent and 56 m perpendicular (offset) to the said tangent. The beginning of the curve is located at 9+070. a. What is the radius of the curve? b. What is the tangent distance of the curve? c. What is the length of the long chord? d. What is the station of point “e”? Draw and plot the curve. Compute all of the necessary elements of the curve. Include the proper units/dimensions and round-off the answers to 3 decimal places.
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A simple curve is connected by tangents that make an angle of 64°. A point “e” along the curve is 220 m along the back tangent and 56 m perpendicular (offset) to the said tangent. The beginning of the curve is located at 9+070.
a. What is the radius of the curve?
b. What is the tangent distance of the curve?
c. What is the length of the long chord?
d. What is the station of point “e”?
Draw and plot the curve. Compute all of the necessary elements of the curve. Include the proper units/dimensions and round-off the answers to 3 decimal places.
![PI
PT
PC
C
Back
tangent
Forward
tangent
R
PI
I
M
I/2
PC
PT
L/2
L/2
R- m
Back Tangent
R
Forward Tangent
20
R
I/2
I
• PC = Point of curvature. It is the beginning
%3D
of curve.
• PT = Point of tangency. It is the end of
curve.
• PI = Point of intersection of the tangents.
%3D
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.
• L = Length of chord from PC to PT. Point Q
as shown below is the midpoint of L.
%3D
Lc = Length of curve from PC to PT. Point M
in the the figure is the midpoint of Lc.
• E = External distance, the nearest distance
%3D
from PI to the curve.
• m = Middle ordinate, the distance from
midpoint of curve to midpoint of chord.
I = Deflection angle (also called angle of
intersection and central angle). It is the
%3D
angle of intersection of the tangents. The
angle subtended by PC and PT at O is also
equal to I, where O is the center of the
circular curve from the above figure.
• x = offset distance from tangent to the
curve. Note: x is perpendicular to T.
• 0 = offset angle subtended at PC between
PI and any point in the curve
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
%3D
equal to 20 m.
• Sub chord = chord distance between two
adjacent full stations.
12
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