I have been wondering about this for a long time, and I wanted to do a thought experiment. This will be very flawed and approximate, and I welcome any input or ideas.
Langstroth Deep Frame – 3,500 cells per side
Queen laying – 1,000 to 3,000 eggs per day
Time for workers to hatch – 19-22 days
Queen lays 2000 eggs per day (She is young and vigorous, right? )
Queen only lays workers (not true)
Using 8-Frame Langstroth Deeps for brood box
Average worker emerge time (from egg) 21 days
Brood frame is about 50% worker brood maximum (I don’t have any evidence, this is just observation), and probably 30-40% maximum across the whole brood box. The rest is honey, pollen, other brood (queens or drones) and empty cells.
How long to fill a single brood box?
So with these starting points, how long would it take a queen to fill an 8-Frame Flow hive deep brood box?
Let’s assume a maximum of 40% of cells is worker brood, which is 40% of 3,500 x 2 sides per frame x 8 frames per box = 22,400 worker cells. Probably an overestimate, but let’s move on…
At a rate of 2000 eggs per day, the queen could fill that box without being honeybound in just over 10 days. Now, that is assuming all comb is drawn, honey flow is maximal, well-established colony, no disease etc.
So in order to give enough space for the queen to maximize laying throughout the nectar flow season, with my very rough assumptions, we will need 2 Deep boxes for all workers to reach maturity.
Now if you have a colder climate, or a nectar dearth, or a slow queen, one box may be enough. I just did this calculation out of curiosity. When we looked into beekeeping my area, I was very surprised that SoCal beekeepers run on 2 deeps or triple mediums (same volume), but now I can get an idea of why that may not be unreasonable.
Please let me know what you think of my amateur musings.