Bill Tindall, E.Tn.
I drilled effortless 3/4 x 3" deep dog holes in my bench with a high quality 3/4" (Greenlee I think) spur bit and 18V Ridgid drill. There is a German bit I have seen demonstrated at IWF that drilled this size hole through many inches of lumber, don't remember what kind, or the drill name.
I have the Lee Valley set through 1/2" supplemented several larger sizes up to 15/16" and then Forstner for bigger than that up to 2 7/8". I power them all with a half inch electric drill of one brand or another. I have installed many lock sets in hardwood doors with these drills and a Forstner bit.
I was drilling a 4" hole in a house plate. It caught and threw me off the ladder.