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Civil Engineering Surveying & Levelling Compound Curves


Compound Curves in Engineering Survey



Combination of two or more simple circular curves of different radius having their curvature in the same direction. Also, A curve that is made up of a series of successive tangent circular arcs is called a compound curve.

Essentially, a compound curve consists of two curves that are joined at a point of tangency and are located on the same side of a common tangent. Though their radii are in the same direction, they are of different values.

tr = perception/reaction time (seconds) Compound Curves
f = AASHTO stopping friction coefficient (dimensionless)
G = roadway grade (dimensionless)
e = superelevation,
fs = the coefficient of side friction,
g = the acceleration due to gravity (=9.81 m/s2) and
v = the vehicle speed.
m = distance from centerline to sight obstruction
L = length of curve
S = sight distance (ds)
R = Radius of centerline
Rv =Radius to driver’s eye (middle of lane)
T = Tangent Length
C= Length of Chord (Long Chord from PC to PT)
E= External Distance
M = Middle Ordinate
Delta = Deflection Angle

Elements of a Compound Curve:

The elements of compound curve are:

  • PC = point of curvature
  • PT = point of tangency
  • PI = point of intersection
  • PCC  = point of compound curves
  • T1 = Length of tangent of the first curve
  • T2  = length of tangent of the second curve
  • V1 = vertex of the first curve
  • V2 = vertex of the second curve
  • I1 =  central angle of first curve
  • I2 = central angle of second curve
  • I angle of intersection = I1 + I2
  • Lc1 = length of the first curve
  • Lc2 = length of the second curve
  • L1 = length of the first chord
  • L2 = length of the second chord
  • T1 + T2 = length of common tangent measure from V1 to V2
  • Θ = 180° – I
  • X and Y can be found triangle V1-V2-PI
  • L can be found from the triangle PC-PCC-PT

Tangent Lengths & Lengths of Curves

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