Navigate / search

How the inverse square law governs the distribution of bee poop

A while back I received an intriguing letter from a homeowner complaining about his neighbor’s beehives. The letter said, in part, “This year the landowner at the rear of my house installed approximately fifteen hives. Consequently, for three months now my house and cars have been smothered in bee poop. The beekeeper has said he will move the hives further along the field and this may alleviate the problem. I wonder if this is true. The nuisance is prolific; all my windows need cleaning daily as well as the cars.”

When I read the letter to my husband, he replied in true engineer fashion, “Tell him the inverse square law applies here.” So helpful.

The gist of the inverse square law

The inverse square law states that “the intensity of an effect such as illumination or gravitational force changes in inverse proportion to the square of the distance from the source.” Loosely (very loosely) translated that means that as you get further and further from the source of the problem, its effect gets less and less.

How the inverse square law explains bee poop.
Imagine S is the hive and each red arrow is a bee.Borb [GFDL or CC BY-SA 3.0], via Wikimedia Commons
While the inverse square law works really well for some things like light and radio waves, it works less so with bees. Still, it’s worth taking a look at this neat little diagram I borrowed from Wikipedia. If S is the source (the hive), and each little red arrow represents a bee, you can see that as the you get further from the hive, the bees become further apart. Bees that are further apart will deposit less poop per unit of area.

So in theory, at least, if the beekeeper moves the hives further away from his neighbor’s house, less bee poop should land on the neighbor’s windows.

Bees do not behave like electromagnetic waves

Unfortunately, unlike electromagnetic waves, bees have a mind of their own, and they do not radiate in perfectly straight beelines from a specific point and keep going forever. Nope. Bees have ideas, and ideas are antithetical to the laws of physics.

Will more distance reduce bee poop?

I can think of several reasons the inverse square law might come up short (or not) in this situation. Let’s take a look of some of the obvious ones. Bear in mind, they are all speculation on my part.

  • Honey bees, I believe, are more apt to drop their load soon after leaving the hive. Carrying it any further than necessary would be energy wasteful, and biological systems do not waste energy. If this is the case, moving the hives further away might help a lot.
  • Honey bees do not radiate evenly from the hive, but go in chosen directions. If a field is in bloom on the other side of the neighbor’s house, the bees may all go there at the same time. Thus, time of the year would play a big part in how much poop landed on the target windows.
  • I learned in master beekeeping class that honey bees compensate for wind speed and direction while navigating. While I haven’t worked out the details, it looks like the wind could have a substantial effect on their flight path.
  • Bees fly around objects. Obstacles in the bees’ path could hurt or help the homeowner, depending on where they are. If trees or buildings funnel the bees over the house, that is bad. If they funnel the bees away from the house, that would be good. Perhaps the homeowner could build a wall around his property. I understand there are people in government who could help.

My answer to the homeowner

When I finally I answered the letter, I wrote:

The inverse square law states that “the intensity of an effect such as illumination or gravitational force changes in inverse proportion to the square of the distance from the source.” This law applies to bee poop as well, with some exceptions.

Because of the inverse square law, a little further away could make a big difference in the number of droppings. Also, I think most bees drop their load soon after they leave the hive, which should also help.

But if the bees are traveling to a certain area, say a field or orchard, and they are passing over your place to get there, the decrease may not be as great as expected. So ultimately, it is impossible to answer your question.

I would recommend that you encourage the beekeeper to move his hives and see if that works. I think there is a good chance it will help. Try to work it out with him because these situations can get messy if you decide to use the courts. If you are reasonable, he may be reasonable too. We hope. And hit him up for some honey when you talk to him. Even if you don’t like honey, it makes a great gift for your friends.

So there you have it. A day in the life of a bee blogger. I never heard from him again, probably because he thinks I’m nuts.

Honey Bee Suite

Hive temperature vs humidity

Back in November, Bill Reynolds of Viking, Minnesota began monitoring the inside of his beehives for temperature. He purchased an inexpensive desktop weather forecasting station with three remote wireless sensors for his project, and he used a fourth sensor to monitor the ambient outside air. The data for the first weeks can be found in the post, “How do honey bees keep their hive warm?

Originally, Bill set up three hives, each with three deeps and a quilt box. One hive contained a colony of Carniolans, one a colony of mutts, and one was empty. The hives were not wrapped, but all three were placed on the south side of a house with a straw-bale wall blocking northwest winds.

On November 22, Bill wrapped the second hive—the one containing the mutts—with 15-pound tarpaper. Then on November 28, he added a humidity sensor to both occupied hives and began to record humidity as well as temperature. Roughly one month later, on December 24, he removed the tarpaper wrap from Hive #2.

Below are some observations Bill made about the experiment, followed by the actual data:

  1. When comparing the data from the two occupied hives, the tarpaper wrap didn’t have much of an effect.
  2. When wrapping and unwrapping, the temperature spiked inside Hive #2. Presumably, this spike was caused by increased bee activity due to human disturbance. Bill writes, “I am surprised that such little interference outside would cause such a large effect inside.”
  3. The outside humidity levels were very high, at one point 99%, but there was no snow. As the outside humidity rose and fell, the internal humidity of Hive #2 followed closely, as did the readings from the empty hive. On the other hand, the humidity of Hive #1 fluctuated much less.
  4. Coincidentally, the outside humidity dropped just after the wrap was removed.

The first graph below goes back to November 1 and continues through December 26. It is easy to see that in the occupied hives, the internal temperature fluctuated with the outside temperature (black bars) but was consistently warmer. The empty hive temperature remained consistent with the outside air. As mentioned above, the temperature of Hive #2 (blue) spiked when the tarpaper wrap was added and again when it was removed.


The second graph shows both temperature (dotted lines) and humidity (solid lines). The outside humidity (green line) fluctuates with outside temperature (black bars). For the most part, the Hive #2 humidity (magenta) followed the outside humidity (green), but Hive #1 (blue) was drier on the humid days and wetter on the dry days than the outside. In other words, have Hive #1 was able to minimize humidity fluctuations.


If you have any questions, please leave a comment and I will let Bill answer them for you. In the meantime, Bill, thanks so much for this fascinating peek inside your hives.

You can purchase the ambient weather station here: *Ambient Weather WS-10 Wireless Indoor/Outdoor 8-Channel Thermo-Hygrometer with Three Remote Sensors


*This post contains an affiliate link.

How do honey bees keep their hive warm?

Honey bees do not heat their hives the way we heat our homes. Instead, they concentrate on keeping the cluster warm by vibrating their flight muscles. The center of the cluster is the warmest part of the hive, and the temperature drops as you move out from the center.

The interior of the hive is warmer than the outside air because heat escapes from the cluster and the hive itself offers a small amount of insulation. But the bees do not attempt to keep the entire space warm. In fact, the air inside the hive can be quite cold.

Because hot air rises, the warmest place outside of the cluster is right above the cluster. A beekeeper can help keep the hive slightly warmer by placing insulation above the cluster to capture some of this escaping heat.

Bill’s hive temperature experiment

In order to help explain this phenomenon to new beekeepers, Bill Reynolds of Minnesota decided to monitor the temperature inside his hives as the colonies plunged into winter. According to Bill, he purchased an inexpensive desktop weather forecasting station with three remote wireless sensors for his project. He used a fourth sensor to monitor the ambient outside air.

The weather cooperated for his experiment. Bill says, “Here in Minnesota we are experiencing bone-chilling temps around zero each morning and mid-twenties, if we are lucky, by noon.”

Bill set up three hives, each with three deeps topped with a quilt box. One hive contained a colony of Carniolans, one a colony of mutts, and one was empty. In each hive he centered the sensor over the third deep but under the quilt box. He did not attempt to place the sensors at the core of the clusters. During the measurement period, the clusters were two deep hive bodies below the sensors.

The hives were not wrapped. All three setups were on the south side of a house with a straw-bale wall blocking northwest winds. According to Bill, “Other than the sensors, there is nothing different between these hives and any other hive one would find in a backyard.”

Partway through the experiment, Bill began recording separate readings for the outside air and empty hive. He made this change because he noticed that the temperatures increased and decreased at different rates inside the empty hive and outside of it. It became apparent that the wooden boxes themselves influenced temperature fluctuations.

Warmer inside, but only slightly

The graph below shows temperature readings for each sensor. It is quite clear from this simple experiment that temperatures inside the active hives rose and fell with the outside temperature, but overall the inside remained warmer than the outside. But far from being cozy, the inside temperatures dropped down into the 30s on the coldest days. It is interesting to see that the two colonies were very consistent with each other, rising and falling in tandem.

It also became clear that the interior of the empty hive box was somwhat warmer than the outside air. I suspect a combination of sun and minimum air movement through the boxes increased the temperature slightly.

Thank you, Bill, for your experiment and awesome graph. Nicely done!

*Ambient Weather WS-10 Wireless Indoor/Outdoor 8-Channel Thermo-Hygrometer with Three Remote Sensors


Graph showing the temperatures inside the three hives, and beginning November 15, outside the hives.
Graph showing the temperatures inside the three hives, and beginning November 15, outside the hives. © Bill Reynolds.
The two populated hives in a warmer time. © Bill Reynolds.
The two populated hives in a warmer time. © Bill Reynolds.

*This post contains an affiliate link.

Shaking larvae from their beds

In third grade my best friend, Kristen, filled the bowl of a soup spoon with mustard. Then, using her finger as a catapult, she fired the mustard into the air. The glistening glob sailed silently above the clattering tables and hit the cafeteria wall just below the ceiling.

Kristen spent the afternoon in the principal’s office. The rest of us were compelled to look at that disgusting splat for the next four years—glossy and yellow at first, devolving to a dull gray-green as the months passed.

As beekeepers, we are frequently urged to “shake the frames free of bees.” For various reasons, we sometimes want to transfer brood from place to place without all the attending bees, and shaking them from the frames is quick and easy.

But shaking—usually a straight up-and-down flick of the wrists—should be a gentle, non-violent sort of motion, just enough to dislodge most of the bees. Shake too hard and you can dislodge your larvae from their little puddles of food. I say this with some authority because I actually tried it.

Some years ago, I watched a beekeeper “shake” his frames by rapping the bottom bars against the edge of the brood box. Bang! Bang! He crashed the frames until not a single bee remained on the wax combs (a guy thing, no doubt). I longed to peek at the larvae after that, but he was impatient and shooed me away.

So the following spring, I tried it myself. I dislodged the bees from a deep frame of brood with a horrific rap on the brood box. Then I looked.

I immediately remembered the mustard. The single impact had flung several dozen larvae onto the walls of their cells—as if their chauffer had driven 30 mph into a brick wall. The victims I could see were small, those not wide enough to fill their cells. The older larvae and eggs were still in place.

Now honey bee larvae don’t wear seat belts or crash pads, and they are not designed to crawl back where they came from. A larva splatted on the cell wall is in serious trouble: separated from its moist pool of food, it begins to desiccate almost immediately. And even if a host of nurse bees could triage the mess, nurses are in short supply—you just shook them off the frames, remember?

So when you shake your frames, do it gently. You don’t have to remove every last bee. In fact, the foragers are the ones you usually want to lose, and they leave easily. Nurse bees hang on a little tighter, but a few nurses transferred to a different hive won’t do any harm.

If you can’t be gentle, you can always use a bee brush. But generally, shaking works fine as long as there is no impact, and as long as you don’t have queen cells on your frames. But please don’t be brutal; don’t launch your larvae into oblivion. Remember, this is beekeeping, not war.


Physics for beekeepers: temperature in the hive

For this fifth installment of the Physics for beekeepers series, I’ve decided to use this recent question, which is representative of several I’ve received this month.

“I’ve heard that some beekeepers leave a medium super of honey on the hive ‘just in case.’ But others say do not leave the hives with an over-abundance of honey because one of two things will happen: They’ll either kill/weaken themselves trying to maintain it, or the honey will simply get too cold and won’t be usable which may or may not result in them dying of starvation with honey inches away from them.”

The cluster stays warm, the hive does not

Natural systems do not waste energy and honey bees are no exception. To survive the winter, a cluster of bees must keep itself warm. While it does this efficiently, it makes no attempt to heat the entire space within the hive.

The warmest place within a hive is in the center of the cluster. The temperature of the cluster decreases as you move toward the outside. The bees on the outside get so cold that they must rotate to the inside. If the inside of the hive were uniformly warm, this rotation would be unnecessary.

Of course, there is some heat lost from the cluster into the surrounding air, and because heat is lost, the bees must continually generate more. If you put your hand close to a heated iron, for example, you can feel the heat. The heat loss from the iron is similar to the heat loss from the cluster. You don’t have to move far away before you no longer feel it. The same is true inside the hive: the temperature drops rapidly as you move away from the cluster.

Nevertheless, the air inside the hive is slightly warmer than the ambient outside air. This is because the hive box itself provides a small amount of insulation. But the R-value of a pine board is not much, which means the difference in temperature between the inside air and the outside air is not great.

Heat rises from the cluster

There is one place in the hive that is warmer than the others, and that is the space immediately above the cluster. That is because warm air rises. One beekeeper in France measured the temperatures in his hive when the outside air temperature was 44°F. He measured 95° in the center of the cluster, 71° immediately above the cluster and 52° in other empty portions of the hive. Other beekeepers have found similar temperature gradients.

For this reason, an insulating layer placed above the bees reduces the rate of heat loss from the hive. Styrofoam, wood chips, or a layer of another material will slow the loss through the roof. But even this has its limits. For one thing, as the internal temperature gets warmer in comparison to the outside air, more heat is lost through the walls, so overhead insulation alone does not conserve as much heat as insulating the top and sides. It is a complex system with no easy answers.

A super of honey will not kill your bees

I often hear people say they don’t leave extra honey supers on their hives because it is too much for the bees to heat. Aside from the fact that the bees will not attempt to heat it, a super of honey is much different than an empty super. An empty super provides more space for the rising heat to go without additional benefit, so it is not a good idea.

But a super of honey has many advantages. Besides being a supply of food, a super of honey is a good overhead insulator. Also, because it is very dense, it has a high heat capacity. That means small or rapid fluctuations in external temperature do not readily change the temperature of the honey. In other words, a large supply of honey stabilizes the internal hive temperature.

Also, a super of honey slows the air flow from bottom to top through the hive. That is because the air passing through the narrow spaces between the frames rubs against the irregular surfaces of the comb, so the air flow is considerably disturbed. This is a good thing: you want some air flow through the hive to remove moisture, but you don’t want a wind tunnel. A super of honey, then, provides food, insulation, temperature stability, and reduced air speed through the hive.

Honey doesn’t need to be kept warm

“If bees can’t eat cold syrup, why can they eat cold honey?” In fact, the honey isn’t cold when the bees eat it.

When you bring groceries home from the store, do you store them in a warm oven? Of course not. And the bees don’t need to store honey in a warm spot either. Remember, heat rises from the cluster, so the honey above the cluster is plenty warm. Even honey close to the sides of the cluster will be warm enough.

As the warm honey is consumed, the cluster slowly moves toward more honey, and as they get close, that honey begins to warm. The bees warm their food on an as-need basis—just like we do. As I mentioned in the beginning, natural systems do not waste energy. It would be a total waste to keep all the honey warm all the time.

In addition, honey in cold storage is far less likely to be ravaged by other insects because they don’t like cold food either. If the bees kept their honey stores too warm, predation would increase.

Moderation in all things

Regardless of the above, I think some degree of moderation is prudent. You don’t need to leave three supers of honey stacked on your brood boxes. In fact, you may not need any. But if you think your bees might run short of food, there is nothing wrong with leaving a super of honey. Would I leave three? Probably not. You can keep one in reserve and add it later, if necessary, or perhaps one super plus supplemental feeding might be enough. Since every situation is different, the beekeeper must use judgement.