Discussion:
Rubbing the tire on the road, is it really mathematically simple?
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micky
2019-05-11 21:13:19 UTC
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When I was in high school I was taught, or I read, that it's bad to turn
the steering wheel when the car is not moving. It's hard on the front
tires, wears out the tread, and one should be moving the car at least a
little when turning the wheel. Did they say that? Do they still?

I've been thinking about this and now I have doubts.

Seems to me any extra wear on the tread because of turning the direction
in which the tires point will be the same whether the car is moving or
still. It's harder to relate to the sliding motion of the tire on the
road surface when the car is moving, but it's clear when the car is
still. That seems to me to be the difference, but the vectors that
indicate rubbing seem the same either way.

I included the math group first because it seems like they would have
opinions.
Paul in Houston TX
2019-05-11 22:09:11 UTC
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Post by micky
When I was in high school I was taught, or I read, that it's bad to turn
the steering wheel when the car is not moving. It's hard on the front
tires, wears out the tread, and one should be moving the car at least a
little when turning the wheel. Did they say that? Do they still?
I've been thinking about this and now I have doubts.
Seems to me any extra wear on the tread because of turning the direction
in which the tires point will be the same whether the car is moving or
still. It's harder to relate to the sliding motion of the tire on the
road surface when the car is moving, but it's clear when the car is
still. That seems to me to be the difference, but the vectors that
indicate rubbing seem the same either way.
I included the math group first because it seems like they would have
opinions.
I would think that total tire wear would be the same but wear per unit
area would be different.
Thomas 'PointedEars' Lahn
2019-05-11 23:26:41 UTC
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Paul in Houston TX amok-crossposted:
^^^^^^^^^^^^^^^^^^
Please post here using your real name, “Paul in Houston TX” #74656.
Post by Paul in Houston TX
I would think that total tire wear would be the same but wear per unit
area would be different.
What is the basis for your assumption?

F’up2 sci.physics
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Twitter: @PointedEars2
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Paul in Houston TX
2019-05-12 01:43:30 UTC
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Post by Thomas 'PointedEars' Lahn
^^^^^^^^^^^^^^^^^^
Please post here using your real name, “Paul in Houston TX” #74656.
Post by Paul in Houston TX
I would think that total tire wear would be the same but wear per unit
area would be different.
What is the basis for your assumption?
F’up2 sci.physics
If you sit in one spot and move the tire L-R repeatedly the tire will
wear down just in that one spot. The rest of the tire would not be
affected. However, if you roll down the road doing the same thing the
tire would have the L-R repeat distributed over its tread surface.
Don't know for sure but I would think that the volume of rubber removed
would be the same as if sitting still.
Thomas 'PointedEars' Lahn
2019-05-12 10:52:53 UTC
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Post by Paul in Houston TX
Post by Thomas 'PointedEars' Lahn
^^^^^^^^^^^^^^^^^^
Please post here using your real name, “Paul in Houston TX” #74656.
Which part of that did you not understand?
Post by Paul in Houston TX
Post by Thomas 'PointedEars' Lahn
Post by Paul in Houston TX
I would think that total tire wear would be the same but wear per unit
area would be different.
What is the basis for your assumption?
If you sit in one spot and move the tire L-R repeatedly the tire will
wear down just in that one spot. The rest of the tire would not be
affected. However, if you roll down the road doing the same thing the
tire would have the L-R repeat distributed over its tread surface.
Don't know for sure but I would think that the volume of rubber removed
would be the same as if sitting still.
That is not so. First of all, a tire never has contact with the ground only
in one spot. Not even a line fits the picture. It is more like this:

_
. ' ' .
' `
' '
. .
. ' ' .
: ' _ ' :
: : :_: : : tire on the road, side view
: . , :
' . . '
' '
. .
._ _. __
_______`---..___..---'__________ |PE


________
.' `. <--- no contact with ground
: ........ :
: .......... : <--- least - " -
: .......... :
: :::::::::: :
: :::::::::: : <--- medium - " -
: :::::::::: :
=: ========== :=
axis of rotation =: ========== := <--- most - " -
=: ========== :=
: :::::::::: :
: :::::::::: : <--- medium - " -
: :::::::::: :
: .......... :
: .......... : <--- least - " -
: ........ :
`. .' <--- no - " -
''''''''

tire on the road, degrees of contact, __
top view |PE

That is, in the worst case (flat tire, low tire pressure and/or heavy
vehicle), approximately ¼ of the tread surface is affected by friction in
all cases.

Second, AISB, when the car is moving, the tire is *rolling* *even if the
wheel is turned*; the rolling resistance is (much) less than the *sliding*
(kinetic) friction of the same tread on the same road. Also, a point on the
bottom front of the tire is continuing to move *backwards* when the wheel is
turned while it is rolling forwards:


| /
1*-._ /
| `*. .'
| /2 `-_.'
| / .*3
.'

* ­— Point on the bottom of the forwards-rolling right-turned tire

As a result, *by far* it does not experience as much friction as when the
wheel is turned while at relative rest to the road, especially if the car is
moving fast (and the wheel is rotating fast, so that the sidewards sliding
friction incurred by turning is negligibly small).

Third, AISB, the tread is designed to be worn primarily in the direction of
axial rotation, NOT perpendicular to that. Therefore, incurring friction on
the tread *perpendicular* to the main tread pattern (which is perpendicular
to the axis of rotation) when turning at rest slowly destroys the pattern:

________
.'/\:/\:/\`.
:\:/\:/\:/\:/:
:\:/\:/\:/\:/:
:\:/\:/\:/\:/:
:\:/\:/\:/\:/:
:\:/\:/\:/\:/:
:\:/\:/\:/\:/:
=:\:/\:/\:/\:/:=
axis of rotation =:\:/\:/\:/\:/:=
=:\:/\:/\:/\:/:=
:\:/\:/\:/\:/:
:\:/\:/\:/\:/:
:\:/\:/\:/\:/:
:\:/\:/\:/\:/:
:\:/\:/\:/\:/:
:\:/\:/\:/\:/:
`./\:/\:/\.'
''''''''
^--^--^--^ main tread pattern

tire on the road, *bottom* tread pattern,
top view |PE
--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
SergIo
2019-05-11 22:19:35 UTC
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Post by micky
When I was in high school I was taught, or I read, that it's bad to turn
the steering wheel when the car is not moving. It's hard on the front
tires, wears out the tread, and one should be moving the car at least a
little when turning the wheel. Did they say that? Do they still?
obviously all the wear is on one spot on the tire
Post by micky
I've been thinking about this and now I have doubts.
Seems to me any extra wear on the tread because of turning the direction
in which the tires point will be the same whether the car is moving or
still.
na, it is distributed all along the tire face, not in one spot
Post by micky
It's harder to relate to the sliding motion of the tire on the
road surface when the car is moving, but it's clear when the car is
still. That seems to me to be the difference, but the vectors that
indicate rubbing seem the same either way.
I included the math group first because it seems like they would have
opinions.
Thomas 'PointedEars' Lahn
2019-05-11 23:14:45 UTC
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micky amok-crossposted to sci.math, sci.physics, and rec.autos.tech:
^^^^^
Please post here using your real name.
Post by micky
When I was in high school I was taught, or I read, that it's bad to turn
the steering wheel when the car is not moving. It's hard on the front
tires, wears out the tread, and one should be moving the car at least a
little when turning the wheel. Did they say that? Do they still?
Yes, of course. However, this is just a rule of thumb; the amount of wear
depends on the surface and the type of tread. For example, the wear from
turning a still tire on ice or snow is negligibly small compared to the
turning on asphalt.
Post by micky
I've been thinking about this and now I have doubts.
You have not thought this through.
Post by micky
Seems to me any extra wear on the tread because of turning the direction
in which the tires point will be the same whether the car is moving or
still.
It is not. When the car is moving relative to the ground surface (road),
and the wheel and tire are rotating the tire’s tread is experiencing mostly
rolling resistance/friction/drag with the road. When the car is at rest
relative to the road, if the wheel is turned, the tread is experiencing
mostly kinetic friction with the road.

The magnitude of the friction (a force) between two surfaces is calculated
as the friction coefficient (commonly: µ, mu) for the contact of the two
surfaces for the respective situation times the magnitude of the normal
force F_n on the body with significantly less mass (lighter body):

F_f = µ F_n,

whereas

F_n = F_g cos α = m g cos α

is the force with which a body is pressed against the ground surface by
gravity (actually the force that the ground surface must exert on the
lighter body to prevent it from continuing to fall freely towards the center
of energy–momentum of the heavier body, e.g. the center-of-mass of Earth).

α is then the angle of the ground surface to the tangent surface of the
heavier body:

.
:`.
: `.
: `.
: `. m
: `* cos(α) = F_n/F_g
: F_n .^:`. F_n = F_g cos(α)
: .' α: `.
: .' : `.
: `. : F_g `.
: `. : `.
: `.: `. ^
:__ v `. : n __
: | α`. : |PE
'--------------------------`----'--

(α = 0 ⇒ F_n = F_g cos(0) = F_g × 1 = F_g as expected, so this works.)

The coefficient of rolling resistance is generally much smaller than that of
kinetic friction – which is why the wheel was invented in the first place.
For example, the coefficient of kinetic friction for car tire rubber on
concrete is 0.6 to 0.85, while the coefficient of rolling resistance is only
0.01 to 0.015.

<https://en.wikipedia.org/wiki/Friction#Kinetic_friction>
<https://en.wikipedia.org/wiki/Rolling_resistance>

For a car that has an average mass of 1 metric ton, on a horizontal road
that makes a difference of friction of at least

F_fs = µ_s m g = 0.6 × m g = 0.6 × 1'000 kg × 9.82 m/s² ≈ 5'892 N

to

F_fr = µ_r m g = 0.01 × 1'000 kg × 9.82 m/s² ≈ 98.2 N,

i.e. at least 60:1. The greater the friction, the greater the wear. So,
roughly speaking, turning a still tire wears it off 60 times more than
turning it while driving, which means that its lifetime is reduced to 1/60
of its normal lifetime if this would be done continuously.
Post by micky
It's harder to relate to the sliding motion of the tire on the
road surface when the car is moving,
A tire is usually *rolling*, NOT sliding, on the road surface.

[If it would be sliding, then the respective vehicle would be out of
control. One possibility for this condition is aquaplaning: the tire
is sliding on the water on the road instead of rolling in proper
contact with the road. Tires with a pronounced profile and suitable
tread pattern reduce or avoid aquaplaning as the water can be displaced
into the tread pattern so that the tire keeps in contact with the
road.

<https://en.wikipedia.org/wiki/Aquaplaning#Prevention_by_the_driver>]
Post by micky
but it's clear when the car is still. That seems to me to be the
difference, but the vectors that indicate rubbing seem the same either way.
Most certainly they are not. In the rolling case there is an additional
non-zero force vector in the direction of the wheel’s axial rotation:

___ ___
: : : :
: .-:----> F_fk : -------> F_fk = F_res
^ : : :
F_fr : : : :
: : :
=:=*=:= =:=*=:=
: : : :
: : : :
: : : :
: : : :
:___: :___:

rolling, at rest,
turning left turning left

(friction is always opposite to the direction of motion)

Since the tread profile is optimized for the wheel rolling in the direction
of axial rotation, NOT sliding, sidewards sliding of the tire at rest is
detrimental to the lifetime of the tire and quality of the tread,
particularly when the vehicle has a great mass and it is done on a
horizontal road (as then the friction is greater; see above). Also, one can
imagine that the greater torque required to turn a still wheel (to work
against the greater friction) produces additional stress and wear for the
steering.
Post by micky
I included the math group first because it seems like they would have
opinions.
Please do not do that again.

“No article in the world is relevant for more than
a few newsgroups. If World War Ⅲ is announced,
it will be announced in news.announce.important.”

–attributed to Peter da Silva

F’up2 sci.physics
--
PointedEars

Twitter: @PointedEars2
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Tom Ivar Helbekkmo
2019-05-12 08:36:44 UTC
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Post by Thomas 'PointedEars' Lahn
Post by micky
It's harder to relate to the sliding motion of the tire on the
road surface when the car is moving,
A tire is usually *rolling*, NOT sliding, on the road surface.
I suspect what the OP was thinking of was that there must be *some*
non-rolling component to this. Any particular little area of front
wheel tire tread that touches the road while rolling will spend a
non-zero amount of time in contact with the road surface before being
lifted back off it. If the steering wheel is being continuously turned
while this goes on, the angle of the wheel to the car, and the diameter
of the car's turn, will both have changed while the bit of rubber in
question was touching the road, so that particular bit of rubber
seemingly cannot have been completely at rest on the road surface during
this time. Furthermore, during a turn, the outside edge of the tire
tread is rolling a longer distance than the inner. Both of these
effects should have a non-rolling aspect. My suspicion is that the
reason it's so much easier to turn the steering wheel while the car is
rolling is that the rubber is, in fact, *not* sliding across the road
surface while in contact with it: both of the mentioned problems are
solved by slight deformation of the tread during the contact phase.

-tih
--
Most people who graduate with CS degrees don't understand the significance
of Lisp. Lisp is the most important idea in computer science. --Alan Kay
Thomas 'PointedEars' Lahn
2019-05-12 11:14:21 UTC
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Post by Tom Ivar Helbekkmo
Post by Thomas 'PointedEars' Lahn
Post by micky
It's harder to relate to the sliding motion of the tire on the
road surface when the car is moving,
A tire is usually *rolling*, NOT sliding, on the road surface.
I suspect what the OP was thinking of was that there must be *some*
non-rolling component to this. […]
Yes, but it is my understanding that the sliding component becomes the more
negligible the faster the wheel (and tire) is rotating (i.e. the faster the
car is moving), because points on the bottom of the forward-rolling tire are
moving/rolling faster backwards than sliding sidewards.
Post by Tom Ivar Helbekkmo
[…]
My suspicion is that the reason it's so much easier to turn the steering
wheel while the car is rolling is that the rubber is, in fact, *not*
sliding across the road surface while in contact with it: […]
At least because points on the bottom front of the tread are mostly
moving/rolling *backwards* instead of sliding sidewards, the sliding should
be negligibly small compared to the rolling.

Therefore, the total friction should be about 60 to 85 times smaller and
about 60 to 85 times less force should be required to turn the wheel (µ_r =
0.01…0.015, µ_k = 0.6…0.85). The steering reduces the required force again
in all cases (I do not know by how much; it would probably be a nice
exercise in mechanics to calculate it).

See also my other follow-up.
--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
Sylvia Else
2019-05-12 05:14:30 UTC
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Post by micky
When I was in high school I was taught, or I read, that it's bad to turn
the steering wheel when the car is not moving. It's hard on the front
tires, wears out the tread, and one should be moving the car at least a
little when turning the wheel. Did they say that? Do they still?
More importantly, it's hard on the steering linkage, which tends to be a
lot more expensive to replace.

Mind you, with modern power steering, clueless drivers, and longer
warranties, manufacturers have probably beefed up that part of the
mechanism.

Still, when you trust your life to a machine, treating it well seems
like a no-brainer.

Sylvia.
Xeno
2019-05-13 13:27:58 UTC
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Post by Sylvia Else
Post by micky
When I was in high school I was taught, or I read, that it's bad to turn
the steering wheel when the car is not moving.   It's hard on the front
tires, wears out the tread, and one should be moving the car at least a
little when turning the wheel.   Did they say that?  Do they still?
More importantly, it's hard on the steering linkage, which tends to be a
lot more expensive to replace.
If it was so hard on the steering, manufacturers would never have fitted
power steering to cars.
Post by Sylvia Else
Mind you, with modern power steering, clueless drivers, and longer
warranties, manufacturers have probably beefed up that part of the
mechanism.
Nope, the parts were sufficiently strong enough before the advent of
power steering.
Post by Sylvia Else
Still, when you trust your life to a machine, treating it well seems
like a no-brainer.
Sylvia.
All driving instructors (should) tell their students to roll the car
fore or aft slightly when turning the steering. It is amazing just how
much of a difference that makes to steering effort. What you are
effectively doing is transferring the energy to the tread blocks and
they are sufficiently flexible enough to absorb the energy involved.
After all, it's the tread blocks that are giving you slip angles at
higher road speeds. https://en.wikipedia.org/wiki/Slip_angle
--
Xeno


Nothing astonishes Noddy so much as common sense and plain dealing.
(with apologies to Ralph Waldo Emerson)
sergIo
2019-05-13 13:46:53 UTC
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Post by Xeno
Post by Sylvia Else
Post by micky
When I was in high school I was taught, or I read, that it's bad to turn
the steering wheel when the car is not moving.   It's hard on the front
tires, wears out the tread, and one should be moving the car at least a
little when turning the wheel.   Did they say that?  Do they still?
More importantly, it's hard on the steering linkage, which tends to be
a lot more expensive to replace.
If it was so hard on the steering, manufacturers would never have fitted
power steering to cars.
power steering is force multiplier, makes it easier to steer.

but along the way companies cheapend out the power steering, mostly the
pump, and it is less reliable, in some cars not replaceable if it
breaks, you can only get another from a junk yard and put it in, but it
is just as bad, plastic tanks that crack....
Post by Xeno
Post by Sylvia Else
Mind you, with modern power steering, clueless drivers, and longer
warranties, manufacturers have probably beefed up that part of the
mechanism.
Nope, the parts were sufficiently strong enough before the advent of
power steering.
true, I think all cars have power steering now, know of any that do not ?
Post by Xeno
Post by Sylvia Else
Still, when you trust your life to a machine, treating it well seems
like a no-brainer.
Sylvia.
All driving instructors (should) tell their students to roll the car
fore or aft slightly when turning the steering. It is amazing just how
much of a difference that makes to steering effort. What you are
effectively doing is transferring the energy to the tread blocks and
they are sufficiently flexible enough to absorb the energy involved.
After all, it's the tread blocks that are giving you slip angles at
higher road speeds.  https://en.wikipedia.org/wiki/Slip_angle
Xeno
2019-05-13 14:10:00 UTC
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Post by sergIo
Post by Xeno
Post by Sylvia Else
Post by micky
When I was in high school I was taught, or I read, that it's bad to turn
the steering wheel when the car is not moving.   It's hard on the front
tires, wears out the tread, and one should be moving the car at least a
little when turning the wheel.   Did they say that?  Do they still?
More importantly, it's hard on the steering linkage, which tends to be
a lot more expensive to replace.
If it was so hard on the steering, manufacturers would never have fitted
power steering to cars.
power steering is force multiplier, makes it easier to steer.
but along the way companies cheapend out the power steering, mostly the
pump, and it is less reliable, in some cars not replaceable if it
breaks, you can only get another from a junk yard and put it in, but it
is just as bad, plastic tanks that crack....
Plastics are the *new vanguards of planned obsolecence*.
Post by sergIo
Post by Xeno
Post by Sylvia Else
Mind you, with modern power steering, clueless drivers, and longer
warranties, manufacturers have probably beefed up that part of the
mechanism.
Nope, the parts were sufficiently strong enough before the advent of
power steering.
true, I think all cars have power steering now, know of any that do not ?
Wide tyres, powerful engines and front wheel drive, with attendant
torque steer, have guaranteed it.
Post by sergIo
Post by Xeno
Post by Sylvia Else
Still, when you trust your life to a machine, treating it well seems
like a no-brainer.
Sylvia.
All driving instructors (should) tell their students to roll the car
fore or aft slightly when turning the steering. It is amazing just how
much of a difference that makes to steering effort. What you are
effectively doing is transferring the energy to the tread blocks and
they are sufficiently flexible enough to absorb the energy involved.
After all, it's the tread blocks that are giving you slip angles at
higher road speeds.  https://en.wikipedia.org/wiki/Slip_angle
--
Xeno


Nothing astonishes Noddy so much as common sense and plain dealing.
(with apologies to Ralph Waldo Emerson)
Xeno
2019-05-13 14:05:12 UTC
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Post by micky
When I was in high school I was taught, or I read, that it's bad to turn
the steering wheel when the car is not moving. It's hard on the front
tires, wears out the tread, and one should be moving the car at least a
little when turning the wheel. Did they say that? Do they still?
I've been thinking about this and now I have doubts.
Seems to me any extra wear on the tread because of turning the direction
in which the tires point will be the same whether the car is moving or
still. It's harder to relate to the sliding motion of the tire on the
road surface when the car is moving, but it's clear when the car is
still. That seems to me to be the difference, but the vectors that
indicate rubbing seem the same either way.
When you are driving along the road, the tread stays gripped to the road
surface. If it didn't you would be in deep shit at the first corner. At
speed, any speed, the tread blocks are sufficiently flexible to allow
the wheels a small change in steering angle yet still remain gripping
the road surface. https://en.wikipedia.org/wiki/Slip_angle
Post by micky
I included the math group first because it seems like they would have
opinions.
Rather than opinions, I'll direct you to relevant texts on the topic;

Tires, Suspension and Handling, Second Edition
John C Dickson
https://www.sae.org/publications/books/content/R-168

This text covers the subject in more detail;

Steering Handbook
Editors: Manfred Harrer, Peter Pfeffer
https://www.springer.com/gp/book/9783319054483

Chapters 1 through 5 should more than adequately cover your needs.

If you really want to delve heavily into the mathematics of it all, then
this book should do it;

The Automotive Chassis
Engineering Principles, 2nd Edition
J Reimpell, H Stoll, J.W. Betzler
https://www.abebooks.com/9780768006575/Automotive-Chassis-Engineering-Principles-Jornsen-0768006570/plp


The above cover steering, including tyres, from an engineering
perspective and I suspect that's what you're after. The Along the way
you'll get a good grounding on all the effects of steering geometry.
--
Xeno


Nothing astonishes Noddy so much as common sense and plain dealing.
(with apologies to Ralph Waldo Emerson)
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