Where I live on South Whidbey Island we have tons of rocks and a mix of soils. Sandy loam to hard pan. And stuff that is in between. My tractor doesn't have down pressure on the 3 point hitch so I have found that getting Slim Pickens to ride the post hole digger for extra weight helps getting it to dig. When he is not available, and since he has been dead for many years, I have found that raising and lowering the auger will get it to drill. I don't have an atom bomb for him to ride anyway.
I use a 9 inch auger, because that's what I have, and my Yanmar YM2310 to spin it, because that's what I have, which is supposed to have 23 HP available at the PTO according to some sources. I have lots of rocks. That tractor just pulls that auger between the rocks and then screws them to the surface. It has, a couple times, gotten stuck on a large root. So I had to shut the tractor down and unscrew the auger. But then, after dealing with the large root, I run the auger back into the hole. With success. Every time. So it seems like 23 HP is good enough for hard pan with rocks.
Generally I use the auger for planting trees and bushes. Posts too, up to 24 inches in diameter. Because of the variable soil I drill holes 3 feet deep. This way the soil is broken up and will drain well. For 3 feet at least. If I need a larger diameter hole it is pretty easy to enlarge the existing hole, especially since the larger hole usually doesn't need to be 3 feet deep, so the soil enlarging the hole just falls into to the deeper hole. It generally takes about 3 minutes to drill a 3 foot hole. That's average. With no rocks I can drill a hole 3 feet deep in a minute. Which leaves me more time to enlarge holes if need be.
The 9 inch diameter auger makes a hole almost 12 inches in diameter because it hits rocks and so does not run true. I don't mind. So maybe you don't need a 21 inch diameter auger if you are only drilling a few holes. Like 10. Augers are expensive so maybe 10 is the breaking point. Maybe your back is ruined, like mine, so maybe 3 is the breaking point. Maybe you don't mind spending the money and you can buy the bigger auger and won't care. If that's the case an 18 inch auger will probably get you a 21 inch hole.
Anyway, have fun drilling holes. I like it. My back is fusing itself and shovel work doesn't make it feel better. That auger is fun to watch, it does such a good and fast job. I have to get out of the tractor seat and sit sideways on the fender to watch the auger because I can no longer twist enough to see it work. So I do. It makes holes way faster than I ever could.
Cheers,
Eric