Contact patch size versus tire inflation
carl...@comcast.net
a bicycle tire increases and decreases linearly according to the tire
pressure.
That is, the contact patch under the same rider will double in size if
the tire inflation is cut in half, and vice-versa.
For example, a 100 lb load on a tire inflated to 50 psi is supposed to
produce a contact patch of 2 square inches, while the same load on a
tire inflated to 100 psi is supposed to produce a contact patch of
only 1 square inch.
Testing suggests that this theory is mistaken.
I clamped a frame with a rear wheel and tire in a vise by the bottom
bracket, leaving the whole frame free to pivot.
A 2x4 attached to the top tube provided convenient leverage. I just
hung enough weights from the end of the 2x4 sticking out past the rear
tire to produce a 100-lb reading on a bathroom scale under the tire.
After rubbing a worn 700x26 tire with a red ink pad, I lowered the
tire onto a sheet of paper on some well-supported sheet metal, and
then let the weight hang, pressing the inked tire down on the paper
with about 100 lbs of force.
The tire was locked in place by brake pads held tight with a zip tie.
Using a floor pump with a dial gauge, I took the tire's fingerprint at
40-60-80-100-120 psi:
http://i7.tinypic.com/2z4wuib.jpg
Even a glance shows that the red tire marks don't shrink at the same
rate that the tire pressure rises.
Here's the data:
3x 2.5x 2x 1.5x 1x
psi 120 100 080 060 040
mm length 76 81 88 96 108
mm width 11 11 11 12.5 13
---- ---- ---- ---- ----
L x W 836 891 968 1200 1404
1x 1.07x 1.16x 1.44x 1.68x
Multiplying the longest diagonal of the mark by its widest section
gives a high approximation of the area of the contact patch (a
rectangle rather than a vague oval).
Even if the extremes are discarded, the size of the contact patch
appears to change significantly less than expected.
For example, pumping the tire up 20% from 80 psi to 100 psi reduces
the approximate size of the patch by only 8%.
The asymmetrical ends of the tire print are likely due to the wheel
not being perfectly vertical, the rope and weight not hanging
perfectly in line with the tire, and the tread being worn. (There was
plenty of ink smeared on the tread--the diagonal lower end of each
mark just shows where the tire was reluctant to touch the paper.)
One possible partial explanation is that pressure varies considerably
in the contact patch, with much lighter pressure toward the edges.
Another possible partial explanation is that casing tension
complicates matters.
Better explanations would be welcome.
Cheers,
Carl Fogel
jta...@nospam.hfx.andara.com
a) a treaded tyre will not give the same result as a smooth one
b) can you get & use a planimiter?
Tim McNamara
carl...@comcast.net wrote:
> A common comment on RBT is that the contact patch for the same load
> on a bicycle tire increases and decreases linearly according to the
> tire pressure.
>
> That is, the contact patch under the same rider will double in size
> if the tire inflation is cut in half, and vice-versa.
>
> For example, a 100 lb load on a tire inflated to 50 psi is supposed
> to produce a contact patch of 2 square inches, while the same load on
> a tire inflated to 100 psi is supposed to produce a contact patch of
> only 1 square inch.
>
> Testing suggests that this theory is mistaken.
<snip>
> Multiplying the longest diagonal of the mark by its widest section
> gives a high approximation of the area of the contact patch (a
> rectangle rather than a vague oval).
That may change the numbers quite a bit and might change the
proportionality of the change in area related to the pressure- e.g., the
contact patch may become more "blunt" at the ends with lower pressure
which would increase the area of the contact patch more than would be
indicated by a simple height x width multiplication.
> Even if the extremes are discarded, the size of the contact patch
> appears to change significantly less than expected.
>
> For example, pumping the tire up 20% from 80 psi to 100 psi reduces
> the approximate size of the patch by only 8%.
I plugged your numbers into a spreadsheet and charted them. The curve
is not quite a curve, being nearly linear for the 40-60-80-100 pressures
and flattening significantly between the 100 and 120 psi data points.
More data points would probably smooth the curves out quite a bit.
Interestingly, the curve does fairly well fit the curves that resulted
from the IRC rolling resistance tire testing data from years ago.
Remember that those curves saw largish reductions in rolling resistance
towards the low pressure end of the graph, and flattened out at the high
end with there being basically diminishing returns from increasing
pressures above 100 psi.
Kinky Cowboy
I'd suggest that the contact patch measured on the interior surface of
the tyre follows the theoretical prediction, but translating this
through a variable thickness of moderately rigid rubber is bound to
give non-linear results. Try calibrating your experiment first with a
thin inner tube with no tyre around it; you'll probably have to run
pressures in the 0.5 - 1.5 bar range, with a corresponding reduction
in load.
Kinky Cowboy*
*Batteries not included
May contain traces of nuts
Your milage may vary
carl...@comcast.net
<tim...@bitstream.net> wrote:
[Carl wrote:]
>> Multiplying the longest diagonal of the mark by its widest section
>> gives a high approximation of the area of the contact patch (a
>> rectangle rather than a vague oval).
>
>That may change the numbers quite a bit and might change the
>proportionality of the change in area related to the pressure- e.g., the
>contact patch may become more "blunt" at the ends with lower pressure
>which would increase the area of the contact patch more than would be
>indicated by a simple height x width multiplication.
[snip]
Dear Tim,
Actually, the picture shows that the blunter and more "rectangular",
and therefore "larger" contact patches are the smaller, higher
pressure examples, not the lower pressure patches. As pressure
increases, the lower dagger-like ends of the patches become blunter
and shorter.
http://i7.tinypic.com/2z4wuib.jpg
So the smaller patches fill out a rectangle more than the larger
patches, which reduces the relative size change even further.
That is, the bottoms of the marks become more and more dagger-like as
pressure decreases and the marks lengthen. Rearrange the long,
dagger-like lower end of the longest 40 psi mark to resemble the
blunter lower end of the 120 psi mark, and you'll get a length and
width of about 97 x 13 mm, for an even smaller rough (high) estimate
of 1261 mm^2 instead of 1404 mm^2.
(The 60 psi mark would shorten a little, too, if its lower end were
re-shaped more bluntly, and so on as pressures increase.)
So again, re-shaping the ends to match the shape of the highest
pressure would only reduce the rough estimates of the area
differences.
Given the extreme length to steady width ratio (about 7.5 to 1) of the
streaks, the somewhat different ends aren't going to change the total
area very much.
If the pressure to contact area relationship were purely linear, the
40 psi mark should have been roughly 3 times the length of the 76 mm
120 psi mark, over 200 mm. But it was only 108 mm, about half the
length predicted by theory.
Cheers,
Carl Fogel
carl...@comcast.net
Dear J.,
I thought about using 1x1 mm graph paper, but it wouldn't really
improve the accuracy to any useful extent.
The air pressure, after all, is only eye-balled on the dial gauge of a
floor pump, and then a little air is lost as the chuck is wrestled off
the Presta valve.
Luckily, the trend is so gross and contradicts simple theory so
obviously that there's no need for greater precision in measurement.
If contact patch area had a purely linear relationship with air
pressure, then the 40 psi patch would be three times the size of the
120 psi patch.
It's plain that the 40 psi patch isn't even twice as big.
http://i7.tinypic.com/2z4wuib.jpg
The 120 psi patch is on the left, the 40 psi is on the right.
Cheers,
Carl Fogel
carl...@comcast.net
wrote:
Dear Kinky,
If you experiment with an inner tube, a pump, and a gauge, I'll be
astonished if you can produce even 3 psi, 0 0.2 bar:
http://groups.google.com/group/rec.bicycles.tech/msg/de34b4e303a152d1
My gauge stubbornly read 0 psi in that post and picture.
Cheers,
Carl Fogel
carl...@comcast.net
Tom Schmitz wrote to point out that he did similar tests with similar
results. Here's a link to Tom's much more detailed data:
http://www.tomschmitz.org/Contact%20PatchFrame1Source1.htm
The obvious point of Tom's graph with area calculated two different
ways versus tire inflation is that roughly doubling the tire pressure
from 60 to 130 psi reduced contact patch area from about 1.80 to about
1.40, a 22% decrease instead of the expected 50% decrease.
Here's where Tom posted his data:
http://groups.google.com/group/rec.bicycles.tech/msg/1e8256ee25dbe90d
Unsurprisingly, Tom was informed that his test results were wrong
because they disagreed with untested theories.
Cheers,
Carl Fogel
carl...@comcast.net
[snip]
http://i7.tinypic.com/2z4wuib.jpg
An email criticized my handwriting in the picture above ("badly
scrawled figures") and then complained that my description of the
contact-patch-test setup was hard to follow.
So here's a picture of the setup. A short rod runs through the hollow
bottom bracket and is clamped in the vise, leaving the bike frame free
to pivot:
http://i7.tinypic.com/47ilsaw.jpg
Holes in the 2x4 let it slip over the head and seat tubes, and a
U-bolt visible near the head-tube anchors the board.
The $2 red ink pad (somewhat dirty now) and the white zip tie locking
the rear brake are visible.
The inside of an old computer case sitting on a portable workbench
provides a smooth surface for the paper.
The four gray 15-lb weights sitting on the upside-down blue plastic
bin (plus the weight of the frame pivoting at the bottom bracket)
produce ~100 lbs on a floor scale under the tire when the weights are
hanging by the rope from the end of the 2x4.
The yellow color of the floor pump reduces pumping effort and
increases psi accuracy by at least an order of magnitude.
CF
jobst....@stanfordalumni.org
>>> Multiplying the longest diagonal of the mark by its widest section
>>> gives a high approximation of the area of the contact patch (a
>>> rectangle rather than a vague oval).
>> That may change the numbers quite a bit and might change the
>> proportionality of the change in area related to the pressure-
>> e.g., the contact patch may become more "blunt" at the ends with
>> lower pressure which would increase the area of the contact patch
>> more than would be indicated by a simple height x width
>> multiplication.
> Actually, the picture shows that the blunter and more "rectangular",
> and therefore "larger" contact patches are the smaller, higher
> pressure examples, not the lower pressure patches. As pressure
> increases, the lower dagger-like ends of the patches become blunter
> and shorter.
> http://i7.tinypic.com/2z4wuib.jpg
> So the smaller patches fill out a rectangle more than the larger
> patches, which reduces the relative size change even further.
I don't understand what sort of tire was used for these ink pad tests.
Why are they parallelograms instead of canoe shaped as my tires make?
What are the diagonal pale stripes in the printed area? Was the tire
worn so that it had a flat zone, as worn rear tires usually have?
Jobst Brandt
jobst....@stanfordalumni.org
> Tom Schmitz wrote to point out that he did similar tests with
> similar results. Here's a link to Tom's much more detailed data:
> http://www.tomschmitz.org/Contact%20PatchFrame1Source1.htm
> The obvious point of Tom's graph with area calculated two different
> ways versus tire inflation is that roughly doubling the tire
> pressure from 60 to 130 psi reduced contact patch area from about
> 1.80 to about 1.40, a 22% decrease instead of the expected 50%
> decrease.
I think Tom's test makes the results more apparent. These are tires
with fairly thick tread and therefore, resist conforming to the ideal
infinitely flexible model of contact patch and inflation pressure. I
believe if you could get a light weight track tubular or better yet,
pull the tread strip off a castoff but inflatable tubular, you would
get closer to the theoretical contact area.
Jobst Brandt
carl...@comcast.net
Dear Jobbst,
I used a worn 700x26 tire. Like most worn tires, it's noticeably
flattened, but if anything that would simplify matters.
The upper ends that were toward the front of the bike tend to be more
rounded, possibly due to the locked wheel descending in an arc onto
the paper.
The trailing ends have a distinct diagonal shape that I suspect is due
to the bike frame being rigidly clamped in a not quite perfectly
square vise-to-workbench-to-cement-floor-to-portable-bench and the
weights hanging not perfectly square and centered from the 2x4
extending from the top-tube of the frame.
Here's the setup:
http://i7.tinypic.com/47ilsaw.jpg
A close-fitting rod through the hollow crank is clamped in the vise.
If things aren't perfectly square, the somewhat flattened tire may
well be tilting slightly, so that the left rear of the tire is very
slightly lifted, enough to show up on ink and paper, with a
corresponding but smaller effect on the upper end, the right front of
the tire:
http://i7.tinypic.com/2z4wuib.jpg
Much of the streakiness and lines visible on the sides is actually
where the tread turns into the sidewall. A very fine chevron pattern
marks the edge of the worn-smooth tread and is visible at much higher
magnifications. The right-hand sides of the marks show more of this
very fine pattern, confirming that the test rig is tilting very
slightly to the right.
An improved setup would probably raise the tire closer to level and
eliminate some of these artifacts, but it's probably not worth the
trouble. At 40 psi, theory predicts that the contact patch should be
about 3 times the size of the contact patch at 120 psi, but it's
obviously nowhere near that large.
Again, it's possible that there's a considerable pressure gradient,
with the raw smear on paper not showing that the edges have only 30
psi while the center has 100 psi, and that the proportion of low to
high pressure area changes with increasing inflation.
Or it could be that there's more than just simple air pressure
involved.
Tom Schmitz showed that the contact patch is considerably larger than
predicted. My crude test suggests the same thing, but I originally
assumed that my figures were too rough to be significant.
At ~120 psi with ~100 lbs load, my contact patch smear is about 76 x
11 mm, roughly 836 mm^2, or 1.30 square inches instead of 0.83, about
56% larger than expected.
At ~100 psi with ~100 lbs load, my contact patch smear is about 81 x
11 mm, roughly 891 mm^2, or 1.38 square inches instead of 1.00, about
38% larger than expected.
At ~60 psi with ~100 lbs load, my contact patch smear is about 96 x
12.5 mm, roughly 1200 mm^2 (the figures just happened to work out with
spurious precision to an even 1200), or 1.86 square inches instead of
1.67, still about 11% larger than expected.
Again, my L x W estimates, pressure measurements, and weight on a
scale are rough, but they do tend to confirm Tom's observations.
Cheers,
Carl Fogel
jobst....@stanfordalumni.org
> Here's the setup:
> http://i7.tinypic.com/47ilsaw.jpg
> http://i7.tinypic.com/2z4wuib.jpg
I think you overlook that tires wear with the crown of the road and
that the flattened area of the tread has a slant. Just the same, as I
mentioned in another reply, tread shape and thickness has too much
influence on contact patch to approach theoretical values.
Jobst Brandt
Werehatrack
>Better explanations would be welcome.
You're past the point of linear returns on this almost before you
start, due to the stiffness of the casing and the limits on lateral
expansion of the contact patch. Try it again with a fat, non-knobby
balloon tire, and you'll get closer to the predicted results for at
least a portion of the range of pressures. And always remember that
in nearly any real-world experiment, there will be variables which
have a bearing on the results but which are not explicitly described
by the theory under test.
--
Typoes are a feature, not a bug.
Some gardening required to reply via email.
Words processed in a facility that contains nuts.
Werehatrack
>The yellow color of the floor pump reduces pumping effort and
>increases psi accuracy by at least an order of magnitude.
Pfui. Paint it black to maximize heat dissipation and minimize
thermally-induced dimensional change.
Phil Holman
<carl...@comcast.net> wrote in message
news:blsfm2t9gp7vjd5rg...@4ax.com...
>A common comment on RBT is that the contact patch for the same load on
> a bicycle tire increases and decreases linearly according to the tire
> pressure.
>
> That is, the contact patch under the same rider will double in size if
> the tire inflation is cut in half, and vice-versa.
>
> For example, a 100 lb load on a tire inflated to 50 psi is supposed to
> produce a contact patch of 2 square inches, while the same load on a
> tire inflated to 100 psi is supposed to produce a contact patch of
> only 1 square inch.
>
> Testing suggests that this theory is mistaken.
Reality includes a bunch of other variables you haven't accounted for.
For one, what area of contact patch do you get with a zero pound load? I
suggest you subtract that area from your results. You should do a
regression of different loads as well as different pressures.
Other variables include the fact that contact pressure varies within the
contact patch. In reality it's an integration of pressure over the area
that must be equal to your 100 lbf.
Phil H
Tosspot
> Carl Fogel writes:
<snip>
>>http://i7.tinypic.com/2z4wuib.jpg
>
>>So the smaller patches fill out a rectangle more than the larger
>>patches, which reduces the relative size change even further.
>
> I don't understand what sort of tire was used for these ink pad tests.
> Why are they parallelograms instead of canoe shaped as my tires make?
> What are the diagonal pale stripes in the printed area? Was the tire
> worn so that it had a flat zone, as worn rear tires usually have?
Jobst, it would be helpful if you could post a jpeg of your tyres under
a similar setup/load so we could compare the two.
Tim McNamara
carl...@comcast.net wrote:
Yes, I note that. How worn is this tire- does it have a significant
"flat spot" from wear that most rear tires exhibit? I wonder if that
makes a difference compared to a basically new tire. It is interesting
that your contact patch shapes are different from those shown in
_Bicycling Science_ 3rd Ed., p 218 esp the second example.
Luns Tee
>in the contact patch, with much lighter pressure toward the edges.
I think this is important to what you're seeing. It takes no
appreciable pressure to transfer ink from your tire tread to the paper.
The curve of the tire outside of the contact patch meets up
tangentially, and the tire beyond the edge of the patch makes grazing
contact with the flat surface. This does not have significant contact
pressure, but the inkblot marks it anyway.
-Luns
carl...@comcast.net
Here are some more contact patch tests with a ~100 lb force on another
tire, same model 700x26, almost new instead of worn, still shows tiny
pebble/cross-hatch surface too small to be dignified as a tread
pattern.
The classic canoe-shape is much clearer, which probably says more
about how real tires that have been used behave than anything else.
The sides of the ink marks are a little harder to measure because of
the faint pebbling.
I did a series at 40-60-80-100-120 psi, and then another series at
30-50-70-90-110 psi, partly to give a little blindness to the test and
partly because I goofed and went to 60 instead of 50 (note the
correction from 50 to 60 on the paper).
I left the chuck on the Presta valve and noticed that what was
supposed to be 40 psi was showing only 38 when I finished (note
that correction, too).
Being easily confused, I thought that the second series was showing
unexpected results when I began multiplying length by width, but I
persevered and found that I'm just dim-witted.
Only the last figure for 110 psi seemed wrong, which it was--for some
reason, I read the scale wrong, using 1 instead of 0 on the scale, so
that's the last correction.
Obviously, the widths are so small that they're much less accurate
than the lengths, but they seemed fairly regular.
http://i15.tinypic.com/4cdn0xi.jpg
Here's the handwritten data in more legible form and in psi order:
estimate
mm mm mm^2
psi widest length L x W
030 11 [1] 122 1342
038 [2] 11 118 1298
050 10 110 1100
060 10 103 1030
070 9.5 98 931
080 9 95 855
090 9 92 828
100 8.5 90 765
110 8.5 86 [3] 731
120 8.5 85 722.5
[1] At 30 psi, widest is 11, but the ink on the left is very faint.
And the paper seemed to wrinkle a bit on the side.
[2] Gauge showed 38 psi afterward, not 40 psi.
[3] First mismeasured as 90, plainly wrong mark on caliper.
The results aren't significantly different than the first test.
At ~40 psi, the mark was ~118 mm long and ~11 mm wide, suggesting a
high rectangular area estimate of ~1300 mm^2.
At ~120 psi, the mark shortened to ~85 mm, the width shrank to ~8.5
mm, suggesting a high rectangular area estimate of around ~723 mm^2.
This is obviously a much smaller change than predicted by the simple
purely straight-line theory of contact patch size versus inflation.
For example, the 60 versus 120 psi estimated areas are 1030 versus 723
mm^2. The patch shrank about 300 mm^2 instead of the expected 515
mm^2.
Again, it could be that the pressure trails off toward the edges, but
something funny is still going on.
At ~100 lbs load, the ~100 psi high area estimate is 765 mm^2, or
1.185 square inches, about 18% larger.
Possibly the 0 psi edge has a border quickly increasing to 100 psi,
which would account for the larger area.
But the effect seems to reverse itself at lower pressures.
Instead of a larger than expected area, there is a smaller than
expected area at low pressure.
At ~50 psi with the same ~100 lb load, the high area estimate of 1100
mm^2 is 1.705 square inches, about 15% smaller (not 18% larger) than
the expected 2 square inches.
Cheers,
Carl Fogel
Joe Riel
Maybe Fogel Laboratories will be acquiring one of these babies,
<http://www.tekscan.com/industrial/tirescan_system.html>,
and will be able to settle the matter once and for all.
I used Carl's data to plot area vs 1/pressure and get a sort of
straight line that intersects the y-axis (pressure=infinity) near 1.2
inch^2. It might be interesting to test this extrapolation with a
tire at infinite pressure; that can be approximated, I believe, by
filling the tube completely with water.
--
Joe Riel
carl...@comcast.net
Dear Joe,
Just in case you missed it, I posted some new data for 30 to 120 psi
in 10 psi increments on a nearly new tire.
I've never filled a tire with water, but this may be my excuse. The
trick, I gather, is to suck up a pump full of water and push it into a
tube already nearly full. A Slime tube with a removable Presta core
would make it easier to get the air out of the tube and fill it, but
I'm not sure how to mount the filled tube in a tire.
I'll start considering one of those pressure sensors just as soon as
certain posters break down and buy spoke tension gauges.
Considering, not buying. I'll wait to buy one when Harbor Freight
offers a discount coupon.
Cheers,
Carl Fogel
jobst....@stanfordalumni.org
http://i7.tinypic.com/2z4wuib.jpg
I think Carl has the home science lab well in hand, especially with
the array of tools and work bench I see in the picture. I have a
truing stand and a bunch of wrenches in my "living room" where my
bicycle is parked.
My results would not come closer to the theoretical pressure vs area
model than Carl's but the shape of contact would be different. My
tires have sufficient tread rubber to also prevent free flexing under
load. Worn tires may be thin in the center, albeit slanted, but the
sides don't wear significantly, making the flexing problem worse.
We don't need no steenkin flawed experiments to prove they don't work.
Jobst Brandt
jobst....@stanfordalumni.org
> Yes, I note that. How worn is this tire- does it have a significant
> "flat spot" from wear that most rear tires exhibit? I wonder if
> that makes a difference compared to a basically new tire. It is
> interesting that your contact patch shapes are different from those
> shown in _Bicycling Science_ 3rd Ed., p 218 esp the second example.
As Carl explained, it is a worn tire and it has a "flat" zone in the
"center" which is off center and slanted from riding on crowned roads.
That is the obvious explanation of the trapezoidal contact patches and
the non-conformity to the theoretical pressure vs area model.
If you have the link or picture of the BS 3rd Ed page to which you
refer, you might put it up on a web page so we can peruse it.
Jobst Brandt
jobst....@stanfordalumni.org
>>> One possible partial explanation is that pressure varies considerably
>>> in the contact patch, with much lighter pressure toward the edges.
>> I think this is important to what you're seeing. It takes no
>> appreciable pressure to transfer ink from your tire tread to the paper.
>> The curve of the tire outside of the contact patch meets up
>> tangentially, and the tire beyond the edge of the patch makes grazing
>> contact with the flat surface. This does not have significant contact
>> pressure, but the inkblot marks it anyway.
> Maybe Fogel Laboratories will be acquiring one of these babies,
http://www.tekscan.com/industrial/tirescan_system.html
> and will be able to settle the matter once and for all.
> I used Carl's data to plot area vs 1/pressure and get a sort of
> straight line that intersects the y-axis (pressure=infinity) near 1.2
> inch^2. It might be interesting to test this extrapolation with a
> tire at infinite pressure; that can be approximated, I believe, by
> filling the tube completely with water.
That probably won't do because, as I have mentioned in the past, I
have filled tires with water on occasion and was unable to tell the
difference when riding. One such event was when a rider with a leaky
tubular and no spare had a slow leak. I filled his tire with water,
making sure there was no air left in the tire, and solved his problem.
He rode the tire for the rest of the ride and the following week,
reporting that it worked well. The other was with my shimmy
experiment, where I was intent on showing that frame twist is what
causes shimmy, not wheel mass or imbalance. I found no perceptible
difference in response while riding and shimmy remained unaltered.
Tire volume does not change significantly when supporting loads and it
is difficult to pressurize a water filled tire. Let's not get farther
into invalid experiments.
Jobst Brandt
jobst....@stanfordalumni.org
> Just in case you missed it, I posted some new data for 30 to 120 psi
> in 10 psi increments on a nearly new tire.
> I've never filled a tire with water, but this may be my excuse. The
> trick, I gather, is to suck up a pump full of water and push it into
> a tube already nearly full. A Slime tube with a removable Presta
> core would make it easier to get the air out of the tube and fill
> it, but I'm not sure how to mount the filled tube in a tire.
This is done with the tire mounted. Using a frame fit pump, like a
Silca Impero. Let the air out of the tire and re-inflate by filling
the pump with water, removing the end cap and piston before pushing
the water into the tire.
When the tire seems full, let out any air that was in it by having the
valve at the top and flattening the tire on top so all air can be
release from the valve. By leaning the wheel to one side and folding
the tire down over the edge of the rim, the valve stem can be made to
be at the highest point of the inner volume. Obviously ALL air will
be hard to remove, but those few cc's won't matter as far as riding
goes. It won't slosh around.
> I'll start considering one of those pressure sensors just as soon as
> certain posters break down and buy spoke tension gauges.
You must mean a tensiometer. I know that the word sticks in many
peoples craw, but that's what it's called.
http://www.m-w.com/dictionary/tensiometer
> Considering, not buying. I'll wait to buy one when Harbor Freight
> offers a discount coupon.
I don't think we are going to discover much from all that testing. I
believe the model of pressure vs contact area is valid and is skewed
by casing and tread stiffness. If it were a small major to minor
diameter tire, cord angle would play a roll, but that is not the case
with 700x25mm tires. They have to little curvature for much bias ply
cord effect. Car tires, on the other hand, have a marked effect, the
narrowest part of the tire being there where one would expect a bulge
as we have on (bicycle or) radial car tires.
I recall how people thought they had a slow leak when they saw the
bulge of their radial tires, a sight they had not noticed with bias
ply tires that bulge adjacent to the ground contact patch.
Jobst Brandt
jobst....@stanfordalumni.org
> Just in case you missed it, I posted some new data for 30 to 120 psi
> in 10 psi increments on a nearly new tire.
> I've never filled a tire with water, but this may be my excuse. The
> trick, I gather, is to suck up a pump full of water and push it into
> a tube already nearly full. A Slime tube with a removable Presta
> core would make it easier to get the air out of the tube and fill
> it, but I'm not sure how to mount the filled tube in a tire.
This is done with the tire mounted. Using a frame fit pump, like a
Silca Impero. Let the air out of the tire and re-inflate by filling
the pump with water, removing the end cap and piston before pushing
the water into the tire.
When the tire seems full, let out any air that was in it by having the
valve at the top and flattening the tire on top so all air can be
release from the valve. By leaning the wheel to one side and folding
the tire down over the edge of the rim, the valve stem can be made to
be at the highest point of the inner volume. Obviously ALL air will
be hard to remove, but those few cc's won't matter as far as riding
goes. It won't slosh around.
> I'll start considering one of those pressure sensors just as soon as
> certain posters break down and buy spoke tension gauges.
You must mean a tensiometer. I know that the word sticks in many
peoples craw, but that's what it's called.
http://www.m-w.com/dictionary/tensiometer
> Considering, not buying. I'll wait to buy one when Harbor Freight
> offers a discount coupon.
I don't think we are going to discover much from all that testing. I
believe the model of pressure vs contact area is valid and is skewed
by casing and tread stiffness. If it were a small major to minor
diameter tire, cord angle would play a roll, but that is not the case
with 700x25mm tires. They have too little curvature for much bias ply
Joe Riel
>
> Just in case you missed it, I posted some new data for 30 to 120 psi
> in 10 psi increments on a nearly new tire.
Thanks, I hadn't seen it. The new data fits quite nicely to the
equation
A = A0 + F/p
with
A0 = 0.81 in^2
F = 41.9 lbf
If you do try the water-filled tube experiment (probably more clever
than useful), insert the tube into the tire before filling it. I've
done this with a standard frame pump that can be disassembled. Remove
the plunger from the pump, fill the body of the pump with water (a
water bottle works nicely), then push the load into the tube. The
difficulty is completely topping it off; with the stem on the inner
circumference of the torus, there is no way to get all the air out.
Freezing the filled tire might solve the problem of the remaining
air-bubble increasing the effective compressibility, however, the cold
rubber would also reduce the compressibility of the tread, which is
what, hypothetically, is generating the A0 term. I suppose if one
were willing to sacrifice an old tire, a hole could be made in the
tire and the stem run through it. That would allow the stem to be at
the top and all the air to be removed. As Jobst suggests, this is
probably not worth doing.
>
> I've never filled a tire with water, but this may be my excuse. The
>trick, I gather, is to suck up a pump full of water and push it into
>a tube already nearly full. A Slime tube with a removable Presta core
>would make it easier to get the air out of the tube and fill it, but
>I'm not sure how to mount the filled tube in a tire.
>
> I'll start considering one of those pressure sensors just as soon as
> certain posters break down and buy spoke tension gauges.
Urrhh, ummm.
> Considering, not buying. I'll wait to buy one when Harbor Freight
> offers a discount coupon.
Alas, the day-after Thanksgiving sale at Harbor Freight is over.
--
Joe Riel
Joe Riel
Carl,
Forgot to mention it earlier: nice pictures and experimentation.
Alas, the annoying divergence of the simple model (A = F/P)
from practive means that the write-up I had been working on
needs some revision.
--
Joe Riel
carl...@comcast.net
[snip]
>Let's not get farther
>into invalid experiments.
>
>Jobst Brandt
Dear Jobst,
Please tell us what's invalid.
Cheers,
Carl Fogel
carl...@comcast.net
[snip]
>As Jobst suggests, this is
>probably not worth doing.
[snip]
Dear Joe,
It's amazing how many things Jobst thinks aren't worth testing, isn't
it? For someone who likes to mention his new, improved tension gauge
design, he's awfully reluctant to use it to check some pretty basic
details.
Cheers,
Carl Fogel
carl...@comcast.net
Dear Joe,
Take my data with a grain of salt.
It's for a single tire of a particular width and thickness.
And while I'm pleased that the even series (40-60-80-100-120 psi) and
the odd series (30-50-70-90-110 psi) worked out so nicely, I'm awfully
suspicious of my own results.
The 110 psi length was "wrong" and clearly turned out to be a
mismeasurement, and it kept coming up just barely "right" when I
re-checked against the 120 psi length.
But I don't like things that work out just barely and ever so neatly.
Those 86 versus 85 mm measurements are exactly what it would look like
if Fogel Labs were fallible and prey to subconscious, unconscious, or
deliberate bias, instead of being fearlessly objective.
I'm tempted to have someone cut the sheet up, marking each contact
patch beforehand with a code, and see what happens when I re-measure
them.
It's a dreadful thing to have seen a psychology professor slyly
influence tape-measure readings of the same lumber by whole classes of
bright young students and several professional carpenters. Shakes your
faith.
But the general trend seems fairly clear. Doubling the pressure
doesn't lead to halving the apparent contact area.
Cheers,
Carl Fogel
Bill S
Has anyone tried using old fashioned carbon paper instead of
ink?(if you can still buy it). It will show variation of
contact pressure across the patch. It does tend to have a
minimum pressure threshold which may not pick up low
pressure areas.
Joe Riel
> On Sun, 26 Nov 2006 07:03:36 GMT, Joe Riel <jo...@k-online.com> wrote:
>
> [snip]
>
>>As Jobst suggests, this is
>>probably not worth doing.
>
> [snip]
>
> Dear Joe,
>
> It's amazing how many things Jobst thinks aren't worth testing, isn't
> it?
In this case it seems a bit of work for a single datum.
--
Joe Riel
Joe Riel
> Has anyone tried using old fashioned carbon paper instead of ink?(if
> you can still buy it). It will show variation of contact pressure
> across the patch. It does tend to have a minimum pressure threshold
> which may not pick up low pressure areas.
Because the Gaussian curvature of the outer half of a torus is
positive, any continuous map to a flat surface (which has a Gaussian
curvature of zero) necessarily distorts the area, by Gauss' Theorema
Egregium*. Applied to the tire, that means there must be a distortion
of the surface of the tire as it rolls on the floor. I've been
wondering whether there is a practical means to measure the
distortion. The simplest feasible method idea I've devised is to
apply white paint to a wire mesh, lay it on the floor, and roll
the tire across it, being car
--
Joe Riel
*For the non Latin scholars, Theorema Egregium = "Remarkable Theorem".
carl...@comcast.net
Dear Joe,
Being carl?
Being carbon?
Being cartographic?
Being car-free?
At 30 psi with a 100-lb load, I thought that the paper wrinkled a
little to the side of the tire, which I assumed was the contact patch
shrinking in size and dragging the trapped paper with it.
My local office supply shop offers carbon paper, but wants about $20
for 100 sheets, which causes my hackles to stand up in outrage.
I looked at the WalMart site for "carbon paper" and was baffled by
this result:
http://www.walmart.com/catalog/product.do?product_id=1299472
What on earth is WalMart doing, selling an $83 highly technical
paperback book like that? At $83 per ~400 pages, the damn thing must
be printed on carbon paper.
Cheers,
Carl Fogel
Joe Riel
> On Sun, 26 Nov 2006 16:01:55 GMT, Joe Riel <jo...@k-online.com> wrote:
>
>>Bill S <bill...@tampabay.rr.com> writes:
>>
>>> Has anyone tried using old fashioned carbon paper instead of ink?(if
>>> you can still buy it). It will show variation of contact pressure
>>> across the patch. It does tend to have a minimum pressure threshold
>>> which may not pick up low pressure areas.
>>
>>Because the Gaussian curvature of the outer half of a torus is
>>positive, any continuous map to a flat surface (which has a Gaussian
>>curvature of zero) necessarily distorts the area, by Gauss' Theorema
>>Egregium*. Applied to the tire, that means there must be a distortion
>>of the surface of the tire as it rolls on the floor. I've been
>>wondering whether there is a practical means to measure the
>>distortion. The simplest feasible method idea I've devised is to
>>apply white paint to a wire mesh, lay it on the floor, and roll
>>the tire across it, being car
>
> Dear Joe,
>
> Being carl?
>
> Being carbon?
>
> Being cartographic?
>
> Being car-free?
The intended continuation was "careful to prevent the wire mesh from
slipping on the floor." Actually, my "explanation" of the Theorema
Egregium is incorrect. One could devise a map that preserves areas,
however, distances are then distorted (and vice-versa). A drawback of
the given procedure is that the measurements have to be made on the
surface of the tire. A nicer, but more difficult, technique would be
to ink a grid on the torus (tire) and then transfer it to the paper.
> At 30 psi with a 100-lb load, I thought that the paper wrinkled a
> little to the side of the tire, which I assumed was the contact patch
> shrinking in size and dragging the trapped paper with it.
>
> My local office supply shop offers carbon paper, but wants about $20
> for 100 sheets, which causes my hackles to stand up in outrage.
>
> I looked at the WalMart site for "carbon paper" and was baffled by
> this result:
>
> http://www.walmart.com/catalog/product.do?product_id=1299472
>
> What on earth is WalMart doing, selling an $83 highly technical
> paperback book like that? At $83 per ~400 pages, the damn thing must
> be printed on carbon paper.
Did you want that in the classic blue gift wrap, with the white
ribbon? Only 30 shopping days 'til Christmas.
--
Joe Riel
Andy B.
<carl...@comcast.net> wrote in message
news:odjjm2l29lmhp4n6t...@4ax.com...
>
> I looked at the WalMart site for "carbon paper" and was baffled by
> this result:
>
> http://www.walmart.com/catalog/product.do?product_id=1299472
>
> What on earth is WalMart doing, selling an $83 highly technical
> paperback book like that? At $83 per ~400 pages, the damn thing must
> be printed on carbon paper.
Firstly you shouldn't be shopping at walmart.
Secondly, they're not selling that book (they're out).
Thirdly, did you look at the cover of the book in the link?
carl...@comcast.net
wrote:
First, no -ly is needed when enumerating pedantic points. "First" is a
noun, an adjective, and an adverb. Appending the unnecessary adverbial
-ly can lead to "thusly" and other nameless horrors. :)
Second, why shouldn't I be shopping at WalMart? Where else can you
obtain a Fury RoadMaster?
Third, yes, I did notice that the book is out of stock. Life is mostly
sorrow.
Finally (which needs the -ly, since "final" is not an adverb), no, I
wasn't shocked that the WalMart site had the wrong picture for an
out-of-stock book whose extremely technical nature and absurd price
made it as out-of-place as a $5,000 time-trial bike would be next to a
Fury RoadMaster.
Cheers,
Carl Fogel
carl...@comcast.net
Dear Joe,
Entertainingly fruitless work!
First I rummaged around for a pump that I didn't care about. I found a
fat plastic "frame" pump with a Schrader head on a flexible hose. I
think that I picked it up years ago on the highway.
Then I groveled through some parts bins for a Schrader-pump to
Presta-valve adaptor. (Now I know where I put them and that they work
reasonably well.)
My first attempt to suck up a pump-full of water failed miserably,
which was instructive. After a perplexed moment or two, I realized
that just sticking the end of the pump in a sink full of water
wouldn't work very well--vast amounts of air rushed down the side of
the pump rod and past the cup valve, so scarcely any water got into
the pump chamber.
I submerged the pump and got much better results, with water rushing
into the pump chamber through the chuck and through the pump handle
and rod.
No matter how I tried, I could never get rid of all the bubbles when I
pumped the water out--at the very end of the pump stroke, a jet of
bubbly water always appeared when I tested things underwater. Maybe
the sink wasn't deep enough to get all the air to the chuck-end of the
chamber, or maybe some porous valve material held a lot of air.
Having figured out how to use a pump as a squirt gun, I moved on to
the inner tube. I rolled it up as tightly as I could toward the valve
stem, letting all the air out, closed the valve, and stuck it into a
sink full of water, with the rest of the tube hanging down to the
floor. I opened the valve underwater and squeezed and rolled the inner
tube between my fingers, trying to get water to flood into the tube.
I got nowhere for quite a while and was wondering how to fill the
stupid tube when I finally looked away from the valve stem and saw
that the rest of the tube dangling down to the floor had filled with
water. Short of pumping more water into it, the rest of the tube up
above the sink wasn't going to fill up.
I closed the Presta valve, stuffed the half-filled tube into place
tire, and had no trouble mounting the tire.
With the tire and its valve sitting in the bottom of a bath tub, I
attached the pump underwater and started filling it.
Eventually, I got some pressure, but never enough to be worth while.
The pump would give tremendous resistance and then the chuck would
come off. My new neighbors have a swimming pool that might allow a
floor pump to be used underwater, but I'm trying to preserve their
illusion that I'm normal.
The result was a curious tire that dented quite easily at first with
finger and thumb pressure, but then gave more resistance.
The obvious explanation was that the water-filled inner tube first
expanded to fill voids inside the tire and rim--bubbles and water came
out of the valve-stem and spoke holes whenever I pressed on the tire.
After the tube squished into those places and filled them, the
resistance increased dramatically.
Of course, that ruined the idea of testing the contact patch. The
water-filled inner tube produces a tire that's pretty much flat
initially and deforms more easily than the same tire at 30 psi, but
then turns into a much stiff tire.
Giving up, I found that the Presta valve empties a water-filled tube
in an amusing fashion. The knurled lock-nut on my valve has a slot cut
through it. Push the valve in just right, and you get two thin streams
of water, sort of like a miniature garden sprinkler. Aim one just
right, and you can startle a dog lying in the sun on the lawn.
Cheers,
Carl Fogel
ctsc...@earthlink.net
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
Tim McNamara
ctsc...@earthlink.net wrote:
> 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
<ctsc...@earthlink.net> wrote in message
news:1164914045.7...@j72g2000cwa.googlegroups.com...
|
| 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
| 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
|
Interesting results. After following the discussion of Carl's experiment, I
reread all the tire articles that I've archived and found one that is
relevant to comparing experimentally determining contact patch areas to
that expected from theory (ie, area = load / psi):
~begin quote
From: "Tire dynamics; rolling resistance is just one critical factor in
tire performance" by Chester R. Kyle [Bicycling, June 1989 v30 n5 p178(3)]
Much can be learned from a tire's "footprint" or contact patch, which is
the area that touches the pavement. From '84 to '86, Paul Van Valkenburgh
and I analyzed the footprints of dozens of bicycle tires at California
State University, Long Beach.
When weight is applied to a tire, it flattens until there is sufficient
area to support the load. If the tire were perfectly flexible like a
balloon, it would be easy to predict the footprint area since the contact
pressure would equal the tire pressure. For example, a tire with 100 psi
supporting a 100-pound weight would have a footprint area of one square
inch.
However, the contact pressure distribution of a real tire is uneven,
varying from zero on the edge of the footprint to a maximum in the center.
Therefore, it has a 10-50% larger footprint than would a perfectly flexible
tire.
~end quote
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...
Jean
Dan Connelly
> 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
Tom Schmitz
"Tim McNamara" <tim...@bitstream.net> wrote in message
news:timmcn-206951....@news.iphouse.com...<snippage>> <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?
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
carl...@comcast.net
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
Tom Schmitz
<carl...@comcast.net> wrote in message
news:hmnum2dcj7i7iqs3v...@4ax.com...
> 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
Tom Schmitz
"Dan Connelly" <d_j_c_o_n_n_e_l@y_a_h_o_o.c_o_m> wrote in message
news:F%Hbh.1039$Ga1...@newssvr12.news.prodigy.net...
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
"Jean" <Je...@spam.not> wrote in message
news:12mui03...@corp.supernews.com...
Jean - you must have an excellent memory to be able to find that article.
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.
I have this nagging feeling that I should know who Chester Kyle is - the
name is somewhat familiar.
Off to Google.
Regards,
Tom
carl...@comcast.net
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
Joe Riel
> 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