I have recently been working on pre-flight inspections of an aircraft with the pilots that take me on scenic rides. The tires are one of a number of items on our pre-flight checklist. So, I told him about the article that my friend sent me. He told me that he thought that the proper tire pressure on the Cessna 172P was about 30 pounds per square inch (psi). He went on to remind me that we had talked about the relationship between tire pressure and hydroplaning and aircraft speed in ground school.
Automobiles can hyrdoplane, as can aircraft. Not a situation you want to be in either vehicle. When you hydroplane, for example on a wet runway, your tire loses contact with the ground and you lose control of the aircraft.
Take a moment and go here and watch a two minute video on NASA's work on hyrdoplaning. You will see a formula in the video:
According to the above formula, a tire with pressure of 30 psi will start to hydroplane at about 49 kts.
Note - apologies for not using proper mathematical notation for the square root symbol. If I can figure out how to include a square root symbol in html code that will show up here, I'll revise the article later.