Tire Contact Patch from Load and Pressure
The tire footprint, and the flotation lever behind airing down: A = W / p, the corner load divided by the inflation pressure. Because the patch carries the load at the inflation pressure, the average GROUND pressure roughly equals the tire pressure independent of load -- which is why airing down floats over sand and cuts soil compaction. A 900 lb corner at 35 psi rides on about 25.7 in^2; drop to 15 psi and the patch grows to 60 in^2 (2.3x) at the same load. An idealization -- the sidewall and tread carry a little load, so the real patch runs a bit smaller than W/p, more so at high pressure. A field estimate, not a measured footprint; the tire, load, and surface govern.
Formula and source
A = W / p; A_cm2 = 6.4516 A. Average ground pressure ~ p.
The first-order tire contact-patch relation A = W / p (ideal air-pressure membrane), first-principles; the tire, load, and surface govern.
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