I have a very large compost pile, about 8 feet tall and 16 ft wide. Would
it work to put a piece of pipe under the pile and hook up my air
compressor
to it to give the pile air? It is just too large to turn by hand and I am
too cheap to buy a tractor.

It's time to break that pile up into a smaller, more manageable pile. If
you take it down, assuming you didn't just recently add all that organic
material, you'll likely find some of it is ready to be used -- I'd go ahead
and use that now.

Since turning it by hand is of course quite a job for one person, find a
local boy scout troop that wants to earn some money for the troop and get
them to come down and do the work for you. It might be a little stinky but
it won't be dangerous so if you offer the troop the right amount of money
they'll probably take you up on it. Of course, if you have any teenage kids
you can try to get them to do it too.

James