Originally Posted by
alpineboard
Let us agree on a few things, one complete revolution of the rim equals one complete revolution of the tire.
If you cut the tire circle at one point and lay it flat on the ground in a straight line, like a belt, one complete revolution of the circle equals
one full length of this belt, this does not change, ever, squish or no squish. This distance does not change if it gets squished under load or no squish under no load.
No one is saying it does. The perimeter of the tire doesn't change.
It's important to keep in mind that the loaded tire
isn't a circle. It's a
deformed circle (there's a flat part at the bottom). It's also important to be clear that circumference is an attribute of an
actual circle (or ellipse).
Originally Posted by
alpineboard
One rev of the wheel equals one circumference distance.
This is where you are making a mistake.
There are
two circumferences to keep mind of: (1) the circle with the tire radius and (2) the circle with the "patch radius" (the vertical distance between the center of the wheel and the ground). (The tire perimeter is a
third thing to keep in mind.)
The circumference that matters is the
second one. This is the 2*(vertical distance) * Pi circle. The vertical distance varies with the load (it's shorter with heavier loads). Thus. the circumference varies with load (as does the horizontal distance travelled). (The tire perimeter is irrelevant.)
Look at my illustration.
Originally Posted by
alpineboard
Let us agree on a few things, one complete revolution of the rim equals one complete revolution of the tire.
The distance travelled in one rotation on a loaded wheel is less than the length of the perimeter of the tire (the length covered by the cut tire laid flat).
Originally Posted by
alpineboard
I fully realize there other variables going on, at the squish load spot, compression, temperature, ect, but all these are irrelevant
until the understanding of the belt theory is understood.
What the "belt" is doing is irrelevant.
The only thing that matters is the distance of the center of the axle and the ground.
Tanks are an extreme example of what is going on. The distance travelled in a rotation is the circumference of the circle with the radius of the wheel axis to the round (not the track length). The tire perimeter is like the track: it doesn't matter how long it is.
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(1) Consider what the deal would be if you removed the tire and just ran on a raw rim. Note that this would be what would happen if you had an extreme load (or no air in the tire).
In this case, the horizontal distance would be equal to the circumference of the rim.
(2) Now, imagine running on a raw rim that was as big as the wheel with a fully-inflated tire. Or on the same rim but with a solid tire that doesn't compress.
In this case, circle and circumference is larger, which means the horizontal distance would be larger than case (1).
So, the circumference of a real wheel is going to be between case (1) and case (2). The circumference will be smaller with more load or less pressure.