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Let's Get Physi-cal

Dave Black


Physics provides a lens that focuses on our honeybee colonies in interesting new ways and a recent paper from Derek Mitchell at Leeds University’s School of Mechanical Engineering does just that. The mathematics is a bit challenging if you’re anything like me, but it’s possible to get through that, and he also has some worthwhile observations we can apply to polystyrene hives.  Mitchell’s current interest (Computational Fluid Dynamics (CFD); his thesis was about differences in heat transfer between natural and man-made honeybee nests using CFD) also has something useful to say about that beekeeping perennial, top vs bottom entrances. This is not the first application of CFD to beekeeping, the Forum has a discussion from a couple of years back about polystyrene hives, and Cory Thompson (with others) studied airflow in Langstroth hives using the method. The results are always interesting, but as important are the assumptions, simplifications and limitations used when devising a workable model.


Honeybees harvest nectar to provide a source of a carbohydrate solution in periods of dearth, typically in the winter, but also during drought periods when flowers may not produce any. In order to store this food effectively they concentrate it to reduce the space it occupies and to prevent spoilage. This concentration is accomplished by doing two things. By adding the enzyme invertase the nominally sucrose nectar is converted to contain smaller sugars, mainly fructose and glucose. Fructose is much more soluble in water (even hygroscopic) and not easy to crystalise; a saturated solution of each of the three sugars (at 25C) will contain 81% fructose, 51% glucose, and 67% sucrose. In addition, a solution containing more than 60% fructose can contain much more glucose than a more dilute fructose solution. In almost all cases honey is a super-saturated fructose solution containing glucose.


The other thing done to concentrate the volume is to remove most of the water. Typically nectar containing perhaps 80% water is reduced to honey, containing less than 20% water, by evaporation. Any change of state, in this case the liquid to gas transition, requires energy. We call this energy ‘latent heat’; the temperature of the body (the solution, the water) remains constant but the added energy changes its volume, from a fluid to a loosely packed gas of excited molecules. To find out how much energy we can just look it up on Wikipedia J, for water it is 2,260kJ/kg (depending on temperature and pressure). This is actually quite a lot, and even more if you think about the quantity of water involved. A colony could evaporate more than 400kg of water in a year, using almost one gigajoule of energy, or nearly 300 kilowatt-hours. Thirty litres of petrol to you.


So where does all that energy come from? A little might come from the warmth of the sun, (and a tiny bit from the invertase chemistry), but given that the ‘bees operate in an enclosed, shaded wooden tree or box a more plausible answer, especially if you can visualise what the ‘bees actually do, is that it is metabolic energy, and it comes from the food itself – nectar. Besides all the other things honeybees do with the energy they harvest; fly, dance, grow, brood, even, waste it, evaporating water might be a very significant one.


It’s reasonable to argue that the survival of the colony depends on the efficiency (energy efficiency) of foraging (the colony must gather more energy that it expends or it dies) but we don’t tend to think about the cost (in energy) of storing and making that food energy available. It must be said that the people and (biological) disciplines that study honeybees aren’t experts in physics or engineering, and may not be the best people to think about things like energy or materials.


In this study, as a starting point, Mitchell considers the model system to be bounded by the nest enclosure, which constantly loses heat to its environs, and the journey to and from the flower patch where the nectar source is at a fixed distance. The nest enclosure does not change (the hive isn't 'supered'). It excludes the honeybee time spent in flower to flower transport energy (which is assumed to be replaced in the flower patch) and flower nectar depletion or dilution. For the sake of simplicity there is assumed to be no variation in energy consumed due to in-flight changes in insect weight or wind speed, nor does it consider significant activities for the honeybees like water and pollen collection or the nest consumption of honey to fuel brood rearing. The model focuses on the Thermal Energy Efficiency (TEE) as determined by the honey ripening rate, nectar concentration, ambient temperature, airflow inside and outside and any behaviour that controls it, and the thermal conductance of the nest (heat lost).


It shows the energy used for nectar conversion is significant, from 20% to 60% of the total energy recovered by nectar foraging. Typical values show that over 50% of the delivered energy may be used in the process of honey ripening and even in exceptionally favourable circumstances for temperate climates, do not use less than 25%. The energy consumption of nectar desiccation limits the maximum foraging distance of honeybees and also changes the energy return for a given nectar source, as well as which nectar sources are viable. The TEE limits nectar conversion so that honeybees can profitably retrieve and refine nectar from either a weaker nectar source or from a greater distance, but not both. A colony that collects nectar at distances, concentrations and TEE outside the break-even line will not add to its honey reserves and may not survive. That much is supported by observations in other studies. As well, improvements in TEE would require less nectar, so less foraging flights, less fanning, and less wing wear.


If you're looking for a 'take-away message', Mitchell is suggesting that thermal conductance of hives, previously thought to be only a consideration for winter, has been shown to be a major factor during the nectar collecting periods of the year, and consequently beekeepers should improve thermal efficiency by changing their hives to ones which lose less heat, and facilitating honeybee behaviours that have the same goal, for example, only using bottom entrances.


Mitchell D. (2019) Thermal efficiency extends distance and variety for honeybee foragers: analysis of the energetics of nectar collection and desiccation by Apis mellifera. J. R. Soc. Interface 16: 20180879. http://dx.doi.org/10.1098/rsif.2018.0879

Mitchell, D. (2017) Honey bee engineering: Top ventilation and top entrances. American Bee Journal, 157 (8). pp. 887-889. ISSN 0002-7626

EPS vs Wooden Boxes (2017),  https://www.nzbees.net/forums/topic/8664-eps-vs-wooden-boxes/

Sudarsan R, Thompson C, Kevan PG, Eberl HJ. (2012) Flow currents and ventilation in Langstroth beehives due to brood thermoregulation efforts of honeybees. J Theor Biol. 1;295:168-93. doi: 10.1016/j.jtbi.2011.11.007. Epub  Nov 25 2011.

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