Is there a way to estimate contact patch size given tire size plus tire volume and rider weight?

Question

Is there a way to estimate contact patch size given tire size plus tire volume and rider weight?

Specifically, I've tried to build a unicycle that maximizes contact patch for riding on soft snow. I have a 26"x3.7" tire with a 65mm rim that I have at 12psi, how can I calculate the resulting contact patch?

For extra credit, I'd like to calculate the contact patch size required to ride across newly fallen snow for a particular rider weight.

This question was previously asked as a comment on my previous question, but I feel it needs its own question...

Answer 1

Basically: weight/psi = square inches.

Has to be combined weight of rider and cycle. And it's approximate. And much easier with a unicyle: with a bicycle you need to know weight distribution, which can change during a ride.

Minor things that make it only an estimate:

• Compression from weight increases psi, making contact patch smaller than estimate.
• thickness of material could increase contact patch size. In fact, I think this math gives you the area of the part of the interior surface of the inner tube that's pressed against the part of the tire pressed against the ground
• stiffness of tire materials could decrease contact patch size
• tread features (knobs, grooves, etc) could do all sorts of things to contact patch size.
• bumps, jumps, etc momentarily increase "weight" (downward force on wheel or upward force on contact patch), contact patch size and psi.

No idea about new fallen snow.