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Tire question for engineers

To: mgs@autox.team.net
Subject: Tire question for engineers
From: James Nazarian Jr <James.Nazarian@colorado.edu>
Date: Mon, 14 Feb 2000 16:35:51 -0700 (MST)
Before I get down to my question, I'll provide a little background.  I
recently had to drop my Mechanical Engineering degree because of the way
my school was handling me (LONG story).  Anyways I have an extra five or
so hours per night when I would have been doing calculus homework.  So
with all this free time I have been working on setting my V8 up to be a
better autocross car. (Read: I have been applying way to much math to
suspension design and upgrades, to keep myself busy-er)

Now for the car content.  I have been working on a formula to calculate
tire size needed for a given amount of power.  What I am trying to do is
figure out how much rubber to I really need to have on the ground given a
set of performance data.  What I am down to now is I have a coefficient of
friction of a set of tires but can't relate that to a tire size.  What I
have is 500lbs on a tire with coefficient of friction of .8 so 400lbs of
traction force (round numbers chosen and ignoring weight transfer etc for
simplicity). So I have this but I don't have a tire size.  Obviously if I
put bicycle tires on the car they would loose traction, but if I put drag
tires on they wouldn't even though both might have Cof of .8

So how do I relate Cof to traction force and to tire contact patch area?
If anyone has some insight, maybe not a solution I would be interested to
hear it.  Also if such a formula for calculating tire size exists I would
like to see it.  Many would suggest just go to bigger tires, but since car
is for autocrossing low unsprung weight is important.  Also big tires =
big $$$.  I don't want to make the car look too fast for insurance reasons
(I'm only 21) but I don't want to pay in handling/acceleration because the
tires are too narrow.  So I want to actually derive the tire size that I
need.  Anyone know more about this stuff than me?  I'll be glad to share
formula with everyone, but I have to figure it out first.

James Nazarian
'71 B roadster
'71 BGT rust free and burnt orange
'74 BGT going by-by soon
'63 Buick 215 


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