Physics Quiz...

[Carlos E.R.]

On 2023-04-24 19:40, Fred Bloggs wrote:

On Sunday, April 23, 2023 at 6:48:05 PM UTC-4, John Larkin wrote:
On Sun, 23 Apr 2023 15:30:24 -0400, bitrex <us...@example.net> wrote:

On 4/23/2023 8:44 AM, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 7:49:24?AM UTC-4, Anthony William Sloman wrote:
On Sunday, April 23, 2023 at 9:01:07?PM UTC+10, Fred Bloggs wrote:
So a vehicle is driving down the road when an entire wheel comes off and continues its direction unchanged rolling alongside the vehicle. Question is why does the wheel end up accelerating, rolling much faster than its original speed, outpacing the vehicle significantly? Answer should be obvious, but you need practical insight.
The only thing that could accelerate it would be the airflow around the vehicle body, which would be associated with trailing vortices.

It seems unlikely than any of them could make the wheel rotate much faster than it\'s original speed - it would outrun the car and the trailing vortices - unless it was moving sideways with respect to the rest of the car, and out into the wake.

Alright, you\'re getting close. From what I\'ve personally observed, a wheel dropping off the vehicle leaves the vehicle behind in the dust, it really takes off.

It seems like a potentially complex process, particularly if it\'s one of
the drive wheels in a modern car with traction control, and/or the wheel
isn\'t in full contact with the pavement when it separates.
If it bounces up before it breaks off, the differential (assume it has
one) could spin it way up.

It\'s too complex to analyze.

You might be on to something there. The nature of the failure somehow gives the wheel a push before it breaks free.

When the wheel losses the weight of the vehicle instantly, the rubber
expands instantly. Like a spring expanding. Maybe that gives a kick to
the wheel, I would guess upwards.

I have no idea how to analyze that.

--
Cheers, Carlos.

 

[John Walliker]

On Tuesday, 25 April 2023 at 12:20:25 UTC+1, Carlos E.R. wrote:

On 2023-04-24 19:40, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 6:48:05 PM UTC-4, John Larkin wrote:
On Sun, 23 Apr 2023 15:30:24 -0400, bitrex <us...@example.net> wrote:

On 4/23/2023 8:44 AM, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 7:49:24?AM UTC-4, Anthony William Sloman wrote:
On Sunday, April 23, 2023 at 9:01:07?PM UTC+10, Fred Bloggs wrote:
So a vehicle is driving down the road when an entire wheel comes off and continues its direction unchanged rolling alongside the vehicle. Question is why does the wheel end up accelerating, rolling much faster than its original speed, outpacing the vehicle significantly? Answer should be obvious, but you need practical insight.
The only thing that could accelerate it would be the airflow around the vehicle body, which would be associated with trailing vortices.

It seems unlikely than any of them could make the wheel rotate much faster than it\'s original speed - it would outrun the car and the trailing vortices - unless it was moving sideways with respect to the rest of the car, and out into the wake.

Alright, you\'re getting close. From what I\'ve personally observed, a wheel dropping off the vehicle leaves the vehicle behind in the dust, it really takes off.

It seems like a potentially complex process, particularly if it\'s one of
the drive wheels in a modern car with traction control, and/or the wheel
isn\'t in full contact with the pavement when it separates.
If it bounces up before it breaks off, the differential (assume it has
one) could spin it way up.

It\'s too complex to analyze.

You might be on to something there. The nature of the failure somehow gives the wheel a push before it breaks free.

When the wheel losses the weight of the vehicle instantly, the rubber
expands instantly. Like a spring expanding. Maybe that gives a kick to
the wheel, I would guess upwards.

I have no idea how to analyze that.

Well, the initial force will be equal and opposite to the downward force from the
car that has just been removed. The force will decrease to the weight of the wheel
as it expands to become circular. You can work out how quickly by considering the
upwards acceleration imparted to the wheel by that decreasing force if you know
the mass of the wheel.
John

 

[Fred Bloggs]

On Tuesday, April 25, 2023 at 7:20:25 AM UTC-4, Carlos E.R. wrote:

On 2023-04-24 19:40, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 6:48:05 PM UTC-4, John Larkin wrote:
On Sun, 23 Apr 2023 15:30:24 -0400, bitrex <us...@example.net> wrote:

On 4/23/2023 8:44 AM, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 7:49:24?AM UTC-4, Anthony William Sloman wrote:
On Sunday, April 23, 2023 at 9:01:07?PM UTC+10, Fred Bloggs wrote:
So a vehicle is driving down the road when an entire wheel comes off and continues its direction unchanged rolling alongside the vehicle. Question is why does the wheel end up accelerating, rolling much faster than its original speed, outpacing the vehicle significantly? Answer should be obvious, but you need practical insight.
The only thing that could accelerate it would be the airflow around the vehicle body, which would be associated with trailing vortices.

It seems unlikely than any of them could make the wheel rotate much faster than it\'s original speed - it would outrun the car and the trailing vortices - unless it was moving sideways with respect to the rest of the car, and out into the wake.

Alright, you\'re getting close. From what I\'ve personally observed, a wheel dropping off the vehicle leaves the vehicle behind in the dust, it really takes off.

It seems like a potentially complex process, particularly if it\'s one of
the drive wheels in a modern car with traction control, and/or the wheel
isn\'t in full contact with the pavement when it separates.
If it bounces up before it breaks off, the differential (assume it has
one) could spin it way up.

It\'s too complex to analyze.

You might be on to something there. The nature of the failure somehow gives the wheel a push before it breaks free.

When the wheel losses the weight of the vehicle instantly, the rubber
expands instantly. Like a spring expanding. Maybe that gives a kick to
the wheel, I would guess upwards.

True. It\'s looking more and more like the instant of release makes a big difference. If, to keep thing simple, it is a 2,000 lb vehicle, with 500 Lbs on each tire, then an instantaneous release starts things in motion with the tire pushing out that flat spot with 500 lbs of force! The reason why the tire doesn\'t immediately shoot 100 ft in the air is that the force is an impulse, and acts through just a small distance before it\'s entirely dissipated, and doesn\'t really give the tire much total effective acceleration upwards. In the wiki articles linked below, you can see that just prior to release the reaction forces acting on the flat spot are both vertical and horizontal. It has to be the stored energy in the air pressure and elasticity of the tire itself, acting through that horizontal component, when suddenly released, gives the tire a horizontal change in momentum impulse, causing it to accelerate. It\'s obviously a substantial kick and, depending upon the myriad of tire and vehicle designs, makes the tire translation motion accelerate more or less. Since the rolling resistance is effectively zero, the tire will roll forever. But even on a perfectly smooth road surface, some kind of resonance occurs causing the tire to start bouncing, the bounces build in amplitude quite rapidly and makes it go airborne more often than it\'s in contact with the road.

https://en.wikipedia.org/wiki/Rolling_resistance

Background on the complexity of tire design and kinetic analysis:

https://www.sciencedirect.com/topics/engineering/rolling-resistance-coefficient

I have no idea how to analyze that.

--
Cheers, Carlos.

 

[Fred Bloggs]

On Monday, April 24, 2023 at 9:31:27 PM UTC-4, Ricky wrote:

On Sunday, April 23, 2023 at 6:17:50 PM UTC-4, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 9:39:16 AM UTC-4, Martin Brown wrote:
On 23/04/2023 13:44, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 7:49:24 AM UTC-4, Anthony William Sloman
wrote:
On Sunday, April 23, 2023 at 9:01:07 PM UTC+10, Fred Bloggs wrote:
So a vehicle is driving down the road when an entire wheel comes
off and continues its direction unchanged rolling alongside the
vehicle. Question is why does the wheel end up accelerating,
rolling much faster than its original speed, outpacing the
vehicle significantly? Answer should be obvious, but you need
practical insight.
The only thing that could accelerate it would be the airflow around
the vehicle body, which would be associated with trailing
vortices.

It seems unlikely than any of them could make the wheel rotate much
faster than it\'s original speed - it would outrun the car and the
trailing vortices - unless it was moving sideways with respect to
the rest of the car, and out into the wake.

Alright, you\'re getting close. From what I\'ve personally observed, a
wheel dropping off the vehicle leaves the vehicle behind in the dust,
it really takes off.
Its diameter changes quite radically when it is no longer being squashed
by the weight of the car and so although it was previously rolling with
constant velocity at radius r when loaded the sudden loss of load means
the tyre expands to about 10-15% larger radius R ~ 1.1r where it is in
contact with the road. The car may also slow down with one wheel missing
if the driver has any road sense at all.

Angular momentum is conserved in the short term so the wheel now has a
linear velocity increase by about 10-15% compared to the car.
Doesn\'t the increased radius increase the angular moment of inertia about the centroid, thereby slowing the rotational speed to conserve angular momentum?
It\'s not the entire wheel that enlarges, just the point of contact with the road. So the delta rotational speed you are talking about is very small.
But you hit on one of two causes for speed increase. Having the weight of the vehicle suddenly removed means the effective friction between the tire and the road, caused by having to overcome that weighted flat spot where road and tread meets, is completely eliminated.
Which is only relevant while driven. Once off the car, and at it\'s full roundness, it has momentum and will tend to preserve that.


The flat spot effect has been traditionally modelled as continuously have to apply translational force to push the tire out of a rut the depth of the flat spot. These days they probably use finite element analysis to make it more accurate, but that\'s essentially it. But it doesn\'t explain the increase in rotational speed.

It would not be the depth of the flat spot, because some of the force is elastic, and pushes the tire faster on the trailing edge.
There\'s a second element hit on by JL, and that is the ability of tire to store energy in its elasticity. These runaway tires almost always break into a bounce, they can bounce really high, and then they really start flying.
LOL Bouncing will not make it run faster at all.
BTW Wheels shouldn\'t drop off properly maintained vehicles.

I only know of one hapless individual with no engineering or mechanical
sense at all who was actually passed by one of their own wheels.
Worst thing is when they bounce into oncoming traffic, which almost always causes a serious wreck. Or they could hit a pedestrian on a sidewalk, which almost always kills them.
You mean like the \"Totally irrelevant\" video of the car that was sent flying some six feet into the air? Then, ironically, the car gets rear ended by the wheel that flew off the pickup! .

This is also what happens when Indy cars run over another\'s wheel in passing.

If you at least attempt to employ some amount of reasoning to justify your baseless pronouncements, you would sound like less of a fool.

--

Rick C.

-+ Get 1,000 miles of free Supercharging
-+ Tesla referral code - https://ts.la/richard11209

 

[Fred Bloggs]

On Tuesday, April 25, 2023 at 7:20:25 AM UTC-4, Carlos E.R. wrote:

On 2023-04-24 19:40, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 6:48:05 PM UTC-4, John Larkin wrote:
On Sun, 23 Apr 2023 15:30:24 -0400, bitrex <us...@example.net> wrote:

On 4/23/2023 8:44 AM, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 7:49:24?AM UTC-4, Anthony William Sloman wrote:
On Sunday, April 23, 2023 at 9:01:07?PM UTC+10, Fred Bloggs wrote:
So a vehicle is driving down the road when an entire wheel comes off and continues its direction unchanged rolling alongside the vehicle. Question is why does the wheel end up accelerating, rolling much faster than its original speed, outpacing the vehicle significantly? Answer should be obvious, but you need practical insight.
The only thing that could accelerate it would be the airflow around the vehicle body, which would be associated with trailing vortices.

It seems unlikely than any of them could make the wheel rotate much faster than it\'s original speed - it would outrun the car and the trailing vortices - unless it was moving sideways with respect to the rest of the car, and out into the wake.

Alright, you\'re getting close. From what I\'ve personally observed, a wheel dropping off the vehicle leaves the vehicle behind in the dust, it really takes off.

It seems like a potentially complex process, particularly if it\'s one of
the drive wheels in a modern car with traction control, and/or the wheel
isn\'t in full contact with the pavement when it separates.
If it bounces up before it breaks off, the differential (assume it has
one) could spin it way up.

It\'s too complex to analyze.

You might be on to something there. The nature of the failure somehow gives the wheel a push before it breaks free.

When the wheel losses the weight of the vehicle instantly, the rubber
expands instantly. Like a spring expanding. Maybe that gives a kick to
the wheel, I would guess upwards.

In the free body diagram in the wiki article. There are horizontal and vertical forces applied. But in the circular coordinates of the tire, all the external forces are either radial or tangential. The horizontal external/ internal forces work out perfectly to apply a tangential force on the tire tread.

I have no idea how to analyze that.

--
Cheers, Carlos.

 

[Fred Bloggs]

On Monday, April 24, 2023 at 1:23:15 PM UTC-4, Ralph Mowery wrote:

In article <o9bd4idr642oadqj1...@4ax.com>, b...@K7IQ.com
says...


My guess is that, mainly, the car slowed down cuz it was missing a
wheel.

Without an absolute measurement of velocity of the car and of the free
rolling wheel in reference to the ground, who knows /


The car I was in when the wheel came off was doing a constant speed as
the wheel passed us.

Right. It was the tire expanding back to its uncompressed shape, after having the vehicle weight suddenly removed, that gives it a forward horizontal motion kick.

 

[John Larkin]

On Tue, 25 Apr 2023 10:50:25 +0100, Martin Brown
<\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

On 24/04/2023 19:11, John Larkin wrote:
On Mon, 24 Apr 2023 09:24:51 -0700 (PDT), Lasse Langwadt Christensen
langwadt@fonz.dk> wrote:

mandag den 24. april 2023 kl. 00.33.17 UTC+2 skrev John Larkin:
On Sun, 23 Apr 2023 15:19:40 -0700 (PDT), Fred Bloggs
bloggs.fred...@gmail.com> wrote:
On Sunday, April 23, 2023 at 1:03:04?PM UTC-4, John Robertson
wrote:
On 2023/04/23 4:01 a.m., Fred Bloggs wrote:
So a vehicle is driving down the road when an entire wheel
comes off and continues its direction unchanged rolling
alongside the vehicle. Question is why does the wheel end
up accelerating, rolling much faster than its original
speed, outpacing the vehicle significantly? Answer should
be obvious, but you need practical insight.
The wheel can\'t accelerate without an external force being
added to it - it has no means of self propulsion. Laws of the
conservation of momentum apply as usual.

Think of a figure skater doing one of those stationary spins.
Arms outstretched is one spin rate, arms brought into the side
and they turn into a blur. No external forces come into play.

The skater must use muscle power to pull her arms in. The work
done in pulling her arms in is converted to energy stored in the
spinning mass of her body, and is recoverable.

Moving the arms in provides the force that spins her up but the
fundamental rule is conservation of angular momentum.

angular momentum is the product of moment of inertia and angular
velocity

angular momentum can\'t just change (newtons 3rd) so when the moment
of inertia get smaller (pulling arms in) the angular velocity has
to increase

no energy added, just \"stored\" differently

She did work pulling her arms in, burned a bit of breakfast and
added energy to the rotating system. When she extends them back out,
work is done on her arms. Of course, muscles don\'t recover energy
when back-driven but some other gadget, a prosthetic arm maybe,
could.

It *is* adding energy to the system by moving her arms against a
resisting force. Though more importantly it is radically changing her
mass distribution so that it is all much nearer the spin axis.

Conservation of angular momentum is more fundamental here which means
that she spins much faster with arms in (and with more stored energy).
Choosing the correct conservation law is essential!

Conservation Of Energy is the Prime Directive.

Given certain relativistic effects, maybe momentum is not conserved.
When in doubt, trust COE.

Moving her arms provides the force and torque needed to spin her up but
doesn\'t alter her total angular momentum at all. She would spin as fast
if she raised here arms above her head as by bringing them to her side.
That state with arms high (and hands clasped together is the fastest
possible spin rate but harder to stay balanced on point) also has more
stored potential energy since her centre of mass has been raised in
addition. This is quite a nice (no maths) review of the physics of ballet.

https://www.discovermagazine.com/the-sciences/the-physicist-who-figured-out-ballet

One could build a robot lady to do the skater spin thing. If it
could recover the energy supplied when it extends its arms, it could
spin up and down forever without needing additional power.

I expect USPTO is just waiting for your application - although ISTR they
are officially no longer accepting patents on perpetual motion machines.

The mechanism would be simple and does not violate COE. It\'s
equivalent to spinning up a DC motor from a battery and spinning it
down to charge the battery. AKA regenerative braking. Absent losses,
the battery-motor system can spin up and spin down forever.

A pendulum has similar behavior, or a spring and a mass. Sometimes it
goes fast and sometimes it stops. The energy is just stored in
different places. It can swing like that for many, many cycles, even
with real losses.

Energy is conserved.

No it isn\'t.

She has to do work against the centrepetal (old school centrifugal)
forces that act on her outstretched arms to move them. By bringing them
in to her side she *is* doing work against that force which results in a
net torque on her body which acts to spin her up so that her angular
velocity increases markedly as her moment of inertia decreases.

Of course; I said that. And when she extends her arms to slow down,
she gets that energy back. If the initial condition were the tight,
high spin rate case, the initial extension would deliver energy that
could be stored to pull the arms in later. Repeat.

Of course her muscles don\'t recover and store energy, but a
motor-battery system could. I said that already too.

 

[RichD]

On April 24, Clive Arthur wrote:

So a vehicle is driving down the road when an entire wheel comes
off and continues its direction unchanged rolling alongside the vehicle.
Question is why does the wheel end up accelerating, rolling much faster
than its original speed, outpacing the vehicle significantly?

The effective diameter of the wheel is proportional to the radius. The
effective radius is from axle centre to road surface. Take away the
load and that\'s quite a significant change in effective diameter.

um, if the wheel\'s diameter (the tire, actually) increases,
its moment of inertia increases. Angular momentum
is presumably conserved, hence the tire SLOWS.

When the car is running normally, there is a
distance between the centre of rotation of the axle and the road.
I\'m calling that the effective radius.

Meaningless.

> The tyre isn\'t a circle, it\'s squished due to the weight of the car.

Right that\'s the key point: the squished tire ISN\'T A CIRCLE.

Every pico degree rotation of the axle corresponds to a distance moved,
proportional only to this effective radius. The parts of the tyre which
are not in contact with the ground don\'t make no never-mind.[1]
Take the weight off the wheel by detaching it and the
effective radius increases. It\'s still spinning at X RPM but it\'s now
\'bigger\'. So it goes faster.

You flunk the geometry exam.

It isn\'t circular. You can\'t cavalierly use the formula converting
angular velocity into linear velocity.

It\'s too complicated to derive the exact road speed as a function
of rotational speed, for this irregular shape. Simplify it: the tire
is a clock face. 12 o\'clock moves at the same speed as (flattened) 6 o\'clock.

Now look at the instants before detachment, vs post-detachment.
12 o\'clock continues turning at rate unchanged. The suddenly
decompressed tire, at 6 o\'clock, turns at that same rate; they\'re
connected, right? Which means the portion in road contact continues
AT CONSTANT SPEED.


> Don\'t overthink it.

ah yes.... \"go with your gut\"

Whenever I hear that, my reaction is: how many organs do you
think with? Have you ever tried your brain?

--
Rich

 

[RichD]

On April 25, Fred Bloggs wrote:

So a vehicle is driving down the road when an entire wheel comes off and continues its
direction unchanged rolling alongside the vehicle. Question is why does the wheel end up
accelerating, rolling much faster than its original speed, outpacing the vehicle significantly?

When the wheel losses the weight of the vehicle instantly, the rubber
expands instantly. Like a spring expanding. Maybe that gives a kick to
the wheel, I would guess upwards.

In the free body diagram in the wiki article. There are horizontal and vertical
forces applied. But in the circular coordinates of the tire, all the external forces
are either radial or tangential. The horizontal external/ internal forces work out
perfectly to apply a tangential force on the tire tread.

You badly misread the (excellent) wiki article, and your physics is deficient.

The external forces are REACTION forces, as the axle drives the wheels.
They aren\'t a power supply! When the wheel detaches, it\'s a free body,
it doesn\'t magically accelerate due to imaginary forces.

--
Rich

 

[RichD]

On April 24, boB wrote:
> My guess is that, mainly, the car slowed down cuz it was missing a wheel.

Has Elon Musk been notified of this revolutionary discovery in automotive
engineering, where a car loses a wheel without losing speed?

Without an absolute measurement of velocity of the car and of the free
rolling wheel in reference to the ground, who knows /

We have an EYEWITNESS account, which as any lawyer could tell you,
is the absolute gold standard -

--
Rich

 

[Martin Brown]

On 24/04/2023 18:34, Fred Bloggs wrote:

On Monday, April 24, 2023 at 5:24:09 AM UTC-4, Martin Brown wrote:
On 23/04/2023 23:17, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 9:39:16 AM UTC-4, Martin Brown
wrote:
On 23/04/2023 13:44, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 7:49:24 AM UTC-4, Anthony
William Sloman wrote:
On Sunday, April 23, 2023 at 9:01:07 PM UTC+10, Fred
Bloggs wrote:
So a vehicle is driving down the road when an entire
wheel comes off and continues its direction unchanged
rolling alongside the vehicle. Question is why does the
wheel end up accelerating, rolling much faster than its
original speed, outpacing the vehicle significantly?
Answer should be obvious, but you need practical
insight.
The only thing that could accelerate it would be the
airflow around the vehicle body, which would be associated
with trailing vortices.

It seems unlikely than any of them could make the wheel
rotate much faster than it\'s original speed - it would
outrun the car and the trailing vortices - unless it was
moving sideways with respect to the rest of the car, and
out into the wake.

Alright, you\'re getting close. From what I\'ve personally
observed, a wheel dropping off the vehicle leaves the
vehicle behind in the dust, it really takes off.

Its diameter changes quite radically when it is no longer
being squashed by the weight of the car and so although it was
previously rolling with constant velocity at radius r when
loaded the sudden loss of load means the tyre expands to about
10-15% larger radius R ~ 1.1r where it is in contact with the
road. The car may also slow down with one wheel missing if the
driver has any road sense at all.

Angular momentum is conserved in the short term so the wheel
now has a linear velocity increase by about 10-15% compared to
the car.

Doesn\'t the increased radius increase the angular moment of
inertia about the centroid, thereby slowing the rotational speed
to conserve angular momentum? But you hit on one of two causes
for speed increase. Having the weight of the vehicle suddenly
removed means the effective friction between the tire and the
road, caused by having to overcome that weighted flat spot where
road and tread meets, is completely eliminated. The flat spot
effect has been traditionally modelled as continuously have to
apply translational force to push the tire out of a rut the depth
of the flat spot. These days they probably use finite element
analysis to make it more accurate, but that\'s essentially it.
The change in moment of inertia is rather small though.
But it doesn\'t explain the increase in rotational speed.
I\'m not sure that there is an increase rotational speed merely an
increase in the effective diameter of the wheel - which separates
from the vehicle with linear speed v and initial radius r. The
rebound of the tyre when the load is removed will make it bounce
into the air as JL pointed out and then the new diameter of the
tyre R where it is only supporting its own weight comes into play.


In the few I\'ve seen in traffic, the wheel comes off, races in front
of the car that lost it, and catches up with the cars in front of it,
with those cars moving at constant speed. I don\'t see any other way
to interpret that other than the wheel picked up speed.

I think it stems from the sudden change in effective diameter when the
tyre is no longer under full load of the vehicle weight.

I only know of one hapless individual with no engineering or
mechanical sense at all who was actually passed by one of their
own wheels.

Worst thing is when they bounce into oncoming traffic, which
almost always causes a serious wreck. Or they could hit a
pedestrian on a sidewalk, which almost always kills them.
Does this happen a lot in the USA?

Probably because U.S. has so many more cars on the road than anyplace
else...

ITYM so many *badly maintained* vehicles.

Is it not an offence to drive around in a vehicle that is falling apart?

--
Martin Brown

 

[boB]

On Tue, 25 Apr 2023 10:38:41 -0700 (PDT), RichD
<r_delaney2001@yahoo.com> wrote:

On April 24, boB wrote:
My guess is that, mainly, the car slowed down cuz it was missing a wheel.

Has Elon Musk been notified of this revolutionary discovery in automotive
engineering, where a car loses a wheel without losing speed?

Without an absolute measurement of velocity of the car and of the free
rolling wheel in reference to the ground, who knows /

We have an EYEWITNESS account, which as any lawyer could tell you,
is the absolute gold standard -

If we didn\'t have so many lawyers... We wouldn\'t need so many lawyers

 

[Clive Arthur]

On 25/04/2023 18:16, RichD wrote:

<snip>

It\'s too complicated to derive the exact road speed as a function
of rotational speed, for this irregular shape. Simplify it: the tire
is a clock face. 12 o\'clock moves at the same speed as (flattened) 6 o\'clock.

No, it doesn\'t. The 12 o\'clock radius is greater than the 6 o\'clock
radius, so its speed is greater.

Maybe that\'s not immediately obvious to you, but consider that the 6
o\'clock portion (and a bit either side) is taking an enforced short cut
along a straight line, the road surface, whereas the 12 o\'clock portion
is going the longer way around the circumference of a circle.

--
Cheers
Clive

 

[Fred Bloggs]

On Tuesday, April 25, 2023 at 4:14:00 PM UTC-4, Martin Brown wrote:

On 24/04/2023 18:34, Fred Bloggs wrote:
On Monday, April 24, 2023 at 5:24:09 AM UTC-4, Martin Brown wrote:
On 23/04/2023 23:17, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 9:39:16 AM UTC-4, Martin Brown
wrote:
On 23/04/2023 13:44, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 7:49:24 AM UTC-4, Anthony
William Sloman wrote:
On Sunday, April 23, 2023 at 9:01:07 PM UTC+10, Fred
Bloggs wrote:
So a vehicle is driving down the road when an entire
wheel comes off and continues its direction unchanged
rolling alongside the vehicle. Question is why does the
wheel end up accelerating, rolling much faster than its
original speed, outpacing the vehicle significantly?
Answer should be obvious, but you need practical
insight.
The only thing that could accelerate it would be the
airflow around the vehicle body, which would be associated
with trailing vortices.

It seems unlikely than any of them could make the wheel
rotate much faster than it\'s original speed - it would
outrun the car and the trailing vortices - unless it was
moving sideways with respect to the rest of the car, and
out into the wake.

Alright, you\'re getting close. From what I\'ve personally
observed, a wheel dropping off the vehicle leaves the
vehicle behind in the dust, it really takes off.

Its diameter changes quite radically when it is no longer
being squashed by the weight of the car and so although it was
previously rolling with constant velocity at radius r when
loaded the sudden loss of load means the tyre expands to about
10-15% larger radius R ~ 1.1r where it is in contact with the
road. The car may also slow down with one wheel missing if the
driver has any road sense at all.

Angular momentum is conserved in the short term so the wheel
now has a linear velocity increase by about 10-15% compared to
the car.

Doesn\'t the increased radius increase the angular moment of
inertia about the centroid, thereby slowing the rotational speed
to conserve angular momentum? But you hit on one of two causes
for speed increase. Having the weight of the vehicle suddenly
removed means the effective friction between the tire and the
road, caused by having to overcome that weighted flat spot where
road and tread meets, is completely eliminated. The flat spot
effect has been traditionally modelled as continuously have to
apply translational force to push the tire out of a rut the depth
of the flat spot. These days they probably use finite element
analysis to make it more accurate, but that\'s essentially it.
The change in moment of inertia is rather small though.
But it doesn\'t explain the increase in rotational speed.
I\'m not sure that there is an increase rotational speed merely an
increase in the effective diameter of the wheel - which separates
from the vehicle with linear speed v and initial radius r. The
rebound of the tyre when the load is removed will make it bounce
into the air as JL pointed out and then the new diameter of the
tyre R where it is only supporting its own weight comes into play.


In the few I\'ve seen in traffic, the wheel comes off, races in front
of the car that lost it, and catches up with the cars in front of it,
with those cars moving at constant speed. I don\'t see any other way
to interpret that other than the wheel picked up speed.

I think it stems from the sudden change in effective diameter when the
tyre is no longer under full load of the vehicle weight.
I only know of one hapless individual with no engineering or
mechanical sense at all who was actually passed by one of their
own wheels.

Worst thing is when they bounce into oncoming traffic, which
almost always causes a serious wreck. Or they could hit a
pedestrian on a sidewalk, which almost always kills them.
Does this happen a lot in the USA?

Probably because U.S. has so many more cars on the road than anyplace
else...

ITYM so many *badly maintained* vehicles.

U.S. has an annual inspection requirement, and the inspection has to be performed by a state licensed inspector. Some of them are really thorough, they look at several dozen parts, and check off their work as they go. And the car gets a windshield sticker, without which or expired, the driver gets a fairly hefty fine- at least 3x the cost of getting the inspection.

Is it not an offence to drive around in a vehicle that is falling apart?

Yes it is. But you have to have something really drastically and visibly wrong before the police take notice and pull you over. They\'re mainly looking for a valid windshield sticker. From what I can find out, most tires end up falling off because a tire shop overtightened and broke the lugs with those over powered pneumatic wrenches they use.

--
Martin Brown

 

[Fred Bloggs]

On Tuesday, April 25, 2023 at 1:31:54 PM UTC-4, RichD wrote:

On April 25, Fred Bloggs wrote:
So a vehicle is driving down the road when an entire wheel comes off and continues its
direction unchanged rolling alongside the vehicle. Question is why does the wheel end up
accelerating, rolling much faster than its original speed, outpacing the vehicle significantly?

When the wheel losses the weight of the vehicle instantly, the rubber
expands instantly. Like a spring expanding. Maybe that gives a kick to
the wheel, I would guess upwards.

In the free body diagram in the wiki article. There are horizontal and vertical
forces applied. But in the circular coordinates of the tire, all the external forces
are either radial or tangential. The horizontal external/ internal forces work out
perfectly to apply a tangential force on the tire tread.
You badly misread the (excellent) wiki article, and your physics is deficient.

The external forces are REACTION forces, as the axle drives the wheels.
They aren\'t a power supply! When the wheel detaches, it\'s a free body,
it doesn\'t magically accelerate due to imaginary forces.

When the vehicle weight is suddenly removed for the tire, the tire pressure decompresses and restores the original shape of the tire with exactly the same magnitude but opposite direction as the reaction forces. If you look at the free body diagram of the whole vehicle in steady state without acceleration, you can see the horizontal component of the tire/ road reaction force exactly equals the wind resistance force acting on the vehicle, plus the force necessary to push the tire off the flat spot, and that\'s heavy duty. That same force is what gives the tire its acceleration when it\'s free.

--
Rich

 

[Carlos E.R.]

On 2023-04-26 12:01, Clive Arthur wrote:

On 25/04/2023 18:16, RichD wrote:

snip

It\'s too complicated to derive the exact road speed as a function
of rotational speed, for this irregular shape.  Simplify it: the tire
is a clock face.  12 o\'clock moves at the same speed as (flattened) 6
o\'clock.

No, it doesn\'t.  The 12 o\'clock radius is greater than the 6 o\'clock
radius, so its speed is greater.

Maybe that\'s not immediately obvious to you, but consider that the 6
o\'clock portion (and a bit either side) is taking an enforced short cut
along a straight line, the road surface, whereas the 12 o\'clock portion
is going the longer way around the circumference of a circle.

Ok, so that means that the speed of the surface of the wheel at any
point that is not under the vehicle weight is actually greater than the
road or vehicle speed. Thus when the wheel is released from the car, it
really is turning faster than previous speed.

So that\'s it.

--
Cheers, Carlos.

 

[John Larkin]

On Tue, 25 Apr 2023 21:13:50 +0100, Martin Brown
<\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

On 24/04/2023 18:34, Fred Bloggs wrote:
On Monday, April 24, 2023 at 5:24:09?AM UTC-4, Martin Brown wrote:
On 23/04/2023 23:17, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 9:39:16?AM UTC-4, Martin Brown
wrote:
On 23/04/2023 13:44, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 7:49:24?AM UTC-4, Anthony
William Sloman wrote:
On Sunday, April 23, 2023 at 9:01:07?PM UTC+10, Fred
Bloggs wrote:
So a vehicle is driving down the road when an entire
wheel comes off and continues its direction unchanged
rolling alongside the vehicle. Question is why does the
wheel end up accelerating, rolling much faster than its
original speed, outpacing the vehicle significantly?
Answer should be obvious, but you need practical
insight.
The only thing that could accelerate it would be the
airflow around the vehicle body, which would be associated
with trailing vortices.

It seems unlikely than any of them could make the wheel
rotate much faster than it\'s original speed - it would
outrun the car and the trailing vortices - unless it was
moving sideways with respect to the rest of the car, and
out into the wake.

Alright, you\'re getting close. From what I\'ve personally
observed, a wheel dropping off the vehicle leaves the
vehicle behind in the dust, it really takes off.

Its diameter changes quite radically when it is no longer
being squashed by the weight of the car and so although it was
previously rolling with constant velocity at radius r when
loaded the sudden loss of load means the tyre expands to about
10-15% larger radius R ~ 1.1r where it is in contact with the
road. The car may also slow down with one wheel missing if the
driver has any road sense at all.

Angular momentum is conserved in the short term so the wheel
now has a linear velocity increase by about 10-15% compared to
the car.

Doesn\'t the increased radius increase the angular moment of
inertia about the centroid, thereby slowing the rotational speed
to conserve angular momentum? But you hit on one of two causes
for speed increase. Having the weight of the vehicle suddenly
removed means the effective friction between the tire and the
road, caused by having to overcome that weighted flat spot where
road and tread meets, is completely eliminated. The flat spot
effect has been traditionally modelled as continuously have to
apply translational force to push the tire out of a rut the depth
of the flat spot. These days they probably use finite element
analysis to make it more accurate, but that\'s essentially it.
The change in moment of inertia is rather small though.
But it doesn\'t explain the increase in rotational speed.
I\'m not sure that there is an increase rotational speed merely an
increase in the effective diameter of the wheel - which separates
from the vehicle with linear speed v and initial radius r. The
rebound of the tyre when the load is removed will make it bounce
into the air as JL pointed out and then the new diameter of the
tyre R where it is only supporting its own weight comes into play.


In the few I\'ve seen in traffic, the wheel comes off, races in front
of the car that lost it, and catches up with the cars in front of it,
with those cars moving at constant speed. I don\'t see any other way
to interpret that other than the wheel picked up speed.

I think it stems from the sudden change in effective diameter when the
tyre is no longer under full load of the vehicle weight.

I only know of one hapless individual with no engineering or
mechanical sense at all who was actually passed by one of their
own wheels.

Worst thing is when they bounce into oncoming traffic, which
almost always causes a serious wreck. Or they could hit a
pedestrian on a sidewalk, which almost always kills them.
Does this happen a lot in the USA?

Probably because U.S. has so many more cars on the road than anyplace
else...

ITYM so many *badly maintained* vehicles.

It\'s very rare to see a junker here. Not 1 in 100. It\'s also rare to
see a Ford (Found On Road, Dead.)

Many US states have periodic vehicle inspection, but that doesn\'t
involve disassembling and inspecting wheel bearings. Do you regularly
inspect your wheel bearings?

It\'s impressive how much ignorance-driven anti-Americanism there is.
Jealousy driven, actually.

Is it not an offence to drive around in a vehicle that is falling apart?

There are Youtubes of runaway tires. Most look like failed, smoking
wheel bearings on cars and multiple-tire rigs coming apart on trucks.

A failed wheel bearing gives little advance warning; sometimes a bit
of noise. The cars involved don\'t look like junkers. My A3 developed
bad rear wheel bearings when the car had about 20,000 miles, still in
warranty. Very noisy!

In most of the vids I\'ve seen, the dropped tire does not accelerate
past the vehicle. When it does pass the vehicle, it\'s usually because
the vehicle is scraping the road on three wheels.

The voice background audio of the dashcams is usually not English.
There are a lot of Russian dashcam disasters, maybe because dashcams
are popular in Russia.

 

[Ricky]

On Wednesday, April 26, 2023 at 7:37:29 AM UTC-4, Fred Bloggs wrote:

On Tuesday, April 25, 2023 at 4:14:00 PM UTC-4, Martin Brown wrote:
On 24/04/2023 18:34, Fred Bloggs wrote:
On Monday, April 24, 2023 at 5:24:09 AM UTC-4, Martin Brown wrote:
On 23/04/2023 23:17, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 9:39:16 AM UTC-4, Martin Brown
wrote:
On 23/04/2023 13:44, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 7:49:24 AM UTC-4, Anthony
William Sloman wrote:
On Sunday, April 23, 2023 at 9:01:07 PM UTC+10, Fred
Bloggs wrote:
So a vehicle is driving down the road when an entire
wheel comes off and continues its direction unchanged
rolling alongside the vehicle. Question is why does the
wheel end up accelerating, rolling much faster than its
original speed, outpacing the vehicle significantly?
Answer should be obvious, but you need practical
insight.
The only thing that could accelerate it would be the
airflow around the vehicle body, which would be associated
with trailing vortices.

It seems unlikely than any of them could make the wheel
rotate much faster than it\'s original speed - it would
outrun the car and the trailing vortices - unless it was
moving sideways with respect to the rest of the car, and
out into the wake.

Alright, you\'re getting close. From what I\'ve personally
observed, a wheel dropping off the vehicle leaves the
vehicle behind in the dust, it really takes off.

Its diameter changes quite radically when it is no longer
being squashed by the weight of the car and so although it was
previously rolling with constant velocity at radius r when
loaded the sudden loss of load means the tyre expands to about
10-15% larger radius R ~ 1.1r where it is in contact with the
road. The car may also slow down with one wheel missing if the
driver has any road sense at all.

Angular momentum is conserved in the short term so the wheel
now has a linear velocity increase by about 10-15% compared to
the car.

Doesn\'t the increased radius increase the angular moment of
inertia about the centroid, thereby slowing the rotational speed
to conserve angular momentum? But you hit on one of two causes
for speed increase. Having the weight of the vehicle suddenly
removed means the effective friction between the tire and the
road, caused by having to overcome that weighted flat spot where
road and tread meets, is completely eliminated. The flat spot
effect has been traditionally modelled as continuously have to
apply translational force to push the tire out of a rut the depth
of the flat spot. These days they probably use finite element
analysis to make it more accurate, but that\'s essentially it.
The change in moment of inertia is rather small though.
But it doesn\'t explain the increase in rotational speed.
I\'m not sure that there is an increase rotational speed merely an
increase in the effective diameter of the wheel - which separates
from the vehicle with linear speed v and initial radius r. The
rebound of the tyre when the load is removed will make it bounce
into the air as JL pointed out and then the new diameter of the
tyre R where it is only supporting its own weight comes into play.


In the few I\'ve seen in traffic, the wheel comes off, races in front
of the car that lost it, and catches up with the cars in front of it,
with those cars moving at constant speed. I don\'t see any other way
to interpret that other than the wheel picked up speed.

I think it stems from the sudden change in effective diameter when the
tyre is no longer under full load of the vehicle weight.
I only know of one hapless individual with no engineering or
mechanical sense at all who was actually passed by one of their
own wheels.

Worst thing is when they bounce into oncoming traffic, which
almost always causes a serious wreck. Or they could hit a
pedestrian on a sidewalk, which almost always kills them.
Does this happen a lot in the USA?

Probably because U.S. has so many more cars on the road than anyplace
else...

ITYM so many *badly maintained* vehicles.
U.S. has an annual inspection requirement,

Pure fantasy. The US government has virtually nothing to do with auto inspections. That is handled at the state level, where some states have an annual inspection, and some don\'t. Virginia used to have an inspection every 6 months! Maryland has mandatory inspections, ONLY when a car trades hands..


> and the inspection has to be performed by a state licensed inspector. Some of them are really thorough, they look at several dozen parts, and check off their work as they go. And the car gets a windshield sticker, without which or expired, the driver gets a fairly hefty fine- at least 3x the cost of getting the inspection.

Maryland has no sticker. They rely on cops observing defects and issuing inspection tickets. So this typically only impacts lights and exhaust systems, resulting in some number of unsafe vehicles being on the road until they are in accidents!

--

Rick C.

++- Get 1,000 miles of free Supercharging
++- Tesla referral code - https://ts.la/richard11209

 

[Ricky]

On Tuesday, April 25, 2023 at 9:42:54 AM UTC-4, Fred Bloggs wrote:

On Monday, April 24, 2023 at 9:31:27 PM UTC-4, Ricky wrote:
On Sunday, April 23, 2023 at 6:17:50 PM UTC-4, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 9:39:16 AM UTC-4, Martin Brown wrote:
On 23/04/2023 13:44, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 7:49:24 AM UTC-4, Anthony William Sloman
wrote:
On Sunday, April 23, 2023 at 9:01:07 PM UTC+10, Fred Bloggs wrote:
So a vehicle is driving down the road when an entire wheel comes
off and continues its direction unchanged rolling alongside the
vehicle. Question is why does the wheel end up accelerating,
rolling much faster than its original speed, outpacing the
vehicle significantly? Answer should be obvious, but you need
practical insight.
The only thing that could accelerate it would be the airflow around
the vehicle body, which would be associated with trailing
vortices.

It seems unlikely than any of them could make the wheel rotate much
faster than it\'s original speed - it would outrun the car and the
trailing vortices - unless it was moving sideways with respect to
the rest of the car, and out into the wake.

Alright, you\'re getting close. From what I\'ve personally observed, a
wheel dropping off the vehicle leaves the vehicle behind in the dust,
it really takes off.
Its diameter changes quite radically when it is no longer being squashed
by the weight of the car and so although it was previously rolling with
constant velocity at radius r when loaded the sudden loss of load means
the tyre expands to about 10-15% larger radius R ~ 1.1r where it is in
contact with the road. The car may also slow down with one wheel missing
if the driver has any road sense at all.

Angular momentum is conserved in the short term so the wheel now has a
linear velocity increase by about 10-15% compared to the car.
Doesn\'t the increased radius increase the angular moment of inertia about the centroid, thereby slowing the rotational speed to conserve angular momentum?
It\'s not the entire wheel that enlarges, just the point of contact with the road. So the delta rotational speed you are talking about is very small.
But you hit on one of two causes for speed increase. Having the weight of the vehicle suddenly removed means the effective friction between the tire and the road, caused by having to overcome that weighted flat spot where road and tread meets, is completely eliminated.
Which is only relevant while driven. Once off the car, and at it\'s full roundness, it has momentum and will tend to preserve that.


The flat spot effect has been traditionally modelled as continuously have to apply translational force to push the tire out of a rut the depth of the flat spot. These days they probably use finite element analysis to make it more accurate, but that\'s essentially it. But it doesn\'t explain the increase in rotational speed.

It would not be the depth of the flat spot, because some of the force is elastic, and pushes the tire faster on the trailing edge.
There\'s a second element hit on by JL, and that is the ability of tire to store energy in its elasticity. These runaway tires almost always break into a bounce, they can bounce really high, and then they really start flying.
LOL Bouncing will not make it run faster at all.
BTW Wheels shouldn\'t drop off properly maintained vehicles.

I only know of one hapless individual with no engineering or mechanical
sense at all who was actually passed by one of their own wheels.
Worst thing is when they bounce into oncoming traffic, which almost always causes a serious wreck. Or they could hit a pedestrian on a sidewalk, which almost always kills them.
You mean like the \"Totally irrelevant\" video of the car that was sent flying some six feet into the air? Then, ironically, the car gets rear ended by the wheel that flew off the pickup! .

This is also what happens when Indy cars run over another\'s wheel in passing.
If you at least attempt to employ some amount of reasoning to justify your baseless pronouncements, you would sound like less of a fool.

Fred, I\'m sorry that all of this escapes you, including your own statements..

--

Rick C.

+-+ Get 1,000 miles of free Supercharging
+-+ Tesla referral code - https://ts.la/richard11209

 

[John Larkin]

On Wed, 26 Apr 2023 04:37:24 -0700 (PDT), Fred Bloggs
<bloggs.fredbloggs.fred@gmail.com> wrote:

On Tuesday, April 25, 2023 at 4:14:00?PM UTC-4, Martin Brown wrote:
On 24/04/2023 18:34, Fred Bloggs wrote:
On Monday, April 24, 2023 at 5:24:09?AM UTC-4, Martin Brown wrote:
On 23/04/2023 23:17, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 9:39:16?AM UTC-4, Martin Brown
wrote:
On 23/04/2023 13:44, Fred Bloggs wrote:
On Sunday, April 23, 2023 at 7:49:24?AM UTC-4, Anthony
William Sloman wrote:
On Sunday, April 23, 2023 at 9:01:07?PM UTC+10, Fred
Bloggs wrote:
So a vehicle is driving down the road when an entire
wheel comes off and continues its direction unchanged
rolling alongside the vehicle. Question is why does the
wheel end up accelerating, rolling much faster than its
original speed, outpacing the vehicle significantly?
Answer should be obvious, but you need practical
insight.
The only thing that could accelerate it would be the
airflow around the vehicle body, which would be associated
with trailing vortices.

It seems unlikely than any of them could make the wheel
rotate much faster than it\'s original speed - it would
outrun the car and the trailing vortices - unless it was
moving sideways with respect to the rest of the car, and
out into the wake.

Alright, you\'re getting close. From what I\'ve personally
observed, a wheel dropping off the vehicle leaves the
vehicle behind in the dust, it really takes off.

Its diameter changes quite radically when it is no longer
being squashed by the weight of the car and so although it was
previously rolling with constant velocity at radius r when
loaded the sudden loss of load means the tyre expands to about
10-15% larger radius R ~ 1.1r where it is in contact with the
road. The car may also slow down with one wheel missing if the
driver has any road sense at all.

Angular momentum is conserved in the short term so the wheel
now has a linear velocity increase by about 10-15% compared to
the car.

Doesn\'t the increased radius increase the angular moment of
inertia about the centroid, thereby slowing the rotational speed
to conserve angular momentum? But you hit on one of two causes
for speed increase. Having the weight of the vehicle suddenly
removed means the effective friction between the tire and the
road, caused by having to overcome that weighted flat spot where
road and tread meets, is completely eliminated. The flat spot
effect has been traditionally modelled as continuously have to
apply translational force to push the tire out of a rut the depth
of the flat spot. These days they probably use finite element
analysis to make it more accurate, but that\'s essentially it.
The change in moment of inertia is rather small though.
But it doesn\'t explain the increase in rotational speed.
I\'m not sure that there is an increase rotational speed merely an
increase in the effective diameter of the wheel - which separates
from the vehicle with linear speed v and initial radius r. The
rebound of the tyre when the load is removed will make it bounce
into the air as JL pointed out and then the new diameter of the
tyre R where it is only supporting its own weight comes into play.


In the few I\'ve seen in traffic, the wheel comes off, races in front
of the car that lost it, and catches up with the cars in front of it,
with those cars moving at constant speed. I don\'t see any other way
to interpret that other than the wheel picked up speed.

I think it stems from the sudden change in effective diameter when the
tyre is no longer under full load of the vehicle weight.
I only know of one hapless individual with no engineering or
mechanical sense at all who was actually passed by one of their
own wheels.

Worst thing is when they bounce into oncoming traffic, which
almost always causes a serious wreck. Or they could hit a
pedestrian on a sidewalk, which almost always kills them.
Does this happen a lot in the USA?

Probably because U.S. has so many more cars on the road than anyplace
else...

ITYM so many *badly maintained* vehicles.

U.S. has an annual inspection requirement, and the inspection has to be performed by a state licensed inspector. Some of them are really thorough, they look at several dozen parts, and check off their work as they go. And the car gets a windshield sticker, without which or expired, the driver gets a fairly hefty fine- at least 3x the cost of getting the inspection.

In New Orleans, the inspection was every six months, a real nuisance.
My MG usually failed the headlight aiming test because the lights were
so low.

When I moved to California I was amazed that there was no vehicle
inspection. The only one now is a smog test every few years, for older
cars.

Mo had a junker when she lived in Germany. To pass inspection, she
left a big bottle of Jim Beam on the rear seat.

Is it not an offence to drive around in a vehicle that is falling apart?

Yes it is. But you have to have something really drastically and visibly wrong before the police take notice and pull you over. They\'re mainly looking for a valid windshield sticker. From what I can find out, most tires end up falling off because a tire shop overtightened and broke the lugs with those over powered pneumatic wrenches they use.

The runaway tires are often smoking, probably from a failed wheel
bearing.

--
Martin Brown