Tire diameter calculations can be way off.

The posts on Tire diameter calculations do not always work for each tire manufacturer. I currently have Michelin XRadial Plus tires (185/65R14) on my '98 Jetta TDI. These tires are sold by Sam's club and are the equivalent to X-ones according to the Michelin guy I talked to. I had contacted Michelin by the contact form on their web site. My question was what are the revolutions per mile for my tires. They called me and told me that it was 901 rev/mile. If you do the calculations for 185/65R14, it comes out to 859.4 rev/mile. (see below for the calculation)

A big difference!

I thought the guy from Michelin gave me erronous information. This weekend I decided to check the tires for myself. I marked the tire and the floor in my garage and pushed the car for one revolution of the tire. I made a mark at the new position on the floor and measured between the marks (70.3125 inches). I calculated it out and the rev/mile is 901.1 rev/mile.

My calculation for rev/mile for 185/65R14:

185 mm x 0.65 = 120.25 mm

120.25 mm /25.4 mm/in = 4.7343 inches

tire diameter = (4.7343 + 7)x 2 = 23.47 inches

Circumference = 23.47 x 3.1416 = 73.728 inches

rev/mile = 5280 ft/mile / (73.728 in / 12 in/ft) = 859.4 rev/mile

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98 Jetta TDI, 93,000+ miles, Highest mpg 53.9

[This message has been edited by Tractor King (edited February 05, 2001).]

Many tire manufacturers have Revs per Mile data for each of their tires on their websites. And the RPMs for a given size do vary not only from manufacturer to manufacturer, but from model to model within one line.

Chris
'96 Passat wagon

Tractor if you can measure the distance a tire turns from a mark on a tire to the 10,000 th of an inch you are the master. I would geus that your 10th of an inch would be in jeapordy of error but you gave us all the way to 10,000 of an inch. They need you doing some atomic radi work with a ruller then we can get rid of the electron microscope.

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2001 4x4 6speed Cummins turbo Ram.

The measurement was actually 70 and 5/16 of an inch which calcutates out to 70.3125000000000000000.... inches. Amazingly enough for my measurement it was right on the 5/16 inch mark. For these calculations, eyeballing the tape measure is just fine.

Greg

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98 Jetta TDI, 93,000+ miles, Highest mpg 53.9

True thats a little nit picky; sorry but when i first read it i thought damn how did he measure that thing to those significant digits. Truncate those erroneous digits!!

That would give a maximum of 70.31 with the .01 as being uncertain I mean icould be .02 but you could never say the digits behind it with certaintity. Indeed you couldnt even say the .01. I thought you were using some laser setup but you are right on your wheel calcs

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2001 4x4 6speed Cummins turbo Ram.

The "engineering" approach to this kind of measurement is certainly to call it "close enough", it's not worth splitting hairs over fractions of a percent of difference here...

Brian P.
'96 Passat TDI mit UPsolute

Here's a thought:

Anyone calculate the revs/mile using the actual radius? Not the calculated one, but the actual one found by measuring the distance from the ground to the wheel center?

We all know that radial tires mush a bit depending on air pressure and tire construction, so the effective radius between tires will change depending on several factors.

My thought is that the difference between the calculated value and the observed value that Tractor King saw is due to the actual radius on the car vs. the radius due to calculations.


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"I love the smell of [burning diesel] in the morning. It smells like ... victory!"

I posted this spreadsheet some ten times by now, but no one ever commented on it ... what´s wrong with it ?
http://www.planet-interkom.de/CFriedriszik/gearcalc.xls

BTW, I use the indicated tire width for calculating, which of course gives an error - 205´ers may very well be 203-208 mm in width ... but then again, hardly any fatalities by that error ...

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´92 VW Polo G40 - 1272ccm / 113bhp
´97 Audi A6 Avant 2.5 TDI - 2461ccm / 140bhp Ad: "Why settle for moving with the times, when you can overtake them ?"
HP: http://www.planet-interkom.de/CFriedriszik

there are a couple web sites that have the calculations in a web format:
http://www.miata.net/garage/tirecalc.html
http://pw1.netcom.com/~sgalaba/tiresize.htm#TireSize
http://www.tolan-hoechst.com/cars/tirecalc.htm

I figure if the tire size is within 1% of stock then I am happy

<BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:</font><HR>Originally posted by Powder Hound:
Here's a thought:

Anyone calculate the revs/mile using the actual radius? Not the calculated one, but the actual one found by measuring the distance from the ground to the wheel center?

We all know that radial tires mush a bit depending on air pressure and tire construction, so the effective radius between tires will change depending on several factors.

My thought is that the difference between the calculated value and the observed value that Tractor King saw is due to the actual radius on the car vs. the radius due to calculations.


<HR></BLOCKQUOTE>

That is essentially what I did by measuring the distance on the garage floor. If you take my number and divide by PI and then by 2 you have the radius. I think my method is more accurate than trying to measure the radius directly.

The numbers for my case are 70 and 5/16 inches divide by PI divide by 2 = 11.2 inches or 284 mm radius.

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98 Jetta TDI, 94,000+ miles, Highest mpg 53.9

[This message has been edited by Tractor King (edited February 09, 2001).]

<BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:</font><HR>Originally posted by CFriedriszik:
I posted this spreadsheet some ten times by now, but no one ever commented on it ... what´s wrong with it ?
http://www.planet-interkom.de/CFriedriszik/gearcalc.xls
<HR></BLOCKQUOTE>

Claus,

There isn't a problem with the math in the spreadsheet (at least the first sheet), the problem is that mathematically inferring tire revolutions per mile (or kilometer) from the tire's generic size designation is only a very rough approximation of the actual RPM of any tire.

To give your example, using your spreadsheet's correctly calculated 63.19 cm overall diameter for a 205/55-16 tire, you would then further calculate a revolutions per mile of 810*. I randomly selected a Bridgestone RE940 tire in that size and Bridgestone lists the RPM as 837. <A HREF=http://www.bridgestone-usa.com/products/RE940tec.htm>http://www.bridgestone-usa.com/products/RE940tec.htm</A>

Tire RPMs shouldn't be calculated if the tire manufacturer's RPM data is available. And different manufacturers have different RPM values for the same size tires relative to other manufacturers and even relative to other tires models within their own product lines.

*5280/(((63.19/2.54)x3.1416)/12)=810

Chris
'96 Passat wagon

[This message has been edited by Chris Bell (edited February 09, 2001).]

<BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:</font><HR>Originally posted by CFriedriszik:
I posted this spreadsheet some ten times by now, but no one ever commented on it ... what´s wrong with it ?
http://www.planet-interkom.de/CFriedriszik/gearcalc.xls

BTW, I use the indicated tire width for calculating, which of course gives an error - 205´ers may very well be 203-208 mm in width ... but then again, hardly any fatalities by that error ...

<HR></BLOCKQUOTE>

I have seen the posts of the various spreadsheets using the tire size to do the calculations. My point is that the tire manufacturers are not making the tires to the same specifications. My Michelin XRadial Plus tires have 185/65R14 on the side wall when the rev/mile really is closer to a 185/60R14 tire size by spreadsheet calculations. If you don't go out and actually measure your tires your calculations may be way off using the spreadsheets.


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98 Jetta TDI, 94,000+ miles, Highest mpg 53.9

[This message has been edited by Tractor King (edited February 09, 2001).]

Chris and Tractor,
that´s what I wrote ... read before quoting ...

<BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:</font><HR>Originally posted by CFriedriszik:
Chris and Tractor,
that´s what I wrote ... read before quoting

...<HR></BLOCKQUOTE>

Yes, but your explanation as to why the formula does not yield an accurate rolling diameter or RPM is not correct. Its not because the actual section width differs from the nominal section width. Actual section width varies with the width of the wheel on which it is mounted. The reason the formula does not predict actual rolling diameters or RPMs is because it does not take into account the dynamic changes to the circumference and "flattening" of the tread footprint that occur with speed and load.

Chris
'96 Passat wagon

Supposing we could agree, what's the point? Will we be better drivers? Will we actually use less fuel? Will anything change? I don't get it. Of course, I don't understand why anyone would waste a day golfing either ...maybe it's just me.

chris,
but by measurement alone you cannot include the changes by speed, too. The rolling diameters of the mft. must be some compromise, too.

Referring to the wheel width problem:
Can you elaborate a little more specifically ? From your post I understand you say that rolling diameter changes with the width of the wheel the tire is mounted ? Ok, I can agree with this is you take into account the use of some absurdly wide wheels out there (prone to chuffing the edges).
But nevertheless a nominally 205 mm wide tire can vary in width for some mm´s.

After all, what results gives us this thread ? That rpm calculation via tiresize is not possible ? Well, my results are exact enough for my uses ...

<BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:</font><HR>Originally posted by CFriedriszik:
chris,
but by measurement alone you cannot include the changes by speed, too. The rolling diameters of the mft. must be some compromise, too.

Yes, thats true. But the most accurate value for figuring the tire's affect when calculating speed/RPM/speedometer values for a particular car and its gear ratios is to use the manufacturer's Revolutions per Mile number. Even if you try to calculate Revs per Mile from the manufacturer's own Rolling Radius value, it will be usually be significantly off from the published RPM value.

Referring to the wheel width problem:
Can you elaborate a little more specifically ? From your post I understand you say that rolling diameter changes with the width of the wheel the tire is mounted ? Ok, I can agree with this is you take into account the use of some absurdly wide wheels out there (prone to chuffing the edges).
But nevertheless a nominally 205 mm wide tire can vary in width for some mm´s.

I think we are mostly saying the same thing. The tires actual section width (not diameter) changes when it is mounted on different width wheels (wider wheel=wider section width). This is why manufacturers usually state the width of the wheel the tire is mounted on when publishing a section width number. There is a usually a 2" range
of approved rim widths and the one they use when measuring section width is usually somewhere in the middle of that range. And you are right, the section width of any given tire can definitely be larger or smaller than the nominal size, at any rim width.

After all, what results gives us this thread ? That rpm calculation via tiresize is not possible ? Well, my results are exact enough for my uses ...

Right, they both work; its just a matter of degree. The mathmatical approach gives a rough approximation of the actual value, which is fine (and it gets you an 'A' in geometry class!). Sometimes you need it to be more accurate (like speedometer calibration, for example) and then the actual Revs per Mile of the specific tire you are using is the value to use.
<HR></BLOCKQUOTE>

Reading this last paragraph raises a question:
A given 205/55-whatever tire should nominally have a tread-width of 205mm and a tread/height-ratio of 55%.
mmh - do they have the same differences concerning the ratio ? which width does every mft. calculate with ? Nominal or measured ?

Aw ! At least they go round in circles, so they shall be known as wheels ...

From looking at various data sheets on tires and comparing the numbers to calculations based on the size, it looks like the manufacturers are getting their data by taking actual measurements and not doing any calculations.

This would explain why my Michelin tire with a quoted 901 revolutions per mile is so far off from the calculated number of 859 rev/mile based on the tire size data. This difference is why I went out in my garage and did a real measurement. My real measurement matched the Michelin number of 901 rev/mile. Michelin had given me good data.

The point of this posting was to draw attention to the fact that manufacturers are not making the tires by the numbers. If you want accurate calculations, you need to go out and measure your tires if you cannot find the manufacturers data for your particular tire.

CFriedriszik I do not have any problem with the spreadsheet. The only thing is if you put in the tire size such as 195/60R14 the calculations can be off because the manufacturers are not making the tires by the numbers.

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98 Jetta TDI, 94,000+ miles, Highest mpg 53.9