Rolling Circumference 235/85 16

[berti1554]

Hey guys!

We had a discussion in another forum (Germany) about different speeds and revs between tyres with different tire pressure. As that discussion went over a couple of pages now w/o a real answer I'll try it here. The main question is whether a tire with a much lower pressure turns more often over exactly the same distance as a tire that is at a higher pressure and with that more round that the one w/ the lower pressure in it.

Please don't add any comments like "too low pressure can cause damange on the tire" and so on. I'm looking for somebody who is really good in physics as I'm completely confused now.

Thanks - Robert

Edited November 15, 2010 by berti1554

[landroversforever]

hmmm.... thats a tough one. thinking one, then the other, and back again...

Sorry I'm no help!

[rtbarton]

The main question is whether a tire with a much lower pressure turns more often over exactly the same difference as a tire that is at a higher pressure

Yes it does.

The rolling circumference c = 2*pi*r

Where r is the rolling radius, ie the distance from the centre of the hub to the ground.

The diatance travelled d = n * c where n is the number of revolutions

so n = d/c thus a smaller c gives a greater n

[jad]

so n = d/c thus a smaller c gives a greater n

this is where the problem lies. the circumference is not technically changing length even though the tyre is changing shape.

I would say that they cover the same distance, assuming the rubber of the tyre does not stretch with an increase in pressure and the ground is flat, then there is still the same length of rubber there.

Im guessing many people will argue either way though. anyone fancy conducting a real life test?

[berti1554]

Thanks buddy, taht's exactly what I was looking for. Do you have any experiece what the radius on a normally inflated tire (3bar/44psi) is when mounted on a standard unloaded 110 or ninty, just roughly. A 235/85-16 has a dia of 806mm => radisu is 403mm. Is 15 to 20mm something that sounds ok to you?

Edit: Now I see the same discussion starting here, only it is supported by math sorry

[jad]

I imagine that would vary from tyre to tyre. I dont really know. 44 psi does sound high though. i run my 235/85's 28 front and 35 rear i think on my 90. Is 44 normal for a 110?

jad

[rtbarton]

this is where the problem lies. the circumference is not technically changing length even though the tyre is changing shape.

I would say that they cover the same distance, assuming the rubber of the tyre does not stretch with an increase in pressure and the ground is flat, then there is still the same length of rubber there.

Im guessing many people will argue either way though. anyone fancy conducting a real life test?

IMHO the only bit that matters is the distance from the centre of the hub to the ground, although I see where you're coming from, I suppose you could say as the tyre flattens it becomes less of a circle and more like a tank track?

In which case the linear velocity of the tyre must be same all the way round or it would bunch up. But this linear velocity is imparted to the tyre by the angular velocity of the wheel, at it's point of contact with the road so I reckon my formulae above still hold.

[jad]

I dont think your wrong, i just think you are saying it in a different way. your formula is correct. a smaller circumference gives a smaller distance travelled. but the change in shape of the tyre does not effect the cirumference (perimeter) of the tyre which remains the same length, whether the tyre is fully inflated, half inflated or cut in half and rolled out.

[western]

I imagine that would vary from tyre to tyre. I dont really know. 44 psi does sound high though. i run my 235/85's 28 front and 35 rear i think on my 90. Is 44 normal for a 110?

jad

for a fully loaded 110 regardless of body type the rear tyres are meant to be inflated to [LR recomend] 48psi with or without a trailer attached, so 44 could be normal for a heavily loaded 110, I run my rears at 40psi when my motorsport recovery kit is onboard.

[rtbarton]

I dont think your wrong, i just think you are saying it in a different way. your formula is correct. a smaller circumference gives a smaller distance travelled. but the change in shape of the tyre does not effect the cirumference (perimeter) of the tyre which remains the same length, whether the tyre is fully inflated, half inflated or cut in half and rolled out.

True, but it's not the circumference that matters, it's the linear speed of the circumference, which will reduce as the tyre flattens.

Going to the extreme, if you fitted the tyre round two small wheels so it became a track the distance from the centre of the driving wheel would be (say) halved so the road speed would be halved, but the perimeter of the tyre would still be the same.

[berti1554]

but the change in shape of the tyre does not effect the cirumference (perimeter) of the tyre which remains the same length, whether the tyre is fully inflated, half inflated or cut in half and rolled out.

This was my first thought too. But then the idea as quoted below came up.

True, but it's not the circumference that matters, it's the linear speed of the circumference, which will reduce as the tyre flattens.

Going to the extreme, if you fitted the tyre round two small wheels so it became a track the distance from the centre of the driving wheel would be (say) halved so the road speed would be halved, but the perimeter of the tyre would still be the same.

The first part is something that sounds logical to me but I doubt your example w/ the tracks. In tracks a sprocket is turning that doesn't change shape at all. Also, the small wheel can turn in the tire but this is not true for a tire fitted to a correct size wheel.

This thing really makes me nuts I have no idea what's correct so I'm still hoping for somebody with engineering background who is good at maths and physics too. Somebody in here

[Daan]

I reckon speed reduces with less pressure, because your effective diameter gets smaller. Your right that the circumference dont change, but what happens is that there is effectively wheelspin at the two points where the tyre goes from round to flat. This gives a lot of heat and tyre wear and that is why you shouldn't run with your tyres deflated at any decent speed on the road.

There is now a trend for energy tyres, which run with more pressure than we used to, which obviously achieves better rolling resistance. So basically, the more pressure the better for rolling ressistance.

I reckon, anyway.

Daan

[ian_s]

if you have the time and the inclination, i'd suggest deflating a tyre and measuring the circumference, then inflate the tyre and measure again.

i'd be very suprised if there is no difference between the two measurements.

how much difference there is will probably vary between tyres, depending on the construction.

i know it's a slightly different subject, but read this article on dragster tyres:

http://www.ehow.com/list_6197524_effects-torque-drag-racing-tires.html

quoting from the link above:

"Believe it or not, most drag slicks are (in effect) a sort of continuously variable transmission. While sitting still, the tires' outside circumference is fairly small but grows larger as centripetal force pushes outward on the tread. A top fuel drag slick can grow as much as 25 percent in size from the head of the track through the traps, which has a huge impact on the car's effective gear ratio."

if the circumference of those tyres can change, it stands to reason that a road tyre will be able to change too, but to a much lesser degree. i realise that it is different forces acting in this example, but it is still a force trying to push/pull the tread away from the centre of the rim.

[Maverik]

Here's my tupenth...

As rtbarton says is correct. The "effective" rolling circumferance of the wheel is changed when the tire is deflated or over inflated.

But you have to take into account that tires have a certain profile at a certain pressure, often the ideal or optimised pressure for that tire profile, i.e optimised for wear/grip etc.

The statment can be proved I guess and we all know the effects of what running woth underinflated tired has "tire with a much lower pressure turns more often over exactly the same difference as a tire that is at a higher pressure" but you have to also take into account that the ammount of pressure relative to tire profile is certaily not linear, i.e higher/overpressure tires don't get larger uniformly, they will tend to "bow" in the middle of the tred thus creating a smaller footprint pattern, but you still have the same load acting through the wheel (weight of car)...

The circumferance of the tire will change within a tolerance of pressure (small length) but with really flat tires the "deflated" circumferance (minimum it can ever be) still exists, so when it passes under the squashed bit of wheel, it must speed up to keep up with the angular velocity of the "effective" rolling circumferance, and when it gets squashed I'm sure it does all sorts of weird stuff, (stretching, contracting, cooling and heating...)

The graphic just illustrates what rtbarton was saying.

Is there any perticular reason for this question or are you just proposing it for giggles?

Mav

[nicks90]

it makes absolutely no difference what the tyre pressure is when considering the distance travelled for a given circumference.

If the circumference of the tyre is 100", it is 100" no matter what shape it is - whether it is perfectlty round or round with a big flat spot on the bottom. It still has 100" circumference. The only way to make that distance any longer or shorter is to spin the tyre or lock the tyre up at some point during its rotation.

the argument:-

IMHO the only bit that matters is the distance from the centre of the hub to the ground,

doesnt work, because you are assuming that if the hub is 1" lower to the ground it is a smaller UNIFORM circle. Mathematically this rings true, but only mathematically. As what you are proposing - by using the maths only - is that if the distance ® from hub to ground reduces from 16" to 15", you are ignoring the fact that the distance r from the hub to the TOP of the tyre remains at 16", not 15" which is what was assumed by using the standard formula for measuring circumference.

when working out distance travelled for a given tyre all that matters is the overall radius of the tyre in its natural uniform state - eg inflated and off the vehicle. Once fitted and 'squished' a bit, you cant get an accurate measurement, but the circumference remains unchanged and therefore the distance travelled remains unchanged.

ignore the bit about dragster tyres. Top fuel dragster rear tyres can be 20" wide. Under extreme centrifugal force the tyre can narrow by up to 6" and hence change the aspect ratio of the tyre and make it physically taller. eg, at standstill the tyre may be a 35"x20"x16" - at 200mph with 1500bhp streaming through them the tyre will physically change to something like 38"x16"x16". This is very different to what we are dicussing regarding tyre pressure and contact circumference, although theoretically it is possible to do with a landrover if you couls get it going fast enough and had a tyre specially made with a super flexible sidewall.

[Mr Ian]

Hi IMO Rolling rad is the only factor to consider, think of it as the effetive pitch circle diameter of the tyre. When calculating a gear ratio the PCD is used not the circumference of the gear. rtbarton has it spot on, Regards Ian

[rtbarton]

After a long think I'm with Maverick and Daan on this one.

My calculation for the rolling radius holds, but as Nick suggests, the same calculation holds for the top of the tyre, so we do have rubber going faster as it forms the footprint. This means we must get skidding and deformation of the rubber, generating stress and heat.

The tyre copes with the stress and heat due to the properties and elasticity of the rubber.

If we increase the load the footprint becomes larger so to bring it back into spec we increase tyre pressure.

If we do a lot of motorway driving the temperature and stresses increase so we increase pressure to reduce the footprint to compensate.

If we reduce the pressure to emergency soft we are probably on slippery ground so the footprint can deform easily without generating heat and we would be driving slowly anyway so not so much stress. Once we hit the tarmac we increase tyre pressure to normal so we can drive at normal speeds.

When a tyre bursts the stress and heat go way out so the tyre quickly destroys itself.

So in conclusion M'Lud, lowering the pressure will reduce the rolling radius, taking it too far will damage the tyre and keeping the pressure within manufacturer's specs won't make any practical difference.

[Range Rover Blues]

Just to chuck my hat into the ring A good few years ago it was proposed to use the rolling circumfrence, or changes in it, to detect low tyre pressures in order to build a pressure warning device.

Experiments within the department I worked in at the time demonstrated that above 5psi there was no measureable change in the rolling circumfrence unless the recomended tyre pressure was exceeded. Some car manufacturers have developed systems that work on a similar principle but how accurate they are I can't say.

the idea was to build pressure warning into the ABS I think.

Anyway, the reasoning behind the results was that the tread is the strongest most heavily constructed part of the tyre, the sidewalls are constructed to flex and stretch but unlike a ballon the tread does not get longer or wider just because you add more pressure. A tyre is more like a spoked wheel, the air inside transfers the load to the tyres plies everywhere but the contact patch, at which point they relax.

[Ruurd]

Yes it does.

The rolling circumference c = 2*pi*r

Ok fine however... a flat tire does not have a constant radius. Ok, let's allow for that by making allowances and take an educated guess. Good approach but I don't think it is a correct one.

I *DO* think that we must really consider the length of the outside of the tyre that touches the road. Does that decrease with lower pressure yes or no? As a matter of fact it might decrease but given the fact that that part of the tyre is quite stiff I think the effect is much less than expected. If we assume that the circumference of the tyre does not decrease then in fact deflating the tyre will not cause it to travel a smaller distance when turned once in respect to a fully inflated one...

The truth probably lies somewhere in the middle I'm afraid...

[rtbarton]

Ok fine however... a flat tire does not have a constant radius. Ok, let's allow for that by making allowances and take an educated guess. Good approach but I don't think it is a correct one.

I *DO* think that we must really consider the length of the outside of the tyre that touches the road. Does that decrease with lower pressure yes or no? As a matter of fact it might decrease but given the fact that that part of the tyre is quite stiff I think the effect is much less than expected. If we assume that the circumference of the tyre does not decrease then in fact deflating the tyre will not cause it to travel a smaller distance when turned once in respect to a fully inflated one...

The truth probably lies somewhere in the middle I'm afraid...

I think we covered that point above. The radius actually changes from the first point of contact (where the rubber starts compressing)with the road to final point where the tyre becomes round again (and expands to its former dimension). Taking the vertical (ie midpoint) rolling radius is going to be the mean value. The rubber has to compress and then expand as it rolls over the contact area.

Whatever the values are, a deflated tyre will have a lower rolling radius and so will cover less distance per revolution.

[berti1554]

Is there any perticular reason for this question or are you just proposing it for giggles?

Sorry for my late reply; I was very busy today...

We were talking about different gear ratios and the impact on engine speed. I got a chart from D. Ashcroft's website and posted it. Then a smart guy came up w/ the theory that the calculations and chart I got from Dave's website are not correct as I used the half dia of a tire of the above dimension

We got over 20 postings in this forum, nearly 6 pages on the German forum and I had a lot of discussion with guys over here in the US. I see some truth in both or in other words both theories make sense to me but I have not idea what's true. Anyhow, thanks for your thoughts...

[Retroanaconda]

So erm, has anyone tried testing it?

Mark a point on a tyre, the same point on the ground, then drive forwards until the point reaches the ground again and re-mark. Then measure the distance between the marks.

Do a test at the highest and lowest levels of inflation you can get away with and it should tell you something.

[berti1554]

Yes, somebody in Germany tested it. The problem there was that it was only a very small difference which could have been a measuring error too. He ran a test at 44psi.

[Daan]

No need to test this, I am running detroit locking diffs, and if there is a difference in tyre pressures left to right (it only needs to be 2 psi difference), it wont drive in a straight line. That should tell something.

Daan

[rtbarton]

No need to test this, I am running detroit locking diffs, and if there is a difference in tyre pressures left to right (it only needs to be 2 psi difference), it wont drive in a straight line. That should tell something.

Daan

Some of that could be due to the difference in grip between tyres with unequal pressures.

You really need to measure the number of revolutions, preferably over a good distance with a wide difference in the pressures to reduce the error factor.