This Aerodynamics page was originally put together fairly quickly and in a rather simplistic fashion, additions made in April 2002 stem from conversations on the now defunct [Bio Bee] discussion group and are shown in red text. The Questioner was Chris Slade, the replies are mine. Owing to the size related aspect of the aerodynamic discussion, a link is provided above left to a document that deals with the mating preferences of drones that vary in physical size.
Much has been said in the vein 'bees cannot fly' whilst it is plain, for all to see, that bees do fly.
The misunderstanding originally came from some work, by an aerodynamicist, that showed superficially that BUMBLE bees should not be able to fly. This work was later corrected when the interior musculature of the Bumble Bee was explained to the person concerned, but by this time the 'story' was well entrenched and nobody took any notice of the correction. This has been translated and misused by the media and has propagated the widely held belief.
We are dealing here not with the mechanics of bee flight, but the relative efficiency of flight of different strains of bee and how that may relate to the body size of the worker bee.
I have a belief that the oversize foundation that we mostly use today has done us no service.
I am coming round to the opinion that the larger bees that result are less efficient fliers.
The mass of a bee is proportionate to it's volume and thus rises at a rate proportional to the cube of any linear reference measurement. If we take cell size as being proportional to bee size, (much work has been done to establish this, but the exact relationship is not known), then a larger bee is disproportionately heavier on a size for size basis.
Does the mass of a bee necessarily increase in line with the volume?
OK the thorax is pretty tightly packed and would probably do so, but the head and particularly the abdomen have large empty spaces, air sacs, and elastic organs, so it is possible that a larger bee would be less dense?
It is not exactly a cubic increase in weight for the reasons that you have specified and the larger bee is therefore less dense, but this reduction in density is itself small, particularly as the larger thorax would be a less rigid box for the muscles to work in... The increase in carapace thickness necessary to compensate for the larger span between muscle attachment points would be greater than a cubic factor, but I do not know by what margin.
Is this increase in carapace thickness fact or supposition?
It is supposition, based on the physics of levers, It is pretty sound supposition...
The increased circumference of the thorax, automatically means greater distances between muscle attachment points and fulcrums.
To maintain the same degree of rigidity that a small drones carapace has, then the larger drone has to increase carapace thickness otherwise the thorax would simply distort rather than the wings being able to flap.
Air resistance is proportionate to the 'frontal area' of a moving body and rises in proportion to the square of cell size.
The drag caused by the cross sectional area of the face.
As the face is largely composed of eyes especially in the drone and the eyes are hairy, does the hairiness trap air to have a 'golf ball' effect, reducing drag?
We are considering size differences in the 10% - 12% region.
The structure of a drones face is the same whether it is small or large and the drag coefficient will increase proportionately to the square of the linear increase. The hairs on insect eyes may well be there to reduce drag, but I favour the theory that they trap a slow moving bubble of air to enhance vision whilst flying (which is important for seeing virgins at a distance) Whatever the exact reason for their existence they have no bearing on flight performance over this narrow range.
Could a large eyed drone have less drag for instance than a small eyed queen?
This is a different ball game, because you are not comparing like with like. If you compare the drag coefficients of queens and drones then another feature raises its ugly head... Sectional density... This is a measure of drag that involves the length, mass, frontal area and surface finish of a projectile like a bullet or missile.
The narrower body of a queen and longer length would give the advantage to the queen here... The differing facial structure will have an effect and so will the relative hairiness of the eye lenses... I do not know which would benefit from these differences, but I have a hunch any such facial effects would be an order of magnitude smaller than frontal area effects (In fact frontal area figures for cars and motorcycles are fudged to iron out such structural differences)
Larger bees contain muscles that are increased in a cubic relationship to cell size. At first sight this looks to be a benefit to the bee, but the increase is only proportionate to the mass of the bee. The relationship between muscle bulk and mass would be proportionate. It has been pointed out that the strength of a muscle is proportionate to it's cross sectional area so our larger bee is therefore using its greater strength proportionate to square of cellsize) in attempting to counter it's own extra weight (proportionate to cube of cellsize). The extra resistance due to the larger frontal area then causes yet more resistance, still to be overcome. This alone seems to me to be a serious and significant disadvantage to the larger bee. But other factors yet further detract from the large bee's performance. The large flight muscles require an amount of oxygen that is increased by a cubic (or even greater) factor, but the orifices which this greater amount of air has to pass through are only increased by a squared factor, whilst the tubes themselves are longer and thus exhibit more resistance due to length. [Editors note... Recent work (2005), as yet unpublished, indicates that tracheal orifices only increase by very small percentages.]
The above factors are rather basic, but are fundamental rules of physics.
Size greatly affects aerodynamics... In my youth I did some aero modeling and found that aerodynamics in a model-size environment are not the same as for full-sized aircraft. A model aircraft is essentially the same shape as its full sized counterpart and both are deliberately streamlined. But because the speed range is very low on models the 'normal' rules do not apply. Insect aerodynamics are a further quantum leap away from 'conventional' or even model aerodynamics, due to completely different ranges of Reynolds numbers. It would seem that our bee is several orders of magnitude too small to apply any of the established rules.
As the larger bee expends more energy to fly a particular distance, compared to a 'properly sized' bee, then it seems likely that the larger bee will have a shorter flying life. The larger bee will probably have a larger nectar carrying capacity per flight, but a lesser total number of foraging flights. I do not know whether the total nectar gathered per bee would be smaller, similar or larger for the oversize bee. As the large bee is disadvantaged by its larger 'total drag' I suspect that the answer is equal or smaller. If it is smaller then this is a disadvantage both to the beekeeper (smaller potential crop) and the bee colony as a whole, owing to a greater number of bees needing to be reared to achieve a given crop.
Firstly the native bee, (at the time that the B.S. Frame was standardised), was physically smaller (by 10% or 12%) which means that there was a capacity available within each frame to generate 10% or 12% more bees. (This equates to more than one frame per box in cell numbers.)
A third reason, and this is pure conjecture, if the individual bees are worn out more quickly it is probable, (possible), that there is a biological feedback mechanism that make the larger bees produce more brood to compensate for the shorter life of the individual bees.
If then our mongrelised stocks with larger individual bees are less suitable for our purpose, then the converse of this is... that we should seek to redress the balance by returning to the 'Natural Native' smaller bee of 120 years ago.
These items >seem to me to all point in the same direction... smaller bees, (natural sized would be a better description), can fly further, potentially gather a larger crop in a smaller and less congested brood nest, with a consequently lower likelihood of swarming.
THIS SEEMS A GOOD IDEA TO ME!
It has been suggested that the viscosity of air may have a bearing on this problem, but as we are dealing with differences of less than 20% in the variation of frontal area I believe that we can ignore this and rely purely on the frontal area/speed/drag coefficients.
Bee wing movements in flight create vortices that create lift in excess of that predicted by aircraft aerodynamics.
Enlarged drones have problems catching up with faster flying, smaller sized, queens. The converse of this is large queens fly slower than small drones and are readily caught. This should enable regressed bees to influence other colonies disproportionately.
As for the fastest drone being the one that mates with the queen, is that necessarily her only selection criterion? She is out there to get mated and so may slow down for the drone(s) she wants.
The above is Chris's answer to his own question.
There is a further complication with Amm which has longer body hair. Some consider this increases the flight envelope but, I am not certain that this applies at the microscopic aerodynamic scale. This may be an attempt to streamline the insect by increasing the 'air smooth' characteristic.
There is another aspect to this... Heather honey gathering is hard work and physically frays bees wings, causing early failure. This often means a very short working (flying) life for individual bees. This would put our long lived bee at a disadvantage as there would be insufficient numbers of bees to gather the expected crop.
I would welcome comments and/or criticisms of the content or logic that I have used here. It is not important to be 'right' or 'wrong', but to try for greater understanding.