treadle feeder question - how much clearance needed above the feeder

[jls6n]

I bought a treadle feeder and am now building a little 4'X4' shed just for the feeder because I want it to be on level ground and not have the feed getting wet. Can anyone suggest a good height for the roof? I don't want the chickens to not be able to get up on the treadle easily, but I don't want the roof so high that it's just a waste of wood for the posts. Thanks!