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Please help "trick " question regarding car tyres
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Posted by: martin_uk

03/01/2005, 19:45:16

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I am hoping someone can answer a technical question, to resolve a long standing argument regarding car tyres.

The question is - what supports the weight of a car, the sidewall of the tyre or the air.

My understanding is that the air is there only to maintain the shape of the tyre, and allow the sidewall to do it's job, holding the weight.

Thinking about it, with a vehicle sitting on the ground, the force due to the weight of the car acts downwards and is equalled by the force of the groud on the tyre. This is acting at the point of contact (ie. the bottom of the tyre) - if the air was supporting the weight of the car then would not the pressure (of the air) be greater at the bottom of the tyre than the top (?) which of course it isn't as pressure in a gas is constant. Further, if say an average tyre pressure is 30psi and the car is jacked up, the pressure remains the same (30psi). Again, if the air was supporting the weight of the car, would this pressure not be expected to increase when the car is on the ground. Effectivly the weight of the car would cause the air to be compressed causing a higher pressure - which is not the case.

If I am wrong, how is it that the pressure stays constant, with or without the weight of the car.

I would be most grateful if you could resolve this for me.

Kindest regards,

Martin Holt







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Re: Please help "trick " question regarding car tyres
Re: Please help "trick " question regarding car tyres -- martin_uk Post Reply Top of thread Forum
Posted by: deepalcatrazz

09/08/2005, 14:15:03

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Hi Martin

The question is misleading. The weight of the car can be held by tube tyres i.e tyres with no air in them as well.

Think of the tyre assembly as a single elastic body with a certain prescribed stiffness. Then, isolate this body as a free body in space. Once you have done that, You will understand that the rubber of the tyre is in a constant state of prestress. Thus, there is an interplay between the pressure exerted by the air and the strain energy stored in the tyre/tube. This pressure does not change..i.e when the car is jacked up, the tyre material restates itself and consequently expands when in contact with the ground.

However, coming back to the question about which one takes the load..its both of them acting as a system!!

Hope this helps

Cheers
deepak







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Re: Please help "trick " question regarding car tyres Smile
Re: Please help "trick " question regarding car tyres -- martin_uk Post Reply Top of thread Forum
Posted by: swearingen

03/22/2005, 09:42:14

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I have the answer: The air does most of the work. Here's why:

This question is very similar to a question about anchor bolts on building columns. I'll explain this one and relate the two. Let's say you have 2 anchor bolts embedded in concrete and set a column over them. You put nuts on the bolts and tighten them until you have 10,000 lbs of pretension in each bolt. Questions:

1. How much tension is in each bolt when you apply 10,000 lbs of tension to the (assumed weightless) column?
2. How much tension is in each bolt when you apply 20,000 lbs?
3. 50,000 lbs?

The answers are 10,000, 10,000, and 25,000. Why? Because the bolts already have 10,000 lbs in them and if you apply anything less, they will only see their 10,000 lb preload. Once you get a load higher than their preload, they will then start to see more stress.

Back to the tire question. Let's assume a rectangular tire configuration - flat bottom and almost vertical sides (they bow out a little from the pressure, but this gives the sides very little vertical stiffness - hence the problem when there's no air).

Looking at an unloaded free body diagram of a cross-section of tire is pretty simple. With, say, 30psi in the tire, you have 30psi pushing on all surfaces. In this condition, the tire actually wants to pull away from the rim because of the internal pressure (30psi pushing up on the rim and 30psi pushing down on the tire). I equate this to the preload in the bolt analogy above - the sidewalls are pretensioned. If I push up on the tire and don't exceed an effective 30psi load over the area I push on (i.e., don't exceed the pretension in the sidewalls), THE PRESSURE IN THE TIRE WILL NOT INCREASE. It's tough to grasp at first, but I'll use a piston analogy to further the cause.

If you have an air-tight piston and put a load on the top, it will indeed go down and the pressure will go up accordingly. However, if you pressurize the piston chamber to 30psi and don't load it, you have to have a mechanism for holding the piston from flying away, so you put a lip over the top and the internal pressure pushes against this lip (think of the bead at the wheel/tire interface). This puts the walls of the piston in tension (the sidewalls of an unloaded tire are in tension, just like the preload on the bolts in the above example). Now, load the piston. Note that until you load the piston with enough weight to overcome the 30psi pushing from underneath, the piston will not move AND THE PRESSURE WILL NOT CHANGE despite having added a load. This is the essence of preload situations and applies for a tire.

Yes, the sidewalls do provide some resistance, but that pales in comparison to what the air does.







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Re: Please help "trick " question regarding car tyres
Re: Please help "trick " question regarding car tyres -- martin_uk Post Reply Top of thread Forum
Posted by: Cragyon
Bart
03/02/2005, 09:23:50

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My understanding is that the air is supporting the weight of the vehicle. Obviously, a tire without internal air pressure would not support the weight of the car. I do know that the design and manufacture of the tire is what maintains the proper shape of the tire under correct internal pressure and when loads are applied during manuvering. In fact, if you have a structural failure in the side wall of the tire, every time you make a turn into the failed tire, the tire will partially lay or bend over due to the side force applied on the tire. I beleive the pressure in a tire is approximately constant. This is due to the changing of shape of the tire under loading. Now, as the air within the tire heats up, you will see an increase in pressure due to the expansion of the the air gas.






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Re: Please help "trick " question regarding car tyres
Re: Re: Please help "trick " question regarding car tyres -- Cragyon Post Reply Top of thread Forum
Posted by: martin_uk

03/02/2005, 14:33:57

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I see your point - but consider the following,

If you lowered the weight of the car onto four (one for each wheel) cylinders with a free moving piston, full of air, the weight would then be supported by the air, and the pressure would indeed rise inside the piston - therefore you would expect this to happen when a car is lowered onto its tyres, but the air pressure does not rise ??? Does this lack of increase in air pressure not show that the air is doing nothing (apart from maintaining the shape).

Or yet another way of looking at it, suppose the tyres were hollow, but very very stiff rubber, almost solid. There is a vacuum inside the 'tyre' - clearly the rubber of the tyre supports the car. Now, replace that vacuum with air, nothing changes, still the rubber supports the car. Now make the sidewalls thinner, eventually they will 'flex' but still support the weight of the car - there is no point at which the support suddenly jumps from the sidewall to the air !! What we have 'created' moving from a solid structure to one with thinner walls that flex, is indeed a tyre !!!

If the air does support the weight, how do you explain te lack of increase in pressure when the car is on the ground.

Indeed a tyre rotating maintains a almost constant volume, yes it changes shape, but volue is near constant. The increse in preesure due to temp. change is valid, but fairly minimal (at least under normal useage.

I was originally told of this as a potential trick university / job interview question, by a mechanical engineer who specialised in fluid mechanics so I have very good reason to believe it is true. My engineering days are 'behind me' (I'm in IT) but have a degree in mech eng. I looked at a couple of tyre manufactures websites, and I really believe that one has it wrong as they state that the air supports the weight, but to me, putting across the views above, do I not have a point.

Thank you for your interest and reply - I may get the books out and see if I can remember enough to prove by maths.

Its a bit like the bike spokes question, the ones 'hanging down' from the top support the weight (well transfer it to the wheel), not the ones 'pointing up' - thats a difficult one to get your head round also.

Thanks,

Martin







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Re: Please help "trick " question regarding car tyres
Re: Re: Please help "trick " question regarding car tyres -- martin_uk Post Reply Top of thread Forum
Posted by: zekeman

03/04/2005, 20:36:59

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The answer is both air and tire contribute to the forces sustainng the load. Assume that the flat area of contact of tire on ground is A. then a free body equilibrium analysis on the flat material yields
W=A*p+s*l
where
W= reaction force
p=air pressure
and where A is the measured area of contact and s is the shear force along the periphery and l is perimeter of contact. Since the tire deforms negligibly overall, the volume remains essentially constant under the loads we are dealing with and therefore pressure p remains essentially constant for this discussion.(obviousy under ambient/driving conditions the temperature changes would change the pressure proportionately)
The way that the reaction force W is delivered to the rim of the tire is thru the tire wall due to the local shear forces and compressive forces manifested in the distorted tire and are very complex but are entirely solvable by finite element analysis.
In the absence of sufficient air pressure the natural forces on the tire at the rim would be compressive and shear which would tend to collapse the tire. Under air pressure the "hoop" stress due to to the air is tensile which reverses the effect of the compressive force , thus holding the tire configuration and preventing collapse.






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Re: Please help "trick " question regarding car tyres
Re: Re: Please help "trick " question regarding car tyres -- zekeman Post Reply Top of thread Forum
Posted by: randykimball
Barney
03/04/2005, 23:13:48

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A simple down to earth answer, if you please....

The air in the tire forces the tire to hold shape. The tire can not stretch much, but it can be depressed. The air pressure resists this depressing of the tire. When the forces of mass weight and depressing of the foot print reach equality the tire holds up its share of the car to that height.

BOTH hold up the car. The side walls have little effect unless the tire is out or near out of air.

-randy-




The worst suggestion of your lifetime may be the catalyst to the grandest idea of the century, never let suggestions go unsaid nor fail to listen to them.


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Re: Please help "trick " question regarding car tyres
Re: Re: Please help "trick " question regarding car tyres -- randykimball Post Reply Top of thread Forum
Posted by: zekeman

03/06/2005, 12:08:17

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I think the author of the thread was looking for a quantitative answer, not qualitative, as you suggest.






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Re: Please help "trick " question regarding car tyres
Re: Re: Please help "trick " question regarding car tyres -- zekeman Post Reply Top of thread Forum
Posted by: martin_uk

03/07/2005, 17:01:37

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Thanks for your help guys ...

I have the answer if I've understod correctly, in summary, as the air pressure is not greater at the bottom of the tyre, the side wall is effectively supporting the load - however, I appreciate the air plays a major part as explained.

Found this from a site ... same thing in different words.

The load transmission on a pneumatic tyre is analogous to that of a bicycle wheel, where the hub hangs on the spokes from the upper part of the rim, which in turn is supported at its lower part by the ground. For an inflated pneumatic tyre, the inflation pressure causes tension to be developed cords comprising the carcass. The load applied through the rim of the wheel hangs primarily on the cords in the sidewalls through the beads.







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Re: Please help "trick " question regarding car tyres
Re: Re: Please help "trick " question regarding car tyres -- martin_uk Post Reply Top of thread Forum
Posted by: randykimball
Barney
03/07/2005, 21:42:19

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Well, we ALL had fun with that, did we not...?



The worst suggestion of your lifetime may be the catalyst to the grandest idea of the century, never let suggestions go unsaid nor fail to listen to them.


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