(Small) Tire Science? Contact Patch Wrinkles?

On Wed, 04 Jul 2007 16:40:04 -0500, Tim McNamara
wrote:

In article ,
wrote:

On Wed, 04 Jul 2007 09:56:13 -0500, Tim McNamara
wrote:

In article . com,
Chalo wrote:

Tim McNamara wrote:

Inflation pressure is one of the most central factors in how
much the tire bulges out at the contact patch. PSI is PSI no
matter the major diameter of the wheel.

The length of the tire's contact patch at a given PSI is a
function of the tire's diameter-- and it seems to vary by more
than the proportional change in diameter. The bigger the wheel,
the lower the feasible tire pressure for any given width, and the
lower the casing deflection (and thus RR losses) for any given
pressure and width.

Interesting point. I was thinking in terms of the area of the
contact patch and didn't think about it's shape. Time for Carl
Fogel to break out his stamp pad and graph paper over at Fogel Labs.

[snip]

Dear Tim,

The contact patch area for a bicycle tire tends toward a favored
size, despite inflation. Straightforward inflation theory works well
for pistons in metal-walled cylinders, but not for inflated
canvas-sided toroids pressed against flat, unyielding surfaces.

Here's a graph, showing measured versus predicted sizes:

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

I remember that discussion and the attempts to explain the observed
information. It's striking how well your measurement's and Tom's fit.
I can't recall- were both of you using the same make/model tire?

snip

As Chalo says, the contact patch tends to lengthen more than it
spreads. Think of the tire as a series of hoops, like rubber cheerios
on a ring. With more load (or lower inflation), the tire works by
squashing the original central hoop a little more so that new hoops
on either side touch the ground, start to bend, and support the new
load.

Yes, that's a simpler and better visual than my explanation would have
been.

Dear Tim,

I measured a single tire, nominally 700x26 from 30 to 120 psi in 10
psi increments.

Tom measured 5 tires of various widths from 60 to 120 psi in 10 psi
increments.

When I averaged the data points for his 5 tires, his results were
ridiculously close to my single-tire data points--the blue and yellow
lines on the graph pretty much match.

I think that the graph of my areas at 30-40-50 psi is jagged,
suggesting that more measurements would produce a smoother curve, but
the general trend seemed to be clear--the tire just didn't spread out
nearly as much as expected.

The sidewall tension probably gives a progressive spring-style
resistance. By the time the tire flattens into impact-puncture
dimensions, the originally round cross-section of the tire has been
enormously distorted against the resistance of the air pressure on the
sidewalls.

Another way to appreciate the sidewall force is to hold a tire off the
ground and then imagine how hard you'd have to pull each sidewall
outward to produce the same flattening at the contact patch. The tire
surface is stretched taut, like a 3-D curved trampoline--bulging it in
either direction takes a lot of force.

At high pressures, the sidewalls bulge very little, and the very edges
of the contact patch press against the ground with less than inflation
pressure because the sidewall is pulling them away from the ground.

But once the load is high enough (or the pressure low enough) to
flatten a good deal of rubber against the ground, the tables turn, and
the sidewall switches to pushing the edges down even harder than
inflation pressure.

Tread thickness and sidewall stiffness probably influence things a
bit, but the main factor is likely to be the cross-section diameter of
the unloaded tire.

Given the same inflation and load . . .

A very wide tire should act like the test tires at high pressure, with
a shorter, rounder contact patch with low-pressure edges that's larger
than pressure x area predicts. (Fewer hoops are bending.)

A very thin tire should act like the test tires at low pressure, with
a long contact patch with high-pressure edges that's smaller than
pressure x area predicts. (More hoops are bending.)

From a practical point of view, the shorter, rounder contact patch
involves less rolling resistance because there's less sidewall
bending.

But the longer contact patch may give better traction because the
pressure is greater than inflation at the edges and the longer strip
_may_ bridge small slippery spots better when cornering.

Here's an exaggerated comparison:

same load, same inflation

narrow tire, wide tire,
slightly larger area slightly smaller area
long, thin contact patch short, wide contact patch

xxxxxxxxxxx XXXXXXX
-bridges- slips
..1234567.. 1234567 --same slippery patch

Cheers,

Carl Fogel

Carl, any idea how this stuff relates to small wheels? 20"? 12"? Wide
and narrow tires? Low pressure, high pressure. Thanks, JP

PS: Carl, have you heard of the bulge/bump in front of the contact
patch? Behind it? How about a concavity after the bulge but before the
patch? --Due to bias ply? Did you see the mention of the losses in
that German research from "tilting over the edge" of the bulge? ---JP

On Thu, 05 Jul 2007 05:10:47 -0700, "Jeff Potter (of
OutYourBackdoor.com)" wrote:

Carl, any idea how this stuff relates to small wheels? 20"? 12"? Wide
and narrow tires? Low pressure, high pressure. Thanks, JP

Dear Jeff,

Contact patches probably work the same way for any round cross-section
tire.

Given a wide enough range of inflation and load . . .

At high pressure the dominant effect will be the ring of low-pressure
contact, where the rubber is curving away from the ground. This
rounder contact patch will have an absolute area smaller than simple
inflation theory predicts. It will have lower rolling resistance
because the sidewalls are hardly bending at all, so they waste less
energy in internal friction. (Similarly, thin sidewalls are more
efficient, since less material is bending.)

At low pressure, the dominant effect will be the high-pressure contact
at the edges, caused by the sidewalls bending enough to function as
C-shaped springs. This long contact patch will have an absolute area
larger than simple inflation theory predicts.

The transition point depends on load, inflation, and cross section. As
load increases (or inflation decreases), the angle of the sidewall
meeting the ground becomes steep enough that the spring-effect becomes
dominant.

In real life, the practical details goof up all sorts of things.

As Sheldon points out, if you have a wide tire and a thin tire at the
same pressure, at least one of them is at the wrong pressure. We use
thin tires on 700c rims because those rims can't handle high inflation
pressures with very wide tires.

A smaller rim can handle higher inflation and reduces wind drag, but
it increases real-life rolling resistance in that it hits real-life
road irregularities at a steeper angle, so more energy goes into
bouncing the bike and rider up and down.

The history of the Moulton small-wheel bicycle offers a good example
of such practical trade-offs. In 1983, Moultons came with 17 inch
wheels:

http://www.moultoneers.net/moultam.html

In 1998, the new series switched to 20 inch wheels:

http://www.moultoneers.net/newnew.html

The size of the rims and tires must deal with the practical problems
of wind drag, rolling resistance, suspension, gearing, and
availability. A very small tire and rim can reduce wind drag and
theoretical rolling resistance, but it can require more suspension,
special gearing, and terrible supply problems.

Cheers,

Carl Fogel

wrote:
On Thu, 05 Jul 2007 05:10:47 -0700, "Jeff Potter (of
OutYourBackdoor.com)" wrote:

Carl, any idea how this stuff relates to small wheels? 20"? 12"? Wide
and narrow tires? Low pressure, high pressure. Thanks, JP

Dear Jeff,

Contact patches probably work the same way for any round cross-section
tire.

Given a wide enough range of inflation and load . . .

At high pressure the dominant effect will be the ring of low-pressure
contact, where the rubber is curving away from the ground. This
rounder contact patch will have an absolute area smaller than simple
inflation theory predicts. It will have lower rolling resistance
because the sidewalls are hardly bending at all, so they waste less
energy in internal friction. (Similarly, thin sidewalls are more
efficient, since less material is bending.)

At low pressure, the dominant effect will be the high-pressure contact
at the edges, caused by the sidewalls bending enough to function as
C-shaped springs. This long contact patch will have an absolute area
larger than simple inflation theory predicts.

The transition point depends on load, inflation, and cross section. As
load increases (or inflation decreases), the angle of the sidewall
meeting the ground becomes steep enough that the spring-effect becomes
dominant.

In real life, the practical details goof up all sorts of things.

As Sheldon points out, if you have a wide tire and a thin tire at the
same pressure, at least one of them is at the wrong pressure. We use
thin tires on 700c rims because those rims can't handle high inflation
pressures with very wide tires.

A smaller rim can handle higher inflation and reduces wind drag, but
it increases real-life rolling resistance in that it hits real-life
road irregularities at a steeper angle, so more energy goes into
bouncing the bike and rider up and down.

The history of the Moulton small-wheel bicycle offers a good example
of such practical trade-offs. In 1983, Moultons came with 17 inch
wheels:

http://www.moultoneers.net/moultam.html

In 1998, the new series switched to 20 inch wheels:

http://www.moultoneers.net/newnew.html

The size of the rims and tires must deal with the practical problems
of wind drag, rolling resistance, suspension, gearing, and
availability. A very small tire and rim can reduce wind drag and
theoretical rolling resistance, but it can require more suspension,
special gearing, and terrible supply problems.

Cheers,

Carl Fogel

very informative summary.

One last part of the question: Does anyone know anything about the
bulges, concavity, wrinkles that relate to the leading and trailing
edges of the contact patch? And maybe relate to the bias-ply
construction vs. radial? As I mentioned the German research mentions
this stuff but no one else has ever said a word about it. Thanks, JP

On 2007-07-08, Jeff Potter (of OutYourBackdoor.com) wrote:

One last part of the question: Does anyone know anything about the
bulges, concavity, wrinkles that relate to the leading and trailing
edges of the contact patch? And maybe relate to the bias-ply
construction vs. radial? As I mentioned the German research mentions
this stuff but no one else has ever said a word about it.

Bicycle Quarterly did a big article on this last year.

--

John )

On Jul 8, 10:00 pm, John Thompson wrote:
On 2007-07-08, Jeff Potter (of OutYourBackdoor.com) wrote:

One last part of the question: Does anyone know anything about the
bulges, concavity, wrinkles that relate to the leading and trailing
edges of the contact patch? And maybe relate to the bias-ply
construction vs. radial? As I mentioned the German research mentions
this stuff but no one else has ever said a word about it.

Bicycle Quarterly did a big article on this last year.

It did?

I thought I had all those... Title? Issue? Thanks, JP