Does a tyre change its CIRCUMFERENCE when underinflated?

[The Natural Philosopher]

All to modern for me. Never seen steering angle sensed yet on any car I've driven.

[Andy Burns]

It's because there are so many inputs available to the electronics, wheel speeds, steering angle, yaw rate, accelerometer(s), that figuring out a flat tyre has just become another part of TCB to the ABS unit.

I thought you have/had a Disco? Surprising if such a relatively high centre of mass vehicle didn't have stability control (or whatever LR call it)

[John Rumm]

Make up your own myths if you like... The 1% seems plausible enough for me.

Stability control programs, collision avoidance system, traction control and various other systems will use it.

Splembib!

We like that.

[Chris Hogg]

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.

[Robin]

Well you were the one to introduce circumference into this, a value which is irrelevant to the relationship between the 2 things measured (the vehicles speed and the angular velocity of the wheel) and what relates them (the rolling radius).

The irrelevance of the circumference can be seen by looking at caterpillar tracks. Ignoring slippage etc a 20m track goes round once when the vehicle moves 20m. But that's true whether it is attached to wheels with a radius of 0.5m or 0.25m. So the circumference tells you nothing about the relationship between speed and the RPM of the wheels. On the other hand, the (effective) radius of the wheels does.

[pamela]

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.

[Tim Streater]

Aren't you overlooking that, with a track, the wheel is only in contact with a part of the track. Whereas with a flat tire, even though the shape of the tire changes, the wheel is still in touch with the tire all the way round (the entire tire, IOW (phew!)).

Thus TNP is right to say that, inflated or not, for one revolution of the wheel, the whole circumference of the tire rotates once. Or, to put it another way, any spot on the tire circumfernce will touch the road just once.

(ignoring slippage on the road, or slippage between the tire itself and the wheel).

[Robin]

Yep. But that's just another way of saying that with a tyre on a wheel the fact that the rolling radius changes with pressure means the "rolling circumference"[1] also changes with pressure. As TNP admitted. So I was and am still unclear why he asked about the circumference. I thought at first it might be because he thought that the steel cords/belts in tyres are like caterpillar tracks. But it can't be that when he volunteered there is an effect.

Of course I may well be missing something. But I _know_ I'm - hic - missing the bottle downstairs, so ...

[1] TM TNP?

[Huge]

Wriggle, wriggle, wriggle.

[Jeff]

It is the only distance that matters with the rotation speed of the wheel. The distance between the axle and the top of the tyre is irrelevant to that.

If you simplify the shape and

But those distances are irrelevant to the rotation speed of the wheel.

But the circumference, perhaps perimeter would be a

Yes, but that isnt what determines the rotation rate of the wheel.

Its irrelevant when deciding if the tyre is under inflated.

does the circumference change between

Not by much at all with steel belted radials and any system that detects under inflated tyres has to work with those.

When I were a lad in

Yes, but the circumference isnt what determines the rotation rate of the tyre on a moving car.

Yes, but the circumference doesn't determine the rotation rate of the tyre.

That's arguable with the very small variations being discussed.

But someone must have checked that the ABS rotation rate does change with under inflated tyres otherwise that wouldn't be used to detect under inflated tyres.

[Jeff]

It is you that doesn?t. That distance is the only thing that matters, it is what determines the rotation rate of the wheel, exactly the same way the diameter of the wheel determines the rotation rate of the wheel, but in this case that radius clearly does vary with the pressure in the tyre. What happens with the rest of the tyre is completely irrelevant.

[Jeff]

Not when the wheel and tyre isnt a perfect circle and it never is with a vehicle wheel and inflated tyre.

No need for any tyre scrub, just the reduced radius under the axle. That is what determines the rotation rate of the wheel.

[Tim Streater]

Dunno what "rolling circumference" means, but the circumference can't change, as it is fixed by the loops of steel belts in the tire (may stretch a bit but not much).

*That* is the point.

[Jeff]

No one said that the change will be the same percentage, just that when the distance between the axle and the ground changes, that the rotation rate will change and that change can be measured.

But enough to measure with RPM so easy to measure differentially.

[Tim Streater]

I'm not disputing that as a method of detecting tire pressure changes. I'm saying that the circumference doesn't change. People have talked about tank tracks etc but that is a red herring. If our tire could stretch (and stay stretched) that would be different. But the important point is that the tire is always in contact with the wheel rim all the way round, regardless of the tire pressure.

[Robin]

Three points:

a. you seem to be assuming the steel is perfectly inelastic. When it usually is made up of thin steel wires woven into cords and then into belts I'd like to know it's actual modulus;

b. I posted a link to a paper which modelled tyres and reproduced observed pressure effects. It noted that "the belt structure strongly influences the effective rolling radius". But it also pointed to the effects of pressure on the deformation of the tread - ie the stuff between the belts and road. It seems to me credible that behaves differently with changes in pressure: eg just look at the sidewall when pressure is low;

c. I introduced the term "rolling circumference" because how iTPMS works can be discussed perfectly well without any reference to circumference. So ISTM it behoves those who introduce "circumference" into it to define what they mean. The circumference of the static, unloaded tyre? Or the distance travelled for one rotation of the wheel - which all the evidence shows does vary with pressure?

[T i m]

But the 'belt's' are parallel loops around the circumference of the tyre but woven diagonally and so form a parallelogram. This parallelogram can change it's shape slightly and therefore allow the tyre to become bigger or smaller due to pressure or whilst carrying a load.

You wouldn't get the point unless it was stuck in you by someone else. ;-)

Cheers, T i m

[Richard]

[Richard]

:)

[Richard]

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.