Physics for beekeepers: heat loss from spheres
. . . or “learning about bees from your cat”
Here is something any feline will tell you: a sphere is a shape with a high volume to surface area ratio. The surface of an object is the part exposed to air, so it’s the surface where things gain or lose heat. Things wrapped up in a ball—like your cat on a cold day—lose less heat to the atmosphere than things stretched out in all directions—like the same cat on a summer afternoon. Basically, your cat is a shape-shifter, changing his volume to surface area ratio depending on the temperature.
Beekeepers often worry about their bees being cold in winter, but bees are brilliantly adapted to staying warm. As the temperature begins to fall they form a cluster to keep warm, as the outside temperature becomes even colder, the cluster becomes tighter and rounder—just like your cat.
But for bees to survive the winter, the cluster must also be large enough. A large cluster contains more bees generating heat, but equally important, a large cluster has a higher volume to surface area ratio than a small one. The reason is simple: as the radius of a sphere increases, the surface area increases with the square of the radius while the volume increases with the cube of the radius. In plain English it means that as your cluster gets bigger, the volume increases more than the surface area.
The lower amount of surface area per volume of bees means the big cluster loses heat at a slower rate than a little cluster, the same way your cat loses heat at a slower rate than the mouse he is stalking, but at a faster rate than the German shepherd stalking him. Small objects lose heat faster than big objects of similar shape and density. (We all know mice shiver, but to know whether they shiver from cold or from fear, you’ll have to consult a mouse.)
In a large cluster, more bees are producing heat and a greater percentage of the bees are on the inside of the cluster where it’s warm and comfy. Conversely, tiny clusters have a small chance of making it through the winter—it is best to combine these with another hive if possible. And in spring, when temperatures are erratic, you should avoid breaking a cluster into smaller units. Reversing boxes when it divides the nest, or opening the brood nest too much, can cause the bees to separate into small clusters or spread themselves into a non-spherical shape. Either one could compromise the health of your hive.