Quote:
Originally Posted by arcosine
Its a law of physics, not a dumb table. The contact pressure equals the inflation pressure of the tire, period. The load equals the pressure times the contact area..........
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I'm sorry, but that is
NOT a law of Physics.
That formula calculates the average ground contact pressure of a tire, but the contact pressure is not equal to the inflation pressure - except coincidentally.
Quote:
Originally Posted by arcosine
......... A narrow tire will had a narrow contact patch, a wide tire will have a wide contact patch. At the same inflation pressure, the narrow tire's belt will deflect more.............
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Not only is that not true, you forgot to add ".....if everything else remains the same." - and unfortunately, things do not remain the same between wide tires and narrow tires. For one, every time you go wider, the load carrying capacity goes up - and that has profound effects on RR.
There are quite a few parameters involved in describing a tire and no matter how you slice it, if change only one thing, something else also changes. Let's follow your example and you will see what I mean.
Quote:
Originally Posted by arcosine
...........Lets take 2 cases; a 1 inch wide tire and a 2 inch wide tire, same pressure, load, construction, and diameter......
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What you didn't mention is that the aspect ratio also changed. And what about the load carrying capacity? Did that change as well?
Plus, if we are using a tire with the same construction, was the construction adjusted to compensate for the fact that we have a physically larger perimeter and NEED a stronger cord in order to keep the same relative strength?
Quote:
Originally Posted by arcosine
...........The one inch tire deflects twice as much....
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I'm sorry, that is not true. The load carrying capacity of the wider tire went up, so the deflection went down because the load on the tire is a smaller percentage of the load capacity.
Quote:
Originally Posted by arcosine
........... but the belt is half as stiff...........
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How can a belt be half as stiff if it is the same?
Quote:
Originally Posted by arcosine
...........But the 1 inch tire can be inflated to twice the pressure without over stressing the cords.................
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Not quite. You need to consider the fact that the tire is not a complete chamber. It is tied to the rim at the bead, so the perimeter isn't quite twice - assuming the same construction.
Tony,
While going through an analysis like you did is helpful in understanding the Physics involved, it is important that the end result match what happens in the real world. The Smithers report to the CEC presents some very valuable insight into how passenger car tires operate relative to rolling resistance - and what it says is that wider tires are ever so slightly better for RR than narrower tires. Why?
Well, if we increase the width of a tire - and try to change nothing else - the diameter goes up (remember, we are keeping the same aspect ratio!). The load carrying capacity also goes up - in proportion to the width increase. Therefore the load on the tire is a smaller percentage of the capacity - and therefore there is less deflection for a given load.
Further, while the width of the tire increased, the width of the tread and belts increased a percentage of that change - not 100%. Put a different way, if the tire is wider by 10mm, the width of the tread and belts will be about 7mm wider!
And one last item: There are still only 2 sidewalls - and while sidewalls do not have much impact on RR, they do have some.
But what about inflation pressure? To date, I have not found any studies where the effect tire size has on RR is adjusted for load carrying capacity. Put another way, if we test for a tire's RR at a given load and inflation pressure, then test an otherwise identical, but larger, tire at the same load, but adjust the inflation pressure according to the load tables to get the same load carrying capacity, what would we get? I suspect an ever so slight reduction in RR - one that might not be able to be measured.
But until we get a study like that, we will have to rely on what informtion is available about what actually happens - and the Smithers report is an excellent source.