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.
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!