196

G. Shailaja and N. Chari

Summary

• By reviewing the eight theories the different mathematical formulae are suggested

for wing beat frequency (νh) of the biological flyers and are tabulated.

• Different authors adopted different mathematical methods to relate νh to different

physical parameters of the flyer.

• Green Walt related frequency inversely to length of the wing with an exponent

‘n’.

• Crawford calculated νh directly linking to mass and indirectly to wing swift area.

• Norberg linked frequency directly to the mass raised to −1/3.

• Penny quick derived νh formula by dimensional analysis method.

• Newton solved differential equation of motion and showed that the νh directly

proportional to the mass of flyer and inversely to the wing area.

• Ellington evaluated νh linking to aspect ratio and coefficient of lift in addition to

other usual wing dimensions.

• In mass flow theory, Chari et al. showed that wingbeat frequency directly depends

on effective mass and inversely on wing length and effective wing breadth.

• Deakin also by dimensional analysis method related wingbeat frequency to the

mass of the flyer directly to the wing area inversely.

References

1. Chari, N. (2015). Bio-aerodynamics of Avian Flight. NDRF Publications.

2. Greenewalt, C. H. (1962). Dimensional relationship for flying animals. Smithsonian Misc Coll.,

144(2), 1–46.

3. Crawford Frank, S. (1972). Comments on the physics and physiology of insect fight. American

Journal of Physiology, 39, 584.

4. Norberg, U. M. (1990). Vertebrate flight: Mechanics, physiology, morphology. Ecology, and

evolution, Vol. 1. Springer.

5. Pennycuick, C. J. (1996). Wing beat frequency of birds in steady cruising flight. New data and

improved predictions. The journal of experimental Biology, 199, 1613–1618.

6. Ellington, C. P. (1999). The novel aerodynamics of insect flight: Applications to micro-air

vehicles. Journal of Experimental Biology, 202(23), 3439–3448.

7. Puranik, P. G., Gopalkrishna, G., Ahmed, A., & Chari, N. (1977). Wing beat frequency of a flier—

Mass Flow Theory. Proceedings of the Indian Academy of Sciences Section A, 85, 327–339 and

Bio-Physics of bird flight (Bio-aerodynamics) (5th ed.).

8. Deakin, M. A. B. (2010). Formulae for insect wingbeat frequency. Journal of Insect Science,

10, 96. Available online: insectscience.org/1096.