Chapter 14

Wingbeat Frequency

Theories—A Mathematical Approach

G. Shailaja and N. Chari

Abstract Eight theories suggested for wingbeat frequency have been reviewed. The

wingbeat frequency is related to body mass, wingspan, breadth and other wing param-

eters (dimensions). GreenWalt used mechanical oscillator theory. He has related

frequency, inversely to length of the wing, with an exponent ‘n’. Crawford calculated

frequency directly linking to the mass and indirectly to wing swept area. Pennyquick

used dimensional analysis method. Newton used differential equations, and mass

flow concept. Ellington evaluated frequency linking to aspectratio and CL in addi-

tion to other wing parameters. Norberg [4] linked frequency directly to mass raised

to 1/3. In mass flow theory, frequency depends directly on mass and inversely on

L and Beff, wingspan loading is a vital factor in insect hovering. Deakin also used

dimensional analysis method for insect in hovering. K value is variable in all theories.

Keywords Mass · Wingspan · Effective breadth · Wingswept area · Disc area

Introduction

The flight of a biological flier is due to Wing beat frequency, and during hovering of

the flier, the forward velocity is zero. There are several theories to explain the wing

beat frequency of biological fliers. Out of these theories, eight have been reviewed for

the calculation of Wingbeat frequency of the biological fliers [1]. The mathematical

considerations of these reviewed theories are of special interest since this may help

in the design of flapping flexib le wing.

The Eight theories on Wingbeat frequency as mentioned are as follows:

1.

GreenWalt’s Theory (1962)

2.

Crawford’s Theory (1972)

3.

Norberg’s Theory (1990)

4.

Pennycuick’s Theory (1996)

G. Shailaja (B)

MRCET, Hyderabad, Telangana, India

N. Chari

Kakatiya Unviersity, Warangal, India

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021

N. Chari et al. (eds.), Biophysics of Insect Flight, Springer Series in Biophysics 22,

https://doi.org/10.1007/978-981-16-5184-7_14

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