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Physics of Insect FlightConcerning the study, modeling, and applications of insect flight to

modern technological advances

Travis Mallett | Physics 205 | Spring 2010

Table of ContentsIntroduction................................................................................................................................................3Types of Insect Flight.................................................................................................................................4

Forward Flight.......................................................................................................................................4Hovering................................................................................................................................................4Passive Flight........................................................................................................................................5Flight Strokes........................................................................................................................................5

Measurement of Forces in Insect Flight.....................................................................................................6Modeling of Insect Flight...........................................................................................................................7

Simple Models.......................................................................................................................................7Advanced Systems Modeling................................................................................................................7

Mathematical Involvement...............................................................................................................9Computer Simulations....................................................................................................................10

Practical Applications...............................................................................................................................11Conclusion...............................................................................................................................................12Bibliography.............................................................................................................................................13

Illustration IndexIllustration 1: Forward Motion - Wing Force has Horizontal and Vertical Components...........................4Illustration 2: Hovering Position................................................................................................................4Illustration 3: Passive Flight Wing Performance Modeled by Free-Falling Paper....................................5Illustration 4: Visual Observation of Insect Flight Aerodynamics.............................................................6Illustration 5: Wing-Fitted Grid Zones.......................................................................................................8Illustration 6: Flapping, Elevation, and Feathering Angles from Kinematic Data Measurements............8Illustration 7: Near and Far Field Flow: Vortex Dynamics and Wake Structures....................................10Illustration 8: Balloon-Assisted Flight of Radio-Controlled Insect Biobots...........................................11Illustration 9: Naval Air Weapons Station China Lake, California – Micro-vehicle Design...................11

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IntroductionInsect flight has long fascinated humans, lay persons and scientists alike. The quick buzzing movements, the agile maneuvers, and the apparent ease at which they seem to ignore the complex physics underlying their ability to fly make the intrigue not without cause. Insects are the most abundant creatures on earth, yet elusive and difficult to catch. Surrounding us with their constant motion and often high-speed flight, they are objects of fascination which effectuate an inspiring force in not only our arts and poetry but also scientific inquiry.

Modern folklore has a tale concerning insect flight. The venerable line about scientists having proved a bumblebee can't fly appears regularly in magazine and newspaper stories. According to legend, a prominent aerodynamicist happened to be talking over dinner to a biologist who then asked about the flight of bees. In response to the question the engineer did a quick “back-of-the-napkin” calculation. After estimating the bee's weight and wing area he calculated the lift generated by the wing. Upon finding that there would not be enough lift generated to enable the bee to fly he jokingly replied, “Well, I guess bees can't fly!”

The myth that “science says a bumblebee can't fly” has its origins in a the 1930s in Germany and appears to be an authentic account of a calculation done by the assistant of a French entomologist Antonine Magnan. In 1934 Magnan referred to a calculation by his assistant André Saint-Lagué, an engineer in his book Le vol des insectes. Magnan mentions in the introduction to his book, “First prompted by the fact of aviation, I have applied the laws of the resistance of air to insects, and I arrived, with Mister Sainte-Lague, at the conclusion that their flight is impossible.”1

Magnan also stated that “One shouldn't be surprised that the results of the calculations don't square with reality.”2 Obviously bumblebees still could fly and the calculations were over-simplified. To keep things simple, the calculations employed assumptions including a rigid, smooth wing, and aerodynamic features similar to those involved in airplane flight. The story of the bumblebee who couldn't fly has become a popular “urban legend” that has taken on various morals and meanings, often in the context of discrediting science. For the most part, the legend has held a certain amount of validity since insect flight has been little understood. It is only in recent years with new applications and motivations that the study of insect flight has become an important field of research.

Whatever the implications of the bumblebee myth, it is useful as an example of the intersection of science, myth, and the intrigue surrounding insect flight. Today with micro-vehicles in development involving wide-spread military application, the study of insect flight is more important than ever. The complexities of insect flight are not trivial and should be studied, if not for the practical applications, then for the knowledge that can be gained about physics and biology as we attempt to better understand the world around us.

1 McMasters, pg. 1642 Ingram, pg. 91

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Types of Insect FlightBefore we dive into the swirling complex of insect flight dynamics, it is instructive to mention the different types of insect flight. For example, the flight of a large moth is very different from that of a fly and neither are like that of the flight of a humming bird.3 Rather than categorize the types of flight of different creatures, it is more useful to divide the flight patterns into different physical aspects of the flight itself. This becomes especially useful since many insects can employ various maneuvers at varying times.

Forward FlightInsects institute forward flight to not only lift themselves upwards, but to move in a particular direction perpendicular to gravitational forces. This occurs when an insects wing beats not only provide some upward thrust but a component of the force generated by the wing is in some direction not parallel with gravity (See Illustration ). Although this is an over-simplified model (with simple, static forces attached to the wings), the general idea holds because on average the forces are as shown. Of course the wings are constantly beating in an oscillatory motion but if we were to ignore this and lump the the complex beat patterns into a net result, we can attach the forces as shown in the following diagrams.

HoveringThe concept of hovering flight might seem like simply a degenerate case of forward flight where the forward velocity is zero. However, the hovering position of insects (see Illustration ) reveals that it is more complicated than a zero forward velocity. As shown, the orientation of the bee is such that the wings not only create an upward lift force, but must also counter the weight of the abdomen and legs which create a torque around the connection of the wings to the body. In effect, the torques must “cancel” such that the insect can remain in one position without moving. The details of this seemingly simple idea become extremely complicated when the motion of the wings that generates the forces involved is taken into account.

3 Although not an insect, the flight of a humming bird (and many birds for that matter) can be modeled much the same way as for insects.

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Illustration 2: Hovering Position

Illustration 1: Forward Motion - Wing Force has Horizontal and Vertical Components

Passive FlightPassive flight is not so much a flight pattern as a physics aspect of wing interaction with the air-fluids. During wing rotation, the forces the twist the wing are not due to a driving force, i.e., the insect is not physically forcing the wing to twist. Instead, the primary forces are due to fluid torque. Isolating this effect is essentially the same as falling piece of paper (see Illustration ). Notice that the paper in air has a periodic motion that rises without a driving force that makes it rise.

Flight StrokesThe flight strokes of insects can be divided into four basic steps. First the downstroke starts up and back and is plunged downward and forward. Then the wing is quickly flipped over during what is called suppination such that the leading edge is pointed backward. The upstroke then pushes the wing upward and backward. Then the wing is flipped again during pronation.

It is important to note that these four basic stroke patterns occur whether the insect is hovering or experiencing forward motion. The difference between the two is the position of the body during these strokes.

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Illustration 3: Passive Flight Wing Performance Modeled by Free-Falling Paper

Measurement of Forces in Insect FlightIt has only been in recent years that the complex nature of insect flight has become more fully understood due to advances in technology such as high-speed video cameras and precision measurement utilities. As the wings of an insect flap, they create swirls of air and generate aerodynamic forces that allow insects to dart forward, to turn, and to hover. Accurately measuring the instantaneous aerodynamic forces on a live insect remains a challenge.

Airflow around insects during flight is perhaps the easiest observed for the tethered insect in a wind tunnel (see Illustration 4). It was in 1868 that E.J. Marey filmed tethered insects using slow-motion film and tracing the wing tips using a glass hair. Today with more advanced equipment we see the tethered insect produces a complex vortex of airflow behind it with each wing flap. However, it is difficult to quantify the forces involved from pictures and it is also thought to not be entirely accurate since the insect is tethered and not allowed to fly in its natural motion.

Methods to accurately measure the time-dependent forces on the wings have involved piezo-electric probes and strain-gauges. One creative method by a team from Tsinghua University of China has allowed a more accurate analysis of the aerodynamic features of insect flight. The team glued a sliver of glass on the top of a bumblebee's body between its wings. The bee was then allowed to fly freely inside a small clear box that was illuminated from above by an array of 49 lasers. As the bumblebee changed direction and orientation, the lasers bounced off the glass and into a screen suspended above the box. Using synchronized cameras surrounding the box, the team was able to calculate the position, velocity, and orientation of the bumblebee with respect to time.4

Using new, innovative methods of observing the forces involved in insect flight, scientists are now able to better understand the complexities of insect flight. However, tracking time-dependent wing kinematics remains a main difficulty in the scientific observations. The complicated setups can be error-prone and it is difficult to know whether the data recorded is really accurate. Despite these adversities, ground has steadily been gained in the study of insect flight.

4 Pennicott (2001)

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Illustration 4: Visual Observation of Insect Flight Aerodynamics

Modeling of Insect FlightArmed with an ever growing repository of data concerning insect flight, physicists actively making attempts to model the flight. Insect flight is a multiplex of physical aspects and interacting systems and involves fluid dynamics, kinematics, morphology, and vortex dynamics, as well as ideas about energy and power. An accurate model must take into account these and many more physics concepts. However, there are some simplified models of insect flight that have been around for many years. More recent models are grossly complex.

Simple ModelsOne “simplified” model of insect flight is called a quasi-steady analysis that originated in 1925 by G.T. Walker. It makes the assumption that the instantaneous forces on a wing are determined by its current motion and is not at all dependent on its history. In other words, it disregards any effect the “swirling” air flows produced by past wing beats might have on the current forces.

The quasi-steady analysis provides a simple framework for quantitative prediction of the forces in insect flight. It was more or less verified by M. Jensen in 1956 who used a high-speed camera and analyzed the motion using a projection method. After sorting through more than 600 sets of observations he concluded that the quasi-steady analysis was consistent within experimental error with the measurements.5

Advanced Systems ModelingAlthough the data available about insect flight has increased dramatically, it is still non-trivial to accurately model the flight. Modern insect modeling no longer uses the single-body Newtonian forces system for analysis. Instead, physicists must use multi-body systems with consideration of dynamically oscillating boundaries of flapping wings and complicated wing-wing and wing-body interactions. The current models must needs employ morphology, kinematics, and aerodynamics to build, evaluate, and test the complex flight models.

To begin, the modern models use complex geometry schemes (see Illustration 5) by surrounding the relevant, interacting components of the insect by so-called zones cones to allow spatial interaction through the fluid. In a recent study by Hao Liu from Giba university, Japan6, the researchers fitted two major grid zones to the body and wings. To further generate high-quality grids, the body grid blocks were further divided into three zones.

5 Z. Jane Wang pg. 1856 Integrated modeling of insect flight: From morphology, kinematics to aerodynamics, pg. 444

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Once the complex geometry system has been determined, the process of modeling the kinematics of the flapping motion can begin. Using a Fourier series, the angles within the stroke plane are modeled below:

The flapping frequency ω can be measured from kinematic data such as that shown below.

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Illustration 5: Wing-Fitted Grid Zones

Illustration 6: Flapping, Elevation, and Feathering Angles from Kinematic Data Measurements

Mathematical InvolvementUnfortunately, this is only the beginning of the insect flight models. Although a detailed analysis is outside the scope of this paper, following is a demonstration of the sheer mathematical complexities involved.7

An important mathematical concept used in modeling insect flight is called the Navier-Stokes equations developed by Claude-Louis Navier and George Stokes. They describe the motion of fluid substances and are a result from applying Newton's second law to fluid motion. The governing equations are the three-dimensional, incompressible, unsteady NS equations:

Although the partial derivative formulas look innocent enough, the formulas quickly become a gross perversion of mathematics when applied to so-called Euler schemes that employ “pseudo time integration.”

Clearly the mathematics involved present a challenge by themselves even without being concerned over the underlying physics involved.

7 Integrated modeling of insect flight: From morphology, kinematics to aerodynamics, pg. 446-457

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Computer SimulationsDue to the sheer complexities involved in the mathematical calculations concerning the physics of insect flight, it is necessary to “test” the final mathematical models using computer simulations. Using computer simulation Liu has created models that take into account vortex dynamics and wake structures of the fluid flow. The following diagram illustrates the development of the vortical structures by an insect for the four parts of the flapping flight, pronation, downstroke, supination, and upstroke.

Advanced computer models and simulations allow us to more fully understand the workings of insect flight and are especially useful in practical applications as these models can be applied to engineering designs.

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Illustration 7: Near and Far Field Flow: Vortex Dynamics and Wake Structures

Practical ApplicationsThe military implications are tremendous. Micro-air vehicles (MAVs) can literally become the proverbial fly on the wall. Spy flies could snap photos and retrieve information undetected. The MAV community has exploded in recent years and has begun to take inspiration from flying insects or birds to create more capable designs.

Not only is insect flight being studied for the purpose of creating miniature flying robots, but it is also being studied for use with “biobots.” An amusing example is the implant of metal wire probes into the brain and thorax tissue of moths. A group of IEEE researchers8 successfully inserted surgical implants into moths and were able to control their maneuvers through joystick manipulation. (See Illustration 8).

Due to the weight of the implants and control systems, the insects required helium-filled balloons to aid in the lift. The modification of the insects provides an interesting example of the applications of the study of insect flight. Technology must still advance to a point that the implants and controls are light enough that the insects do not require additional lift.

Potential military use is one of the driving motivations behind research into and design of MAVs that mimic insect flight. The U.S. Air Force has developed several prototypes of miniature flying robots to evaluate their short-range scouting capabilities (See Illustration 9). However it is speculated that it will still take years for micro-vehicle designs to achieve the capabilities of insects. MAVs must be able to carry a wide range of sensors and be able to fluently perform complex maneuvers in flight to be useful.

The research and design involved in the development of micro-vehicles is not trivial and remains an active field of study and constant change today.

8 Balloon-Assisted Flight of Radio-Controlled Insect Biobots, pg. 2

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Illustration 8: Balloon-Assisted Flight of Radio-Controlled Insect Biobots

Illustration 9: Naval Air Weapons Station China Lake, California – Micro-vehicle Design

ConclusionHumanity has long been reflecting on insects. The marvels of their flight and effortless maneuvers has been the cause of much awe and delight. But it is only now, in more recent years, with complex modeling capabilities and data available are we able to understand the concepts behind insect flight more fully than ever before. Even so, the amazing complexities of insect flight have been revealed to be even more complicated than ever thought and only prompts us to further question and probe how it works. The advanced mathematics behind insect flight only makes their flight more marvelous. Our most advanced engineering designs cannot even come close to approximating the capabilities of a small insect.

Today with our great technological advances, insect flight remains a complex subject that is still not fully understood. It is without doubt that the study of insect flight will continue for much time to come and will enable us to even further advance our designs of micro-vehicles and provide a greater understanding of the physics behind flight. The study of insect flight is important in the long run not only for the purposes of design and engineering, but also for adding yet another set of physics principles and mathematical tools to our arsenal of physical understandings.

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BibliographyIngram, Jay The Barmaid's Brain, Aurum Press, 2001

McMasters, J.H. 1989. The flight of the bumblebee and related myths of entomological engineering. American Scientist 77(March-April)

Peterson, Ivars 2004. Flight of the Bumblebee, Mathematical Association of America:

http://www.maa.org/mathland/mathtrek_09_13_04.html

Lijang Zeng et al 2001 Meas. Sci. Technology. 12 1886

Lasers illuminate the flight of the bumblebee – Physics World, 2001: http://physicsworld.com/cws/article/news/3410

Walker GT. 1925. The flapping of birds. J. R. Aero. Soc. 29:590–94

Dissecting Insect Flight – Z. Jane Wang – Theoretical and Applied Mechanics, Cornell University

Weis-Fogh T, Jensen M. 1956. Biology and physics of locust flight. Proc. R. Soc. pg. 239:415–58

Balloon-Assisted Flight of Radio-Controlled Insect Biobots, IEEE Trans Biomed Eng. 2009 Sep;56(9):2304-7.

Hao Liu, Integrated modeling of insect flight: From morphology, kinematics to aerodynamics, Journal of Computational Physics, Volume 228, Issue 2, 1 February 2009, Pages 439-459, ISSN 0021-9991,

http://www.sciencedirect.com/science/article/B6WHY-4TN0M2J-1/2/98af058450b2ad713464cd352f38f64c

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