# Thread: Scientific numerics in complex systems

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Aug 2002
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## Scientific numerics in complex systems

I realize everyone would like to think what they are measuring is scientific. Things like weight, temperature, volume are simple to quantify and therefore seem very scientific when trying to prove something one way or the other. The problem is that even fairly simple systems are more complicated than just a simple measurement. We often express these more complex things with vague statements such as "it's not heavy, it's just awkward". This is a way of expressing that although we know (from a scientific point of view) that if we put this item on a scale it will not say that it weighs much more than objects that we can easily lift, this object is very difficult to lift. We feel that weight should translate into how difficult it is to lift, but we also know that the reality is that it doesn't.

Weight is only one aspect of how difficult something is to lift. Any object where we end up with a lot of weight a long ways from our body is "awkward". The leverage of the weight is against us in such a way as to put far more stress on our backs than the weight of the object would seem to indicate. That's because how difficult something is to lift or move, is not just about weight. It's about leverage and mechanical advantage and disadvantage. It's also about how quickly we can set the object down or how gently we have to set the object down.

Moving fifty pound bags of grain where I can drop them or throw them into a pile, is much easier than fifty pound boxes of bees and honey that need to be set down gently. It's also about how far we have to bend over to get to it and how far we have to bend over to set it down. Weight is only one small aspect of the whole issue.

An eight frame box is much easier to handle than it's weight would indicate. True it weighs less than a ten frame box of otherwise equal circumstances (full of honey, same depth etc.), but the weight you eliminated was the two frames furthest from your body, meaning that the mechanical disadvantage of those two frames was much greater than the rest of them. So looking at it from one simple measurement (weight) is misleading. We need to take into account many other things. These are things that probably can be quantified, but doing so is much more complex. Trying to figure out the "mechanical weight" (meaning the weight times the mechanical advantage or disadvantage) is much more complicated than just putting it on a scale and weighing it.

I bring this up, not just to talk about boxes, but about things in general and about other things like the thermodynamics of a wintering hive. I am not attempting here to explain the answer to the thermodynamics of a hive, but merely to try to outline the question and show that metrics is more complicated that it appears. Lets see how many significant aspects of the thermodynamics of a wintering hive we can list.

o Temperature. This is the simple one. It's easy to measure temperature by putting a thermometer where you want to measure it. Measure the temperature of the distant points in the hive and in the cluster and on the edge of the cluster and outside the hive. These are the "facts" usually used to try to explain the thermodynamics of a winter hive. These facts are one very small piece of the whole picture.

o Heat production. The cluster is producing heat. You can argue all day that they don't heat the hive, and obviously that is not their intent, but they do produce heat in the hive and that heat dissipates into the hive and, depending on other factors, into the outside, at some rate. This is a "thermostatically" controlled source of heat in that the bees will produce more heat as the temperatures decline to make up for heat loss, or less as it warms up. The temperature in your house is the same with the back door open or closed, but that doesn't mean that leaving it open doesn't matter. A thermostatically controlled environment can be misleading when we try to measure it in temperature and don't take into account heat loss.

o Respiration. There is a change in humidity in the hive cause by the metabolic processes of the bees. This water is put into the air by respiration. It is warm and moist air. This changes the humidity and the humidity changes other aspects.

o Humidity. The moisture in the air changes many other aspects of the thermodynamics as it causes more heat transfer by convection, more heat that is stored by the air, more condensation and less evaporation. We express this difference when referring to the weather in things like "it was hot but it was a dry heat" or "it wasn't the cold, it was the dampness".

o Condensation. Condensation of water gives off heat. There is water condensing on the cold sides and lid of the hive all through the winter and this affects the temperature. Condensation is caused by a temperature difference between a surface and the air contacting that surface. It occurs when the humidity of the air is high enough that when the air is cooled on the surface, the air (now cooler) can no longer hold that amount of humidity.

o Evaporation. Water that has condensed and run down the sides to the bottom or dripped on the bees, evaporates. This absorbs heat as it evaporates. Wet bees have to burn up a huge amount of energy to evaporate water that has dripped on them. Puddles of water on the bottom continue to absorb heat until they evaporate.

o Thermal Mass. The mass of all of the honey in the hive holds heat and dissipates heat over time. It changes the time period over which changes in temperatures occur. It holds a lot of the heat that is in the hive. A lot of cold honey can keep a hive cold even when it's warm out. A lot of warm honey can keep a hive warmer even when its cold out. It moderates the effects of temperature changes and it holds and gives off heat. This is more related to the amount of heat in the system than the temperature. A large mass of moderate temperature may actually hold more heat than a small mass of higher temperature.

o Air Exchange. I am splitting this out from convection, although convection is involved, because I am differentiating an exchange of air with the outside as opposed to convection taking place within the hive. Outside air coming into the hive is essential to the bees having enough oxygen for aerobic metabolism , but the more of it there is the more it affects the temperatures in the hive. If this is minimized during winter, the temperature in the hive will exceed the temperature outside the hive. If it is too minimized the bees will suffocate. If it is too maximized the bees will have to work much harder to maintain the heat of the cluster. Even if you were to increase this gradually to the point of the inside and outside temperatures being indistinguishable, more air exchange from that point would not change the temperatures, inside, outside or of the cluster but WILL cause more heat loss to the cluster thereby causing them to make more heat to compensate. If you rely only on measuring temperature you will not see this difference.

o Convection within the hive. Convection is how an object with some thermal mass and therefore some kinetic heat, loses it's heat to the air. The air on the surface either picks up or gives off heat (depending on the direction of the heat difference) and if the air heats up it rises bringing more cool air into it's place. If it cools it sinks bringing more warm air into it's place. Things that block air or divide it into layers will add to warmth. That's how things like blankets and quilts work. They create dead space where the air can't move so easily. A vacuum thermos works on the principle that if there is no air, it can't carry away the heat by convection. The more open space there is in the hive, the more convection can take place. The more you limit things to layers the less convection takes place. We sometimes refer to an excess of convection in our houses as "it was 70 degrees in the house but it was drafty".

o Conduction. Conduction is how the heat moves through an object. Take the outside wall of a hive. At night if it's colder outside, it absorbs heat from the inside that comes from convection (warmer air against it's surface) and heat from radiation (heat radiating from the cluster) and that heat warms the wood. The rate at which that heat moves through the wood to the outside is its conductivity. The heat is conducted to the outside where convection carries off the heat from the surface. On a sunny day on the South side, the sun will heat the wall, the heat will move by conduction through the wall to the inside where convection will transfer the heat to the air. Insulation or Styrofoam hives will slow down conduction.

o Radiation. Radiation is the process in which energy is emitted by one body, transmitted through an intervening medium or space without significantly affecting the temperature of the medium, and absorbed by another body. A heat lamp or heat from a fire are tangible examples of this. In the case of a wintering hive the two main sources of radiant heat are the cluster and the sun. During a sunny day the radiant heat of the sun hits the side of the hive and turns into kinetic heat and is transferred by conduction to the inside of the hive. The radiant heat from the cluster hits the surrounding combs of honey and walls, cover and bottom. Some is absorbed by the honey and walls, and some is reflected back. The amount is dependent on how close the cluster is and how reflective the surface is. Real life experience of radiant heat would be being in the sun on an otherwise cool day or putting a thermometer in the sun and getting a dramatically different reading than one in the shade.

o Temperature differences. The amount of the difference in temperatures between the cluster and the outside is a significant factor. If your outside temperatures in winter average say 32 F and your lows are rarely 0 F the significance of some of these things may be minimal. On the other hand if your winters often have subzero temperatures of -20 to -40 F for long periods then these issues are much more significant.

The real question is, "How do all of these interact in a wintering hive?"

One clue to understand some of it is by watching the bees. They adjust based on what they are experiencing as far as heat loss, rather than what it says on the thermometer. The cluster is drawn to the place where they lose less heat. This should be a clue to us on where and how they are losing heat.

My point is, if you look at most things they are much more complicated than a simple measurement and yet we have a tendency to try to reduce them to that.

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Sep 2007
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## Thermodynamics

Michael,

Excellent introduction in how heat moves through systems.

The only thing I would like to add relates to conduction. Radiation moves heat (energy) through space using electro-magnetic waves. Examples would include visible light, but primary mechanisms are infra-red waves. Dark (black) surfaces absorb energy from radiated sources at a higher rate than light (white) surfaces. In the absence of a radiating source, dark surfaces emit radiated energy more than light surfaces.

I don't know if this helps you with your beekeeping skills.

Mike

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