Contact patch size versus tire inflation

Here is the data that I collected last weekend for several different
tires.

Pressure> 60 70 80 90 100 110 120
Tire and Contact Patch Area
Carl's 26mm 1.60 1.44 1.33 1.28 1.19 1.13 1.12
Vitt Tecno 23mm 1.43 1.36 1.31 1.25 1.12 1.06 1.05
Pan Pasela 35mm 1.82 1.62 1.54 1.45 1.38 1.31 1.26
Mich Hi Lite 23mm 1.08 0.94 0.83 0.79 0.77 0.73 0.72
Perf Tubular 1.87 1.71 1.55 1.49 1.33 1.33 1.18
Perf ST2 1.62 1.57 1.55 1.45 1.33 1.25 1.23
Calculated 1.67 1.43 1.25 1.11 1.00 0.91 0.83

This is the characterization of the data:

The Vittoria, Panaracer, Michelin, and Performance Tubular were all in
new condition, having zero mileage.

Carl's 26mm tire and the Performance ST2 tire were both used tires.
The data from both of these tires was not taken in the same set-up as
the other tires, but is presented here for completeness.

The Michelin Hi-Lite has a unique construction. This tire does not have
a conventional bias-ply construction. Rather, it has a woven
construction. The woof and warp are at right angles, and the weave is
at 45 degrees to the tread.

The Sew-up was a bit canted on the rim; evident from the imprint.

All areas (except Carl's) were calculated as the area of an ellipse,
as that is what the imprint most looked like to me.

You can see the images of the imprints, the test set-up,, the Michelin
"carcass" and the chart of the above data at:

http://www.flickr.com/photos/34424013@N00/

I chose Flickr because it will allow you to download different sizes,
which I couldn't figure out how to do with other photo hosts.

Regards,

Tom

In article <[email hidden]>,

Quoted message said:

Here is the data that I collected last weekend for several different
tires.

Pressure> 60 70 80 90 100 110 120
Tire and Contact Patch Area
Carl's 26mm 1.60 1.44 1.33 1.28 1.19 1.13 1.12
Vitt Tecno 23mm 1.43 1.36 1.31 1.25 1.12 1.06 1.05
Pan Pasela 35mm 1.82 1.62 1.54 1.45 1.38 1.31 1.26
Mich Hi Lite 23mm 1.08 0.94 0.83 0.79 0.77 0.73 0.72
Perf Tubular 1.87 1.71 1.55 1.49 1.33 1.33 1.18
Perf ST2 1.62 1.57 1.55 1.45 1.33 1.25 1.23
Calculated 1.67 1.43 1.25 1.11 1.00 0.91 0.83

<snip>

So, if I understand correctly the bottom line ("Calculated"😉 is the area
of the contact patch predicted, compared to what was actually measured
using different tires.

Interesting. But why the variation? Does the thickness of the tread,
stiffness of the rubber compound and tire casing, etc, affect the
results? Is there an issue with how are is calculated (the shape of
some of the imprints being lanceolate rather than elliptical)? Etc?

Jean said:

His explanation pretty much explains why most results show measured areas
being higher than theory. That just leaves figuring out why some results
are lower than expected from theory...

Any elastic force due to deformation of the tire will reduce the contact
patch area. Consider a steel tire, perfectly stiff, at atmospheric
pressure. The theoretical patch area is infinite, but the actual patch
are can be extremely small. Of course, rubber isn't steel, but the
effect is still there.

Dan

"Tim McNamara" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

In article <[email hidden]>,
[email hidden] wrote:

<snippage>> <snip>

Quoted message said:

So, if I understand correctly the bottom line ("Calculated"😉 is the area
of the contact patch predicted, compared to what was actually measured
using different tires.

Interesting. But why the variation? Does the thickness of the tread,
stiffness of the rubber compound and tire casing, etc, affect the
results? Is there an issue with how are is calculated (the shape of
some of the imprints being lanceolate rather than elliptical)? Etc?

Hi Tim -

Yes, the "calculated" is the theoretical value calculated by load/inflation
pressure.

"But why the variation?" OK - that's what makes this interesting.

I find it difficult to swallow that the thickness of the tread, the
stiffness of the rubber, et al account for the difference. An un-inflated
tire is really quite limp. It will barely hold it's shape under it's own
weight.

Further, the average tire is pretty well uniform in construction with about
3/32" of tread rubber and about 1/8" total thickness of tread and carcass.
Perhaps a specialty tire like the Schwalbe Marathon (built for longevity)
might have more tread thickness and a bit more stiffness. Even the Michelin,
which in it's day, was known as a tire that nearly approached sew-ups in
ride, does not deviate significantly in these dimensions.

Somehow, I think that the mechanics by which a standard tire casing supports
a load is playing in to the observed results. I say this partly out of
intuition and partly due to the results seen from the Michelin, wherein the
significant difference is in the casing construction. At this point I have
wandered into the area labeled "Here be dragons", for the math and physics
is way over my head.

Is there an issue with how the area is calculated? Clearly, yes. The best I
can do is to use the ellipse formula. There may be another way, however. It
would take some work by someone familiar with graphics work. Imagine that we
take the image of an imprint and turn everything in the image that is "not
black" to red. Scan the image and determine what percentage of the image is
red and what percentage is black. Since we can accurately know the area of a
rectangular image we can calculate the area of the imprint much more
accurately. Again, I'm off my personal map of skills and abilities.

Regards,

Tom

Quoted message said:

Here is the data that I collected last weekend for several different
tires.

Pressure> 60 70 80 90 100 110 120
Tire and Contact Patch Area
Carl's 26mm 1.60 1.44 1.33 1.28 1.19 1.13 1.12
Vitt Tecno 23mm 1.43 1.36 1.31 1.25 1.12 1.06 1.05
Pan Pasela 35mm 1.82 1.62 1.54 1.45 1.38 1.31 1.26
Mich Hi Lite 23mm 1.08 0.94 0.83 0.79 0.77 0.73 0.72
Perf Tubular 1.87 1.71 1.55 1.49 1.33 1.33 1.18
Perf ST2 1.62 1.57 1.55 1.45 1.33 1.25 1.23
Calculated 1.67 1.43 1.25 1.11 1.00 0.91 0.83

This is the characterization of the data:

The Vittoria, Panaracer, Michelin, and Performance Tubular were all in
new condition, having zero mileage.

Carl's 26mm tire and the Performance ST2 tire were both used tires.
The data from both of these tires was not taken in the same set-up as
the other tires, but is presented here for completeness.

The Michelin Hi-Lite has a unique construction. This tire does not have
a conventional bias-ply construction. Rather, it has a woven
construction. The woof and warp are at right angles, and the weave is
at 45 degrees to the tread.

The Sew-up was a bit canted on the rim; evident from the imprint.

All areas (except Carl's) were calculated as the area of an ellipse,
as that is what the imprint most looked like to me.

You can see the images of the imprints, the test set-up,, the Michelin
"carcass" and the chart of the above data at:

http://www.flickr.com/photos/34424013@N00/

I chose Flickr because it will allow you to download different sizes,
which I couldn't figure out how to do with other photo hosts.

Regards,

Tom

Dear Tom,

Here's a graph showing the calculated/predicted contact-patch area,
the average for your 5 tires, and my single tire results:

http://i17.tinypic.com/2j3jpqc.jpg

Click on the lower right in Explorer to show the graph full size.

The average for your 5 tires matches my single tire results so closely
that they overlap.

Below 70 psi, the calculated/predicted area is larger and larger than
what either of us measured. (I added my results for 30-40-50 psi). At
30 psi, the calculated/predicted area is around 55% larger than what I
measured.

At 70 psi, our measurements match the calculated/predicted area.

Above 70 psi, the calculated/predicted area is smaller and smaller
than what either of us measured. At 120 psi, the calculated/predicted
area is only about 75% as large as what we measured.

Cheers,

Carl Fogel

<[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Quoted message said:

Here is the data that I collected last weekend for several different
tires.

Pressure> 60 70 80 90 100 110 120
Tire and Contact Patch Area
Carl's 26mm 1.60 1.44 1.33 1.28 1.19 1.13 1.12
Vitt Tecno 23mm 1.43 1.36 1.31 1.25 1.12 1.06 1.05
Pan Pasela 35mm 1.82 1.62 1.54 1.45 1.38 1.31 1.26
Mich Hi Lite 23mm 1.08 0.94 0.83 0.79 0.77 0.73 0.72
Perf Tubular 1.87 1.71 1.55 1.49 1.33 1.33 1.18
Perf ST2 1.62 1.57 1.55 1.45 1.33 1.25 1.23
Calculated 1.67 1.43 1.25 1.11 1.00 0.91 0.83

This is the characterization of the data:

The Vittoria, Panaracer, Michelin, and Performance Tubular were all in
new condition, having zero mileage.

Carl's 26mm tire and the Performance ST2 tire were both used tires.
The data from both of these tires was not taken in the same set-up as
the other tires, but is presented here for completeness.

The Michelin Hi-Lite has a unique construction. This tire does not have
a conventional bias-ply construction. Rather, it has a woven
construction. The woof and warp are at right angles, and the weave is
at 45 degrees to the tread.

The Sew-up was a bit canted on the rim; evident from the imprint.

All areas (except Carl's) were calculated as the area of an ellipse,
as that is what the imprint most looked like to me.

You can see the images of the imprints, the test set-up,, the Michelin
"carcass" and the chart of the above data at:

http://www.flickr.com/photos/34424013@N00/

I chose Flickr because it will allow you to download different sizes,
which I couldn't figure out how to do with other photo hosts.

Regards,

Tom

Dear Tom,

Here's a graph showing the calculated/predicted contact-patch area,
the average for your 5 tires, and my single tire results:

http://i17.tinypic.com/2j3jpqc.jpg

Click on the lower right in Explorer to show the graph full size.

The average for your 5 tires matches my single tire results so closely
that they overlap.
<snippage>
Cheers,

Carl Fogel

Carl -

Nicely done - I should have thought to look at it that way.

By the by, what is this tire you're using?

Regards,

Tom

"Dan Connelly" <d_j_c_o_n_n_e_l@y_a_h_o_o.c_o_m> wrote in message
news:[email hidden]...

Quoted message said:

Jean said:

His explanation pretty much explains why most results show measured areas
being higher than theory. That just leaves figuring out why some results
are lower than expected from theory...

Any elastic force due to deformation of the tire will reduce the contact
patch area. Consider a steel tire, perfectly stiff, at atmospheric
pressure. The theoretical patch area is infinite, but the actual patch
are can be extremely small. Of course, rubber isn't steel, but the effect
is still there.

Dan

Dan -

I know all of the words in the sentences above, but when they are all put
together the only ones I could understand were "rubber isn't steel".

Can you explain what you mean by "Any elastic force due to deformation of
the tire will reduce the contact patch area" and "The theoretical patch
area is infinite"?

Regards,

Tom

Tom Schmitz said:

<[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Quoted message said:

Here is the data that I collected last weekend for several different
tires.

Pressure> 60 70 80 90 100 110 120
Tire and Contact Patch Area
Carl's 26mm 1.60 1.44 1.33 1.28 1.19 1.13 1.12
Vitt Tecno 23mm 1.43 1.36 1.31 1.25 1.12 1.06 1.05
Pan Pasela 35mm 1.82 1.62 1.54 1.45 1.38 1.31 1.26
Mich Hi Lite 23mm 1.08 0.94 0.83 0.79 0.77 0.73 0.72
Perf Tubular 1.87 1.71 1.55 1.49 1.33 1.33 1.18
Perf ST2 1.62 1.57 1.55 1.45 1.33 1.25 1.23
Calculated 1.67 1.43 1.25 1.11 1.00 0.91 0.83

This is the characterization of the data:

The Vittoria, Panaracer, Michelin, and Performance Tubular were all in
new condition, having zero mileage.

Carl's 26mm tire and the Performance ST2 tire were both used tires.
The data from both of these tires was not taken in the same set-up as
the other tires, but is presented here for completeness.

The Michelin Hi-Lite has a unique construction. This tire does not have
a conventional bias-ply construction. Rather, it has a woven
construction. The woof and warp are at right angles, and the weave is
at 45 degrees to the tread.

The Sew-up was a bit canted on the rim; evident from the imprint.

All areas (except Carl's) were calculated as the area of an ellipse,
as that is what the imprint most looked like to me.

You can see the images of the imprints, the test set-up,, the Michelin
"carcass" and the chart of the above data at:

http://www.flickr.com/photos/34424013@N00/

I chose Flickr because it will allow you to download different sizes,
which I couldn't figure out how to do with other photo hosts.

Regards,

Tom

Dear Tom,

Here's a graph showing the calculated/predicted contact-patch area,
the average for your 5 tires, and my single tire results:

http://i17.tinypic.com/2j3jpqc.jpg

Click on the lower right in Explorer to show the graph full size.

The average for your 5 tires matches my single tire results so closely
that they overlap.
<snippage>
Cheers,

Carl Fogel

Carl -

Nicely done - I should have thought to look at it that way.

By the by, what is this tire you're using?

Regards,

Tom

Dear Tom,

I first used a worn 700x26 Forte tire from Performance, flattened by
wear.

The data in the graph is from my second test, which used another
700x26 Forte tire from Performance, almost new.

The tires have a Kevlar bead, an internal Kevlar belt, and a faint
pebble-like tread pattern that wears off quickly, but is still visible
on the new tire.

I've tried to figure out a mathematical explanation for the odd change
at 70 psi, with the predicted area being larger than the measured area
at lower pressure and smaller at higher pressure, but I can't make
sense of it by anything as simple as a steady exaggeration or
understatement of the area.

That is, our measurements aren't larger (or smaller) than the
predicted area at all pressures.

Cheers,

Carl Fogel

Tom Schmitz said:

I question, though, that Kyle has explained anything. He has made a
statement that he supports with what seems to be a contradiction in terms.

He says that the foot print will be larger than calculated because the tire
is more flexible. Yet it would seem logical that if the tire were more
flexible that the it would deform more and produce a larger patch.
Conversely, an inflexible tire would not deform and the resultant patch
would be smaller than predicted.

Your reasoning is sound, however, Kyle has assumed (implicitly) that
the maximum contact pressure (Pmax) in the footprint is less than or
equal to the air pressure in the tire. Given that, then because the
pressure is not uniform throughout, it is should be easy to see that
the actual area has to be greater than F/Pmax. For the inflexible
tire you imagined, Kyle's assumption would not hold.

--
Joe Riel