Skid Marks and Accident Reconstruction and Investigation - The
Skid Mark Equation
In a college algebra course, we may learn that "the stopping
distance of a car is directly proportional to the square of its
speed." The formula for this is:
D = k●V2 where D is
the stopping distance in feet, V is the speed in miles per
hour, and k is a constant that depends on the frictional force
of the pavement on the wheels of that particular vehicle. To
accurately use this formula, one must:
- Experimentally determine the constant k for the particular
vehicle in question driven on the same pavement, in the same driving
conditions. Drive at a known speed V. Brake suddenly.
Measure the skid mark D. Use this data to
solve for k. The algebraic solution of D
= k●V2 for variable k is
- Measure the skid mark D for a different speed.
- Substitute the value of D into the equation
My Own Skid-Mark Experiment (Watch
My brother-in-law (a former law enforcement officer), myself, and my
sons decided to try out this formula by conducting
experiment. As the test driver, I locked up the brakes on my 2003
Kia at a speed of 30 MPH several times to get an average skid mark of
33 ft, 4" or 33.33ft. Plugging into
this results in a value of k = 33.33/(302) = 0.037
So, for this particular vehicle on this particular pavement,
D = 0.037●V2
I then increased the speed to about 35 MPH and locked the brakes.
Surprisingly, the extra 5MPH resulted in a skid mark of 50ft!
According to our formula
Plugging D=50, we get V = 36.8 MPH. Not Bad!
I have found this formula referenced
internet, and my brother-in-law
Deputy Murray also used this formula and other mathematics
while on the job.
NOTE: When measuring the skid mark, you need to measure from
where the mark first begins, however faint. This was pointed out to me
by retired Deputy Murray as we were conducting this experiment.
Factors To Consider
In the tests shown on the video, the skid mark equation worked quite
well because we obtained the constant k using the actual vehicle on
the actual pavement. Other factors to take into account include:
- Is the pavement wet or slippery? Investigators account for
this by actually doing a pavement test at the scene.
- What are the condition of tires? Again, investigators account
for this and adjust calculations.
- Is there an incline to the pavement up or down? If so,
this must be recorded and the calculation must be adjusted.
- Did the car impact some other car or object while skidding? If
so, a modified formula must be used.
See this story.