I would like to hook up my school back to the bike, so then I can commute without having the weight on my shoulders, but... the 'above the rear wheel racks' at bike shops I have seen are just far too small for my bag (a lot of homework). I don't want to tie it down with ropes because it takes too much time, and is always flimsy.

Whats the best solution, except buying a new bike bag, and I don't want to carry anything on my shoulders because that can develop aches and pains in the back if you're riding every day 25kilometres or so.