Bumblebee Paradox

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The bumblebee paradox describes an apparent paradox in aerodynamics according to which bumblebees cannot fly.

History and description

In popular literature there is a legend that a bumblebee can not fly according to the laws of aerodynamics . The story circulated at the beginning of the 1930s as a joke among students of the renowned aerodynamicist Ludwig Prandtl at the University of Göttingen and was eagerly received by the press. According to this story, a biologist is said to have asked an aerodynamicist one evening in a restaurant why a bee or a bumblebee could fly. After a brief calculation on a beer mat or a napkin, the aerodynamicist's answer should have been something like this:

The bumblebee has 0.7 cm² wing area and weighs 1.2 grams. According to the laws of aerodynamics, it is impossible to fly at this ratio.

In addition, subsequent sentences such as:

The bumblebee doesn't care and it flies anyway. or
Since the bumblebee does not know the laws of aerodynamics, it still flies.

The aerodynamicist is said to have reconsidered his calculations against the background that he had mistakenly assumed the wings of the bumblebee to be stiff. The later answer, however, was unlikely to make a headline. It is controversial who this aerodynamicist was. In some sources it is assumed that it could have been the Swiss gas dynamist Jacob Ackeret (1898–1981). According to other sources, it was André Sainte-Laguë , a mathematician and collaborator of the French entomologist Antoine Magnan . The latter mentions a similar statement made by his assistant on the flight of insects in 1934 in his book Le Vol des Insectes (German The flight of insects ).

Physical explanation

In fact, there is no paradox here . Bumblebees are much smaller than airplanes. However, they move in the same air with the same density and viscosity . As a result, the Reynolds number for flying a bumblebee is many orders of magnitude smaller than that for flying an airplane. This means that the shapes of the flow field around the blades differ considerably. Theories on this were already developed in the 1930s. In particular played vertebral a decisive role. Experimental evidence for this was provided in 1996 when Charles Ellington from the University of Cambridge carried out experiments on insect flight: the flapping of the wings creates eddies that give the bumblebee the necessary dynamic lift . With the help of a super slow motion camera, Ellington found out that the bumblebee moves its wings in a circle up to 200 times per second, creating a tornado-like air vortex (tornado effect). This creates a negative pressure and the bumblebee rises into the air. A speed of 20 km / h is no problem for them. In 2012, a small joint was discovered in the middle of the wing, which, like the rest of the wing, is made of the protein resilin . The wing can be bent with the joint. If it was put out of action in the experiment, the bumblebees were able to carry 8.6% less weight.

Individual evidence

  1. ↑ Ivars Peterson : Flight of the Bumblebee. In: sciencenews.org. September 9, 2004, accessed January 30, 2015 .
  2. ↑ Extensive article by Peterson in his column Mathtrek, MAA ( Memento of July 2, 2013 in the Internet Archive )
  3. ↑ Theresa Moebus: Are bumblebees really too fat to fly? In: Spektrum.de. March 20, 2015, accessed September 30, 2018 .
  4. ↑ Andrew M. Mountcastle, Stacey A. Combes: Wing flexibility enhances load-lifting capacity in bumblebees. In: Proceedings of the Royal Society B. March 27, 2013, accessed on March 28, 2016 .