Wheelchair Ramp Slope, Post Height, and Handrail Length
A community center is building a wheelchair ramp to a door 2.4 ft above the sidewalk. The available horizontal distance is 30 ft. The local code says the slope may not be steeper than 1:12, and the ramp angle must be reported on the permit. The contractor proposes using the full 30 ft as the horizontal run and puts a vertical support post under the ramp at a horizontal distance of 18 ft from the bottom. The contractor's permit application states the slope is 1:12.5, the ramp angle is 5.0°, and the post must be 1.8 ft tall. A second door will be raised to 3.0 ft, and the architect wants to keep the same ramp angle as the first ramp rather than the maximum legal slope. The center also needs a straight handrail along the sloped surface from the bottom to the top.
1. Check the contractor's three claims for the first ramp: the slope ratio is 1:12.5 and is legal, the ramp angle is 5.0°, and the support post at 18 ft horizontal distance should be 1.8 ft tall.
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Slope = rise/run = 2.4/30 = 0.08, which is 8%. As a ratio, 0.08 = 1/12.5, so the contractor's 1:12.5 is correct. The maximum legal slope 1:12 equals about 0.08333, and 0.08 < 0.08333, so the ramp is legal, but only slightly flatter than the limit.
The ramp angle is θ = arctan(0.08) ≈ 4.57°, not 5.0°. The contractor rounded up by about 0.43°, so the permit value should be corrected.
The post height comes from similar right triangles: the post and the full ramp have the same angle, so h/18 = 2.4/30. Thus h = 18(2.4/30) = 1.44 ft, not 1.8 ft. The 1.8-ft figure would place the top of the post above the ramp surface.
2. For the second door, the rise is 3.0 ft and the architect wants the same ramp angle as the first ramp. Find the required horizontal run and compare it with the minimum run allowed by the 1:12 code.
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The first ramp's slope is 2.4/30 = 0.08. To keep the same angle, the second ramp must also have rise/run = 0.08:
3.0/run = 0.08 run = 3.0/0.08 = 37.5 ft.
The code maximum slope is 1:12, so the minimum legal run for a 3.0-ft rise is 12(3.0) = 36.0 ft. The 37.5-ft run is legal because it is gentler than 1:12, but it is not the minimum legal run. If the site has only 30 ft available, the second ramp cannot keep the same angle and will need a different design, such as a turn or landing.
3. The straight handrail follows the sloped surface of the first ramp from the bottom to the top. The contractor orders exactly 30 ft of handrail. Is that enough? If the code requires a 12-in extension beyond each end, what total length should be ordered?
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The handrail length is the hypotenuse of a right triangle with horizontal run 30 ft and vertical rise 2.4 ft:
L = √(30² + 2.4²) = √(900 + 5.76) = √905.76 ≈ 30.096 ft.
Exactly 30 ft is short by about 0.096 ft, or about 1.15 in, so it is not enough even before extensions.
With a 12-in extension at each end, add 1 ft + 1 ft = 2 ft:
Total ≈ 30.096 + 2 = 32.096 ft.
Order at least 32.1 ft, and preferably round up for cutting and fittings.