Whilst what you say is true, it is only for *ideal* or theoretical friction.
Tyres
do not conform to the theory - there are two additional effects
1) Micro surface area
2) chemical forces
Micro surfaces on the road are conformed to by soft rubber making the
contact area much larger than the simple Area = Weight/Pressure.
Racing rubber also is characterised by bonding forces between the rubber
and the road surface. Think of this as a weak "glueing" force that increases
the coefficient of friction behond the theoretical max of 1 (even if you
take
into account the real surface area as per 1)
Having said all this, I don't think either effect would change significantly
with
increased width and constant weight (i.e. wide but short contact patch vs
narrow and longer contact patch), in an instantaneous single measure
but energy dissapation does come into it.
If you have a long narrow contact patch, then any given area of rubber will
be
in contact with the ashphalt for a longer time than for the wide short
contact patch.
Racing rubber has a high hysterisis (i.e. the deformation of the rubber is
non
elastic i.e. it absorbs energy (as heat) during deformation instead of
giving it all
back on rebound). Both the chemical and physical forces that generate heat
during the power transfer from wheel to road will be acting for a longer
time
per cycle. This will lead to breakdown of the grip and eventually the rubber
sooner
for the narrow tyre than for the wide tyre.
Another impact is on the centrifigul loading on the tyre. Drag tyres
increase working
diameter by a very significant margin. I'd hazard a guess that the
deformation of the
tyre's cross section could be a significant factor. Although it seems
counter-intuitive
I'd guess that they must be able to keep the contact area flatter on the
wide tyres
though some tricky layup techniques. If they couldn't then the advantage
*would*
swing back to the narrow tyres.
I'm not at all sure of the relative magnitudes of these effects or what
other effects
may come into it. This is just my guess - take it for what its worth...
Mike
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Mike Gigante mikeg@vicnet.net.au
Watsons Creek Vineyard http://www.vicnet.net.au/~mikeg
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-----Original Message-----
From: Scott Gardner <gardner7@pilot.infi.net>
To: mgs@autox.team.net <mgs@autox.team.net>
Date: Saturday, January 24, 1998 4:26 PM
Subject: Another physics question (Help me out on this one...)
Since the list did so well on the water-displacement/painted cylinder
questions, maybe you can help me out on one that my Dynamics profesor
asked us about eight years ago. I still haven't found a definitive
answer. It IS automobile-related, but not necessarily LBC.
First, some background information: The coefficient of friction
between to surfaces does not rely on the amount of surface area in
contact, only on the weight of the object being moved. This is why a
tall, skinny box is not any easier to slide across a floor if you
have the small surface in contact with the box than if you have the
big side in contact with the floor. This is true whether you're
talking about sliding friction or static friction. (sliding friction
is the box sliding across a floor, static friction is like a wheel
rolling across the floor--no points on the floor and wheel ever
actually slide relative to one another, but there's still friction,
also known as rolling resistance).
Here's his question. If the coefficient of friction is only
dependent on the two surfaces in question and the weight of the
object being moved, and not the amount of surface area in contact
with the ground, why do drag racers use such wide tires? Discount
anything having to do with cornering, since drag racers are just
interested in straight-line movement. Those of you who still
remember any dynamics classes you may have had can do the math
yourself--On paper, a car should be able to generate the same
forward force whether it is fitted with bicycle tires or 30" wide
Mickey Thompson Slicks, as long as the rubber used in both tires is
the same, and the weight of the car remains the same.
I have an idea, but I don't want to prejudice the list.
I'll post my hypothesis for confirmation or ridicule in a day or two.
Scott
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