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The terrible flying lizard

The parameters that characterize steady horizontal flight of birds, insects, bats and flying dinosaurs include the wing span L (a length), the wing area A, the animal’s weight W, the frequency of wing beating f (in cycles per unit time), the forward speed V, the air density ρ and the air viscosity μ.
a) Choosing A, V and ρ as repeating parameters, determine all appropriate dimensionless groups for this problem. If possible, convert some or all of these groups into groups which are commonly used in fluid mechanics.
b) Consider building a robotic, flying model of a quetzalcoatlus, a prehistoric dinosaur considered to be the largest ever flying animal (quetzalcoatlus would, presumably, be capable of carrying Raquel Welch to its nest, unlike the much smaller pterodactyl, which would hardly be able to do such a thing). It is estimated that this creature had a wing span of 11 m and weighted 1350 N. Further assume that it flapped its wings 20 times per min and had a steady forward flight speed of 10 m/s. The model will be geometrically similar to the animal, as reconstructed from fossilized remains, but, for obvious reasons, it will be made with the smaller wing span of 2 m. Determine the weight, the forward speed and the wing beat frequency of the model, as required in order to preserve dynamic similarity. Do you foresee any difficulties with the operation of the model? If so, can you recommend some solution that may be acceptable?.


Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada.

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