# Teaching Tires?

#### sharming14

I have to teach Tires to my class and I want to do something innovative and new that will tie in to Physics. Please help and any ideas you have that I could use would be greatly appreciated

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#### berkeman

Mentor
I have to teach Tires to my class and I want to do something innovative and new that will tie in to Physics. Please help and any ideas you have that I could use would be greatly appreciated
Welcome to the PF.

What kind of class? Is this like for an automotive technician training class? Or a high school science class? Who is the audience? Why/What do they need to learn about tires?

#### sharming14

Hello thanks for replying, this is a highschool grade 11 class just learning forces I need a good way to introduce friction while giving them something they can really relate to

#### berkeman

Mentor
Hello thanks for replying, this is a highschool grade 11 class just learning forces I need a good way to introduce friction while giving them something they can really relate to
So the friction forces with the road, okay. I guess that's not a good group to show links about racing tires and dragster slick physics, eh? Not good to encourage their antics too much... :-)

You can cover F = mu * N stuff to explain braking forces, and talk about how the mu varies between soft/sticky racing tires and hard truck tires. You could talk about how anti-lock braking systems work, and how they help vehicles to still steer under (almost) maximum braking....

#### lalbatros

My post to answer the initial question in post #1 was deleted and I even received a warning for it.
This post was deleted as it was considered as nonsense.
Actually, it was perfectly to the point since it answered specifically the wish to come with a fresh approach.

The eye pressure is (classicaly) measured by applying a transparent plate on the eye and measuring the contact surface as a function of the applied force.

Theoretically, a (mathematical) Abel inversion of this measurement leads to the evaluation of the eye internal pressure.
Practically, this is a routine and very simple examination.

Furthermore, I discovered myself this topic of eye pressure measurement when I worked on the mechanical contact on cement kiln tires. These tires are not from rubber, but are huge steel rings used to support the rotary kilns in cement plants. The contact surface is the main factor to reduce constraints in the kiln shell as well as the deformations. It depends on the gap between kiln shell and the tire.

In summary, rubber tires, kiln tires and eye pressure measurement share a common mechanical behaviour.
It is about forces, deformations, elasticity, contact.
No need to stress that good tire contact is important for driving safely.

I hope that this further explanation will cancel the unjustified warning that I received.
In the meanwhile, I'm really shocked.

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#### xxChrisxx

It's tricky teaching tyres and focusing on friction, as it's perpetuated many into a misunderstanding about how tyres grip and created huge (and needless) debates about contact patch area.

What sort of thing would you like to focus on in the class? What are the aims?

In summary, rubber tires, kiln tires and eye pressure measurement share a common mechanical behaviour.
How on earth are you justifying that a big steel ring (steel is generally pretty stiff) is in anyway similar in mechanical behaviour to a pneumatic rubber tyre?

It is about forces, defromations, elasticity, contact.
No need to stress that good tire contact is important for driving safely.
Would you care to explain what you mean by this?

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#### lalbatros

Hello xxChrisxx,

That's very positive!

How on earth are you justifying that a big steel ring (steel is generally pretty stiff) is in anyway similar in mechanical behaviour to a pneumatic rubber tyre?
This big steel ring is used to support the rotary kiln which is a huge cylinder weigthing typically 2000 tons up to 10000 tons. This ring also serves to rigidify this kiln shell. Without this ring being almost in full contact with the shell, the shell would collapse completely.
In this system you have many forces at play. The similarity with rubbers tires, except for the name, and with the eye pressure measurement is that the contact surface depends on the force applied on the system: the weigth of the car, the weigth of the kiln or the force used to measure the eye pressure. If you look at the equations, these are from elasticity theory, and are all similar.

I would add to this that the Hertz pressure widely used in mechanical engineering is also related to this topic. Here the application usually deals with micro contact between curved surfaces like in many (if not all) mechanical system. On wiki you find many examples: http://en.wikipedia.org/wiki/Contact_mechanics.

Another famous example is that of a spike heel on an elastic floor. This is a mathematical problem known for its signulaties on the border of the heel. The funny think, is that I encountered almost the same equations, long ago, when studying radio frequency antennas. same singularities on their edge. Could I have suggested that radio-frequency antennas can be used to discuss tire physics? Maybe that would be a bit too far fetched?

No need to stress that good tire contact is important for driving safely.
Would you care to explain what you mean by this?
I have little knowledge in this domain.
However, it is clear that a few aspects play a big role here:

- the friction force is proportional to the contact surface
- the friction force/unit surface migh proportional to the pressure
- can we conclude that the friction does not depend of the contact surface?
. . nice to discuss in classroom
- wear could also be an interresting topic
- what happens if the tires over-inflated? contact surface will depend on rubber elasticity
- what happens if the tires at under-inflated?
- what about dissipation of heat in the tire, due to friction, due to periodic deformation?

Of course, we all know that the working of tires is much more complex than that.
I know that the major tire manufacturers are all studying tire physics with super computers (crays in the good old times). Not only they simulate deformation, contact, water flow, geometry, but they also try to analyse noise generation.

Tires can indeed be used to talk about physics!

Michel

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#### xxChrisxx

You are making the classic mistake that all people do, and are trying to apply rigid body (or at least low deflection) characteristics to a highly flexible rubber tyre.

Tyres load and friction charateristics are non linear, basically when you apply load to them they behave in no way like a steel ring.

The method you desicrbe about measureing contact patches underload are used to determine tyre characteristics, it's qute similar to the way they measure slip angles at varying loads.

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#### lalbatros

I don't know so much about tires, indeed, except how they burn in cement kilns, and their impact on the final product and on the process.

However, I did not mention the most interresting topic that could occur when studying the deformation of a kiln shell strengthened by a tire: the buckling of the shell. When this occurs, the contact surface may split into several contact surfaces. I did not go deep in studying this, because this quite too far from real-world interrest. However, in a sense, this could be called "large deformations", at least practically. I had to forced myself not to continue playing further on this topic.

#### jack action

Gold Member
Hello thanks for replying, this is a highschool grade 11 class just learning forces I need a good way to introduce friction while giving them something they can really relate to
This is a nice experiment: http://www.fearofphysics.com/Friction/friction.html" [Broken]

It shows that:

• the weight of the vehicle does not change braking distance
• changing the surface type, changes the friction coefficient
• the kinetic energy of the vehicle (½mv²) has been transformed into heat by the friction force (force X distance)
• maximum braking force depends only on the tire-road properties (and not the brake system)

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#### xxChrisxx

This is a nice experiment: http://www.fearofphysics.com/Friction/friction.html" [Broken]

It shows that:

• the weight of the vehicle does not change braking distance
• changing the surface type, changes the friction coefficient
• the kinetic energy of the vehicle (½mv²) has been transformed into heat by the friction force (force X distance)
• maximum braking force depends only on the tire-road properties (and not the brake system)
Before showing this it's got to be made clear the differences between braking with rolling wheels and braking with sliding wheels. As point one only really applies with sliding wheels and the same compound rubber and assuming a linear friction effect.

I do realize that when teaching a new concept you do have to omit some assumptions to not confuse the teaching aim. I'm not really sure what could be omitted here, I'd be a dreadful teacher.

I suppose that the most important thing would be to teach that if you want to stop quicker fit better tires before you fit bigger brakes.

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#### jack action

Gold Member
Before showing this it's got to be made clear the differences between braking with rolling wheels and braking with sliding wheels. As point one only really applies with sliding wheels and the same compound rubber and assuming a linear friction effect.
First of all, changing rubber compound is like changing road condition; It changes the friction coefficient as pointed in my second point. Usually, large truck tires will have a lower friction coefficient than car tires, hence longer braking distance.

Second, for a highschool grade 11 class just learning forces, assuming a linear friction effect for tires is a fairly good approximation.

Finally, I totally disagree with your point where weight would play a significant role with rolling wheels but not with sliding wheels. Again, assuming the braking system can produce enough torque to reach the maximum tire force.

True, in real life, truck takes longer to stop than cars (as shown http://www.jmu.edu/safetyplan/vehicle/generaldriver/stoppingdistance.shtml" gives an explanation for why a truck takes more time to brake than a scooter.

Again, for high school students, I think the experiment I proposed with these simplified assumptions is good enough for teaching purposes.

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#### cjl

With tires, weight does play a significant role though. Rubber tires deform and behave in ways which do not really follow the simple linear relation that is usually taught in physics. This is also related to the fact that sports cars and racing cars use very wide tires. If rubber behaved in the way a lot of people are assuming here, then there would be no point to this. The standard friction equation does not care at all about surface area. However, because rubber has some "stickiness", the width of the tire actually does matter. Similarly, the weight on a given set of tires matters.

#### jack action

Gold Member
With tires, weight does play a significant role though. Rubber tires deform and behave in ways which do not really follow the simple linear relation that is usually taught in physics. This is also related to the fact that sports cars and racing cars use very wide tires. If rubber behaved in the way a lot of people are assuming here, then there would be no point to this. The standard friction equation does not care at all about surface area. However, because rubber has some "stickiness", the width of the tire actually does matter. Similarly, the weight on a given set of tires matters.
I agree that if you put your 2-ton truck on mini cooper tires, these tires won't behave the same way as they were on the mini cooper. But comparing 2 vehicles with different weight AND with appropriately sized tires of similar construction and compound (and with size, I refer mostly to the http://en.wikipedia.org/wiki/Tire_code#Load_index"), both vehicles will have similar friction coefficients. Anyway, close enough for teaching high school students.

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#### rcgldr

Homework Helper
the weight of the vehicle does not change braking distance
Because of tire load senstivity, the heavier car takes longer. Wiki link (although it shows some numbers for lateral force, the same issue affects forwards and backward forces):

The kinetic energy of the vehicle (½mv²) has been transformed into heat by the friction force (force X distance)
Static friction force at the tires does not generate any heat. Deformation of the tires due to load factor, weight and braking forces, generates heat (hysteresis) but most of the heat lost when braking is due to dynamic (kinetic) friction at the brakes.

maximum braking force depends only on the tire-road properties (and not the brake system)
Assuming the brakes are not overheated, which reduces their coefficient of dynamic friction.

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