The Ramp That Does Not Fit
Students are designing a wheelchair ramp for the community center's side door. The door sill sits 0.90 m above the sidewalk, and the only available space is a straight run of 9.0 m along the wall. The town rule states that ramps may not be steeper than 1:12, meaning 1 m of rise for every 12 m of run. The team has $600 for surface materials and railings.
To choose a surface, they release a 5 kg sled, wetted to simulate rain, from the top of a test ramp built at 1:12 and measure how far it slides along the flat ground past the bottom:
- Smooth aluminum: 2.4 m
- Painted wood: 1.1 m
- Rubber mat: 0.3 m
Costs per square meter are $14 for aluminum, $6 for painted wood, and $22 for rubber mat. Rubber mat holds water and is expected to need replacement every three years.
1. Check whether the proposed straight ramp satisfies the town rule in the space available. Show the calculation and name a workable alternative if it fails.
Read the worked answer
The required run for a 0.90 m rise at 1:12 is 0.90 × 12 = 10.8 m. Only 9.0 m of straight run is available, so a single straight ramp would have a slope of 0.90/9.0 = 1:10, steeper than the rule allows. The design fails a hard constraint before surface choice even matters, which is exactly the kind of problem that should be caught before ordering materials.
Options include a switchback or L-shaped ramp with a flat landing, which gains run by turning along a second wall; extending the ramp into the sidewalk area with a variance and a protected landing; lowering the door sill or raising the walkway to reduce the rise; or installing a platform lift if space cannot be found. Each option carries a new constraint to check, such as landing size, door swing clearance, drainage, and cost, so the students should measure the second wall before committing.
2. Assuming the ramp can be built, choose a surface using the sled data and the stated constraints. Explain the trade-off rather than just picking the lowest number.
Read the worked answer
Rubber mat produced the shortest slide (0.3 m) and is the safest wet surface, but it costs the most at $22 per square meter and needs replacement every three years, which strains a $600 budget over the ramp's life. Aluminum is cheapest per square meter but slid 2.4 m wet, the worst result, and a slippery ramp is a safety failure, not a saving. Painted wood sits in the middle at 1.1 m and $6 per square meter.
A defensible choice is rubber mat, or painted wood with a roughened, sealed finish plus a lower-cost strategy such as matting only the sloped sections, if the math fits the budget. The trade-off is upfront cost and maintenance against slip risk for people using wheels, canes, or walkers.
The sled is only a proxy. It does not model wheelchair wheels, braking, handrail use, or a person's strength, so the students should treat the rankings as a screening tool and confirm the choice with a test using an actual wheelchair and a wet surface.
3. Describe one test the team should run before installation and state what result would change their decision.
Read the worked answer
Build a full-scale section of the chosen surface at the final slope, wet it with the same amount of water, and have a wheelchair user test going up, stopping midway, and coming down with and without handrails. Record whether the user can start from a stop, whether the chair drifts sideways, and whether the user reports effort or loss of control.
The decision should change if the surface fails this test. For example, if the rubber mat is too soft and makes pushing exhausting, or if the painted wood becomes slick after ten minutes of wetting, then slip distance from a sled is not capturing the real requirement and the team should switch surfaces, add a textured strip, or add a landing to break up the slope. A test that cannot change the decision is not worth running; this one can.