I love me some hulls out of the water but I have a quibble with the term “flying” when there’s still something in the water and taking everything out of the water is dangerous, even of it is only a tiny fraction of the boat… have hydrofoils always been spoken of as flying or is that more recent hype?
In the context of a planing catamaran, flying refers to allowing the windward hull to lift out of the water in order to minimize wetted surface area. These boats, especially the Hobie 16, were quite popular in the 70s and 80s.
They call it flying because foils are flying through a medium, generating lift, just as the wings of airplanes do.
A big difference is that these wings lift the main body out of that medium (water) into a much less dense one (air), hugely decreasing resistance.
And yes, this doesn’t lift the boat completely out of the water, but airplanes do not get completely out of the medium they use (air), either.