Welcome to the love of pigeons!
Mine "live" in what used to be a pen for one breed of my bantam chickens. Its 8' x 16', roof is 7'-8' high. The pen shares a fence with my ducks pen, which is covered with netting. I can close the duck pen, and allow the pigeons to fly into it, but still not be open to fly away. I have never let them free-fly because I'm not too sure what my cats would do (they never bother my ducks and chickens, but they do show some interest in the pigeons lol)
As you can see in this video, though they fly very well, they don't stay in the air very long. They prefer to fly and land, fly and land.