Hi. My. Name is Michael Dickinson I'm a professor of biology and, bioengineering at, the California, Institute of Technology and, this, is the first of three lectures, on how flies, fly, in this, lecture I'm going to be focusing, on lift that is how, the air how the flies and other insects, generate, sufficient, aerodynamic. Force to, remain in the air and to maneuver, but. Before getting started let's. Consider about, flight, in general, within biological, systems. Flight. Evolved, exactly, four times in, the history of life in pterosaurs. Birds. Bats, and insects. And each time that flight evolved, it was associated with an enormous, radiation. Of species, flight, is extraordinarily, useful. Form. Of locomotion it's a very cheap form of locomotion which, allows animals, to, generate. New niches, and ways of finding food ways, of migrating, across the globe ways, of gathering. Mates, and other resources. So. It's not surprising that, every time that flight has evolved. It's. Been associated with enormous. Species, diversity. Today. Though what, I'd like to focus on is in. Our insects, which. Are my favorite creatures because, I think in many ways they. Excel, in aerodynamics. Flight. Control, as, is. Demonstrated, by this high-speed video sequence, that you're seeing. Which. Was shot at. Seven-and-a-half. Thousand. Frames per second, in infrared, lighting, it shows, two flies on a collision course and the entire sequence lasted. Only 200. Milliseconds. Which is approximately, a fraction. Of a human eye blink the, two flies were on a collision course but they saw each other with their eyes and, were able to initiate, evasive, maneuvers. To keep from crashing, it's just such types of behaviors, that have inspired me throughout my career and, have, allowed me to focus, 30, years of war of research on the problem of insect. Flight. It's. Also worth mentioning. That. Insects, are unique among flying, animals, and that they haven't transformed. Their legs into, wings rather, they have evolved the completely, different, appendage, so, they can walk and fly we. Call these things flies, but we could just as easily call, them walks because they're capable of terrestrial. Behavior, as well so in many ways insects. Are somewhat like mythical. Creatures that we write about as humans. Like, this. Pegasus. That has both legs and wings, and again. Before getting into the details of insect flight it's worth remembering.
That. Insects, are the most species-rich. Group, of organisms on the planet and, this is largely due to the fact that they can fly. So. How do, you fly what does it take to fly well. To ask this question and answer it we, really can think about the devices, that humans, have built over the last century, to fly so here's the famous picture of Wilbur and Orville on. The, beaches of North, Carolina, with their famous a, Wright, brothers flyer and in, order to fly the Wright, brothers had to basically solve three, problems the. First problem was lift they needed to make a system, in this case these canvas. Wings that. Were sufficient, to make aerodynamic, forces that could keep their flyer in the air in order, to do so they needed a source of power in, in, this case an engine, that ran the propeller, that pulled the airplane. Through the air that generated. The velocity, that the craft needed, to generate the lift and finally. They. Needed some way of steering, and maneuvering, the device so that it didn't crash and of course in this case it was either Wilbur, or Orville, who was at the controls of the device to, keep it in the air so. Lift power and control. But. Really the three topics that we have to understand, if we're going to understand, not just human flight but also the flight of organisms. Such, as flies so, in the first of three lectures on this topic I want to focus on this, question, of lift, how, do flies and other insects, generate, enough, lift to, stay in the air. Well. Many. People have heard a story as. They go through life that, an engineer once proved a bumblebee couldn't. Fly. This story goes back to the to the 1930s. But. I can guarantee, you that we actually do, know how insects, fly it is true however that when you apply standard. Conventional. Aerodynamic. Theory, it is difficult to explain the flapping flight of insects and I'd like to begin, my lecture, by diving into why, exactly that is the case so, first however we have to go over some definitions, that are going to be useful for, the lecture. So. It's. Useful to visualize, the, wing of an insect or an aircraft as, a, tiny, section, that we call a wing cord and then we can draw, diagrams, of this wing cord and all the forces that it generates, as it moves through the air so here's that section, of the wing and, as. It moves through the air it does so at a certain velocity and, at. A certain angle that we call the angle of attack and, as we'll see a velocity.
And Angle attack are very critical, for determining, how much lift and drag, this, structure is going to make so as it sweeps through the air it generates. A force, that. Is roughly, perpendicular to, the surface of the wing, and. We can break that force into two components of an. Upward, force that we call lift that. Is perpendicular, to the direction of motion and a, parallel. Force that we call drag that is parallel to the direction of motion. So. Let's take another view of this where. We have the wing moving, at a velocity U, at a given angle of attack and it has a surface area s. Imagine. That. As the wing moves through the air it's intercepting. A volume, of air. Which. I might make the mistake of calling it fluid because to a fluid mechanician, air is, a fluid but. We imagine this this wing is intercepting. This this, bolus of air and it deflects, that bolus downward, so in order for it to change. The momentum of, that flow of air a force. Has to be generated, and that force is manifest. As the upward force on the, surface of the way and, we. Can determine, how much force that is from, Newton's laws that is that the force, is equal to the change in momentum in, this case the change in the fluid momentum the. Fluid being deflected, downward. And it's equal to the surface area of the wing the, density, of the fluid and the, velocity, squared we, can turn this proportionality, into, an exact equation by, introducing, a term called the force coefficient which. Basically tells us how good is any particular wing, a generating. Lift or in this case how good is that wing and deflecting, the flow of air downward. It's. Often, convenient, as well to, divide the, force coefficient into, the, two terms representing. Lift. And drag, so we can talk about a lift coefficient and, a, drag coefficient and, we have this nice equation, that says the lift is equal to one-half times this lift coefficient the. Density, of the fluid in this case air the, surface, area of the wing and the velocity, squared, and we have a comparable, equation, for drag. Now. Getting, back to that drag coefficient. You can imagine a nice streamlined. Wing like. This one, to, my left and a sort, of more ugly wing right, to my right and you, can imagine that perhaps that streamline. Wing, would generate more lift and less drag and that's exactly what it does that's to say that it would have a higher lift. Coefficient and. How. Would we study, and measure the lift coefficient of, an object, like, an airplane wing or perhaps an insect wing well, we would start with a wind, tunnel and this is what someone studying aerodynamics.
Would Use to, study a wing a wind, tunnel basically, generates, a. Uniform. Flow, of. Air and it's instrumented. With four sensors, that allow one's to measure lift, and drag so. We take our wind tunnel in our, wind tunnel we put a wing at a particular, angle of attack and we, have sensors that can measure the lift and drag we, can then vary the angle of attack and, we'll note that lift and drag change, as we change the angle of attack at, which the wing is hitting, the airflow so, we can then plot these measurements. So. For each angle of attack we, can measure the lift and drag as I've done here with the red and blue points and, then we change the angle of attack and, measure, different. Values for the lift and drag and we can do this over a whole range of angles of attack and, this is how many, many aerodynamic. Experiments, begin its. Conventional. Within, the study of both, human, aircrafts, and and, animals. To, reap, lot these data in the following way if I plot the lift coefficient, against. The drag coefficient at, each angle of attack as, I'm. Doing right. Now we. Present, we construct, something rather that, we call an aerodynamic. Polar so again each point of an aerodynamic, polar represents. The, value. Of lift at a given value of drag. For. A particular, angle of attack and, in, this design. Of aircraft aerodynamic. Polar's are very useful, for example if you draw a line from. The origin of, such a plot, tangent. To the curve that's. Actually the highest lift-to-drag, ratio that. That wing can produce and many times aircraft, are designed to operate at the highest lift-to-drag. Ratio. Now. Before going forward with, why. It's, hard to explain how insects, can fly I want to introduce a slightly different, way, of deriving, the lift that's generated, by a wing so imagine I put a wing in an airflow and that. Airflow is going to be distorted, by the presence, of the wing because obviously the air can't flow directly through the wing and the, way it's distorted. Means. That the flow. Of air on top, of the wing actually. Has to travel over a longer distance than, the flow, of air beneath that. The wing, and. As. A consequence. Of this, velocity difference there's, a slight pressure difference, this is a.
Phenomena. Known as the Bernoulli effect which. Explains why wings, are actually sucked, upwards but, another way of thinking about this is because, there's a differential, in velocity. On the top surface of the wing relative, to the bottom surface of the wing it's as, if there's a net circular, flow around, the wing and this is what introduces a very very important, topic which, is called circulation. Which measures, this net flow, of air. A wing and it turns out that one of the most important, equations, in. Aeronautics. Is the so called kutta. Joukowski theorem. That says that the amount, of lift generated, by any tiny, section, of the wing is proportional. To circulations. Proportional. To sort of how, big a velocity, differential. The, wing can create, and we'll, see that circulation, plays a big. Role in, our understanding of, how insects, fly. Okay. So, let's get back to trying, to explain what the basic, problem, is well, back in the 60s, 70s and, 80s, researchers. Had some of the first access. To high. Speed movies. And now high speed videos of flying, flies and yes indeed this is a fly, that's pooping. As it's hovering, there in the air answering, the questions do flies poop, when they fly and the answer is absolutely yes but, the main reason I'm showing you this is to get a sense that it would be possible to. Take a high speed a movie, or video of an insect and determine. What the motion. Of the wing is at each instant, in time, one. Could then take such a data. And. Try to reconstruct how, much force, the, wing, is gennadiy rather the insect is generating, throughout an entire stroke. And this is an exercise that was done by a real, pioneer, in our understanding of, insect. Flight a torque, vice, vogue who. Unfortunately had. A rather tragically, short life but he, worked on. On. Locusts, and other insects, and he did the following exercise, which is to say if I, took the, wing, at a particular. Time in the wing stroke when it's moving at a given velocity moving. At an angle of attack I have everything I need to know to, generate how much forces, it's, producing, at that time because. I have this nice equation that says the lift is equal. To one-half the lift, coefficient times, the density of air times the surface area of the wing times velocity squared and I can do that exact same exercise at a bunch of different points, along the wing, so, this is what is called a quasi. Steady, analysis. Because you're making the assumption that each point, time.the. The wing is acting, as if it would under steady state conditions. Then. The next part of the exercise is simply to add up the contributions of. All those points in time and ask the question, does the insect generate enough lift to, sustain, body. Weight which is the bare minimum for, staying in the air. When. This exercise. Was, done on, many many different, for. Many different insects by, Charlie Ellington who happened to be a protege, of torque LaVon vice vogue and he worked in the 80s published, a monograph and, he came to the resounding conclusion. That. The, wings just don't generate enough lift to keep the animals in the air so what you see here is a series, of those aerodynamic. Colors again where, we're plotting lift as a function. Of drag. Or. Locus. Wings fruit, fly wings crane, fly wings and so forth but the problem, is that, in order to stay. In the air. Insects. Have to generate, enough lift. In. This high range, so, the measurements, of real insect, wings show that it's just their insufficient to produce enough force to stay in the air so this is a big problem because we're off by almost a factor of two. So. This is about the time where, I became, interested in this problem and I'd like to tell you a little bit about my, research and the research of others working. In the, early 90s, that helped to solve, this enigma, of of, insect, flight before, I do so I need to introduce a, topic that we call dynamic scaling. Because it turned out that large. Robotic. Insects, played, a big role in our. Understanding. Of how insects, can fly so. If you imagine an, object, in the, air there, are two types of forces that are on that object and one, which is easy to sort, of Intuit, if you're imagining a kite, that you're, flying, has, to do with inertial, forces because as the kite is in the air the. Flow, of air is pushing against, the the, the, kite so. The forces are really coming from the fact that air has density, it has, mass and, that mass is pushing, against the the the. Surface of the kite creating, a force, another. Type of force that's very important. Our. Viscous, forces so for this imagine, a spoon. In a jar of, honey. And these viscous forces are not due to the fact, that the honey. Has mass they, have to due to the fact that the honey is sticky that, the different molecules, of honey are actually, exerting, a force on each, other and so as you try to stir, that, spoon, and the honey it's very, very difficult to do so well.
It Turns out that the, ratio, of these forces, the ratio of the inertial forces to the viscous forces which is a force divided, by a force is a very, very important, dimensionless. Number, called Reynolds number and it, turns out that if the Reynolds number is the same then, the forces. For. Any particular, problem, are identical. So what, do I mean by that well what, I mean is it's possible, to, take, a large airplane. Determine. The. Particular. Reynolds, number the ratio of inertial forces and I can make a more convenient, scale. Model. For example I might want to make a smaller, model that I could put in a wind tunnel and as long as I modify. The viscosity. Or the velocity, and, keep the Reynolds number the same that I know that the physics, are identical, and this is why you may have seen in automobile, ads or on National, Geographic specials. Researchers. That, are putting model. Fish model, cars even model, cities, to understand, how, air flows around skyscrapers. This can all be done with the principle, of dynamic, scaling so. In the case of insects, because, they're so small and because they flap their wings so quickly, it's, often, convenient, to work with larger. Models, and this is just a simple. Drawing of one of the first models that that, I constructed with Carl goods back. In the, early. 90s, it was just a simple paddle, that moved through a tank, of sticky, sugar, syrup but, we were very very very careful, to make sure that it matched the Reynolds number so it had exactly the same ratio, of inertial, to viscous forces as, the, tip of a fruit, fly wing. As a fly was flying through the air so. What I'm going to show you is the actual movie that Carl goats and I took. And. What you're going to see is a wing which, is shown here I'm, just pointing. Out where it's going to appear with the red line this, wing is going to move through the fluid at, a Reynolds, number the same as a fruit fly wing and at a very high angle of attack and, what I want you to notice is a swirling. Structure. On the top of the wing which is something we call a leading, edge vortex, which turns out to be really. In many ways the secret to insect, flight because, it generates so, much circulation. So. I'll play the video and, there. You can see the wing and you can see this very large vortex, on the top surface this leading-edge vortex, and I'll play it one more time so.
To. Get a quantitative. Sense of what's going on what I'd like to show you in the next slide are the measurements. That we made while we were making these, videos. And so, what you're seeing here is just the time history of the, lift, generated. By, this simple. Insect. Model, wing as it, moves through the fluid and at a very low angle of attack you. See that generally it produces. A steady, amount of lift but something, very different happens, if you do, the same experiment, at a higher angle of attack and you can see that the lift trace has, a wiggle, in it and particularly a, bump. At the beginning and this, is the increase. In force, that's due to the presence, of this, leading-edge, vortex, this leading-edge vortex, that appears, when. The wing flaps at a high angle of attack and, so. We repeated. These measurements, for many angles, of attack and, we could see exactly at, what angle of attack this leading-edge vortex, begins to appear and then when we plot the, lift, as a function, of angle, of attack I'm, showing, here two curves because, one curve represents. The time when the leading edge vortex, was attached to the wing and the other, represents. The time later, when the leading at vortex has shed and is not contributing, to the generation, of lift and you can see a very. Large augmentation. Producing. Lift coefficients. That are of sufficient magnitude. To, explain, how. The insect, can stay in the air, now, shortly after call goats and I did these sorts of experiments, Charlie, Ellington who is a real pioneer, and our study of insect flight was, able to do some very elegant, visualizations, of, insects, in particular, moths flying. In wind tunnels and was able to show that moths do, actually, produce leading-edge. Vortices, as they, fly. Since. This time, we've. Generated. Lots, and lots and lots of evidence showing. The importance, of leading-edge vortices, and this has mostly been done by creating more, and more complicated robots, so. What I'm showing you here are movies of various versions of, what, we call in my laboratory, Robo. Fly which, flaps its wings and a giant to metric, ton tank of mineral. Oil. Instrumented. In such a way that we can measure the, forces and flows that it generates, very, very accurately. So. We know from these sorts of experiments, Oh. Before. I get there let me just show you some. Of these measurements. Of the leading edge vortex, and visualizations, that. Have come from such experiments. So you're showing, you in this. One movie, what. You would see if your eyeball, was staring, down the. The axis, of the wing as the, wing was flapping back and forth and you can see this swirling, structure, that develops, right, at the leading edge in, this. Animation, immediately. To my right, this. Is actually a simulated. Flow, I'm from, a computer model done by a former. Student in the lab Sean, Humber and you can see this leading-edge vortex, an important. Fact. About it and that's, the fact that the leading-edge vortex, develops, on one surface of the wing the wing then flips over and the leading-edge vortex, develops, on the other surface so, the wing the insect actually is sweeping, it swing back and forth and every time it flips over it generates, a new leading edge vortex, which is producing, this high circulation. And producing. These very large forces. So, leading, at vortices, seem to be the, real. Reason. That insects. Can can fly and and since this early work on insect, flight leading at vortices, have been found in a variety of different organisms, they're, used by Swift's. As Swift's, can. Glide quickly. Through the air they're, generated, by bats when bats are hovering they're. Produced even by the tails of fish as fish are flapping back and forth they're, flapping their tails back and forth fairly quickly leading, edge vortices are even, generated, by plant, seeds such as maple seeds when they swirl. To the ground so this seems to be a common. Trick that, evolution. Has found, again, and again to produce very. Very large forces. Now. In the next couple, of movies what I'd like to show you is really why. We. Got this wrong for so long and it has to do with exactly. How an insect flaps its wings so an insect doesn't flap its wing or move it's going like an airplane that, is it doesn't simply, translate. Through, the, air but, rather it rotates, more, like the wing or the fan, blade of a helicopter, so here you see a wing, of Robo. Fly. Translating. Through an oil tank and this was a movie taken by David Lent Inc winningly is my laboratory and you can see the leading edge vortex. Develop. As the wing starts to move but, then the vortex gets shed quickly. As it moves through this is the mechanism. Or rather the process, that we call stall, however. You take that exact same wing and you move it in a different way you revolve. The wing as it, does on a would, revolve on a helicopter, and then you see a nice, stable, leading-edge, vortex. That. Is not shed. As. Long as the wing continues, to revolve so.
Really One of the key things is this the, fact that insects, revolve, their wings rather than translating. Them so, to just give a summary of that if you take a wing and and translate. It through the air as it would on an airplane what, you see is a leading edge vortex, it's very unstable and quickly, sheds if you take that same wing and revolve, it as it, would on the, rotor of a helicopter, what you see is a leading-edge, vortex, that stays, attached, as for. The duration of motion. So. We should really think about insects, as being like, a little tiny helicopters, but instead of revolving, their wings continuously, they revolve, their wing in one direction flip, it over revolve, it back flip it over revolve, it back and so, forth now. That's, not the only thing. That's going on with insect, flight this mechanism. I'm sometimes called, delayed stall involving. The leading edge vortex, this, is certainly very important, in the middle, of each stroke. As. The, insect is flapping its wing but because, an insect, has to actually. Stop. Revolve. Its wings stop, its wings and move in the other direction, there, are some opportunities, for other interesting, aerodynamic. Mechanisms, and, one, of them has is, something we call rotational. Lift because the wing actually has to flip. Over before, it begins translate, in the other direction and that process of flipping over is able to generate even higher, forces, the leading-edge vortex, can even get larger, and these forces are somewhat analogous to the, forces that are generated when a baseball, or tennis ball, spins, as it moves. Through the air in, addition. As the. Wing stops, and starts to move in the opposite, direction it, intercepts, the weight generated. By the previous, stroke and if it does so in an efficient, way it's, actually able to extract energy from the, wake something, we call wake, capture, and it, turns out that for certain insects, a particularly, insects. That have very very very short strokes.
So They're basically always flipping. But flipping, the wing over, that. These so, called rotational. Mechanisms, play, a large role for. Example in this honeybee. And you can see just how brief, its strokes are before, it flips over and honeybees make use of these rotational, forces, as they, fly. So. The last thing I want to say is that as you imagine, an insect flying through the air and this is going to be important, when we consider a, Epic's such as power and control. But, the insect, can vary. The way the, the wing is moving it can modify the angle of attack it. Can change, slightly, the velocity, from one stroke to the next and as a consequence. It can. Vary the direction, of the forces, that are being produced by the stroke, so it can for, example fly. Backwards. Or, forwards. Via, subtle, modifications. In. The way that it's moving its forces, and whether, the way that it's moving its wings through. The stroke, so. I hope by. The end of this lecture you have a much better understanding, about the aerodynamic, mechanisms, that flies, and, other insects, use, to, stay in the air and maneuver. If you. Want to learn more about other topics related to insect flight in particular, where, the fly gets its power required. To flap its wings and, how, its able to control, its wing motion, you, can see the two other lectures, in this, series. Thanks. For your attention, and remember, to think before you swat. You.
2020-05-02