There you have a key. 23 in the limber chest with the howitzer, and then three more chests with the caisson and its limber. At 3/minute that is only about half an hour of firing without resupply. Also, just popping away as fast as you can, except maybe at massed troops such as in the example Keith gave, is wasteful. Better to take a bit extra time to lay the piece and get off one accurate round than to fire off three in that same time and have all of them miss.
That 11 rounds in one minute must have been something to see. I wonder what the projectiles were? Case? Shell? Canister?