Several years ago, I made a study of tire surface area versus inflation pressure. This information was most helpful when driving in sand and in extreme off-road conditions. Many times my brother, his family and I went out to the southern California desert to roam and drive around. It was a good time. More than once, I pulled someone out in either a 2-by or who hadn’t reduced their tire pressure to something that would work in sand.
My short article on tire inflation actually shows the tire footprint relative to the inflation pressure. This graphically shows how different the footprint can be.
This article here by Harry Lewellyn is a more complete mini-tretise on why reducing tire pressure works.
Granted, I’ve never taken my 2005 Tacoma up Elephant Hill in Utah. That would have been an ultimate test of tire inflation vs grip. It’s a notorious vehicle wrecker. As I walked up, I could see serious scrape marks on the rocks with lots of drained oil or other vehicle fluids. I’ll stick with simple sand driving and medium off-roading.