The Americans with Disabilities Act stipulates that wheelchair ramps cannot have an incline surpassing a ratio of 1:12. An architect is designing a ramp that allows handicapped persons to get to a door’s level that is 12 feet off the ground. What is the maximum angle of elevation for the ramp, rounded to the nearest hundredth of a degree? What is the shortest possible length of the ramp, rounded to the nearest tenth of a foot?
1: maximum angle of elevation for the ramp
2: Explanation for ramp angle
3: shortest possible length of the ramp
4: Explanation for ramp length
Maximum slope for hand-propelled wheelchair ramps should be 1" of rising to every 12" of length (4.8-degree angle; 8.3% grade).
Maximum slope for power chairs should be 1.5" rise to 12" length (7.1-degree angle; 12.5% grade).
Minimum width should be 36" (inside rails) - (48" is ideal).
1. The max angle is given by this :
arctan (1/12) = angle ≈ 4.76°
2. The tan is the rise over the run.....hence 1 ft rise / 12 foot run
The tan inverse (arctan) will tell us what an angle with this rise and run is
3. Ramp length can be found by this
sin (4.76°) = 12 / ramp length .....rearrange as
ramp length = 12/ sin (4.76°) ≈ 144.6 ft
4. The sine gives the ratio of the opposite side from the angle to the hypotenuse which is the ramp length