# Collision reconstruction

Question: How is the constant of 30 in the minimum speed formula derived?
This is in collision reconstruction where the speed of the vehicle is determined by taking the square root of the product of 30 times the distance travelled (skid) times the drag factor (coefficient of friction) times the braking efficiency.

First of all let me say that I do not know the formula. Maybe if you could send me a bit more background, including an explanation of the formula I could be of more help.

However I have made up some ideas which may be useful and below is a link to a web site that you might like to look at before, or after, reading my ideas.

Collision reconstruction

### Looking at a car braking

The two variables involved in calculating the distance of skid are:
(i) the coefficient of friction between the car and the road (f)
(ii) the initial speed of the vehicle (v)

Braking force (F), mass of car (m), normal reaction between car and road (R = mg), stopping distance (d)
Take the acceleration due to gravity (g) to be 9.8 m/s2

But F = fR
Using energy considerations: Fd = ½ mv2 therefore fmgd = ½ mv2 and this gives:

Speed of vehicle before braking (v) = (2fgd)1/2

So if f = 0.72 (asphalt) and d = 20 m we have for v:

Speed (v) = (2x0.72x9.8x20)1/2 = 16.8 m/s or 37 mph.

If the car had barked on grass (f = 0.35) the distance travelled (from the same initial speed) would have been:

Braking distance (d) = ½ v2/[fg] = 41.1 m

This is a very simplistic answer and does not take into account of the braking efficiency of the car. It rather looks as if my 2g in the formula is replaced by your 30 but I have no idea why. Sorry!

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