Ramp Design and Slope Compliance
A community centre is installing a wheelchair ramp to a door whose threshold is 0.6 m above ground level. Building regulations require the ramp slope to be no steeper than 1:12 (rise:run), and the available horizontal space along the wall is only 6.5 m. The contractor proposes a straight ramp 6.0 m long horizontally. A volunteer measures the diagonal walking surface and reports it as 6.03 m, arguing this satisfies the rules because the surface is 'about 6 metres'. The centre manager wants to know whether the proposal is compliant and what alternatives exist if it is not.
1. Determine whether the proposed straight ramp meets the 1:12 slope requirement, and compute the actual slope ratio and angle of inclination.
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Slope ratio = rise : run = 0.6 : 6.0 = 1 : 10.
Required maximum is 1:12, i.e. run must be at least 12 × 0.6 = 7.2 m. The proposed run of 6.0 m is shorter, so the ramp is too steep and non-compliant.
As a decimal slope: 0.6/6.0 = 0.1. Angle = arctan(0.1) ≈ 5.71°.
Compliant angle: arctan(1/12) ≈ 4.76°. The proposal exceeds this.
The volunteer's 6.03 m figure is the hypotenuse √(6.0² + 0.6²) = √(36 + 0.36) = √36.36 ≈ 6.03 m. Measuring the diagonal does not change the horizontal run; the regulation is about rise-to-run, so the argument fails.
2. The centre cannot extend beyond 6.5 m horizontally. Evaluate whether a compliant straight ramp is possible and describe a switching (zig-zag) design quantitatively.
Read the worked answer
A straight compliant ramp needs 7.2 m of run, but only 6.5 m is available. So no compliant straight ramp fits.
A switchback with two flights, each rising 0.3 m, needs run per flight ≥ 12 × 0.3 = 3.6 m. Two flights side by side require about 3.6 m of horizontal run plus a turning landing (commonly ~1.5 m). Total footprint length ≈ 3.6 + 1.5 = 5.1 m, which fits within 6.5 m.
Each flight's walking length = √(3.6² + 0.3²) = √(12.96 + 0.09) = √13.05 ≈ 3.61 m. Total walking distance ≈ 7.22 m plus the landing.
Conclusion: a two-flight switchback with 3.6 m runs per flight and a 1.5 m landing is compliant and fits the space.