Speed Hump and Speed Table Geometry

A speed hump's height and length set the speed a driver finds comfortable, and getting the proportions wrong produces either a device nobody slows for or one that bottoms out a fire truck. THE RAMP IS TREATED HERE AS A PARABOLA, which has a constant second derivative -- so the vertical acceleration a wheel feels is constant across the ramp and works out to eight times the height times the square of the speed, over the square of the transition length. Two things follow, and both are the design. Length matters more than height, because it enters squared: doubling the length quarters the acceleration at the same speed, while halving the height only halves it. And the speed at which a given ramp reaches a stated comfort limit falls straight out of the same relation, which is what a design speed actually means for a vertical deflection device. A classic twelve foot hump three inches high reaches a quarter of gravity at about sixteen miles an hour, which is why it works. THE FLAT TOP IS A SEPARATE MECHANISM AND IT IS THE REASON SPEED TABLES EXIST. A table with the same height and the same ramp slope has the same ramp acceleration and a materially higher tolerable speed, and the difference is not in the ramp at all: a short hump lifts one axle at a time and pitches the vehicle, while a flat top long enough for the whole wheelbase to sit on removes that pitching entirely. That is what this reports as the ground clearance question. A vehicle whose wheelbase spans the crest has its belly lifted above the line between its axles, and the amount is the crest height less the profile height under the wheels -- zero when the wheelbase sits entirely on the flat, and the full device height when the wheelbase is longer than the device. A long low vehicle on a short hump is where a device becomes a hazard. Emergency access is the constraint that usually settles the argument in a neighbourhood. Each short hump costs a fire apparatus seconds, and a corridor with six of them costs meaningful response time; departments object legitimately, and tables and cushions are the compromises that come out of this same geometry. That delay is NOT quantified here -- it needs the fire department's own apparatus and route data. This is a geometric screen. It does not design a traffic calming installation: device selection, spacing, placement relative to driveways, intersections, drainage, bus and emergency routes, signing and marking, and the public process are all part of a program this arithmetic supports rather than replaces. Device dimensions are set by the agency's standard drawings and by ITE traffic calming guidance and they vary, and taking dimensions from another jurisdiction is a common source of devices that do not perform as expected. It does not evaluate drainage, which a hump across a gutter line disrupts, or pavement construction and durability, and it does not address speed cushions or chicanes. The agency's standard drawings, ITE traffic calming guidance, the fire department, and the adopted MUTCD for signing and marking govern.

ramp length = (total length - flat top) / 2; ramp slope = height / ramp length; wheel vertical acceleration over a parabolic ramp = 8 x height x speed squared / transition length squared, constant across the ramp; the comfort speed is that relation inverted at an entered acceleration limit; the ground clearance required is the crest height less the parabolic profile height under the design vehicle's wheels.

The parabolic vertical-deflection geometry as standard traffic calming practice, by name, with ITE traffic calming guidance and the agency's standard drawings named as governing dimensions. Emergency response delay is NOT quantified; it needs the fire department's own apparatus and route data. The agency's standard drawings, ITE traffic calming guidance, the fire department, and the adopted MUTCD for signing and marking govern.

A slope, one squared term and a parabola evaluated at the wheelbase; no agency standard drawing is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: height_in, total_length_ft, flat_top_length_ft, crossing_speed_mph, comfort_limit_g, wheelbase_in, ground_clearance_in, target_ramp_slope_pct, ramp_length_ft, ramp_slope_pct, vertical_accel_g, comfort_speed_mph, clearance_required_in, ramp_length_for_target_ft

• A parabolic profile circular-arc devices differ modestlythe agency's standard drawings
• Device dimensions are entered taking them from another jurisdiction is a common source of devices that do not performITE traffic calming guidance
• Emergency response delay is not quantified each short hump costs an apparatus seconds, and a corridor of them costs real timethe fire department's apparatus and route data