This issue has been bugging me since it came up on one of my mailing lists a while back. The common wisdom in A/R circles says that skid marks are a result of oils coming to the surface as the skidding tire heats the pavement while passing over it, and perhaps bits of tire grinding being trapped in a molten roadway surface layer which cools immediately after the tire passes. I have been skeptical of both explanations - if I swing a torch over pavement (open propane flame being clearly hotter than a skidding tire) I don't get a black stripe. And what about concrete? why do we get similar marks on concrete.....So. Having not learned from that curious cat, I decided to calculate the energy dumped into the ground by a skidding car, and see how much it would heat the pavement.
Let's start with a 2500 lb car travelling 60 mph, assume a drag factor of 0.8. For severity and simplicity, let's assume that the rear wheels are in the air, and the fronts do all the work - this means all the heat input on one side is through one contact patch in one event, so there's no cooling between tires, and no second event to mess with.
If the brakes are locked, we will dissipate all the kinetic energy [(mass*v^2)/2] in the skid. this gives us 300,600 ft-lbs. Each skid gets half of the energy, or 150,300 ft-lbs.
The total expected skid length works out to be:
So, if we assume even distribution of the energy along the skid length, we get:
According to the Asphalt Institute (asphaltinstitute.com) the heat capacity (Cp) of pavement is about 0.22 cal/gram-degC which is equivalent to 0.22 BTU/lbm - F which equals 171.2 ft-lb / lbm - F
Typical wear-course pavement density is 14.20 in^3/lb , or 0.071 lb/in^3 (see http://www.highwaysmaintenance.com/Bitdata.html for this info)
If the energy dumped into that one-square-inch area of pavement heats a layer say 0.01 inches deep (which is on the order of pavement roughness acording to several websites regarding texture and mean profile depth, see http://www.greenwood.dk/html/profilo/macro.htm, http://www.vti.se/nordic/1-00mapp/100dk1.html, and http://www.tfhrc.gov/hnr20/rosan/rosandoc.htm), it's heating 0.01 square inches, or about 0.00071 lb of asphalt, recalling that
= 137 degrees F.
It has been suggested to me that the fact that a brake disk is hot after a long (non-locked) stop is proof of this theory. I disagree. A disk or drum is absorbing the entire 190-or so BTUs (presuming the rear brakes suck) in the several seconds that it takes to stop, with a mass of around 8 pounds, and a relatively small surface area (yielding at best modest convection cooling during the event and only modest heat conduction through the disk thickness). This is NOT even close to being the same as 150 foot long piece of pavement, with the car passing over each one-inch length in a tiny fraction of a second (about 0.001 seconds at about 60mph).
Mechanical Forensics Engineering Services, LLC.
This page created on 21-NOV-2001 and last modified 21-NOV-2001