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Calculating Tire Height mathematically
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Thornton
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PostPosted: Sat Jul 18, 2009 8:04 pm    Post subject: Calculating Tire Height mathematically Reply with quote

Tire Height questions pop up here in the forum often so I am posting the math equation so anyone can figure out the height of a tire.


This Simple math equation can tell you the height of a tire without air and vehicle weight on it.

We will do the tire size 205-70-15

you take the width 205, Divide it by 25.4 (25.4 is how many millimeters are in a inch)

205/25.4 = 8.07086614

Now you take the Series of the tire, in this case its 70
70 represents that the side wall height is 70% of the tread width

you take the 8.07086614 times it by 0.7

8.07086614 x 0.7 = 5.6496063

you then times this number by 2 meaning above wheel and below wheel

5.6496063 x 2 = 11.2992126

take that number and add the rim diameter to it

11.2992126 + 15 = 26.299

so a 205 / 70 / 15 has a rolling diameter of 26.299"



you can do the math like I always tend to do

OR

use this link below for the non math people Wink

http://www.wallaceracing.com/tire-aspect-calc.php
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booch
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PostPosted: Mon Jul 20, 2009 6:37 pm    Post subject: Reply with quote

Here is another link for the non-Mensa crowd. You can compare two sizes at the same time, complete with graphics.

http://www.rims-n-tires.com/rt_specs.jsp
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CoastalDefender
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PostPosted: Wed Oct 21, 2009 9:02 pm    Post subject: Reply with quote

And if you are a complete dolt like myself, this should do you well...

http://www.miata.net/garage/tirecalc.html
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sactojesse
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PostPosted: Tue Dec 01, 2009 11:17 am    Post subject: Reply with quote

I prefer to do the math myself, but I have a simpler method.

(Width in mm) x (double the aspect ratio) = sidewall height in mm
Divide by 25.4 mm/inch to get sidewall height in inches
Add to rim diameter in inches to get total diameter

For example, 165R15 is a P-metric (82 series) tire:

165 mm x 1.64 = 270.6 mm/25.4 = 10.65 in. + 15 in. = 25.65 in.
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schunacher
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PostPosted: Wed Jan 20, 2010 4:52 pm    Post subject: Tire math "without air" Reply with quote

@Thornton (or anyone),

What are the implications of measuring the tire without air? Does it get smaller when you add air?

Stephan
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Thornton
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PostPosted: Wed Jan 27, 2010 2:33 pm    Post subject: Re: Tire math "without air" Reply with quote

schunacher wrote:
@Thornton (or anyone),

What are the implications of measuring the tire without air? Does it get smaller when you add air?

Stephan


Looking on Tirerack.com it says this about tire measurement

Overall Diameter

A tire's overall diameter is the outer diameter of the tire measured in the center of the tread. This measurement is made without any load placed upon the tire and after the tire has been properly mounted on its industry assigned measuring rim and has been inflated and reset to its test pressure after 24 hours.


If you take a tire without them mounted on the rim and compare the same tire to one mounted on a wheel they are going to seem to be different heights. the mounted version on wheel has some sidewall stretch for the rim width.

So depending on the width of your rim, i guess your tire can get smaller if your stretching it on a wide wheel
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sammystics
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PostPosted: Thu Feb 18, 2010 10:51 pm    Post subject: Tire size Reply with quote

Here's another place to go to. It will calculate the tire size for you.
Also if you put in the rim size,width and et it will give you the backspacing too.


http://www.wheelsmaster.com/rt_specs.jsp
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KellyH
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PostPosted: Thu Feb 25, 2010 7:51 am    Post subject: Tire size calculator and charts Reply with quote

This site has another calculator as well as charts that list tire dimensions of the older tires.

http://vw.zenseeker.net/Wheels-TireSizing.htm
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schunacher
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PostPosted: Thu Feb 25, 2010 1:34 pm    Post subject: Reply with quote

There is another interesting "tire height" dimension listed in the VW service manuals called "Rolling Radius" (12.09") which is substantially less than the 5.60x15 tire's calculated radius (12.65"). I assume that the reduced radius is because of gravity acting on the flexibility of the sidewall. I guess it only matters if you are calculating the ride height of the car, but the interesting part is that VW chose to publish this number.
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KellyH
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PostPosted: Thu Feb 25, 2010 10:25 pm    Post subject: Reply with quote

schunacher wrote:
There is another interesting "tire height" dimension listed in the VW service manuals called "Rolling Radius" (12.09") which is substantially less than the 5.60x15 tire's calculated radius (12.65"). I assume that the reduced radius is because of gravity acting on the flexibility of the sidewall. I guess it only matters if you are calculating the ride height of the car, but the interesting part is that VW chose to publish this number.


Calculated height and true height are different. There is also static height, which is measured when weight squishes the tire a bit. This changes the true rolling diameter of the tire, which in turn changes the final gearing of the car and the speedometer reading.

Image may have been reduced in size. Click image to view fullscreen.


Rolling radius is
"Tire-rolling radius is the distance from the center of the wheel to the road. Static radium applies when the vehicle is standing still. Dynamic rolling-radius described wheels in motion. The latter is used to measure tire revolutions per mile and is usually slightly higher than static radius. "

This would be a little harder to measure than static, as the car needs to be moving to measure it and will differ in regards to tire pressure, axle load, speed, tire size, tire composition, etc.

The effective rolling radius
Tyre and vehicle dynamics
The automotive chassis: Components design
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schunacher
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PostPosted: Fri Feb 26, 2010 4:00 pm    Post subject: Reply with quote

KellyH wrote:
Calculated height and true height are different. There is also static height, which is measured when weight squishes the tire a bit. This changes the true rolling diameter of the tire, which in turn changes the final gearing of the car and the speedometer reading.

I don't have any real expertise but here are some thoughts off the top of my head. Once you start accounting for distortion of the tire you can no longer rely on calculations that assume that the tire is a circle. In other words the reduced radius due to distortion of the tire does not affect the speedometer or gearing since the circumference of the tire remains the same as it was in a distortion free calculation (reduced radius does not result in reduced "circumference" since the tire is not a circle anymore). Therefore we are still pulling along the same amount of road with each revolution of the axle and tire. Does that make sense or am I missing something?
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KellyH
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PostPosted: Fri Feb 26, 2010 9:04 pm    Post subject: Reply with quote

There is a great deal of chemistry and physics that goes into tire science.

I think that knowing how to calculate the size of a fully inflated tire and knowing that this is really just a ball park estimate of what you will have in the end is really all most of us will find useful.

Lucky for folks like me, there are charts and calculators available on the web, as well as lots of other car owners who have already experimented with different tire/wheel configurations who have posted their results and photos on the web.
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PostPosted: Sun Feb 28, 2010 8:30 pm    Post subject: Reply with quote

Tire selection is definitely voodoo in more ways than one. Tire selection is one thing that makes Formula One racing so interesting (it used to be even more interesting when F1 had competition between multiple tire manufacturers). One aspect (unintended pun) that seems counterintuitive is that F1 cars use relatively tall profile tires to produce their phenominal handling.
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strelnik
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PostPosted: Tue Nov 16, 2010 1:15 pm    Post subject: Re: Calculating Tire Height mathematically Reply with quote

Thornton wrote:
Tire Height questions pop up here in the forum often


Thanks for doing this, I figured it out on my own and made a chart, but I have another question:

What happens if you have one of the 1950's era tires that were 165 mm x 400mm?

Unfortunately, they never showed the aspect ratio of the tire Sad
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PostPosted: Thu Nov 27, 2014 12:22 pm    Post subject: 65 beetle project Reply with quote

I just had my 65 painted and I bought everything new to replace the old. I replaced the wheels with 15 in BRM 5 in wide wheels I'm using 195/60/15 on front and rear it has 67 fenders on front it already was lowered a lil in the front but when I put the new wheels on the front my driver side tire scrubs any suggestions on what I can do to fix this problem?
Thanks David
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FRNKNSTNGHIA
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PostPosted: Mon Jan 27, 2020 8:07 pm    Post subject: Re: Calculating Tire Height mathematically Reply with quote

I've been a fan of this site. You can play with offsets, widths, tire sizes and see how the wheel should sit in the fender well.

www.willtheyfit.com
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Car32
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PostPosted: Fri Oct 09, 2020 7:23 am    Post subject: Re: Calculating Tire Height mathematically Reply with quote

Another other other other site:

https://www.rimsntires.com/specspro.jsp

This one's nice 'cause you can compare two potential tires and rims side-by-side.
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PostPosted: Wed Mar 16, 2022 4:59 pm    Post subject: Re: Calculating Tire Height mathematically Reply with quote

I haven't seen this case yet, so I'll grit my teeth and ask:

Im running 185/ 60 R15 on the front of my slightly lowered bug. (205/ 60 R15 on the back)

I am looking for Bias Ply look (piecrust) radials. It seems the smallest is the 560 R15. I have been told they are too big for my lowered bug.

Is there a calculator that compares 2 different types of tires? I can't find one that converts the XXX/ XX R15 to a YYY R15 tire format. (This shouldn't be too hard, I realize, but I dont get the different tire formats. Appologies)

Summary:
I'm just trying to figure out what size "Bias Ply look" radial that I can safely fit on a car that's got 185/ 60 R15 as the smallest size.
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