Strangest Tire Question EVERRR...
Has anyone ever calculated or estimated the area, in square inches/square cm, of the *surface of the inside* of a tire?
Does at least an average exist out there, for broad categories: passenger car, SUV-light truck, and commercial truck?
Just curious, Thanks!
Tire manufacturers would have this as it would be the same as the inner build die they use when laying up a tire. However the number would vary a lot because of the myriad of sizes, Take a 205 75R 15, it would have a larger surface area than a 205 60R 15 simply due to the aspect ratio change.
Steve W.:
I went to several tire mfg. sites, but could not find such information. I guess it's time for some E-mails & phone calls.
What tools do we have to solve the problem? o Let's start with shape & terminology:
That gives us these perhaps relevant terms: o Tread width o Section height o Aspect ratio o Rolling circumference etc. Where for now I'll ignore there's a difference between o free (i.e., unloaded), and, o loaded
Then, using this tire-size calculator: And ignoring sig fig approximations (so I can just cut & paste numbers)...
Assume a P200/50R15 for easy numbers & using only the 1st URL above: o Diameter = 582mm (22.9") o Width = 200mm (7.9") o Sidewall = 99mm (3.9") o Circum. = 1,824mm (71.8") o Revs/Mile = 882 Also noting: o Rim diameter = 381mm (15")
Assuming the carcass inside & outside surface is "similar" in both shape & surface area, we easily arrive at a gross _approximation_ of: o Tread area = ~200mm wide times ~1,824mm around = ~364,800?sq mm o Sidewall area = ~99mm times ~1,824mm around times 2 = ~361,152sq mm Which calculates to... o Total U shaped carcass = ~364,800?sq mm + ~361,152sq mm Which comes to roughly ~725,952?sq mm
Given the sidewall area is probably more accurately done with donuts:
Where the terms appear to be: o Diameter of the Whole Area = 582mm o Diameter of Inside Area = 381mm Which calculates out to: o Area = 152,023.9sq mm o Outer Perimeter = 1,828.4mm o Inner Perimeter = 1,196.9mm o Total Perimeter = 1,196.9mm
Using these numbers for sidewall area in the previous calculation: o Tread area = ~200mm wide times ~1,824mm around = ~364,800?sq mm o Sidewall area = ~152,023.9sq mm times 2 = ~304,047.8?sq mm o Total U shaped carcass = ~364,800?sq mm + ~304,047.8?sq mm Which comes to roughly ~668,847.8?sq mm
In summary, and knowing the inside dimensions must be smaller than the outside dimensions, I'd guess it's around 600,000sq mm to 700,000sq mm.
But that's only a gross approximation. o How much accuracy does the OP need?
Arlen Holder - wow! You went to town on the math!
How precise? Ohh, just an average. It's something I'm working on, so an average sized automobile tire is all I'm asking about. 215/6R16ish.
Thanks for the hard work though.
I just noticed something interesting when it comes to 'averages'. o All you need is the tread width & the aspect ratio & rim size.
That is... o For a 40 series tire, it's 2x40, i.e., tread area times 180% o For a 50 series tire, it's 2x50, i.e., tread area times 200% o For a 60 series tire, it's 2x60, i.e., tread area times 220% etc.
Notice an aspect ratio of, oh, say, 50 is 50% of the tread width. o So the surface area is a function of the tread width & aspect ratio.
If the tire is a 50-series tire, the sidewall area is approximately 100% more than the tread area (i.e., 50% times 2 sidewalls).
For a 60 series tire, the sidewall area is approximately 120% more than the tread area (i.e., 60% times 2 sidewalls).
In short, for a quick mental calculation all you need is the tread area and the sidewall-to-tread ratio, where the tread area is simply the width times the circumference of the tire.
So, for your P215/60R16, this calculator tells me:
The area of the tread would be its width time the circumference: o Tread area = 8.5" times 26.2" = 222.7 sq inches
Since it's a 60-series tire, the sidewall area is 120% of that. o Sidewall area = 222.7sq inches time 120% = 267.24 sq inches
In summary, you just take the tread area and multiply it by the percent: o For a 40 series tire, surface area is tread area times 180% o For a 50 series tire, surface area is tread area times 200% o For a 60 series tire, surface area is tread area times 220% etc.
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