"carl mciver" wrote:


"Jeff Wisnia" wrote in message
...
| Ned Simmons wrote:
|
| In article ,
| says...
|
| On Thu, 18 Aug 2005 13:09:28 -0400, Ned Simmons
| wrote:
|
|
| In article ,
| says...
|
| The "NPR "Car Talk" show's "Puzzler" a couple of weeks ago gave an
| answer stating that some car's computer "knew" a front tire was low on
| air because the ABS system noted that wheel was rotating "a heck of a
| lot faster" than the other wheels when the car was driven.
|
| I didn't buy that one.
|
| Sure, the rolling radius of a low tire is less than that of a fully
| inflated one,

The distance from axle to ground is less, but calling that distance a
radius (rolling or otherwise) is misleading. In the first place, that
distance does not equal half of the deformed diameter, so it's not a
radius in any conventional sense; secondly, and more importantly, the
shape of the under inflated tire is not circular, so even the
semi-diameter of the deformed shape does not have a 2 pi relationship
to the tire's circumference.

but the overall circumference, particularly on a steel
| belted tire, remains the same. Barring slippage, that circumference
must
| lay its whole length on the road once per revolution, just like the
| circumference of a full tire does.

Yes.

| But if the circumference remains constant as the rolling
| radius decreases there has to be slippage.

No. You're assuming that the relationship between the circumference
and the axle-to-ground distance (what you call the "rolling radius")
remains constant; it does NOT.

under inflated
| tires run hot, and some of that heat surely comes from
| excess flexing of the tire, but I imagine a large
| proportion is a result of the rubber scrubbing against the
| pavement.

I doubt there is much slippage at all. The car will tend to pull in
the direction of the under inflated tire because there is more
friction, not less, as would be the case if the tire were slipping.
(Of course, the lean of the car also contributes to the pull.)

| "a heck of a lot faster" may be exaggeration, unless the
| tire is seriously under inflated, but I'm sure the effect
| is measurable under controlled conditions even with small
| changes in pressure. I guess the question is how sensitive
| can the system really be without causing nuisance alarms?
|
| Ned Simmons
|
| Picture a spoked wheel with string instead of spokes, and the strings
| 1/2" too long. Just because the axle is closer to the road doesn't
| mean the tire is slipping,

Nor does it mean that the radius has changed.

| I don't think it's the fact that the axle is closer to the
| road that's causing the tire to slip relative to the
| pavement. When the tire deforms the radial distance from
| the axle to the ground across the length of the contact
| patch is not constant. So either the linear velocity or the
| angular velocity of the rubber on the road has to vary - in
| other words, something's got to give.

Neither the linear velocity of the rubber nor the angular velocity of
the hub has to vary. What "gives" is the mathematical relationship
between the two, due to the departure from a circular form.

The sidewall probably
| absorbs most of the difference when the tire is properly
| inflated, but can only do so much. Keep in mind that
| underinflated tires wear more rapidly, which implies at
| least some scrubbing.

That is true, but the scrubbing occurs during turns, not during
straight travel. Because the under inflated tire has a longer distance
between the foremost and aftmost points of contact with the road, more
scrubbing will be involved when turning, compared to a properly
inflated tire. Hence, more wear.

| Your example of a loosely strung wheel with a rigid (I
| assume) rim really isn't analogous since the rim only
| contacts the road at a point.

It also isn't analogous because the rigid rim retains a circular
shape.

| or that the tire's radius has actually
| changed.
|
| If the axle is closer to the ground, hasn't the effective
| radius of the wheel been reduced?

No. The only meaningful definition of "effective radius" in this
context is c/2*pi. If the circumference doesn't change, the effective
radius doesn't change.

The question is, how much does the circumference change as the
pressure changes? Will it change enough for the sensors to classify
the associated change in rotation speed as significant? Anyone have a
compressor and a tape measure handy to gather a little empirical data?

| The heat is probably almost exclusively from the flexing,
| primarily in the sidewall.

And from scrubbing during turns.

| I'm skeptical, especially in a seriously underinflated
| tire.
|
| Ned Simmons
|
|
| I didn't prased my OP post clearly. I know that that part of the ABS and
| couputer sytem will report a difference in the revolutions of the wheels
| after integrating the revolutions over some time period long enough to
| let you make a few consecutive turns in the same direction without
| trigering a warning.
|
| What I was incredulous about was the part of the puzzle's answer saying
| the tire with low air pressure would be rotating "a heck of a lot faster".
|
| The specific wording of the answer, by Ray, of Bob and Ray's "Car Talk"
| show was:
|
| ***************
|
| RAY: But when a tire loses air pressure and its diameter gets smaller,
| when the car is going down the road, in order for that tire to keep up
| with all the others and not get left behind, it has to turn faster. And
| your car does have something that is constantly monitoring the speed of
| all the wheels and comparing them to one another.
|
| What most modern cars have is ABS-- antilock brakes. And there's a
| sensor at every wheel that's reading how fast each of the wheels is
| turning. So, if it notes that the right front wheel is going a heck of a
| lot faster than the other wheels, it can either assume that you're
| making a lot of left hand turns or driving around a circle...or that
| your right front tire is going flat.
|
| **************
|
| It sounded to me like Ray somehow tricked himself into thinking that the
| increase in rotations per unit distance would be in direct proportion to
| the decreased rolling radius, and I don't believe that could be the
| case, for the reasons I already stated.

It could be that you're not giving enough weight to Ray's penchant for
hyperbole. Maybe by "a heck of a lot" he really means "a little
bit"...

If the tire is low, the axle is therefore lower to the ground. That
means the effective radius is shorter. Since the radius is shorter, the
effective circumference must be smaller. Following the progression of basic
geometry, more revolutions are required to move the same distance.

No. See discussion above about effective radius. As for the "effective
circumference", that's just the circumference, since each point will
contact the road during each revolution. The circumference will change
a little due to the change in pressure, and possibly a little due to
compressive effects within the contact zone, but not because the axle
is closer to the ground.

When a tire is low, the contact patch is not necessarily larger, once
you discount the lack of equal pressure in the middle of the contact patch.

I'm not sure if I buy the notion that the area of the contact patch
would remain unchanged, but in any case, the *length* of the patch
will be longer, resulting in a greater deviation from a circular
shape, and thus a greater deviation from the relation c = 2*pi*r,
especially if you're using the axle-to-ground distance as r.

The circumference is still the same, it's just not round, so there's a
bubble in the middle of the contact patch. Anyone who has seen a flat (and
mounted) tire sitting for a long time will see it clearly when it's rolled

That's a static condition. I don't know if that bubble would be
maintained under rolling conditions, since that would require each
point on the circumference to travel up and over the bubble (kind of a
standing wave thing). My hunch is that the bubble would be diminished
when rolling, but I could be wrong...

over. Since the tire's still rolling, that excess slack as it passes
through the patch "humps up," and you will see the sides of the tread worn
more than the middle, since the pressure is so much lower in the middle.
Since a tire with normal pressure has a given diameter, it follows that a
tire with lower pressure will have a slightly smaller diameter, although the
bulk of the movement is taken up by the sidewall's expansion (due to the way
the wires route.) There's obviously a lot of flexing, and you can see the
sidewall flexing and wrinkling in a very low tire being driven slowly. This
kind of flexing in rubber, strung with steel belts, gets really hot and the
rubber starts to break down, even pulverizing itself. At some point, the
flexing becomes so much that the bead wrinkles and breaks. At that time the
tire deflates rather violently and at that point how smart or stupid you are
determines the rest, and who lives and who dies. The stresses on a tire
when it's way low are incredible and I thank God for steel belted radials
every time I have a flat!

Bert