# OT - Rotations of a low tire?

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.
Sure, the rolling radius of a low tire is less than that of a fully inflated one, 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.
From my TSD rallying days I remember that low tire pressures made some slight differences in odometer measurements, but these were in the second decimal place, hardly "a heck of a lot".
Jeff
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Jeffry Wisnia

(W1BSV + Brass Rat '57 EE)
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I don't buy it either. I know a GM mechanic and he states there are sensors in the wheel that transmit tire pressure to the computer. His bitch is that it complicates simple things like rotating tires because now he has to connect the scan tool and tell the computer how he rotated the tires.
cs
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This is indeed the "indirect" tire pressure rotation system. You're right, it actually requires that the pressure be so low that the outermost belts are sort-of buckled in, but this is what happens if you are 5 or more PSI down on a big vehicle.
I think SUV's are soon (already?) required to have a "direct" method (after the tire fiasco of a few years ago), an actual pressure sensor.
Tim.
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This morning on the way to work a car came up beside making all kinds of funny tire noises. One front tire was almost running on the rim and the driver was oblivous to it all.
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snipped-for-privacy@conversent.net says...

But if the circumference remains constant as the rolling radius decreases there has to be slippage. Underinflated 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.
"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
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wrote:

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, or that the tire's radius has actually changed. The heat is probably almost exclusively from the flexing, primarily in the sidewall.
Pete Keillor
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Pete Keillor wrote:

I like the free wheel with rubber band spokes. When you shine a strong beam of light onto the spokes on just one side of the wheel it heats them up, they shrink, the wheel goes out of balance, and it rotates, continuing to turn as long as the light is on.
"They Shrink when heated?", you ask.
Yep. I thought I knew about lots of things but I lived over 60 years before I learned that about rubber. It is composed of funny molecules that do the opposite of what I'd come to think of as normal, like shrinking when heated.
If you've never tried this one it might suprise you.
Stretch a rubber band between your hands, hold it stretched for a few seconds to let it come to near room temperature and then touch your upper lip to the center of the band and bring your hands together quickly.
Feel it get colder?
Jeff
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Jeffry Wisnia

(W1BSV + Brass Rat '57 EE)
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On Thu, 18 Aug 2005 17:37:52 -0400, Jeff Wisnia

Yup, learned that in P-chem about 33 years ago. Weird.
Pete Keillor
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snipped-for-privacy@chartermi.net says...

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. 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.
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.

If the axle is closer to the ground, hasn't the effective radius of the wheel been reduced?

I'm skeptical, especially in a seriously underinflated tire.
Ned Simmons
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Ned Simmons wrote:

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.
Jeff
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Jeffry Wisnia

(W1BSV + Brass Rat '57 EE)
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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. 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. 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 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!
Hairy story: I was in a company Astrovan on a freeway in Dallas rush hour, inches from the zipper barrier, doing ~70 when a dumb bitch in front of me blew a tire. In the minivan, bolted to the floor, was 1000+ pounds of scale test weights (500 was too little for the way I liked to calibrate scales) and lots of tools, so when she slammed on her brakes, I about shit my pants 'cause traffic was asshole to belly button and FLYING. I stopped short of her by two feet and was surprised that no one hit me from behind. As I'm chewing her out for being so phenomenally stupid, I was removing her spare from the back seat (???) and changing it as fast as I could. I could barely touch the old rim, it was so damn hot! The sidewall was all but gone, and when the wheel flipped to the ground in front of me there was a pile of steaming rubber powder on the ground some four inches high and six or so inches around. I'm sure some of this was from the sidewall that ground away when she stomped on the brakes, but I can't see the tire providing any stopping effort given its condition, so I'm confident most of it was rubber that crumbled before the tire blew and was trapped inside the tread by centrifugal force. The tread, of course, was hotter than fuck and intact. About the time I got her tire back on I started to "come down" and the transportation truck showed up to (more kindly) explain to her how to brake safely after a blowout. I looked back at the million car traffic jam and there, a few cars back, were a couple folks exchanging information and sour looks. The difference between a royal fuckup of massive proportions was merely milliseconds at that speed and it could have all been averted if that \$%^&*! had used her brain instead of her foot. Thinking back on it, I'm sure my normal scatterbrained self would have just run over her, but for some reason, at that very moment, I had my head screwed on right. Still get that intense feeling when I think about it.
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carl mciver wrote:

Now Carl, that explanation is what I had trouble with in the first place.
Imagine if you would that the tire had side to side notches on the tread like an inside out timing belt and the pavement had mating pitch grooves on it. (Sort of like the ones which make a warning sound if you start to wander off the side of the road?)
That would create a "rack and pinion" configuration.
Would you still say that the number of revolutions per mile that tire makes would vary with the air pressure in it, or as you put it "the effective radius".
That's where my skepticism to the "Car Talk" answer stemmed from. I don't doubt that second order effects come into play to make the rotations per unit distance increase somewhat with lower tire pressure, but I'm willing to bet that the effect is nowhere near as large as being fully inversely proportional to the rolling radius, at least not until the tire jumps right off the rim.
Jeff
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Jeffry Wisnia

(W1BSV + Brass Rat '57 EE)
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| Now Carl, that explanation is what I had trouble with in the first place. | | Imagine if you would that the tire had side to side notches on the tread | like an inside out timing belt and the pavement had mating pitch grooves | on it. (Sort of like the ones which make a warning sound if you start to | wander off the side of the road?) | | That would create a "rack and pinion" configuration. | | Would you still say that the number of revolutions per mile that tire | makes would vary with the air pressure in it, or as you put it "the | effective radius". | | That's where my skepticism to the "Car Talk" answer stemmed from. I | don't doubt that second order effects come into play to make the | rotations per unit distance increase somewhat with lower tire pressure, | but I'm willing to bet that the effect is nowhere near as large as being | fully inversely proportional to the rolling radius, at least not until | the tire jumps right off the rim. | | Jeff
Believe me, I have a bit of trouble getting it, even visualizing it, but there's really no other way to see it. The difference in rotational speed has to be taken up in the wrinkling in the tread and all the sidewall flexing, which is why a low tire is a very bad thing, since all that action creates a lot of heat.
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| > Would you still say that the number of revolutions per mile that tire | > makes would vary with the air pressure in it, or as you put it "the | > effective radius". | | I think Carl has explained the paradox. Imagine that as your inside out | timing belt engages with the rack it develops a bubble in the center of | the engagement such that there are x+1 pitches of belt between x teeth | on the rack. The overall length of the belt hasn't changed, but its | effective length has been reduced by one tooth.
Thank you for making it clearer than I did. I was so wrapped up in the big picture I missed the simple explanation!
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snipped-for-privacy@nedsim.com says...

^^^^^^
Sorry, F*r...
Ned Simmons
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wrote:

r is not constant because the tire has a flat patch. C = pi *2 r comes from integrating dC = r(theta) d(theta) thru 2 pi radians with r constant. If r(theta) is not constant, then the formula for circumference of a circle (C = pi *2 r or C = pi * D) is no longer valid.
Even a properly inflated tire has a flat patch. An underinflated tire just has a bigger flat patch. Circumference can remain unchanged, so revs/rolled_distance also can remain unchanged.
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snipped-for-privacy@NOSPAMgoldengate.net says...

^^^^^F*r

Then where is the length of tread that compensates for the length that is lost to the flat spot? It seems to me that it either must be in an inward wave in the middle of the contact patch, or causing an outward bulge just outside the contact patch, or possibly both.
Note that we all seem to be accepting the fact that the tread length is fixed. Do we really know this to be the case? I'm sure the belts are pretty effective at limiting the length of the tread in tension, but how do they really behave in compression? If the tread can compress slightly as it rotates into contact with the road that would resolve the entire controversy.
In any case, I just can't accept that the car travels anything other than 2*pi*r per rev (as before, r is the distance between the axle and the road), regardless of what the tread does. To carry the torque and work argument further, consider that the horizontal reaction of the driving tire on the road is equal in magnitude to the horizontal force at the axle pushing the car forward, call it F. Work is equal to F * d, d being the distance the car travels. Work is also equal to Torque * angular displacement in radians, T * theta. The torque at the axle is F * r. So... F * d = T * theta = F * r * theta
But if d per rev is greater than 2*pi*r, the work moving the car forward is greater than the work input to the system by the torque turning the axle.
Ned Simmons
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wrote:

If the radius is less at the flat spot, then it must be greater elsewhere. No length of tread is lost, it just isn't all at the same distance from the axel.

This is true if you use the r that the tire had when it was circular in shape.

These formulae were derived for circular geometry. The tire covers once circumference per rev regardless of its shape, so work output work input (minus losses that go to heat the tire). Torque is exerted on all partsof the periphery, not just the part that touches the road. The parts of the tire not touching the road still have torque due to "pulling" the tread around with circumferential tension.
The total torque is the sum of the various moments (at various radii) around the axel.
It is true that the *average* radius is always r, which is the (constant) radius of the tire when it is circular in shape. If you use that r in your assertion, then your assertion is correct. If r varies with theta, then the average radius is (1/(2*pi)) * integral ( r(theta) d theta) integrated over 2pi radians. If r is constant, as in a circle, this comes out to r, fancy that!
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Don Foreman wrote:

With my nearly last breath I just rescinded my DNR document and asked to be kept on life support until this one gets settled.
Don, I definitely would have picked you to be on the topside end of 100 feet of manilla line back around 1960 when we thought it great fun to SCUBA dive under the ice around here.
http://home.comcast.net/~jwisnia18/temp/ice2.jpg
That's me on the left. All that's left from those halcion days are some great memories and that very same length of manilla line, which I used just yesterday while felling a tree in the backyard.
Jeff
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Jeffry Wisnia

(W1BSV + Brass Rat '57 EE)
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On Sun, 21 Aug 2005 13:31:12 -0400, Jeff Wisnia

Topside is exactly where I'd rather be, Jeff. Brrrrrr!