## Find out how maths can transform your beekeeping

I am no maths (‘math’ in the USA) genius, but I do like to mess about on a spreadsheet. The magic happens when data and calculations morph into a chart that conveys something useful. I have fiddled with plotting honey bee colony numbers over the season more times than I care to say, continually trying to match what I see in hives to my theoretical model. Recently, I have been thinking about hive sizes, prolific queens and how to ‘stay ahead of the bees’ in spring. It’s autumn here now, and I won’t visit my hives until the December oxalic acid treatment, but that can’t stop me thinking about bees.

### Laying rate of queens

I don’t know where it comes from, but I often hear or read people saying that a good queen lays 2,000 eggs per day. I doubt that I have ever had such a creature. It’s a fun exercise to consider how much space a colony needs in relation to how prolific the queen is. Even if a queen is pumping out 2,000 eggs per day at her peak, it’s unlikely to be something that lasts for more than a few weeks. Brood must be fed and kept warm by workers of a certain age, so there can be a big difference between a queen’s potential and her reality. As the workforce grows, so the number of eggs laid can grow too, until a point is reached when the queen is in top gear.

During the night the hive is pretty crowded, with all the foragers packed indoors, so I reckon the queen probably doesn’t lay much at this time. Let’s assume that her peak laying time will be for 16 hours in the daytime, when foragers are flying. This gives her majesty 57,600 (16 × 60 × 60) seconds per day of laying time. Dividing this by 2,000 shows that she lays an egg every 28.8 seconds for all of that 16-hour window. That means dropping two eggs per minute, every minute, for sixteen hours. It seems a lot, but I’m not a honey bee queen, so my feelings are irrelevant.

### Amount of brood and bees

How much brood can there be in a hive? One interesting side issue is that some colonies have two laying queens, by accident or design. I’m going to ignore that situation, but there are people who deliberately use a two queen system to get monster colonies. Given that worker brood takes 21 days to transform from an egg to a bee, it’s easy enough to calculate the theoretical maximum amount of brood (21 x laying rate). What’s more, as bees live about 6 weeks (42 days), the maximum number of bees should be twice the maximum brood (max brood x 42/21) – see table below.

How many bees fit in a box? I did some searching on that and got quite a wide spread of alternatives, depending on the hive type, obviously. I ended up looking at the size of foundation for different brood boxes, then calculating the area, in square inches. Then I could work out how many bees can fit on both sides, using my estimation of the length and width of a typical worker bee. While I was at it, I calculated how many cells should be on each frame.

The table below shows my results for number of cells and bees per brood box of different types. I took the theoretical maximum number of cells and reduced it a bit to get my ‘realistic’ number (blue/grey). I then took 65% of this to be the space available for brood, assuming that cells are also used for stores. In some cases, in National hives, the bees more or less fill the whole box with brood, so the 65% would not apply. I think it’s safe to say that a National hive has 31,200 to 45,000 cells available for brood, depending on the stores situation.

### Enough space in the brood box

Taking my two charts together, we can see how different brood boxes measure up in terms of space for bees and brood. If a queen can lay up to 1,500 eggs per day at peak times, we could need 31,500 cells available for brood, and ultimately, we’d also need space for up to 63,000 bees. It looks as if a National brood box would be just about big enough for the brood. The Langstroth has plenty of space, and the others are cavernous.

Clearly, 63,000 (theoretical maximum) bees are not going to fit into a single brood box of any type. My charts below show what I see in my strong colonies. The arrows depict when supers need to be added based on the size of the boxes. This means supers for bees, not honey. Once honey starts piling in (late April & May), they require yet more space. To me, an advantage of the Langstroth hive is that a single brood box is great for the brood nest, and the supers (I use mediums) are much bigger than Nationals, meaning I require less of them. I have had Langstroth hives taller than me (6 feet (1.83 m)) and I can’t begin to imagine how that lot could fit into Nationals. Of course, many people extract honey through the season, or once in spring and once in summer, which reduces the need for so many honey boxes.

### What’s the point?

Firstly, you can use these measurements (or make your own – mine are bound to be imperfect, and nature varies considerably anyway) to remind you how early and how often you should be adding supers in spring and summer. You require space for bees and then space for honey too. I’m not certain how true it is, but I’ve heard it said that it takes bees three supers of nectar to make one of honey. With strong colonies you need to get a super on pretty early with a small hive type such as a National. If you don’t and they start swarm cells, it’s a whole lot of work.

Secondly, when you check on how many frames of brood you have, you can figure out roughly how many eggs per day your queen is laying. That will also give you a guide as to what to expect in terms of bee numbers once that brood emerges. Number of brood cells x 2 equals expected number of bees, once emerged.

I could have just said, “add supers early and frequently to stay ahead of the bees” – but where’s the fun in that? The whole ‘National vs. Langstroth’ or “double brood vs. single’ debate really boils down to how prolific your queens are, and what suits your way of working.

ElaineLove a good piece of analysis! V interesting and thanks for sharing Steve.

WalrusThanks Elaine. and thanks for sharing on the beekeeping forum, albeit to a fairly unenthusiastic reception 😀