Re: Tire marks on road

[David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>]

Regarding Hasan's question:

> A tire mark on a road due to hard braking is dark at one end and
> fades out at the other.  Which way was the vehicle moving when the
> brakes were slammed?
>
> This morning I wondered when I saw such marks.
>
> Hasan Fakhruddin

This is an interesting question whose answer I do not know for
certain.  But I suspect we can probably figure it out.

We can probably conclude that the brakes were locked since there was
a tire mark in the first place that was caused by abrasive shearing
of the rubber comound off of the tire.  Because of this we know that
the vast majority of the vehicle's kinetic energy (w.r.t. a frame in
which the pavement is at rest) was dissipated as heat at the rubber/
pavement interface.  (But some of the energy was also used to do the
work of  tearing off the rubber compound from the tire.)  All this
concentrated thermal energy must have resulted in a large local
temperature increase in the tire compound near the interface such
that the temperature increased as the skid proceeded and the
vehicle slowed.  I suspect that the resistance to abrasive shearing
in the tire rubber declines with increasing temperature.  So as the
surface heats up I would expect that more compound is torn off per
unit length of sliding.  Also, I would expect that the tire's
frictional sticking to the pavement would increase with this
temperature and this increase in friction would increase the
braking force and thus increase the deceleration rate near the end
of the skid.  Also a slower speed mismatch at the interface would
presumably result in better rubber/pavement contact with less
local surface skipping than at higher speeds.  This increase in
friction force would presumably be more effective in causing
further tearing of the compound off of the tires.  The upshot of
all of this seems to suggest that the skid marks on the pavement
ought to be thicker at the end of the skid than at the beginning
(with a sort of positive feedback mechanism contributing to the
effects).

David Bowman

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.