Quoted message said: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.
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
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
