The car ramp

A car is a rigid body on two axles, and its nose runs ahead of the front wheels. Where a flat floor meets a 20 % slope directly, the nose of the test car touches the ramp before it can climb it, and at the top its belly comes close to the crest.

So a ramp begins and ends with a gentler transition, with the steeper middle between them. With 10 % transitions the same car passes with clear room.

The test car is an approximate mid-size electric crossover: wheelbase 2.89 m, front and rear overhang 0.93 m, ground clearance 0.17 m. All of these values are unverified.

The regulation fixes three things: a transition is at least 5.00 m long, its slope is at most 10 %, and the middle slope is at most 20 %. Each transition gains 0.50 m at most, and the middle climbs the rest.

A rise of 3.20 m needs at least 21.00 m. On a shorter site no profile complies, however the points are moved, and on a longer one every slope eases.

Between the two there is a third state with a name of its own: at the limit. The profile complies, with no tolerance left for construction. It is neither a warning nor an error. This experiment calls a slope at the limit when it reaches 90 % of its maximum or more; that threshold is a choice of the experiment, not of the regulation.

The two transitions together gain 1.00 m. When the level difference is that much or less they cover it alone and the middle disappears: the ramp becomes one gentle slope.

For a rise of 0.80 m, for example, a single run of 8.00 m at 10 % is enough.

Above the foot of the ramp is the slab of the upper floor, which stops at the opening the ramp comes out of. Headroom is the vertical distance from the ramp surface to the underside of that slab.

The tightest point is neither at the bottom nor at the top but under the edge of the slab: there the ramp has already risen and the slab is still overhead. The minimum is 2.00 m over the full width.

The slab thickness of 0.30 m is a working value, unverified.

The slope rules do not know the plan shape. Straight, switchback and helical ramps lay the same developed length on the ground in different ways.

In a switchback the runs are joined by a flat semicircular landing. On the centreline it is at least 21.21 m long, because its inner edge keeps the minimum inner radius of 5.00 m, and it uses length without gaining height.

A landing is itself a flat surface, so are transitions needed on both sides of every landing or only at the two ends of the ramp? The required length changes with the answer.

A helical ramp does not save area. It saves a dimension: its footprint is roughly square and stays the same as the height grows, while the other two get longer.

On a circular path the inner edge travels a shorter distance than the outer edge for the same rise. So a helical ramp has three slopes at once: inner, centreline and outer.

With an inner radius of 5.00 m, a width of 3.50 m and one full turn, the lengths are 31.42 m, 42.41 m and 53.41 m, and for a rise of 3.20 m the slopes are about 10.2 %, 7.5 % and 6 %. The limit is checked on the inner edge, the steepest.

The effect shows here: the inner slope of 10.2 % is just over the transition limit of 10 %, so one turn at this radius is not enough.

Cross slope is outside the scope of this experiment.

Move the two break points wherever you like. The limit that applies to a point depends on where it is, not on the segment it belongs to: anything within one transition length of a flat surface is held to the transition limit, everything else to the middle limit. A segment that crosses that line is checked in two parts.

Every value of the generic rule is unverified: a transition of 3.05 m and a maximum slope of 16 %. Its point is one relationship: the transition limit is 0.5 of the slope the ramp is actually designed at, not of the maximum. A ramp designed at 12 % needs 6 % at its ends, so an 8 % transition fails.