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Subject: What Holds the Rim Off the Ground?
From: Jobst Brandt

What forces keep the rim of a wheel with pneumatic tires off the ground? It obviously can't be the air pressure because that's acting from top as well as from below.

As has been pointed out, the casing walls pull on the rim (or its equivalent) and thereby support the load. The casing leaves the rim at about a 45 degree angle, and being essentially a circular cross section, it is in contact with the rim over its inner quarter circle. At least this is a good representative model. The visualization may be simpler if a tubular tire is considered. It makes no difference whether the tire is held on by glue or is otherwise attaches to the rim such as a clincher is. Either way the tire is attached to the rim, a relatively rigid structure.

Under load, in the ground contact zone, the tire bulges so that two effects reduce the downward pull (increase the net upward force) of the casing. First, the most obvious one is that the casing pulls more to the sides than downward (than it did in its unloaded condition); the second is that the side wall tension is reduced. The reduction arises from the relationship that unit casing tension is equivalent to inflation pressure times the radius of curvature divided by pi. As the curvature reduces when the tire bulges out, the casing tension decreases correspondingly. The inflated tire supports the rim primarily by these two effects.

Tire pressure changes imperceptibly when the tire is loaded because the volume does not change appreciably. Besides, the volume change is insignificant in small in comparison to the volume change the air has undergone when being compressed into the tire. In that respect, it takes several strokes of a frame pump to increase the pressure of a tire from 100 psi to 101. The air has a low spring constant that acts like a long soft spring that has been preloaded over a long stroke. Small deflections do not change its force materially. For convenience car and truck tires are regularly inflated to their proper pressure before being mounted on the vehicle.

Jobst Brandt

Also see our article on tires

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More Articles by Jobst Brandt
Next: Measuring the Circumference of a Wheel
Previous: Shimmy or Speed Wobble

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