@article {OSBORNE221,
author = {OSBORNE, M. F. M.},
title = {Aerodynamics of Flapping Flight with Application to Insects},
volume = {28},
number = {2},
pages = {221--245},
year = {1951},
publisher = {The Company of Biologists Ltd},
abstract = {1. General formulae are derived giving the lift, thrust and power when the wing motion is specified. The formulae are applied to twenty-five insects for which quantitative data are available. Average values for lift and drag coefficients, CL and CD, are derived by equating the weight to the vertical force and the thrust to the horizontal drag of the body. 2. The large drag and lift coefficients obtained for insect flight are attributed to acceleration effects. There is a distinct correlation between (C2L,+ C2)D){\textonehalf} and the ratio of the flapping velocity of the wings to the linear velocity of flight. When this ratio and therefore the accelerations are small, the force coefficients do not exceed those to be expected for flat plates. Owing to the nature of the assumptions and approximations made, the values derived for CD, CL and CD/CL are minimum values. 3. Other characteristics of insect flight are discussed. In general, insects fly in such a way as to minimize the mechanical power required. In most, but not all cases, the useful force is the one perpendicular rather than parallel to the relative wind. The wing tips should move in a figure 8, the down beat should be slower than the up beat, and the majority of the necessary force must be supplied on the down beat. 4. Figures are given using the data from the twenty-five insects considered, showing average relations between power, specific power, mass, acceleration forces, force coefficients and geometrical dimensions. The power per gram, the {\textquoteleft}wasted power{\textquoteright}, and the force coefficients all increase as the importance of the acceleration forcesincreases. 5. When plotted as functions of mass, quantities involving the power show much less dispersion than quantities involving the geometrical dimensions. This is taken to mean that despite the diversity of insect form, as {\textquoteleft}power plants{\textquoteright}, they are all essentially similar. 6. A table of the observed or adopted flight parameters (frequency of beating, mass, wing area, velocity of flight, amplitude and orientation of wing motion) is appended.},
issn = {0022-0949},
URL = {https://jeb.biologists.org/content/28/2/221},
eprint = {https://jeb.biologists.org/content/28/2/221.full.pdf},
journal = {Journal of Experimental Biology}
}