194

G. Shailaja and N. Chari

R is wing length (m)

CL is the coefficient of lift

Ar is aspect ratio of wing

m is mass of insect (kg).

7.

MASS FLOW THEORY (1977, 2015)

Amongst all theories Mass Flow Theory suggested by Puranic et al. [7] is more

reasonable since observed and experimental results are in good agreement. Chari

and Achary et al. considered mathematical aspect, and further this was reviewed by

Chari [1]. For sustained flight during hovering, lift must be equal to the body weight.

The comparison of basic aerodynamic forces of insects, bats and birds can be the

basis for understanding and designing bio-mimicking aerial vehicles with flapping

flexible wings.

In mass flow theory frequency of biological flier is based on mass of the flier (Mf ),

squareof thewingspan(L²) andbreadthof thewing(Beff ). Hereall thefour dynamical

forces namely weight and lift, thrust and drag are taken into account. The rate of flow

of air ( ^dm

dt ^{) displaced by the flier is mathematically related to frequency. The constant}

of proportionality is shown as 2086. In this Mass flow theory the constant 2086 is

calculated by empirical formula and has been verified experimentally. The calculated

and observed frequencies are in good agreement.

The formula for wingbeat frequency is

vh = ^{K 1M f}

L²Bef f

where K^′ = 2086, Mf = mass of the flier,

L = wing span, Beff = maximum wing breadth.

The value of K^′ is determined experimentally by drawing a log–log graph of Mf νh

ν0L²Bef f and the graph is a straight line. In brief, the equation can be summarized

as follows:

M f g = K Sd Beffρνh/2, where Sd = ^L2

4

Finally νh =

8g

K

M f

L²Bef f

Wing span loading = ^{Wing loading}

Aspect ratio

=

M

A

L²

A

= ^M

L²