How to work out speed from skid marks, and why the answer should be a range

Put the measurements into SKID as ranges rather than figures — the lowest the drag factor could be and the highest, the shortest the skid could be and the longest — and every answer comes back as a band. A skid of 22 to 24 metres at a drag factor between 0.65 and 0.75 is not "38 mph". It is between 37.5 and 42.0 mph, and that is the sentence that survives cross-examination. Nothing is uploaded and it works at the roadside with no signal.

The arithmetic is not the problem

The equations in collision reconstruction are old, published and undisputed. Speed from a slide is v = √(2 f g d): the drag factor, gravity, and the distance. There is no controversy in it and there has not been for decades.

What goes wrong is the inputs. The drag factor is one somebody remembered or took from a table. The skid length was paced, or measured with a tape held at one end by a colleague. The middle ordinate of a yaw was read off a curve nobody could stand in the middle of. Those numbers go into an equation that does not care how they were obtained, and out comes a single confident figure that goes into a statement and gets read out in court as though it had been measured.

A range in, a range out

The honest answer to "how fast was it going" is almost never a number. Here is the same skid worked at the corners of a realistic set of measurements:

Four and a half miles an hour of width, from measurements nobody would call sloppy. Quote the midpoint and you have invented a precision that does not exist; quote the band and you have said something true that will not fall apart under questioning.

The width of the band is frequently the real finding. Where it exceeds about a quarter of the answer, the page says so — because knowing that the measurements are doing more to the result than the collision is worth far more before a hearing than during one.

Why the band is sampled rather than cornered

For a simple slide, the extremes of the answer do sit at the extremes of the inputs, and evaluating the corners would do. That is not true of every calculation here.

The radius of a yaw is R = C²/8M + M/2 from the chord and the middle ordinate, and it is not a monotonic function of the middle ordinate. Over the values anyone measures at a scene it happens to be, but a corner method is only safe if somebody has checked that it is monotonic over the range they were actually given — and nobody checks. So the whole input space is sampled instead. It costs nothing, and it cannot be quietly wrong on the one calculation where an honest band matters most.

Critical speed in a yaw, and why it carries a warning

The critical speed equation, v = √(f g R), is the most over-trusted thing in the subject. The reason is the radius: it is derived from a chord and a middle ordinate, and it is brutally sensitive to that ordinate.

Half a metre of error in a measurement taken at the side of a road, in the dark, on a curve, moves the answer by twenty-five miles an hour. That is why the warning sits beside the equation on the page rather than in a footnote: it is confidently wrong in the middle of its range more often than anything else in the field.

Several surfaces, and the mistake that gets made

A vehicle that slides across tarmac, then a verge, then gravel does not have an average drag factor. Energy is what adds, not friction: each segment contributes 2 f g d and the speeds combine as the square root of the total.

Averaging the drag factors gives the right answer only when the distances happen to be equal, and the wrong one — sometimes badly wrong — whenever they are not. This is one of the commonest errors in amateur reconstruction and it always flatters the shorter, higher-friction segment.

No drag factors are built in, on purpose

There is no table of surfaces in this tool. A drag factor belongs to that surface, that tyre, that temperature and that day. A figure inside a piece of software is not evidence of any of them, and quoting one as though it were is how a reconstruction becomes indefensible.

If the number matters, it should come from a skid test at the scene, a drag sled, or a published figure you can name and stand behind — entered as the range it honestly is.

The question usually being asked

Often the real question is not "how fast was it going" but "could it have stopped". That is thinking distance plus braking distance, and the perception-and-reaction time is itself a range, not the 1.5 seconds everybody quotes. The tool gives the distance and, more usefully, the speed still on at the point of the hazard — which is the figure that decides whether a collision was avoidable.

The short version