Ramp Slope and the Switchback Illusion
A school is installing a wheelchair ramp at a side entrance. The door threshold is 24 inches above the sidewalk. The available straight-line horizontal distance from the building to the sidewalk is 20 feet. The facilities director proposes a straight ramp using all 20 feet, producing a slope of 24 inches over 240 inches, or 1:10. A contractor suggests a switchback with two 10-foot runs separated by a 5-foot by 5-foot level landing; the contractor says the landing 'breaks up the slope' and makes the design compliant. The district requires compliance with the ADA standard of a maximum 1:12 slope and a 5-foot level landing at the top. The bottom sidewalk is level and can serve as the bottom landing. The principal can remove a planter to gain 10 additional feet of horizontal space, but only if the math justifies it. The school also has a $12,000 budget; a platform lift costs $18,000.
1. Calculate the minimum horizontal run required for a 24-inch rise at 1:12. Determine whether the 20-foot straight ramp and the contractor's two 10-foot switchback runs comply. Show the slope for each run.
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At 1:12, run=12×rise=12×24=288 inches=24 feet. The 20-foot ramp has slope 24/240=0.10=10%, or 1:10, which is steeper than 1:12 (about 8.33%), so it does not comply. For the switchback, each 10-foot run rises half of 24 inches, or 12 inches, over 120 inches. Slope=12/120=0.10=1:10. The 5-foot landing is level and does not change the slope of either run. Splitting the total rise in half while splitting the total run in half leaves the same average slope, so the switchback as proposed is also noncompliant.
2. If the planter is removed and 30 feet of horizontal distance is available, design a compliant straight ramp with the required 5-foot top landing. The bottom sidewalk is level and can serve as the bottom landing. Show the arithmetic and state the margin.
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Required ramp run=24 feet. Add the 5-foot top landing: 24+5=29 feet. This is 1 foot less than the available 30 feet, so the design fits with a 1-foot margin. The ramp slope is 24 inches over 288 inches=1:12, exactly at the maximum. The top landing is level and at least 5 feet long. The level sidewalk at the bottom serves as the bottom landing. Because the design uses the maximum allowed slope, construction tolerances should be checked so the as-built slope does not exceed 1:12; a small additional margin, if available, would be safer.
3. If the planter cannot be removed, what maximum rise can a 20-foot straight ramp accommodate while including the 5-foot top landing? Compare with the 24-inch threshold and recommend an action.
Read the worked answer
Available ramp run=20−5=15 feet=180 inches. At 1:12, maximum rise=180/12=15 inches. The threshold is 24 inches, so the ramp would fall 9 inches short. A 20-foot straight ramp cannot meet the door with a compliant slope and top landing. Options: remove the planter to get 30 feet (preferred, since 24+5=29 feet fits); regrade the sidewalk to reduce the rise to at most 15 inches; or use a platform lift, which costs $18,000 and exceeds the $12,000 budget. The mathematically defensible recommendation is to remove the planter, because it is the only option that meets both the slope standard and the budget.