How to Calculate Length of Vertical Curves
Vertical curves are used in engineering for a variety of purposes, including the design of highways and in construction work zones, dam spillways and even roller coasters. The curves are parabolic, which means that the initial rate of change increases steadily. One of the most common vertical curves is the crest vertical curve, which connects two inclined sections of road. The equation necessary to determine the length of this curve (if S<L) is L=(2S-(200(sqrt(h1)+sqrt(h2))squared)/A).
Instructions
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1
Note that square h1 is the height of the driver's eyes above the road surface (in feet). Use a common stopping sight distance of h1=3.5 feet, so 3.5*3.5=12.5.
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2
Note that square h2 is the height of the object above the ground (in feet). Use a common stopping sight distance of h2=0.5 feet, so 0.5*0.5=0.25.
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3
Add Step 1 and Step 2 together: 0.25+12.5=12.75.
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4
Square the result from Step 3: 12.75*12.75=162.5625.
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5
Multiply Step 4 by 200: 200*162.5625=32,512.5.
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6
Divide Step 5 by "A," the change in grades as a percentage. Set this number aside for a moment. If the change in grade is 20 percent, then 32,512.5/20=1,625.625.
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Multiply the sight distance by 2. A reasonable sight distance might be 1,000 feet, so 1000*2=2000.
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Subtract Step 6 from Step 7: 2,000-1,625.625=374.37500.
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Tips & Warnings
Sight distances for roads and highways are usually controlled by state or local governments. See your state guidelines for the appropriate sight distances to use.
