I was in formation with a hawk at Hemet-Ryan years ago; I was solo in a 150, in the pattern, I think turning base to final - he was inside my turn, a few feet lower, in perfect formation during the whole turn, and looking over at me - like, his was head turned, looking at me. . .weird, and kinda cool. He never flapped a wing to stay in place; I think his shorter turn radius made up for the difference in our speed, and we were descending, which I guess gave him some more energy, as well.
Just danged odd that his relative position never changed during 90 degrees of turn. . .that was a weird airport, back in the 70's - wild dogs/coyotes eating the fabric off sailplanes, the taxiway being landed on all the time 'cause it was better looking than the runway, wires across one end of the runway, fairly close as I recall; a bluff, or a kinda flat ridge just north, if I remember, and you could "skim" over it and get a dramatic effect as the edge dropped away. Did my first solo there . . .