Biomedical Engineering Reference
In-Depth Information
conclude that if a certain feature exists on a bird
wing, and the bird flies well, then that feature is
essential for flight. An example of this reasoning
is to conclude that feathers on birds, by virtue
of their beneficial aerodynamic properties, must
have evolved to enable flight. However, it is
now a widely accepted fact that birds evolved
from theropod dinosaurs, and feathers evolved
for several reasons before the ancestors of birds
could fly. Some of these reasons include thermal
insulation, water repellancy, and coloration to
attract a mate. Numerous fossils have confirmed
that feathers existed in nonavian dinosaurs.
These early feathers reflect the stages of feather
development predicted by theoretical reasoning
based on evolutionary developmental biology
[5]
. It has been stated that “proposing that feath-
ers evolved for flight now appears to be like
hypothesizing that fingers evolved to play the
piano”
[6]
.
This chapter describes recent developments
in the area of manmade microflyers, along with
fundamental limits to their performance.
Because the focus is on biomimicry, scaled-
down versions of conventional aircraft, such as
fixed-wing micro air vehicles and micro-heli-
copters, are not discussed.
dimension. The surface area of the aircraft,
and other parameters related to the area, vary
directly with the square of the representative
dimension.
As a result, the wing loading
W
/
S
of an air-
craft, which is the ratio of its weight
W
to the
area of its wings
S
, varies approximately linearly
with the representative dimension
l
as
l
3
l
2
∝
l
∝
W
1
/
3
.
W
/
S
∝
(5.1)
The cruise speed
V
is related to the wing load-
ing by
W
/
S
∝
V
2
.
(5.2)
As a result, it can be seen that a heavier aircraft
tends to have a higher cruising speed.
A number of trends can be deduced using
similar scaling arguments. Tennekes
[7]
dis-
cussed several of these scaling laws and devel-
oped the Great Flight Diagram (
Figure 5.1
),
which plots a number of natural as well as man-
made flyers on the basis of their weight, cruising
speed, and wing loading. It is quite remarkable
that manmade aircraft, birds, and insects all fol-
low a common trend line quite closely. Specially
developed aircraft—for example, solar-powered
or human-powered aircraft—do not follow this
trend because they have been engineered to
achieve specific requirements. In a similar way,
the spread of aircraft around the trend line is a
result of specific mission or operational require-
ments. Note that the spread is the largest for
insects, which perhaps have to satisfy numerous
other requirements that are not considerations
for birds or aircraft. Another remarkable feature
of this diagram is that the trend line is the same
regardless of the mechanism used for flight, that
is, fixed-wing manmade aircraft follow the same
trend as flapping-wing natural flyers. Although
the diagram does not explicitly indicate bats,
they fall within the range of small birds on the
trend line.
Scaling laws and trends such as this are use-
ful in developing conceptual designs of new
5.2 DESIGN SPACE FOR
MICROFLYERS
Manmade microflyers typically have dimen-
sions on the order of 10 cm and a gross mass
on the order of 100 g or less. Based on con-
ventional fixed-wing aircraft that range in size
from single-passenger light aircraft to large civil
transport aircraft such as the Boeing 747, it is
possible to develop scaling laws for the size and
performance of an aircraft of given dimension.
These parameters are broadly governed by the
square-cube law. That is, the mass of the aircraft,
and other parameters related to the mass, vary
directly with the volume of the aircraft, which
is proportional to the cube of its representative
