The Hall Ramp
A council is building a wheelchair ramp to a community hall doorway. The floor inside the doorway is 0.90 m above the path outside.
Building rules require a ramp gradient no steeper than 1:12 - that is, 1 m of rise for every 12 m of horizontal run. The flat space available in front of the door is 9.6 m long, and the ramp must finish exactly at the doorway, so no extra run can be gained beyond that 9.6 m.
The builder proposes three options: keep the 0.90 m rise using the 9.6 m available; lower the doorway floor to 0.80 m; or keep 0.90 m and insert a 1.5 m flat landing at the top of the ramp. The ramp deck will be 1.2 m wide and is priced at $46.50 per square metre.
1. Check whether the builder's first option (0.90 m rise over a 9.6 m run) complies with the rule.
Read the worked answer
Required run for a 0.90 m rise at 1:12: run = 12 × 0.90 = 10.8 m
Available run: 9.6 m - this is 1.2 m short.
Actual gradient: 0.90 : 9.6 = 1 : 10.67 (dividing both by 0.90), which is steeper than 1 : 12.
Verdict: it does not comply. A useful quick test is that at 1:12 a 9.6 m run can only lift 9.6 ÷ 12 = 0.80 m, so 0.90 m is too high for the space available.
2. For the option where the doorway is lowered to 0.80 m, find the length of the sloping ramp surface.
Read the worked answer
At 1:12 the required run is 12 × 0.80 = 9.6 m - exactly the space available, so this option just complies.
The sloping surface is the hypotenuse of a right triangle with run 9.6 m and rise 0.80 m: L² = 9.6² + 0.80² L² = 92.16 + 0.64 = 92.80 L = √92.80 ≈ 9.63 m
Notice that the slope length is only about 3 cm more than the run - for shallow ramps the hypotenuse is nearly equal to the run. Treating the slope as 9.6 m would be a small error, but it must still be rounded up for ordering material, never down.
3. Using the compliant 9.63 m ramp, cost the deck, and explain why the landing option fails.
Read the worked answer
Deck area: 9.63 × 1.2 = 11.556 ≈ 11.56 m² Cost: 11.56 × $46.50 ≈ $537.54 (about $538)
If a supplier quotes on 9.6 m instead, the area is 11.52 m², a difference of only 0.04 m² - small, but rounding down would leave the deck short, so order from the 9.63 m figure.
The landing option fails: a 1.5 m flat landing eats into the horizontal space, leaving a run of 9.6 − 1.5 = 8.1 m for the slope. The gradient would then be 0.90 : 8.1 = 1 : 9, far steeper than 1 : 12, and the maximum rise would be only 8.1 ÷ 12 = 0.675 m. A landing can only be added by first lowering the doorway or extending the total footprint beyond 9.6 m, so it cannot be combined with the 0.90 m rise in this space.