Hmmmmm, I think you are asking the wrong question. See the previous very
verbose thread about the tire contact patch size NOT being related to
tire width or diameter. Also, I think you will find that the tire
*compound* has a very large effect on your "coefficient of friction". And
I would think that "power" is hardly the key factor for tire use in
autocrossing... you might want to consider vehicle inertia and desired
target lateral G (we won't even get into inflation pressures and spring
rates)... I think your mathematical model is going to need to get a great
deal more complex!
Given that you're starting with an MGB, your limiting factors for tire
width are your wheel rim width and the clearance in the wheel wells. Your
limiting factors for tire diameter are the sizes available for your rims,
ground clearance, and well clearance. These are also the effective limits
to the tire profile, or "how low can you go?". Within these rather severe
constraints, I think it would be more profitable to query other
autocrossers as to what tires they have found effective, rather than to
waste time calculating the ineffable. Besides, even if you somehow manage
to figure out an "optimum" size using arcane mathematics, that still
doesn't tell you (1) if that size is even available, or (2) which brand
to buy for best performance.
Don't mean to throw a wet blanket on your mathematical engineering
exercise, but I think if it was that simple, someone would have published
it by now. Anyway, there is such a limited range of sizes that even fit a
stock B that you hardly need a computer to sort them out. IMHO, etc.
James Nazarian Jr had this to say:
>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
>
>
--
Max Heim
'66 MGB GHN3L76149
If you're near Mountain View, CA,
it's the red one with the silver bootlid.
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