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.
"When one man dies it's a tragedy. When thousands die it's statistics."
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.
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.
But the circumference does not increase when the radius where
the wheel touches the ground reduces significantly and visibly.
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
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).
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,
"I am inclined to tell the truth and dislike people who lie consistently.
This makes me unfit for the company of people of a Left persuasion, and
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.
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.
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.
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
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 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)?
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.
reply-to address is (intended to be) valid
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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