This is
the first in a series of occasional articles I hope to write about dragonfly and
damselfly flight. My intention is
to make a connection between the physics and biology of flying, and to
eventually cover many of the different aspects of flight in our favorite group
of insects. I spent about 30 years
working as an aeronautical engineer, and have been interested in flight in
nature for most of that time, so will be bringing some of that baggage along
with me. I will try to make the
technical aspects of my discussions accessible.
I
welcome comments and feedback. There
are a number of folks in the DSA who have been watching dragonfly flight and
doing research into it for a long time, and I hope that they will feel free to
contribute comments, criticism or clarification to help make this a useful,
instructive, and entertaining endeavor. Now
to the topic at hand.
Why the
title “wings as wings”? Well,
one of the fundamental differences between airplanes (and most attempts to study
insect and bird flight have used aerodynamic theory of wings as it was developed
for application to airplanes) and insects is that insects use their wings for
moving them forward (generating
thrust) and for “holding them up” (generating lift).
In most airplanes, the lift is generated by wings and the thrust (the
force that causes the airplane to move forward through the air) is generated by
a completely separate system (jet engine or propeller).
Insects, of course, generally flap their wings to both move forward
(wings as propellers) and to hold them up (wings as wings).
For the purposes of this introductory discussion, we will restrict
ourselves to wings as wings, not as propellers, and will assume for the moment
that our insects are not flapping their wings, but are gliding.
Suppose
we watch an Anax junius male gliding over a pond without flapping his
wings. If he is flying at a
constant speed and height above the water (not climbing or descending or
accelerating or decelerating), we can envision that his weight is being balanced
by some force. We call that force
lift. It is the result of a
difference in air pressure on the ventral and dorsal surfaces of the wings.
(We’ll take up just how the pressure difference is generated next
time.) The pressure of the air flowing past the underside of the wings is
greater than that of the air flowing over the top of the wings.
Suppose
the dragonfly’s mass is 1 gram. His
weight is then about 0.01 Newtons. If
his four wings total 2000 square mm (0.002 square meters), then his wing
loading, that is, the average pressure that must be exerted by the air on the
surface of his wings, is the weight (W) divided by the wing area (S):
W/S= 0.01/0.002 = 5 N/m2.
(For those of you more familiar with English weights and measures, that
is about 0.1 pounds per square foot.) Thus,
to fly, our Anax junius needs to have an average air pressure of 5 N/m2
acting on the surface of its wings.
This
simple ratio, the wing loading, can be figured for any odonate by weighing the
live insect, and by measuring its wing area, then dividing the weight by the
area. (Area measurement has become
a lot easier in these days of computers and scanners. By scanning a set of wings at high resolution and then using
an image processing software program like NIH Image (available for free from the
National Institutes of Health web site: < http://rsb.info.nih.gov/nih-image/
>), the total wing area can be very accurately figured.)
Figure 1 will allow you to figure the wing loading if you know an insect’s weight in grams and wing area in square centimeters. I have also plotted the wing loadings for a number of odonates based on data I have measured.
Several
papers have been published that record wing loading values for different
odonates (see References) also. Rüppell
and Hilfert (1993) have summarized some values for different taxa:
What
do these values tell us about how these insects might fly? A trip to a wind tunnel with an assortment of wings would
eventually lead us to find that the lift generated by any given wing is directly
proportional to the density of the air, and the projected area
of the wing. It is also proportional
to the square of the velocity of the wing with respect to the air. We could
thus say that:
L (the lift) is proportional to ρ (the density of the
air) times S (the wing area) times V2 (the
square of the velocity)
This
can also be written down as an equation:
L = C (a constant of proportionality) times ρ times
S times V2 =
C ρ S V2
A
measure of the kinetic energy possessed by a moving mass of air is a quantity
called the “dynamic pressure”, usually written as:
q = ½ ρ V2, so the equation for lift is usually
written:
L = ½ ρ V2 CL S
where now we have used CL
to denote the constant of proportionality.
This constant is called the “lift coefficient”, and one of the goals
of our testing would have been to determine a value for that constant.
(The value of the lift coefficient is determined by the geometry of the
wing and the angle it makes with the moving air – we will investigate this in
more detail at a later date.)
Let’s
suppose that our dragonfly is gliding along at 3 m/s, and is at sea level, where
the density is 1.2256 kg/m3 . Then
we can figure out what lift coefficient is needed for each wing to generate its
share of the lift supporting our Green Darner.
Remember
that we calculated the wing loading was as 5 N/m2. This is just lift divided by wing area, or L/S.
We could write our equation as:
CL = [L/S]/[½ ρ V2 ] = [5]/[(½)(1.2256)(3)2]
= 5/5.515 = 0.91
We
will see in a future column that values of around 1 (one) for lift coefficients
are perfectly achievable for wings of various shapes and sizes.
Figure
2 shows the
speed of the air moving past the wings that would be necessary to generate lift
to support insects of various wing loadings for values of lift coefficients from
0 to 1.5. At a CL of
1.0, we see that an insect with a wing loading of 1 could glide at speeds as low
as around 1.3 m/sec, while an insect with a wing loading of 4 could only glide
as slow as around 2.6 m/sec. The
wing loading thus gives us a very rough indication of whether an insect is a
high or low speed flyer.
Key
facts:
Next
time: More about the pressure distribution on wings and how it is generated.
Rüppell,
G. & D. Hilfert, 1993, The flight of the relict dragonfly Epiophlebia
superstes (Selys) in comparison with that of the modern Odonata (Anisozygoptera:
Epiophlebiidae), Odonatologica, 22(3):295-309.
Grabow,
K. & G. Rüppell, 1995, Wing loading in relation to size and flight
characteristics of European Odonata, Odonatologica, 24(2):175-186.
Wakeling,
J.M., 1997, Odonatan wing and body morphologies, Odonatologica, 26(1):35-52.