"Rolling Radius" vs Circumference of Deflated Tyres and Tyre RPM.
Submitted: Saturday, Sep 25, 2021 at 16:13
ThreadID:
142627
Views:
8797
Replies:
12
FollowUps:
55
This Thread has been Archived
Frank P (NSW)
Being in lockdown and having plenty of time for the mind to wander I thought more about the side discussion in the space-saver spare wheel thread ....
While Zippo and others made me doubt my understanding, having thought about it more I am again convinced that deflating a tyre causes it to spin slightly faster than its fully inflated mate of the same nominal size at the same roadspeed.
Consider a tracked vehicle and its driving sprocket. The track length stays the same. For a given road speed a larger sprocket will spin slower than a smaller one to maintain the roadspeed. Ie, at a given roadspeed the RPM of the sprocket is directly related to its radius.
Now consider a tyre. The tread of the tyre is a fixed length, just like a track. As you continue to deflate a tyre, the tread with its fixed circumference becomes a little more like a track with its elongated contact patch and a little less like a perfectly round wheel . The distance from the centre of the axle to the ground is effectively the radius of the pseudo-sprocket, if I can call it that. As you deflate the tyre that radius decreases and consequently just like a tracked vehicle, to maintain a given roadspeed the wheel (sprocket) has to turn faster.
Of course the extent to which this can happen is limited by the connection of the tread to the rim by the sidewalls - they kind of get in the way (and get hot as a result) - but I think the principle is there nonetheless.
Discuss if you wish, or travel if you can. LOL
Reply By: Allan B (Sunshine Coast) - Saturday, Sep 25, 2021 at 17:46
Saturday, Sep 25, 2021 at 17:46
.
Frank,
Your tracked vehicle analagy does'nt do it for me I'm afraid. The track is no more than an interface between the sprocket and the ground. Neither its length, nor even its existence has any consequence upon the the progression of the sprocket which is simply rolling along the ground, albeit with a track interface.
A tyre has a defined circumferential length. One revolution of the wheel, and hence the tyre, moves that circumferential length along the ground by 1 unit, i.e. its length. It matters not what the shape of the tyre may be, it will retain the same circumferential length as it would if perfectly circular. Accordingly, 1 revolution should produce the same progress length regardless of a varying distance between axle and ground.
I say "should" because I know that it does not. I know that a 'flat' tyre rotates more for a given ground distance. The discrepancy, I believe, can be accounted for by compression of the flexible tyre as it is rotated by the wheel. The tyre, being more flaccid in its underdeflated state is being compressed as it is fed under the wheel thus shortening its effective length and hence its progress on the ground. Essentialy, its circumference is reduced in the same proportion as the reduction in radius.
Some of that heat you refer to is doubtless generated in this compression and recovery of the tyre as is rotates, as
well as the contribution from sidewall flexing.
Do you see any legitimacy in my thinking Frank?
AnswerID:
638068
Follow Up By: Frank P (NSW) - Saturday, Sep 25, 2021 at 18:27
Saturday, Sep 25, 2021 at 18:27
Allan,
We agree 100% on the tread length (circumference) being the constant.
The distance the tread will move the vehicle forward in one complete revolution will be the same on each side regardless of inflation because the treads are equal and fixed in length (circumference). On this we also agree.
The issue is what drives the tread to rotate. Think about a Caterpillar D9 or whatever with the driving sprocket at the top of a triangular arrangement of the track. A smaller sprocket will have to spin more to make the track complete one revolution, a larger sprocket less so.
Now consider the tyre. The driving "sprocket" is the rim and the sidewall. Deflate the tyre and the radius of the "sprocket" is reduced as the sidewall bulges and the axle gets closer to the ground. Therefore the "sprocket" has to spin more to make the tread do one complete revolution. (As the "sprocket's" axle gets closer to the ground it is a bit like the triangular track arrangement on the Cat D9, only inverted.)
So the wheel travels the same distance as its fully inflated mate on the other side, but the axle (and "sprocket") that drives it must spin more to make it happen because of its reduced effective radius.
Whether the "sprocket" is rolling or driving it makes no difference - with a deflated tyre it must increase RPM to keep up with or drive the fixed-length tread.
Is this more paradoxical than Aristotle's wheel? LOL
FollowupID:
916298
Follow Up By: Zippo - Saturday, Sep 25, 2021 at 18:41
Saturday, Sep 25, 2021 at 18:41
Allan, in my (engineer's) view you are partly correct. The analogy I prefer is the tracked vehicle. The track has a fixed circumference. Similarly the modern tyre has a belt of definitely fixed circumference, buried under the outer casing topped with tread.
On the tracked vehicle, if you fitted a 50mm block of -say- wood to each track element, what would be the change in effective circumference? My answer is NONE.
With the tyre, the overlaying tread deforms at the point whereas it is forced into contact with the road under the belt, and a similar -but opposite- deformation as it escapes from the road surface. These cancel out, the net effect of this deformation is zero creep, so the effective circumference remains dictated by the underlying belt.
This is largely unaffected by tyre inflation except in extreme situations like a flat. Have you ever observed a flat tyre being driven on very slowly? I have, and it was interesting that the tread contact area was "interrupted" - there were TWO separate contact patches, with the belt going concave between them, not what I had expected. In that scenario you will get a departure from the "constant circumference" scenario, but reductions in tyre pressure that are less dramatic (than a flat) won't alter it.
That's my 2.2c worth.
FollowupID:
916299
Follow Up By: Allan B (Sunshine Coast) - Sunday, Sep 26, 2021 at 11:18
Sunday, Sep 26, 2021 at 11:18
.
Exactly Zippo, attaching the wood blocks has raised the track but the "wheel", the sprocket, has not changed. One rotation will still propel it along the track, which is in close relation with the ground, for the same distance as before.
Bear in mind that the sprocket is a 'wheel' in itself.
On an automobile, the 'wheel' is composed of a metal centre firmly attached to an outer rubber tyre. The whole assembly is the effective 'wheel' and must be considered as such in contemplating the physics.
FollowupID:
916321
Reply By: Peter_n_Margaret - Saturday, Sep 25, 2021 at 20:31
Saturday, Sep 25, 2021 at 20:31
I have (copyright) data for the Michelin tyres that I run on the OKA.
It quotes (amongst other things) the relationship between Road Contact area (cm2), Laden Radius (mm) and Rolling Circumference (mm) when these tyres are operated at reduced pressures.
Road contact:------------- 493,,,,,541,,,,,599,,,,741.
Laden Radius:------------- 428,,,,,423,,,,,417,,, 402.
Rolling Circumference: 2820, 2810, 2800, 2760.
Conclusion? Michelin say the rolling circumference reduces with reduced pressure at the same load.
Cheers,
Peter
OKA196 motorhome
ps the extra commas and stuff was an attempt to line the numbers up :)
AnswerID:
638071
Follow Up By: Frank P (NSW) - Saturday, Sep 25, 2021 at 20:55
Saturday, Sep 25, 2021 at 20:55
Thank you Peter.
That says to me that there is a correlation between reduced tyre pressure which causes a reduced radius and therefore a reduced effective circumference.
Therefore the tyre at reduced pressure must revolve more frequently to cover the same distance as a tyre at a higher pressure given the same load, nominal size, etc.
FollowupID:
916304
Follow Up By: RMD - Saturday, Sep 25, 2021 at 22:31
Saturday, Sep 25, 2021 at 22:31
Peter,
That info is only from a small tyre company, what would they know eh? Anyone who thinks a deflated tyre doesn't revolve faster and hotter should go straight to
the Pool Room and stay there.
PS, my Corolla has Michelin tyres. and now they are not talking to me! Must be SUB standard.
FollowupID:
916307
Follow Up By: Allan B (Sunshine Coast) - Sunday, Sep 26, 2021 at 09:46
Sunday, Sep 26, 2021 at 09:46
.
So Frank, how do you account for Boobook's video clip where it shows (before your very eyes) that the distance travelled per wheel rotation did not change with decreased tyre pressure?
p.s. Please forgive delayed response. I have been off-line. Bloody NBN!!
FollowupID:
916312
Follow Up By: Briste - Sunday, Sep 26, 2021 at 10:25
Sunday, Sep 26, 2021 at 10:25
Allan - as I posted in other follow-up, "The fact that the rolling circumference doesn't change doesn't negate Frank's initial point in the original post in this thread - that an under-inflated tyre will rotate faster, because its effective radius - from the centre of the hub to the road surface - is less than the other fully-inflated tyres. That tyre tread is going to cover more distance than the others."
FollowupID:
916314
Follow Up By: Frank P (NSW) - Sunday, Sep 26, 2021 at 10:51
Sunday, Sep 26, 2021 at 10:51
Allan, I never disputed the circumferential thing. The tank track analogy I used supports it. What I am trying to come to terms with is the rotational speed of the axle supporting a deflated tyre. Is there a difference between that and its mate on the other side supporting a fully inflated tyre?
Let me ask you a question.
Given the video and our agreement on same, how do those OEM built-in tyre pressure warning systems (ie, those without actual pressure sensors) work?
PS Forgiven. I, too, have been subject to the vagaries of NBN. 12 weeks Nov '20 to Jan '21 and intermittently this year.
FollowupID:
916319
Follow Up By: Allan B (Sunshine Coast) - Tuesday, Sep 28, 2021 at 13:51
Tuesday, Sep 28, 2021 at 13:51
.
Yes Frank, I have no doubts that a wheel not fully inflated must rotate faster than its fully inflated mate on the other end of the axle. And that is demonstrated by the successful operation of the inferential TPMS systems which operate by sensing the rotation of each tyre and performing a comparison. I suspect that the difference in effective 'rolling radius' is not great with inflation change but enough to be sensed and resolved.
Boobook's video presentation, which aims to demonstrate that an under-inflated tyre rolls the same distance as a fully inflated one, fails to convince as it is performed over one rotation only which is insufficient sampling data for the required accuracy. As I said above, the differentiation is not great and more rotations would be needed to resolve the issue. I suspect also that the significance may vary between a slowly rolling tyre and one travelling at speed with dynamic forces at play. But if so, I could not hope to predict in what way or magnitude. Just a suspicion, as dynamics often do modify the the simple geometrical reasoning.
FollowupID:
916380
Reply By: Allan B (Sunshine Coast) - Sunday, Sep 26, 2021 at 10:44
Sunday, Sep 26, 2021 at 10:44
.
A flaw in reasoning of this subject is that the tyre is being treated as a circle when it is not. Not when distorted by a laden vehicle.
The formula of c=2*pi*r is for application to a circle, a perfect circle. A distorted tyre is a not a 'circle' so that formula cannot be applied.
A tyre attached to a wheel has a given perimeter length, even when distorted by load. If the supporting wheel is rotated by one turn, then the tyre's perimeter will describe a distance equal to its perimeter length, regardless of its deviation from a perfect circle. This surely is obvious by observation not by conjecture.
Using the formula based on 'r' is a notion based on that formula for a circle when it is not.
Frank's caterpillar track analogy is false in that the sprocket is not 'attached' to the track which is simply an interface between the sprocket and ground. One turn of the sprocket does not produce one rotation of the track as is the case with a tyre affixed to a wheel. The sprocket rolls along the track as if it were on the ground and being a 'perfect circle' the c=2*pi*r can be applied to this case.
So how does the TPMS sensing based on tyre rotation work? Dunno, I'm still working on that!
AnswerID:
638082
Follow Up By: Frank P (NSW) - Sunday, Sep 26, 2021 at 11:34
Sunday, Sep 26, 2021 at 11:34
From the link in Michael H9's post immediately above about VW's indirect tyre pressure warning system:
"The tire pressure monitoring system looks at the ABS wheel speed sensors and uses that
information to track the rotational speed of the tires. Any time a tire has lower pressure, it will roll at a different number of revolutions per mile than tires that have the correct tire pressure. If one tire’s rotational speed seems off compared to the rest, the TPMS will alert the driver that one of the tires has low pressure."
If we forget Dieselgate and accept this then how can it be reconciled with the fixed tread length argument?
The only variable as the tyre deflates is the radius of the rotating parts - the vertical distance from the contact patch to the axle. For the rotating parts with a smaller radius of rotation to cover the same distance, which is controlled by the fixed circumference of the tread, they MUST rotate more - a fact that VW uses in its indirect TPMS.
So if the wheel is doing more rotations and the tyre is of fixed circumference and therefore ostensibly travelling further, what is happening to the extra distance that the tyre should be travelling but is not because it is fixed to the vehicle that is being "held back" by three (or more) normally inflated tyres?
Perhaps that distance is simply lost to the tyre scrubbing or slipping on the road, which shows up as accelerated wear of the tyre.
FollowupID:
916323
Follow Up By: Briste - Sunday, Sep 26, 2021 at 12:59
Sunday, Sep 26, 2021 at 12:59
I only got into this thread because of my experience with the run-flat warnings on vehicles with RFT but no TPMS. Believe me, these systems work, that's why manufacturers use them as a poor man's TPMS. Under-inflated tyres rotate faster.
Why is that? If we had a mechanical engineer here to sort us out, like Allan_B does for electrical matters, then we wouldn't be having this classic online slugfest. Without that, everyone is going to have to come to their own understanding of why this is. I'm with Frank. Reduced effective radius. YMMV (pun intended).
FollowupID:
916325
Follow Up By: Allan B (Sunshine Coast) - Sunday, Sep 26, 2021 at 13:08
Sunday, Sep 26, 2021 at 13:08
.
Yes Frank, I agree that 'inferential' TPMS using wheel rotation sensing does work.
Because of this, I cannot ignore that a deflated tyre with unchanged circumference rotates faster than its fully inflated mates.
But I cannot accept that the measured distance from the hub to the ground surface (rolling radius) can unconditionally be seen as a radius in simple c=pi*2r computation of a circumference.
Surely, if you were to dismantle a tyre such as to enable the tread (circumference) to be laid out straight on the ground then that would be the distance that the vehicle would travel with one revolution of a wheel.
I am missing something but cannot see it! Think I'll go and take my pills!
FollowupID:
916326
Follow Up By: RMD - Sunday, Sep 26, 2021 at 14:08
Sunday, Sep 26, 2021 at 14:08
We all recognize that the tread length remains the same if partially deflated, and many know the wheel rotates faster, to keep up, with opposite side. However, it seems many will not recognize that as deflation increases, so does the degree of tyre squirm and deformation and tread scrubbing at the road surface as the tread length is forced to slip and abrade past the road surface. With this squirm the heat increases/rises at an alarming rate. Maybe it doesn't happen with American TIRES but it happens with Australian TYRES. The tread buckles up in the centre in relation to the now lower sidewalls, that constant tread deformation has to occur for the wheel to rotate faster "cos the sidewalls are lower.
Q, why does a flatish tyre begin to make two parallel scrublines and the tread isn't touching much at all. Run a partially deflated tyre over a flat section of clay and you will see. Anyone been offroad and hit mud or clay with lower pressure would know. Perhaps they don't!
FollowupID:
916327
Follow Up By: Allan B (Sunshine Coast) - Sunday, Sep 26, 2021 at 14:15
Sunday, Sep 26, 2021 at 14:15
.
OK, I took my pills and am now convinced that I have the answer.
As the tyre rotates and a given section makes contact with the road, it dynamically changes from being an arc (curved section of circle) and becomes a chord (straight line connecting two points on a circle). This chord is shorter than an arc joining those same two points therefore the circumference is shortened. If the circumference is shortened then the forward progress of the axle will be less per rotation of a wheel of perfect circle shape (no flat section as bottom). Or conversely, the wheel will need to rotate faster for a given progress.
This shortening of the circumference is only accomplished by compression of a section of the tyre (the flat bit in contact with the road). This constant compression/relaxation will generate heat which contributes to that being generated bu sidewall flexing.
This proposition satisfies all (sensible) argument. Yes, the 'effective radius' (dislike 'rolling radius') changes and yes the actual circumference changes. "Everybody wins a prize"!!!
FollowupID:
916328
Follow Up By: Frank P (NSW) - Sunday, Sep 26, 2021 at 14:24
Sunday, Sep 26, 2021 at 14:24
Allan,
I wrote a follow-up to yours (916326) above. It was along the lines of RMD's content (Follow-up 916327) about tyre squirm absorbing or partially absorbing the increased RPM, but you posted the above which, along with RMD's, makes my contribution redundant so I deleted it.
I had not considered the arc-chord thing and doubt that I would have got to it. As with all good engineering solutions, it is simple!
An interesting discussion, thanks for hanging in there!!
FollowupID:
916330
Follow Up By: Allan B (Sunshine Coast) - Sunday, Sep 26, 2021 at 15:08
Sunday, Sep 26, 2021 at 15:08
.
Frank,
I had said in Reply 638068 above that "The discrepancy (in circumference), I believe, can be accounted for by compression of the flexible tyre as it is rotated by the wheel". I realised that could be the only explanation but had not at that time reasoned it scientifically. It really was staring us in the face.
FollowupID:
916331
Follow Up By: RMD - Sunday, Sep 26, 2021 at 16:53
Sunday, Sep 26, 2021 at 16:53
Mathematically, if you think that way, but tyres are not mathematical at all, they are flexible. To the eye it may seem as a chord at road surface but, it sure isn't and that chord line will be a fluctuating suddenly with a severe induced S bend of sorts. The rubber has to go somewhere in that instant trip under the rim. If you cut a tyre open in the tread after a deflation failure you will see the belt has been severely massaged and it was hot and delaminated.
The flapping your may hear on some isn't the sidewall, it is the tread doing Yoga under the rim. If it doesn't recover before the road hits it again then the flapping is more.
FollowupID:
916335
Reply By: Member Kerry W (Qld) - Tuesday, Sep 28, 2021 at 13:55
Tuesday, Sep 28, 2021 at 13:55
Thinking out loud here...
One thing which would be interesting to consider - In lowering the profile of the wheel, generally, by deflating the tyre. Is there a (significant) increase in the power/torque being delivered. Or rather what is the increase?
If so, is this a trade off/implication in the distance the tyre covers or doesnt cover during a single rotation compared to a fully inflated tyre?
A few of the laws of physics need to be considered but I'm guessing/hoping someone else has the time to consider from this point of view...
The maths involved is a bit over my pay grade but I can see there are more factors involved than just distance travelled.
AnswerID:
638111
Follow Up By: RMD - Tuesday, Sep 28, 2021 at 14:25
Tuesday, Sep 28, 2021 at 14:25
Kerry
All depends if it is a front wheel free rotating or a driven rear wheel providing traction force forward.
Flat but free it will soak up power, On the rear it will be using power/torque at a certain rate to create heat and noise and the additional rotation is provided by differential action, where the crownwheel and carrier is going faster than the deflated side and slower than the inflated side. The differential gives and takes, ie directly proportional.
Net feeling with one wheel deflated is, engine RPM same, but some loss of forward speed.
FollowupID:
916382
Follow Up By: Member Kerry W (Qld) - Thursday, Sep 30, 2021 at 09:46
Thursday, Sep 30, 2021 at 09:46
Yes RMD I agree RPM same but less foward speed theoretically more power available....Interesting RMD that you mentioned the freewheeling tyre - I thought I explained
well enough. The deflated wheel(s) being driven "should" or could display an increase in torque/power/gearing being delivered in proportion to the reduction in diameter. Just as changing tyre size affects gearing and torque. It is simply a question to ponder....largely irrelevant but none the less an interesting question for those above who have taken an interest in the physics involved.
thanks for your thoughts.
FollowupID:
916436
Reply By: Geoff (Newcastle, NSW) - Tuesday, Sep 28, 2021 at 16:15
Tuesday, Sep 28, 2021 at 16:15
There must be some relationship between tyre pressure and rotation.
The reason I say this is my mate bought a new VW Toureg back in the early 5cyl diesel days.
One of the dealer fitment software options was a tyre abnormality warning. You paid your money, the dealer was issued a code by VW and the dealer entered that into the Toureg's plastic brain. It could be added any time in the vehicles life.
Once done you had VW's TPMS option.
The only way my mate and I could see for this to work using the vehicles existing array of sensors was the ABS ring.
As I said, there appears some form of measurable differing relationship between a correctly inflated tyres speed of rotation and an underinflated tyres speed of rotation.
| Geoff,
Landcruiser HDJ78,
Grey hair is hereditary, you get it from children. Baldness is caused by watching the Wallabies.
Lifetime Member
My Profile My Blog Send Message |
AnswerID:
638113
Follow Up By: RMD - Tuesday, Sep 28, 2021 at 19:12
Tuesday, Sep 28, 2021 at 19:12
G'day Geoff.
First hand you have seen the reality of it all. Good to see users know what is the reason. It seems though, many people have infinitely more knowledge than ALL the world car companies who use ABS rings etc to
check rotation speed and report, if difference is more than the full tread wear depth.
Definitely smart some of those Aussies.
FollowupID:
916392