Tvrdnju da bumbar ne bi trebao moći letjeti izgovorio je tridesetih godina XX stoljeća jedan fizičar u razgovoru s jednim biologom. Iz konteksta razgovora bilo je jasno da se misli na to da bumbar sa svojom masom (oko 1 g), površinom krila (oko 1 cm²) i brzinom kojom se kreće (oko 1 m/s), ne može letjeti tako da klizi po zraku, dakle na način na koji lete velike ptice ili avioni. Naravno, bumbar ne leti poput aviona s raširenim nepomičnim krilima, već on njima maše (zato se i čuje zujanje), što mu onda ipak omogućuje da leti po zraku.

Nešto više detalja o toj priči može se naći na Internetu, u tekstu koji prenosimo ovdje u cijelosti (iz razloga što dotične stranice često 'nestaju' ...):

One favourite subject people raise is the old line about scientists having proved that the bumble bee cannot fly, a much-beloved piece of urban folklore. There it is, the humble Bombus Terristris, plainly flying around us all through the summer and those crazy know-all scientists with their noses in their test-tubes say it cannot possibly fly. What utter nonsense! It is obvious to any scientist that the bumble bee can fly as experiment proves it. So what is this business about proving bees cannot fly? And who started it?

First let's look at the physics behind the story. If you are asked about flight the first thing you do is to use the equations which describe how much lift an object has. You compare the lift to the weight of the object. If the lift is greater than weight then the thing can fly. Bumble bees are pretty big, weighing almost a gram, and have a wing area of about a square centimetre. Tot up all the figures and you find that it cannot generate enough lift at its typical flying speed of about one meter per second. But that doesn't prove bees cannot fly. It proves that bees with smooth, rigid wings cannot glide. Experiment has proven this too. With the aid of dead bees and a little lacquer it is easy to show that they really cannot glide.

So how do they fly? Actually that turns out to be a very interesting question and one that reveals a lot of physics. Why do bees flap while jumbo jets have fixed wings? It is a question of size and this is revealed in a figure called the Reynolds Number. Osborne Reynolds was a Victorian engineer who was interested in what happens when you place an object in a stream of liquid or gas. The number named after him is a ratio which tells us, for a particular object, how much lift you get compared to how much drag or resistance you get. A low Reynolds number means little lift for a lot of drag and a large Reynolds number means a lot of lift.

The Reynolds Number depends on the size of the wing. Bigger wings give bigger Reynolds numbers. Now if, again, you put in all the numbers you find that bees work at very low Reynolds Numbers (1000 or so for a honeybee, as little as 15 for the aphid-eating chalcid wasp). This means that their flight is very inefficient because as a wing starts to move to create lift the drag holds it back. It is fairly straightforward to show that birds can generate enough lift to fly once they are in motion with air flowing smoothly over their wings, but many of them would have great difficulty taking off. Small insects, according to this model, cannot fly at all. Of course, all this proves is that the model is incomplete.

Some brilliant work by Torkel Weis-Fogh has shown us how small insects do fly and it has led to some rather neat insights into nature's cunning. If you are small and want to fly you have a problem. The Reynolds Number is against you so you cannot glide and flapping is very hard work. A wing is a device which encourages the air to flow over it so that when it leaves the rear wing edge, the air moves downwards. That produces a thrust upwards on the wing. A smoke-filled wind tunnel shows this beautifully with curling eddies of smoke flicking off the wing edges. Unfortunately to make a good eddy takes time. The wing has to move a few times its own length to get things started. This makes it tricky if you are going to flap as the maximum travel of a wing is about its own length and very little lift is generated for most of the stroke. Nature has come up with a number of interesting solutions to this problem of which the "clap-fling" is a good example. When a small bird or insect wants to take off it needs a lot of lift. What it does is bring its wings together above its back so they clap, expelling air from between them. As the wings are separated, air is drawn quickly in to fill the void. The wings are flung apart and lift is generated immediately as the air is already in motion in the correct way. You can hear the clap. The characteristic whirring of a pheasant taking off is caused by its wings clapping. Almost 2000 years ago Virgil recorded in The Aeneid that a rock dove claps its wings as it takes off - a passage he stole from Homer but he added the bit about the clapping.

So in asking how bees fly we find that they are remarkably clever about it. Aircraft can generate enough lift that they do not need such tricks, but they do need long runways. Birds get enough lift to fly but for take-off need a boost. Just the poor old bee and about a million different species of winged insect need some extra trickery to stay aloft.

But how did it all start? Where does the story date back to? J.H.Mcmasters states that the story was prevalent in the German technical universities in the 1930's, starting with the students of the aerodynamicist Ludwig Prandtl at Göttingen. The story he tells is that a noted Swiss aerodynamicist, whom he does not name, was talking to a biologist at dinner. The biologist asked about the flight of bees and the Swiss gentleman did a back-of-the-napkin calculation of the kind I described. Assume a rigid, smooth wing and so on. Of course, he found that there was insufficient lift and went away to find out the correct answer. In the meantime the biologist put the word around, presumably to show that nature was greater than engineering, and the media picked it up. The truth, as now, wasn't newsworthy so a correction has never been publicised. The man on the Clapham omnibus, therefore, continues to tell me that science is a load of crock because it once proved that bumble bees cannot fly. And he will not hear otherwise, especially not from a scientist. Perhaps if I became a journalist he might listen?

Odgovorio:
mr.sc.M.Basletić, PMF