Accuracy of cycle computers

[Ambrose Nankive]

In news:[email protected],
Dr Curious <[email protected]> typed:
> "Doctor J. Frink" <[email protected]> wrote in
> message news:[email protected]...
>> On Tue, 15 Jun 2004 13:45:16 +0100, Dr Curious
>> <[email protected]> wrote:
>>> So the outside circumference of an inflated tyre is
>>> larger than that of a flat tyre is it?
>>>
>>> Curious
>>
>> Take bike.
>>
>> Deflate front tyre.
>>
>> Wheel descends to floor to rest on rim.
>>
>> Note distance r_flat from hub to floor (ie the radius of
>> the circle that we would be rolling on).
>>
>> Pump up tyre.
>>
>> Wheel rises from floor as tyre inflates.
>>
>> Note distance r_inflated from hub to floor (ie the radius
>> of the circle that we would be rolling on).
>>
>> You'll find that r_inflated > r_flat.
>>
>> The actual circumference of the tyre itself may not
>> change but the effective wheel radius does, and that's
>> what we're really measuring (ok, labelling it
>> Circumference wasn't totally accurate but it's close
>> enough).
> I'm sorry but this all totally irrelevant.
>
> The radius of the wheel is irrelevant.
>
> When a tire is flat, all this means is that the wheel/tyre
> is no longer circular. It's now a part circle with a flat
> at the bottom. And so there's more surface area in contact
> with the ground. But the actual outside circumference
> remains exactly the same. It wouldn't even matter if you
> were riding on oval wheels. All you ever need measure are
> the number of revolutions multiplied by the circumference
> of the tyre.

The thing is that the squashing causes the tyre to slip
slightly, so it does actually follow the path of a circle of
the effective radius of the wheel. So it's not irrelevant.

In general it's better to be right before you call other
people's reasoning irrelevant.

A

 

[Mike Dodds]

> > (circumferance) to 2180 for a 700 x 38. I then did my
> > usual morning
commute
> > and found that instead of 6.35 miles the distance shown
> > was 6.27 miles
or
> > abotu 100 yards less.
> >
> > That must entirely down to my weight bearing down on the
> > rear tyre
(assuming
> > both computers can count and calculate correctly. The
> > Astale 8 magnet is
on
> > the rear wheel, but the Halfords magnet is on the front
> > wheel.
>
> As has already been mentioned (I think), the front wheel
> actually does go slightly further than the rear. Ride
> through a puddle and it will be very obvious. Weight
> distribution may also make a difference, I have not
> thought about their relative magnitudes.
>

But in this case the computer showed that the front wheel
did less... I think....

Previously I'd been wondering if it was rounding errors in
the calculations of one, but I think it more likely to be
the additional compression of the rear tyre.

Mike

 

[Doctor J. Frink]

On Tue, 15 Jun 2004 15:57:29 +0100, Mike Dodds
<[email protected]> wrote:

>But in this case the computer showed that the front wheel
>did less... I think....
>
>Previously I'd been wondering if it was rounding errors in
>the calculations of one, but I think it more likely to be
>the additional compression of the rear tyre.

The rear wheel, being the drive wheel, may slip more than
the front one. Hence the computer detects a certain
number of revolutions and records that exaggerated
distance whilst the front wheel just rolls along
recording fewer revolutions. How much of a difference
this makes will depend on surface, grip etc. Might be
bugger all for all I know ;0).

I suspect there are many factors at play that affect the
assumption of "wheel goes round once, we've gone C metres".

Frink

--
Doctor J. Frink : 'Rampant Ribald Ringtail' See his mind
here : http://www.cmp.liv.ac.uk/frink/ Annoy his mind here :
pjf at cmp dot liv dot ack dot ook "No sir, I didn't like
it!" - Mr Horse

 

[Pete Biggs]

Dr Curious wrote:

.............
> I'm sorry but this all totally irrelevant.
>
> The radius of the wheel is irrelevant.
>
> When a tire is flat, all this means is that the wheel/tyre
> is no longer circular. It's now a part circle with a flat
> at the bottom.

But it's not just flat at that one point of the tyre for the
revolution. The tyre is flatter throughout the whole
revolution so it's effectively smaller when ridden. Have you
noticed that tyres are squashy things?

> And so there's more surface area in contact with the
> ground. But the actual outside circumference remains
> exactly the same. It wouldn't even matter if you were
> riding on oval wheels. All you ever need measure are the
> number of revolutions multiplied by the circumference of
> the tyre.

It's fun when people can't get their head round this one.
You're wrong mate.

It doesn't matter what the actual circumference of the tyre
tread is because you're not riding that distance per wheel
revolution. You're riding on the point where the tyre is
being compressed to. The rest of the tyre's resting outer
position is irrelevant. You are NOT riding on an oval wheel
or a wheel that is effectively oval. The wheel is
/effectively/ round, just oval at any one point in time.
Distance as a concept doesn't exist in any one point in
time. We're only concerned about distance travelled in one
wheel revolution here not the actual length of your tread.
You're not riding on the whole of the tread at once. It's
where it goes that counts.

Imagine an exaggerated case: a tiny wheel with a huge soft
tyre, even a totally flat tyre; or wheels with loose floppy
caterpillar track. Are you travelling the length of that
track once per wheel revolution?

~PB

 

[Mark Tranchant]

Simon Brooke wrote:

> This really is not an issue. Both the seven year old
> wireless computers on my bikes are still on their first
> batteries.

Wow! I assume they stopped working about six years
ago, then? ;-)

What computers are these? My VDO Cytec C10+ is excellent,
but needs new batteries annually.

--
Mark.

 

[dazzle96]

Originally posted by Pete Biggs
FranklynMint wrote:
> Greetings fellow cyclists I have a mid-price cycle
> computer, which is set up according to instructions (double-
> checked and triple checked). On a long ride, recently
> (recommended by a friend, who said it was about 40+ miles,
> he hadn't measured it) i was quietly impressed by the
> distace i rode, which was longer than he'd said. But
> looking at a map later, I thought something was amiss. I
> reckon that the computer is about 1 mile out every 15. Is
> that par for the course with these gadgets? I'm not
> interested in measuring to the millimetre, nor do I have
> more than a passing interest in the average speed, etc,
> but it's nice to have an idea of how far you've done.
> Arrivederci FM

Modern cycle computers tend to be as accurate as each other
so don't worry about the model. Just make sure it's working
and that the tyre circumference setting is correct. The
result will be true.

Bike ride distances will be greater than map measurements
because you can't measure all the bends properly on a normal
map, and all the little micro-turns and wobbles add up.

~PB

Map distances will always be shorter also because of gradients. Your wheel will measure the slope distance which will inevitably be geater than plan distance

 

[davek]

dazzle96:
>Your wheel will measure the slope distance which will inevitably be geater than plan distance

Good point. One of those [few] occasions where Pythagoras comes in handy.

d.

 

[Dr Curious]

"Doctor J. Frink" <[email protected]> wrote in message
news:[email protected]...
> On Tue, 15 Jun 2004 14:38:03 +0100, Dr Curious
> <[email protected]> wrote:
> >
> >The radius of the wheel is irrelevant.
> >
> >When a tire is flat, all this means is that the
> >wheel/tyre is no longer circular. It's now a part circle
> >with a flat at the bottom. And so
there's
> >more surface area in contact with the ground. But the
> >actual outside circumference remains exactly the same. It
> >wouldn't even matter if you were riding on oval wheels.
> >All you ever need measure are the number of revolutions
> >multiplied by the circumference of the tyre.
>
> Sorry, but that's wrong for these measurements. Try it!
> Take a bike, do a rolling test (unloaded) a few times,
> measure the distance covered. Deflate the tyre until it
> deforms significantly. Do the rolling test again. You get
> different results.
>
> A severe test I just did (with a pumped and ~75% deflated
> tyre so it's deformed but not squishing about) made a
> difference of a few cm on just one revolution. It's likely
> to be less in real world conditions but it's still going
> to be a few mm out.
>
> I'm probably backtracking, but it's not really the
> absolute circumference we're interested in, it's how
> far the bike goes for one revolution of the wheel the
> sensor is attached to (ie the effective circumference)
> and that distance definitely (and I've physically
> proved it to myself) depends on tyre pressure/load.
> We're dealing with real things that deform here, not
> pure mathematical models.
>
> Frink

...

With a tyre which is fully inflated, unless the bike is
being ridden around a banked track etc the area in contact
with the the ground i.e the effective circumfreance will be
a 3mm strip running down the centre of the tyre. This is
simply becuase the tyre is rigid. So if the tyre is opened
up it this will form a straight line running down the middle
of the tyre.

When a tyre is soft the area in contact with the ground may
be a 25 + mm strip across the width of the tyre. And the
effective circumferance will be the mid point of this strip.
Because the tyre is no longer rigid, and so can roll, this
strip and thus the midpoint can meander sideways. So that if
the tyre was opened up it would form a slight snaking
pattern. And thus the effective circumference would indeed
be marginally longer.

Oops!

This would probably be more pronounced on the back wheels
where the effect of the riders shifting weight could be
expected to have more side to side impact, while not being
so immediately noticeable. On the front wheel where the
sensor is situated, any such rolling motion would probably
be noticeable straightaway in its effects on the steering.

That's my story anyway.

Curious

...

>
> --
> Doctor J. Frink : 'Rampant Ribald Ringtail' See his mind
> here : http://www.cmp.liv.ac.uk/frink/ Annoy his mind here
> : pjf at cmp dot liv dot ack dot ook "No sir, I didn't
> like it!" - Mr Horse

 

[Dr Curious]

"Ambrose Nankivell" <[email protected]> wrote in
message news:[email protected]...
> In news:[email protected], Dr Curious
> <[email protected]> typed:
> > "Doctor J. Frink" <[email protected]> wrote in
> > message news:[email protected]...
> >> On Tue, 15 Jun 2004 13:45:16 +0100, Dr Curious
> >> <[email protected]> wrote:
> >>> So the outside circumference of an inflated tyre is
> >>> larger than that of a flat tyre is it?
> >>>
> >>> Curious
> >>
> >> Take bike.
> >>
> >> Deflate front tyre.
> >>
> >> Wheel descends to floor to rest on rim.
> >>
> >> Note distance r_flat from hub to floor (ie the radius
> >> of the circle that we would be rolling on).
> >>
> >> Pump up tyre.
> >>
> >> Wheel rises from floor as tyre inflates.
> >>
> >> Note distance r_inflated from hub to floor (ie the
> >> radius of the circle that we would be rolling on).
> >>
> >> You'll find that r_inflated > r_flat.
> >>
> >> The actual circumference of the tyre itself may not
> >> change but the effective wheel radius does, and that's
> >> what we're really measuring (ok, labelling it
> >> Circumference wasn't totally accurate but it's close
> >> enough).
> > I'm sorry but this all totally irrelevant.
> >
> > The radius of the wheel is irrelevant.
> >
> > When a tire is flat, all this means is that the
> > wheel/tyre is no longer circular. It's now a part circle
> > with a flat at the bottom. And so there's more surface
> > area in contact with the ground. But the actual outside
> > circumference remains exactly the same. It wouldn't even
> > matter if you were riding on oval wheels. All you ever
> > need measure are the number of revolutions multiplied by
> > the circumference of the tyre.
>
> The thing is that the squashing causes the tyre to slip
> slightly, so it does actually follow the path of a circle
> of the effective radius of the wheel. So it's not
> irrelevant.

...

Leaving aside the validity of that particular line of
reasoning would you kindly explain how the radius of the
wheel is in any way relevant to measuring the circumferance?

...

>
> In general it's better to be right before you call other
> people's reasoning irrelevant.
>
...

When you've provided an answer to the above question
you'll be better placed to demonstrate just who's
reasoning is relevant.

And who's isn't.

Curious

...

 

[Ambrose Nankive]

In news:[email protected],
Dr Curious <[email protected]> typed:
> Leaving aside the validity of that particular line of
> reasoning would you kindly explain how the radius of the
> wheel is in any way relevant to measuring the
> circumferance?

Well, the distance travelled by a wheel is equal to the
height of the axle (the radius) multiplied by 2 pi. If the
wheel was moving in a shape other than a circle, this
wouldn't be true, but it is.

If the bike were travelling the distance of the length
around the unsquashed rubber, then the tyre would have to be
rotating slower than the wheel, which would mean it slipped
round. What happens is that the rubber slips a bit between
the point where it contacts the ground and the point where
it is bearing the full weight. I could draw diagrams to show
this but it would be quite an involved thing to do, so I'm
afraid I can't make it any clearer than tat.

A

 

[Dr Curious]

"Ambrose Nankivell" <[email protected]> wrote in
message news:[email protected]...
> In news:[email protected], Dr Curious
> <[email protected]> typed:
> > Leaving aside the validity of that particular line of
> > reasoning would you kindly explain how the radius of the
> > wheel is in any way relevant to measuring the
> > circumferance?
>
> Well, the distance travelled by a wheel is equal to the
> height of the
axle
> (the radius) multiplied by 2 pi. If the wheel was moving
> in a shape other than a circle, this wouldn't be true,
> but it is.

...

Yes indeed. With you so far. If there was no tyre on the
wheel this would be true.

...

>
> If the bike were travelling the distance of the length
> around the
unsquashed
> rubber, then the tyre would have to be rotating slower
> than the wheel,

...

No sorry. Once you put a tyre on the wheel all bets are off.
The rim without a tyre you mentioned before is a totally
differnt thing altogether.

There is no longer any "wheel" for the tyre to be rotating
slower than.

Now you've got a wheel with a tyre (fairly) firmly
attached to it.

...

> would mean it slipped round. What happens is that the
> rubber slips a bit between the point where it contacts the
> ground and the point where it is bearing the full weight.

...

It may indeed roll sideways but that isn't what you seem to
be talking about. Are you claiming that the tyres slowly
rotate, around the rim?

...

> I could draw diagrams to show this but it would be quite
> an involved thing to do, so I'm afraid I can't make it any
> clearer than tat.
>
> A

...

Fair enough.

Curious

...

 

[Peter Fox]

Following on from FranklynMint's message. . .
>thought something was amiss. I reckon that the computer is
>about 1 mile out every 15. Is that par for the course with
>these gadgets? I'm not
In themselves extremely accurate. If you tell it 2031 pulses
then it registers exactly 2031 pulses. (May not apply to
cordless - I wouldn't know.)

Quite simply you have to sit on the bike and measure one
or more wheel revolutions on the ground. You should get
1%-2% accuracy.

--
PETER FOX Not the same since the deckchair business folded
[email protected]
www.eminent.demon.co.uk/wcc.htm Witham Cycling Campaign
www.eminent.demon.co.uk/rides East Anglian Pub cycle rides

 

[Ambrose Nankive]

In news:[email protected],
Dr Curious <[email protected]> typed:
> "Ambrose Nankivell"
> <[email protected]> wrote in
> message news:[email protected]...
>> would mean it slipped round. What happens is that the
>> rubber slips a bit between the point where it contacts
>> the ground and the point where it is bearing the full
>> weight.
>
> It may indeed roll sideways but that isn't what you seem
> to be talking about. Are you claiming that the tyres
> slowly rotate, around the rim?

No, that they slowly slip on the ground. It'd be obvious
if you had a completely flat car tyre to hand, but apart
from that it's a bit difficult to think of an experiment
to show it.

A

 

[Dr Curious]

"Ambrose Nankivell" <[email protected]> wrote in
message news:[email protected]...
> In news:[email protected], Dr Curious
> <[email protected]> typed:
> > "Ambrose Nankivell"
> > <[email protected]> wrote in
> > message news:[email protected]...
> >> would mean it slipped round. What happens is that the
> >> rubber slips a bit between the point where it contacts
> >> the ground and the point where it is bearing the full
> >> weight.
> >
> > It may indeed roll sideways but that isn't what you seem
> > to be talking about. Are you claiming that the tyres
> > slowly rotate, around the rim?
>
> No, that they slowly slip on the ground. It'd be obvious
> if you had a completely flat car tyre to hand, but apart
> from that it's a bit
difficult
> to think of an experiment to show it.

...

So the idea of letting air out of the tyres in order to
increase traction in unfavourable conditions is totally
wrong then?

I must admit that I don't keep up with this stuff but if you
intend to cite some recently published paper fron some
obscure Research Institute establishing precisely that
point, then I believe I have the right to a reference of
some kind.

Curious

...

>
> A

 

[Chris Malcolm]

Ian G Batten <[email protected]> writes:

>In article <[email protected]>,
>FranklynMint <[email protected]> wrote:
>> Greetings fellow cyclists I have a mid-price cycle
>> computer, which is set up according to instructions (double-
>> checked and triple checked). On a long ride, recently
>> (recommended by a friend, who said it was about

>> But looking at a map later, I thought something was
>> amiss. I reckon that the computer is about 1 mile out
>> every 15.

>Over ten miles this morning mine agreed to within about
>0.05 miles (~100 yards) with the GPS box I had clipped to
>the handlebars. Given they're measuring different things in
>different ways, given I was running the GPS at a slow
>update rate and given the fact that the computer had
>recorded 100 yards _more_ I'd say that's about bang on. The
>more is reassuring, as the GPS box will be measuring a
>succession of short chords to the route.

I tested mine over several 3 mile journeys by comparing it
to GPS distance readings, and got a similar result -- error
always less than 1%.
--
Chris Malcolm [email protected] +44 (0)131 651 3445 DoD #205
IPAB, Informatics, JCMB, King's Buildings, Edinburgh, EH9 3JZ, UK
[http://www.dai.ed.ac.uk/homes/cam/]

 

[FranklynMint]

Tell you what....I'll make sure to keep my tyres pumped up, shall I?
;-)

 

[Doctor J. Frink]

On Tue, 15 Jun 2004 18:45:00 +0100, Dr Curious <[email protected]> wrote:
>
>"Ambrose Nankivell"
><[email protected]> wrote in
>message news:[email protected]...
>>
>> No, that they slowly slip on the ground. It'd be obvious
>> if you had a completely flat car tyre to hand, but apart
>> from that it's a bit
>difficult
>> to think of an experiment to show it.
>
>So the idea of letting air out of the tyres in order to
>increase traction in unfavourable conditions is totally
>wrong then?

Depends who you ask but some people swear by it (others
don't but I'm not getting into that!)

The two principles of a lower tyre rolling radius involving
some slip and increasing traction by reducing pressure
aren't mutually exclusive. The amount of slip could be
insignificant compared to the increase in traction from
surface area and the softer tyre moulding to the floor
contours. Remember that for a normal (bike) situation we're
probably talking ~1% per revolution (pressure and load
dependent) which isn't going to degrade grip by much, but
over thousands of revolutions will add up to a systematic
effect on odometer readings *on top* of other errors.

Anyway, do a Google for ``tyres "rolling radius" odometer''
and you'll see it's not a new idea that the rolling radius
of your tyre (height of wheel centre from bottom edge of
tyre, *not* the actual tyre circumference) and its effect on
odometers is not new and not limited to bikes. Or just
perform the bike tyre experiment I outlined in a previous
post and see it for yourself (if you do it on a shiny
surface like I did you can *hear* the tyre slipping and
squeaking but that's an exaggerated case).

Try it. You have a bike (and a pump ;0).

Frink

--
Doctor J. Frink : 'Rampant Ribald Ringtail' See his mind
here : http://www.cmp.liv.ac.uk/frink/ Annoy his mind here :
pjf at cmp dot liv dot ack dot ook "No sir, I didn't like
it!" - Mr Horse

 

[Doctor J. Frink]

On Tue, 15 Jun 2004 18:32:09 GMT, FranklynMint
<[email protected]> wrote:
>Tell you what....I'll make sure to keep my tyres pumped up,
>shall I? ;-)

Best all round I think ;0).

Frink

--
Doctor J. Frink : 'Rampant Ribald Ringtail' See his mind
here : http://www.cmp.liv.ac.uk/frink/ Annoy his mind here :
pjf at cmp dot liv dot ack dot ook "No sir, I didn't like
it!" - Mr Horse

 

[Dr Curious]

"Doctor J. Frink" <[email protected]> wrote in message
news:[email protected]...
> On Tue, 15 Jun 2004 18:45:00 +0100, Dr Curious
> <[email protected]>
wrote:
> >
> >"Ambrose Nankivell"
> ><[email protected]> wrote in
> >message news:[email protected]...
> >>
> >> No, that they slowly slip on the ground. It'd be
> >> obvious if you had a completely flat car tyre to hand,
> >> but apart from that it's a bit
> >difficult
> >> to think of an experiment to show it.
> >
> >So the idea of letting air out of the tyres in order to
> >increase traction in unfavourable conditions is totally
> >wrong then?
>
> Depends who you ask but some people swear by it (others
> don't but I'm not getting into that!)
>
> The two principles of a lower tyre rolling radius
> involving some slip and increasing traction by reducing
> pressure aren't mutually exclusive.

...

I'm sorry but I must beg to differ. "Slip" and "traction"
are indeed mutually exclusive.

...

> The amount of slip could be insignificant compared to the
> increase in traction from surface area and the softer tyre
> moulding to the floor contours.

...

If the soft tyre moulds itself to the floor contours, as you
admit, then that makes it less likelty to slip than a fully
inflated tyre.

...

> Remember that for a normal (bike) situation we're probably
> talking ~1% per revolution (pressure and load dependent)
> which isn't going to degrade grip by much, but over
> thousands of revolutions will add up to a systematic
> effect on odometer readings *on top* of other errors.

...

Which phenomenon are you referring to here ? The ~l% per
revolution of slip that isn't going to occur anyway
because the soft tyre more easily molds itself to the
floor contours?

...

>
> Anyway, do a Google for ``tyres "rolling radius"
> odometer'' and you'll see it's not a new idea that the
> rolling radius of your tyre (height of wheel centre from
> bottom edge of tyre, *not* the actual tyre
> circumference) and its effect on odometers is not new
> and not limited to bikes.

...

You've succeeded insofar as I've been induced to consult
one or two sources with repect to rolling radii in car
tyres. First up the rolling radius is used simply as an
easier method of calculating the circumferance of tyres
which are known to be perfectly round. According to these
"experts" anyway - the rolling radius in car tyres is
affected by two factors -

" Because of this, bias-ply tires that increase their
rolling radius on the road,
largely_through_centrifugal_force
which_makes_them_grow_larger at higher speeds, are not
preferred for serious rallying. Also, as a tire
heats_up_with_use, and the temperature within the tire
increases, so will the
tire_pressure,_further_increasing_the_tire_radius."

http://www.jcna.com/library/rally/chapter5.html

Neither of which factors are of any relevance here, I hope
you'll agree.

So that basically I'm suggesting that rolling radius is only
of use, as a shortcut to calculation the circumferance in
wheels which are known to be perfectly round. And that
otherwise its of no use whatsoever in respect of wheels
which aren't round. i.e flat or partially inflated. So it
isn't the case that a flat tyre has a reduced rolling
radius, more a case that by virtue of its being flat, roling
radius is no longer an appropriate maeasurement. Phew!

...

> Or just perform the bike tyre experiment I outlined in a
> previous post and see it for yourself (if you do it on a
> shiny surface like I did you can *hear* the tyre slipping
> and squeaking but that's an exaggerated case).
>
> Try it. You have a bike (and a pump ;0).

...

Yeah sure! The experiment troll. Did you know mobile phones
work under water as well? Anyway. Oh yes. One practical
difficulty with all such tests is to keep the bike perfectly
straight. The simplest way presumably would be to lock the
steering. This would render the bike unrideable to all
intents and purposes and so the effects of a rider shifting
their weight over the back wheel and causing tyre roll would
need to be simulated with weights. So anyway, you first!

Curious

>
> Frink
>
> --
> Doctor J. Frink : 'Rampant Ribald Ringtail' See his mind
> here : http://www.cmp.liv.ac.uk/frink/ Annoy his mind here
> : pjf at cmp dot liv dot ack dot ook "No sir, I didn't
> like it!" - Mr Horse

 

[Doctor J. Frink]

On Tue, 15 Jun 2004 20:51:04 +0100, Dr Curious
<[email protected]> wrote:
>
>"Doctor J. Frink" <[email protected]> wrote in
>message news:[email protected]...
>
>> Or just perform the bike tyre experiment I outlined in a
>> previous post and see it for yourself (if you do it on a
>> shiny surface like I did you can *hear* the tyre slipping
>> and squeaking but that's an exaggerated case).
>>
>> Try it. You have a bike (and a pump ;0).
>
>Yeah sure! The experiment troll. Did you know mobile phones
>work under water as well? Anyway. Oh yes. One practical
>difficulty with all such

What, exactly, has that got to do with anything?

>tests is to keep the bike perfectly straight. The simplest
>way presumably would be to lock the steering. This would
>render the bike unrideable to all intents and purposes and
>so the effects of a rider shifting their weight over the
>back wheel and causing tyre roll would need to be simulated
>with weights. So anyway, you first!

It's quite possible. You use the weight of the bike as the
load. You deflate the tyre to artifically enhance the
deformation. It's quite easy to then roll the bike walking
along side, keeping it straight (I did it along a tiled
floor so I could follow the line). We then have two
situations: (almost) perfectly circular tyre and tyre with
flat bit at bottom. Effect of wheel wobble is minimal (and
statistically reduced by repeated measurements).

The inflated one consistently and visibly went further in
one revolution

Live in your mathematical dreamworld, the rest of us seem to
grasp it and have experimental evidence to back it up.

Frink

--
Doctor J. Frink : 'Rampant Ribald Ringtail' See his mind
here : http://www.cmp.liv.ac.uk/frink/ Annoy his mind here :
pjf at cmp dot liv dot ack dot ook "No sir, I didn't like
it!" - Mr Horse