QuestionThe subject came up that one of our employees was driving around with his rear passenger side tire, approximately half deflated. “Party B” stated that, with the tire partially deflated, it will need to go around more times to cover the same distance. “Party A” stated, no, the circumference of the tire is unchanged and will go around the same number of times to cover the same distance. A heated argument ensued, so we made a bet that parties agreed to. Who’s right, and why?
The specifics of the bet are as follows:
The bet
Party A:
With 1 rotation of the wheel, the car goes forward by one circumference of the tire. And that the tire rolling circumference is not *significantly reduced by low air pressure.
*by more than .5%
That the radius from the wheel hub to the ground has no impact on the calculation of rolling circumference
Qualifiers:
Party A states, that in the case of a radial tire, there is a very small 1/200th ish belt deformation which directly effects circumference, 1 extra rotation every 200 times around. In the case of a balloon or bias ply the percentage of circumference change may be slightly higher but that the distance from the wheel hub to the ground still has no impact on the calculation of rolling circumference.
Party B:
When the radius is changed such that the hub of the wheel is closer to the ground, the wheel needs to go around more times to travel the same distance.
AnswerTim,
I don't think you are going to like my answer but here goes:
You asked:
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Party A:
With 1 rotation of the wheel, the car goes forward by one circumference of the tire. And that the tire rolling circumference is not *significantly reduced by low air pressure.
*by more than .5%
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I don't know what the percentage is, but some Tire Pressure Monitoring Systems (TPMS) rely on the difference in rolling circumference to trigger an alert that a tire is low.
But to add further confusion - if you were to take a tape measure and measure the circumference of the tire at the center of the tread (freestanding), you would find that when the tire rolls when loaded, it only rolls 97% of that circumference. Some folks think this is because the belt - which is relatively inextensible - is what controlls the rolling and it behaves much like a tank track - in the it doesn't matter how you distort it from a circle, it still has the same length - and the tread merely sits on top and deforms as the belt goes through the footprint.
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You also said:
That the radius from the wheel hub to the ground has no impact on the calculation of rolling circumference
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It's a little more complex than that as the "Static Loaded Radius" - what you called "radius from the wheel hub to the ground" - has a some affect on the rolling circumference, but clearly the relationship is not as simple as the ratio of diameter to circumference of a circle. I should also point out that the the hub is off center compared to the tire.
Put another way, if you were to take a mounted tire, put in on a car, and slowly lower the car to the ground, not only would the ground distort the shape of the tread at the bottom and the hub get closer to the tread, but the tread 180 degress opposite to the ground moves away from the hub. The amount is affected by a great many things, and I don't think anyone has explored what those things are.
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Further, you said:
Qualifiers:
Party A states, that in the case of a radial tire, there is a very small 1/200th ish belt deformation which directly effects circumference, 1 extra rotation every 200 times around. In the case of a balloon or bias ply the percentage of circumference change may be slightly higher but that the distance from the wheel hub to the ground still has no impact on the calculation of rolling circumference.
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As I stated earlier, I don't know the percentage, but a bias ply tire would be more affected.
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And you continued:
Party B:
When the radius is changed such that the hub of the wheel is closer to the ground, the wheel needs to go around more times to travel the same distance.
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That's somewhat true, too. The problem is that tires distort and the hub is off center, the tread is flat to the ground, etc.
OK - Bottomline? No one wins the bet - it's a standoff!!! There are elements of truth in both positions and the issue is really complex - so much so, that I've had similar conversations with other tire engineers and we get into some interesting debates about cause and effect and whether what I have just stated above is 100% true.
