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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.

Rusty
HoneyBeeSuite

Too warm to be decent.
Too warm to be decent.

How much honey for a warm winter?

Lots of folks want to know if bees consume more food in warm winters or cold winters. I’ve been searching for scientific data on this for quite a while but I haven’t found any. So, for what it’s worth, I hereby offer my opinion.

Based on hearsay and my own beekeeping experience, I believe that bees expend more energy—and so eat more food—in warm winters than in cold ones. As counter-intuitive as that may seem, I’m convinced it’s a common occurrence.

In very cold winters the cluster remains intact for long periods, brood production is extremely low or non-existent, and all other hive activities come to a standstill. The bees vibrate their wing muscles to create heat and the highest temperatures are found in the center of the cluster, but that temperature can be lower than when brood is present.

In warm winters, however, with occasional balmy days and temperatures that rise into the 40-60°F (4.5-15.5°C) range, the bees begin doing other things. They may take cleansing flights, some search for pollen, the undertaker bees carry dead bodies from the hive, house bees clean debris from the nest and sweep cobwebs from the corners. Brood production may increase, and with increased brood production comes the need for consistently higher temperatures in the nest along with constant feeding and tending of the larvae.

All of these activities require energy even though some of them are not very effective. Foraging for pollen, for example, requires lots of energy and it may or may not produce good results. The higher than normal temperatures seem to “trick” the bees into searching for something that may not be there—or may not be found in sufficient quantities to make the trips worthwhile. We’re talking cost/benefit ratios here, and the benefits will depend on local conditions.

And don’t forget, the nights are still cold. The cluster resumes warming itself during the long winter nights, so it is still expending a lot of “keep warm” energy even though the daylight hours are warmish.

In addition to tricking the bees, I think beekeepers, too, get lulled into thinking that warm weather means the bees will have plenty of food. I, for one, have been seduced into believing that winter stores would last longer during a balmy winter. But experience has shown otherwise, and I now check for honey stores earlier in warm winters than in frigid ones.

Rusty
HoneyBeeSuite

The bees were flying from this top-bar hive one day after the photo was taken.
The bees were flying from this top-bar hive one day after the photo was taken.

Why so many starving bees?

It was a winter of bee starvation. In the past few weeks I’ve heard countless tales of beekeepers losing all or nearly all their hives to starvation. Many of these hives had not a drop of honey left. Others had full frames of honey remaining, but the bees starved anyway.

During cold weather, the bees cannot leave the cluster in order to find food. Oftentimes, honey stored just beyond the edge of the cluster is never touched. As the bees move upward, they consume the food the cluster encounters. The resulting pattern resembles a vertical tunnel through the stored food.

Warm periods during the winter allow the bees to move around and find more of the food. Sometimes the cluster may move toward one side of the box and eat the honey there. But after it becomes cold again, they are even further from the stores remaining on the other side of the box–which is why you sometimes see the dead cluster on one side or in one corner of the brood box.

A similar type of movement occurs in top-bar hives. Although the bees don’t move up, they may gradually move left or right. But if they eat their way to one end of the hive, they can’t turn around and traverse the empty combs to get to the other end. So they starve.

The cluster of bees won’t leave brood unattended, so even though there is very little brood in the winter months, it anchors the cluster to one spot. It seems like the bees would move freely inside their box, but instead, they are always attached to the nursery.

Placing feed–especially hard candy–just above the cluster is very effective because that is where the bees are most likely to find it. In addition, heat from the cluster keeps that area warmer than the surrounds, so bees can move onto the candy without freezing.

A lack of honey may be due to over-harvesting, but it may also be due to paltry nectar flows or particularly long winters. Whatever the cause, feeding sugar is a long, time-consuming, and expensive ordeal–but it may be the only way to keep your bees alive.

The photo below shows what typical starved bees look like. The bees–still in the shape of a cluster–all died head-down in a cell with their little butts sticking up in the air. Each is trying to survive by licking every last molecule of sugar from the bottom of a cell, but when that gives out, they die from lack of fuel or freezing to death. It is a very sad sight to see. The photo was kindly provided by Jared Watkins.

Rusty

A frame of bees that starved. Photo courtesy of Jared Watkins.
A frame of bees that starved. Photo courtesy of Jared Watkins.

Temperature regulation in a winter cluster

A winter cluster can be thought of as a ball of bees dissected by sheets of honeycomb. Clusters begin to form when the outside air temperature falls to about 57°F (14°C). Bees in these clusters are in no way hibernating but are actively moving, eating, and performing hive duties.

The comb in the very center of the ball contains a small amount of brood and the queen bee. The brood and the queen are kept at the correct temperature by the surrounding workers. The workers have several ways of regulating temperature and air flow throughout the cluster.

The cluster is not of uniform density. The outermost layers of the cluster form the densest portion, whereas the bees in the core are able to move freely and carry out the regular chores of brood rearing and caring for the queen. Although brood rearing may be almost non-existent in early winter, as the day length increases, so does the amount of brood rearing.

When no brood is present, the core temperature is kept somewhat less than 85°F (29°C), but brood needs to be kept warmer—at a constant temperature of about 93°F (34° C).

To warm the cluster, the workers vibrate their wing muscles—an action which burns calories and gives off heat. The temperature in the brood rearing area is further regulated by the expansion or contraction of the cluster. If the “nursery” becomes too hot, the cluster expands which increases the air flow around each bee and cools the nursery. If the nursery becomes too cold, the cluster contracts which decreases the air flow.

Bees on the exterior surface of the cluster become so cold that they appear motionless and dead. However, in a way that is not completely understood, these outside bees get pushed towards the center of the cluster by warm bees who then exchange places with them.

Clustered bees need a constant supply of food and, as the winter progresses, the cluster will slowly move toward stored honey. If the cluster loses contact with the stored honey, the bees can quickly starve. Clusters of bees that are too small—that is, they don’t have enough bee bodies to maintain adequate nest temperatures—will soon die as well.

Rusty

Why are all my bees at the top of the hive?

Yesterday a reader wrote to say that all her bees were in the top brood box and she didn’t recall this happening last year. She wanted to know if this was normal.

The fact is that winter bees kept in a vertical hive will move up as they consume their stores. Remember that the bees stored their honey overhead all summer long. First they filled in the area around the brood nest, and next they went into the honey supers and filled them as well. It is only natural that they will search for honey in the place they stored it—which is overhead.

However, if the bees have plenty of honey, this upward migration occurs slowly over the course of the winter. Only when they deplete the honey in their immediate area do they move up to look for more.

If a cluster is large it extends to cover more of the frames. These large clusters may consume all the honey in all the frames because it is right in front of them. Sometimes, however, the cluster is small and occupies only some of the frames. These bees may “miss” the honey that is stored several frames to the left or the right—and move up early instead. You can picture this as a chimney built through the honey. Colonies have been known to starve in this situation—especially in very cold weather when the bees can’t leave the cluster to go in search of food.

In my experience, colonies that have chimneyed through the honey and gathered on top of the frames to starve usually have smaller, less populous clusters. It’s a question of probability. More bees covering more area are more likely to run into the food stores than small, compact clusters.

My recommendation is this: if you find bees clustered on top of the frames, feed them with some type of winter (non-liquid) feed such as candy cakes, fondant, or granulated sugar. Or, if it is warm enough, open the hive and move any remaining honey close to the cluster where they can find it. You may be able to reverse your brood boxes. That is, put the cluster on the bottom and place any frames of honey on either side and directly above the cluster.

Bees kept in a horizontal hive, such as a top-bar hive, are already as high up as they can go. They will move laterally to get the honey, but they usually move in only one direction. Let’s say, for example, that the cluster started in the middle of the hive and moved to the right. Once all the honey in that direction is eaten, they will not normally turn around and traverse the empty space to find the honey at the other end—especially when it is too cold to break cluster.

One trick some top-bar beekeepers use is this: at the beginning of the winter they rearrange the top bars so the cluster it at one end of the hive—not in the middle of the honey. This way, the bees are always moving in the same direction and always finding more honey. No backtracking is required.

In any case, if your bees are all clustered at the top or on one end of your hive this early in the winter, you will almost certainly have to do some intervention to keep them alive until spring.

Rusty
HoneyBeeSuite