Had a bit of a play in some mud today. I kept my street tyre pressures, partly because I was feeling lazy, but the others dropped theirs by varying amounts. Turned out we all got through okay but it prompted me to dig out and post this diagram showing the effect of lowering tyre pressures. This one was stolen from a Mickey Thompson brochure, as if you can't tell from the "Baja Claw" tread pattern. When you look at a part-deflated tyre, it seems from the "bulge" that the extra contact area is lateral, but the diagram shows that the big footprint gain is in added fore and aft contact.
Tyre pressures between 16 and 28psi are often recommended for mud, although some drivers go much lower when using tubes and/or beadlockers. On the other hand, you may not even need to lower pressures. The most suitable pressure depends very much on the type of mud, the steepness of slope and what sort of base lurks under the mud. That's both my experience and what the Mickey Thompson brochure says. If it's thick mud, with a loose, deep base, lower pressures and less wheelspin with some decent momentum may get you through best. If the mud is watery with a solid base, you can maintain higher pressures, maintaining momentum without going fast enough to either lose control, hit something or wreck the track. Higher pressures will be required when carrying heavy loads.
Politically correct disclaimer: Remember, whenever you reduce pressures, re-inflate as soon as you drive back to the road.
Here's another take on tyre footprints, this one from Andy Cockroft's book, 4WD North Island: 102 Off Road Adventures (Shoal Bay Press, 2002).Effect of tyre pressure on length of footprint. (Measurements taken from Land Rover Series IIa with Dunlop Mud Rovers fitted.)
1. Over-inflated to 35psi, Reduces the footprint to 7.5 inches (-6.25%)
2. Normal inflation of 25psi. Footprint measures 8x8 inches.
3. Halving pressure to 12psi increases length of footprint to 11.5 inches (+43.75%).
4. Halving again to 6psi increases footprint to 15 inches (+87.5%).