Chapter 6

Theories on Hovering Flight of Insects

N. Chari, Prasad Mukkavilli, A. G. Sarwade, and D. Sandhya

Abstract Seven classical theories have been suggested for calculating wingbeat

frequency in hovering state of flight. In Mass flow theory of Hovering, frequency is

calculated based on the rate of mass flow of air; and insect is in dynamic equilibrium.

This was suggested by Puranik et al. The value of K is variable in different theories.

In Mechanical oscillatory theory, the oscillating wing is considered as a mechanical

oscillator. Wing length is in millimetres and K is 3540. This theory was suggested

by Greenwalt. Crawford’s theory is a modified Mass flow theory where wing swept

area replaces wingspan square and stroke angle is small. This is applicable for small

insects. Norberg’s theory is based mainly on the mass of the flier (and other flight

parameters) which is related to power of the flier. Pennycuick’s theory is based on

multiple regression and dimensional analysis. Theory based on Newton’s Law is on

mass flow concept. Deakin’s theory, he applied dimensional analysis concept. This

is particularly applicable to insect hovering.

Keywords Disc area concept · Harmonic oscillator · Wing swept area · Wingspan

loading (WSL) · Dynamic equilibrium

Introduction

The hovering flight requires normally more power than does the forward flight.

However, the discrepancy may become less significant for the insects which weigh

far less as compared to birds and bats. Understanding a detailed study of flying insects

that seem to hover effortlessly helps in the development of flapping flexible wings for

winged nano-scaled MAVs useful for surveillance over small areas. Forward speed

being zero in hovering flight, the lift has to be sufficient to balance the total weight

N. Chari (B)

Kakatiya Unviersity, Warangal, India

P. Mukkavilli · D. Sandhya

SNIST, Hyderabad, India

A. G. Sarwade

MRCET, Hyderabad, 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_6

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