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Re: Rim and Tire sizes (long)

----- Original Message -----
From: Robert B. <robbrauns@bb.eulink.net>
To: Quattro List <quattro@audifans.com>
Sent: Friday, August 20, 1999 4:11 PM
Subject: Rim and Tire sizes (long)

> Hello Q-List:
> someone posted off list to me and so I thought I would share this
> information on upgrading to bigger rims and tires. Sorry if it's long,
> but it is a detailed mathematical formula and explanation on how to
> calculate the rolling circumference of any tire and rim combination.
> I think there is a formula somewhere on the web, but you can calculate
> rolling circumference pretty easily...
> Firstly, it is not the size of the rim only that makes a difference, but
> rather the rolling cicrumference (RC from now on) of the rim PLUS the
> tire size. For example, a 175/65HR15 tire has a RC of 61.2". A
> 205/45SR17 tire has a RC of 64.8", so these are almost the same RC, but
> your speedo will read too low by about 6%. A larger RC means your car
> will accelarate slower, but have higher top end speed and lower highway
> rpms. Your speedo will read too low if the RC of your new tire/rim combo
> is bigger than the RC of the stock tires. Now for the math:
> The formula for the circumference of a circle is: 2TTr, where
> TT=pi=3.14169 and r=radius of the circle (rim + tire).
> So, to calculate the RC (how long the tire would be if you cut it and
> laid it on flat on the ground), you have to add the diameter (which is
> 2x the radius) of the rim PLUS add the diameter of the tire. Since the
> 175/65 are in millimeters, you first have to convert the 175/65 to
> inches. BUT before you do that, the 175/65 number has to first be
> converted to the actual tire height. 175/65 means that the tire (or
> tread?) width is 175mm and the height of the tire is 65% of the tread
> width. BTW, this ratio of 65% to the tread width is called the aspect
> ratio. So, the height of the tire would be 175x65/100=113mm. Now take
> this figure and divide by 25.4 to get the height of the tire in inches.
> 113.75/25.4=4.47". So the diameter of the rim + tire (called the RC) is:
> TTx (15" [rim] + 4.47" [tire]) = 61.2".
> If you have a spreadsheet program, enter values for rim size in A1
> (15"), the tread width in A2 (175) and the aspect ratio in A3 (65) and
> then enter this formula in A4 to get the RC: =
> (3.14169*(A1+(A2*A3/100)/25.4))
> Think of rolling circumference this way: for every ONE revolution of the
> tire, the car will move forward exactly 61.2".
> The letters, HR, SR, TR, VR are speed ratings (H being the lowest and Z
> being the highest) and R simply means a radial tire (as opposed to say,
> bias-ply tires). (BTW, are these still made?)
> If you plan on upgrading your rims to a larger diameter, you need to get
> a tire with a smaller aspect ratio or else your speedo will be off. A 5%
> difference is the most you can change without worrying about your
> speedo, since there are variations between tire companies of about 5%.
> HTH.
> Rob
> Germany

Actually, that's the wrong number for pi.  Off the top of my head it's about
3.141592653589793238462643383279502884197169399 .

I used to get really bored in my calculus class.