Duke rubbed off some of his mane!

Hi so my horse Duke has rubbed off a part of his mane on a rough board.He has a bald patch there about four inches long. How long until it grows back? He had such a beautiful thick mane!

It could be a few months. My pony mare rubber parts of her mane so I decided to roach it (shave it all off) sometime in mid september (and she used to have the prettiest mane you'd see) and it's grown back about 3-4 inches now-it's still sticking straight up like a Norwegian Fjord though!