Does a tyre change its CIRCUMFERENCE when underinflated?


https://www.youtube.com/watch?v=_2l5bOhHNxU

Answer. not by very much, if at all.
This seems to be a perpetual urban myth.
It tyre pressure sensors are using this, it has to be a very very complicated bit of software to detect - say - less than 1% change in RPM relative to the other wheels.
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But the radius clearly does vary significantly.

It can't be given that Andy and others have had a number of warnings that have turned out to be accurate every time.

Yes, but that isn't hard to measure when its relative to other wheels.
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Does it? The perimeter certainly changes shape from being near-circular to having a significant flat side against the ground, but if the radius changed significantly, that would also mean a circumference change, and the read-outs from the various gauges such as speedometer and odometer would no longer be accurate. There are also steel reinforcing belts beneath the tread that would have to stretch if the circumference increased.
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It clearly does with the distance between the axle and the ground.
The perimeter certainly changes shape from being

No it does not. What happens is that the distance between the rim and the outer flat surface of the tyre changes a lot. That is very clearly visible with a flat tyre still on the car.
and the read-outs from the various gauges such

That inaccuracy wouldn't be noticed even if it was done from the wheel which has the flat tyre.
There are

But the circumference does not increase when the radius where the wheel touches the ground reduces significantly and visibly.
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I think we're at cross-purposes here. Obviously, as you say, when a tyre is flat, the axle is nearer the ground. But is it reasonable to regard that as the radius of the tyre? If you simplify the shape and call it an ellipse, then you have two radii; quite how many radii would be needed to describe a tyre with a flat on one side, I wouldn't like to speculate. But the circumference, perhaps perimeter would be a better word, won't have changed significantly. It'll just become distorted, i.e. no longer circular.
But that assumes there is a weight pressing down on the tyre, which I grant you, would be the case for a loaded tyre on a vehicle. But I was thinking of an unloaded tyre; does the circumference change between under-inflated and fully- or even over-inflated? When I were a lad in the days when tyres had inner tubes, we used to go to our local garage and get old tubes that were no longer serviceable, patch them where necessary, inflate then and use them as super-sized rubber rings for taking down to the beach (and probably getting blown out to sea!). As they were inflated, the radius and circumference most certainly did increase; they blew up like a balloon. But put them into a tyre and there'd be no significant change in the circumference as they inflated and deflated. The structure of the tyre wouldn't allow that to happen.
Likewise, I suggest that the circumference (perimeter if you prefer) of a modern tubeless tyre doesn't change significantly as it inflates or deflates.
Every full rotation of the hub must correspond to a full rotation of the perimeter, regardless of the state of inflation of the tyre, otherwise serious slippage will be occurring between the tyre and the rim, which would result in friction heating and fairly rapid failure. So as far as speedometers and odometers are concerned, state of inflation won't make a significant difference.
(What amounts to 'significant' as I've used it here, I'm not sure; it depends on the pressure difference being considered between under and fully inflated, and the elasticity of the structures within the treaded surface of the tyre, amongst other things, but others in this thread have mentioned figures of around 1% for the stretching of the perimeter as the tyre is inflated. In this context, I would regard that as not significant).
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On 23/06/18 13:42, Chris Hogg wrote:

Not if you have any understanding of mechanics. The whole tread, up to and including a caterpillar track, goes round once per revolution of the track or tyre.
THAT is what determines the RPM/speed relations ship.
What happens with tyre pressures is quite clear. The tread stretches slightly under higher pressures. How much will be a function of the tyre construction. And this is what the sensors rely on.
Since no wheel is circular using radious as a concept is plain wrong. At best you can calcualate a '*radius it would be if it were round*,' from the actual circumference.
For it to be any other way the tyre must slip on the rim or on the road, substantially.
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On Sat, 23 Jun 2018 17:01:38 +0100, The Natural Philosopher

Which is what I was trying to say in a rather clumsy way, in the bit you snipped. I'm not complaining; you put it more succinctly.
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On 17:01 23 Jun 2018, The Natural Philosopher wrote:

Surely the circumference changes because the area in contact with the road is a chord and not an arc.
The length of the chord increases when the tyre is underinflated on account of compression of more of the former arc in contact with the road. The circumference is reduced.
Only if all the compression of the former arc occurs at the leading edge of contact would the speed be unaffected.

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Nope, not when the circumference doesn’t stretch and it doesn’t with steel belted radials.

Not with steel belted radials.

The circumference is irrelevant. What determines the rotation rate of the wheel is the distance between the axle and the road.

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On 23/06/18 17:01, The Natural Philosopher wrote:

A revolution is the movement of one object (*point* on circumference) around a centre (hub). Your caterpillar track is supported by wheels, each of which will do many revolutions for one revolution of the track. The circumference of the track is many times the circumference of each wheel.

No.

The use of radius is completely right. The circumference doesn't change. The centre of the instantaneous circle moves closer to the radius. The tyre is a three dimensional structure and this debate is being conducted in a two dimensional manner.

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On 24/06/18 08:03, Richard wrote:

I hope no one ebver emp;loys you in an engineering capacity.
The use of radius is meaningless. The the tyre is not round.
Go and get a technical education
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On Mon, 25 Jun 2018 18:02:49 +0100, The Natural Philosopher

That's why 'most people' that know what they are talking about use the terms 'rolling radius' (effective loaded radius) and have done for years, and all without your understanding or permission!
From this dynamic value you can extrapolate the rolling circumference or even measure it (as it's a real thing of course).
Plug an OBD reader into your ABS equipped car and pickup one of the sensor ring outputs.
Measure the unloaded circumference of the tyre.
Use the output of the ABS ring to count the wheel revs, calculate the theoretical distance traveled and compare that with a GPS or road marked value. Report back here with your findings. ;-)
Cheers, T i m
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On 25/06/18 18:02, The Natural Philosopher wrote:

I hope so too, as I am not an engineer.

It doesn't have to be. The radius is the distance between the centre of the object and a point on the perimeter (circumference). In our case, the point closest to the centre. 20P and 50P coins have a constant diameter despite not being circular.

I did, but am always learning.
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On 26/06/18 06:31, Richard wrote:

No, it is not.

No, they do not.

No, you are not.
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On 26/06/2018 09:06, The Natural Philosopher wrote:

They do for the normal meaning of "diameter" (which is not confined circles, spheres or other n-spheres)
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I must admit, I would tend to confine the word "diameter" to circular (or spherical) objects. But let's leave semantics aside.
I had never realised that the flats on a 20p or 50p coin were arranged so the distance between one edge and the other, for any line that goes through the centre, was always the same, irrespective of which part of the flat or point the line happened to go through and even though the middle of that line may not always coincide with the centre of the coin.
Do all polygons with an odd number of sides have the property, or is it unique to heptagons (7 sides)?
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On 26/06/2018 10:40, NY wrote:

Fair enough - but the general meaning of "diameter" does apply more widely. And "diameter" is a lot shorter than eg "the distance between one edge and the other for a line that goes through the centre" :)

I'm old enough to have "done" the design of the original 50p coin at school before it was in circulation :(

I _think_ it's possible to achieve it with any odd number of corners but couldn't tell you the parameters that can be fiddled with.
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NY wrote:

the usual phrase is 'curves of constant width', but in real terms (e.g. a coin mechanism measuring coins) they do have a constant diameter, but a varying radius.

Never play with multiple 50ps and two rulers at school?

No, its a class of Reuleaux prisms, even 'better' are solids of constant width
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No. I must have missed out on that bit of geometry. Tell me more: I'm intrigued. I've lived with decimal coins for 47 years and never knew that 20p and 50p coins had constant diameter. I realised that the sides are slightly curved rather than being flat, but not that the curves were so arranged as to create a constant width object.
It's just the sort of thing that my old maths teacher (who taught me from from 1974-77) would have revelled in, so I wonder why he never mentioned it.

Yes, "the concept that something could roll but not be round totally messes with your head" :-)
I hadn't realised that the rotor of a Wankel engine was a constant width shape, only that it was an equilateral triangle with curved sides. Indeed I thought that the sides were only curved to make the corners slightly less sharp and so reduce the stress on each corner.
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<snip> >I had never realised that the flats on a 20p or 50p coin were arranged so

I think that was so they would be acceptable in slot machines.
Cheers, T i m
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