Ramp Slope, Unit Conversion, and Code Compliance
A building entrance has a 30-inch vertical rise from the sidewalk to the door threshold. The available horizontal run is 26 feet, and the site can extend the run to at most 32 feet. A designer proposes a straight ramp and writes the slope as 30/26≈1.15, concluding that because 1.15 is greater than 1/12, the ramp is compliant. A second designer says the calculation is wrong because the run should be measured in inches, but then computes 30/26≈1.15 again after converting only the rise. The local code requires a slope no steeper than 1:12, and the ramp must be a straight run with no landings. You are asked to review the proposal before it goes to permitting.
1. Diagnose the unit error and compute the actual slope as a ratio. Is the proposed 26-foot run compliant?
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Both designers compare inches with feet. Convert the run: 26 ft=312 in, so the slope is 30/312=0.09615, or about 1:10.4. The code maximum is 1/12≈0.08333. Since 0.09615>0.08333, the ramp is steeper than allowed and is not compliant. A compliant 30-inch rise requires a run of 30·12=360 in=30 ft. The current 26-foot run is 4 feet short. The site allows up to 32 feet, so a compliant straight run is physically possible if the run is extended to at least 30 feet.
2. The contractor proposes shortening the rise to 26 inches while keeping the 26-foot run. Is that compliant? Explain using proportional reasoning.
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The new slope is 26 in divided by 26 ft. Converting the run, 26 ft=312 in, so the slope is 26/312=1/12 exactly. This meets the code maximum. The shortcut is to keep units consistent: 26 inches of rise over 312 inches of run reduces by 26 to 1/12. Shortening the rise while holding the run fixed decreases the slope proportionally, so the change from 30 inches to 26 inches is enough. If the door threshold cannot be lowered, the run must instead be extended to 30 feet.
3. A supplier offers a modular ramp rated at 7.5 degrees. Is that equivalent to a 1:12 slope? Support your answer with a comparison.
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No. A slope of 1:12 corresponds to an angle whose tangent is 1/12≈0.08333, so the maximum angle is arctan(0.08333)≈4.76 degrees. The supplier's 7.5-degree ramp has tangent tan(7.5°)≈0.1317, which is about 1:7.6, much steeper than 1:12. The 7.5-degree ramp would not satisfy the code. This also shows why slope ratio and angle are not interchangeable: for small angles they are close, but at 7.5 degrees the difference is large enough to matter for compliance.