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 Geometric Design: Example Problems

 
Sag Vertical Curves

If a stopping sight distance of 400 ft. is to be maintained on a sag vertical curve with tangent grades of -3% and 0%, what should the length of the curve be? Assume a headlight beam upward divergence angle of 1°.

[Solution Shown Below]

 

 

 

 

 

 

 

 

 

 

 

Solution

Since we know everything that we need to know to solve this problem, we'll jump straight into the equations.

If S > L then

L=2*S - (200*(H + S*tan(B)))/A

If S < L then (invalid because L < S)

L=(A*S^2)/(200*(H + S*tan(B)))

Where:
L = Curve length (ft)
S = Sight distance, 400 f.
B = Beam upward divergence, 1°
H = Height of the headlights, 2 ft (assumed as 2 ft)
A = Change in grade, 3% (|G2-G1| as a percent)

Solving the equations above results in a curve length of 201 feet. You can find the elevation of any point along the curve once you have the curve length. See the crest vertical curve example problem.