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ITAI COHEN: My name is Itai Cohen. And I am obsessed with motion, motion on all different length scales, ranging from the kinds of things that you see here to your left. These are colloidal particles. They're spherical plastic spheres that are essentially a fiftieth of a hair diameter. And by looking at them and seeing them under the microscope, we can tell and we can learn a lot about many of the same processes that go on in atomic systems. They do all the same things that atoms do. But they're bigger and slower, so we can watch them and track them in real-time.
I'm also interested in things like origami. Trying to understand how, by folding something, we can give it mechanical properties that are different from the material that it's made out of, and how those folds inhibit or allow the material to move differently.
I'm interested in biological tissues. So up here on the upper right, what you're seeing is cartilage from your knee-- actually, this is from a cow's knee, but this is the same thing. It's the soft tissue that coats the bones in your knee. And I'm watching how it moves when we deform the tissue to try to learn something about what is it that makes cartilage in our knee last so long, on the order of 60 years. But cartilage that's artificial seems to break down after something like only a few years, if that.
And then finally, I'm interested in motion on large length scales. What happens when a group of people attend a heavy metal concert and spontaneously form a mosh pit? What are the rules that get them to interact with each other to get these organized behaviors?
So I'm obsessed with motion. And I begin with this quote by Aristotle, who says, "to be ignorant of motion is to be ignorant of nature." And what I love about this quote is that Aristotle, of course, had the laws of motion completely wrong. And so what that goes to show people in the audience, especially the students, is that you don't necessarily have to be right to be famous. You just have to say something that's interesting.
Today I'm going to tell you about fruit flies. I'll tell you about some interesting things. And hopefully, some of them are even right. This is Drosophila melanogaster. Isn't he beautiful? OK, I have some skeptics in the audience. But let me try to convince you of why this animal is doing something incredible.
I'm going to start by trying to balance a meter stick on my fingertips. You guys have probably done this at some point in your life. I'm doing pretty good. Does anybody have a pen with them? Oh, man. OK, I'm now going to try the same thing with this pen. And this one's a lot tougher.
Why is it a lot tougher? What's the problem that I'm trying to solve here? The pen wants to tilt over. It's unstable. I have a certain amount of time for my motor reflexes to move my hand so that it stabilizes the pen. What's the difference between the meter stick and the pen? The meter stick is a lot longer. What else? What does that change if it's a lot longer?
AUDIENCE: Center of mass.
ITAI COHEN: Center of mass. Well, I can put them at the same spot. Has anyone ever seen an ice skater pulling her hands? What does she do when she pulls out her hands?
AUDIENCE: She rotates slower when she pulls her hands out.
ITAI COHEN: Yeah, so she's slower when she's out. When she pulls her hands in, her moment of inertia goes way down. And she starts spinning really, really fast. Same thing is happening here. This stick has a large moment of inertia, that corresponds to a very slow timescale for rotation. This pen has a much, much smaller moment of inertia. This goes the distance here.
And now I want you to think about Drosophila melanogaster. This meterstick is a meter. This pen is 10 centimeters. Drosophila melanogaster is one millimeter long. Its rotation speed is extremely fast. But it is subject to aerodynamic instabilities that essentially are problematic, in the sense that the timescales of those instabilities are set by the rotation time of the insect. A meter stick, a pen, one millimeter. OK, this is an amazing animal.
I'm going to tell you about work today that's been done by my students-- Leif Ristroph, Attila, and Gordon, and my postdoc, Tsevi. And this is really a collaboration that came out of interactions with colleagues here at Cornell. So everything I'm going to tell you about is really the work of many people that came together for these results.
So my story of flight in general starts with a conversation that I had with Jacob Israelachvili. Does anybody know who Jacob Israelachvili was-- is. He's still alive. So anybody heard of van der Waals forces?
AUDIENCE: Yes.
ITAI COHEN: Yes. Jacob was one of the first guys to measure it. So he's a pretty famous dude. He was nominated for the Nobel Prize. And the conversation that I had with Jacob went something like this. Jacob sat me one day and asked, Itai, what do you want to do when you grow up? And I said, Jacob, I want to study flight. And he said, Itai, you can't study flight. I said, Jacob, why can't I study flight? And he said, because it's all been done.
And when you look at the literature, you see that, to a large degree, he was right. There is over 50 years of literature on insect flight, many papers looking at the way that these animals flap their wings and produce forces. And yet, when we took a closer look at the literature, we found that even simple things like, for example, how does a fruit fly propel itself forward, not known. How does a fruit fly produce forces to move sideways or elevate itself? Not known.
So despite this 50 years of literature, there are still glaring open questions in the field. And I tried to understand why. So to explain why this is, I'm going to tell you about a pioneering experiment. This is an example of one of them. This is a fruit fly. This is an image that comes from Michael Dickinson's lab. And what you can see here is a pin that's glued to the fruit flies back. I see some of you are a little bit worried, it's not going through the fruit fly. See, the fruit fly is still flapping its wings, so nobody called PETA yet.
This pin right here is attached to a magnet at the very top, and it allows the fruit fly to rotate about this axis. And what's nice about these experiments is that now you can show the fruit fly movies, and you can play some psychology experiments. For example, you can show the fruit fly a movie of its world moving to the right. And the fruit fly will think, oh, no, I'm moving to the left, so I better start rotating to the right. OK, or vise versa, a movie that goes to the left, and then it starts rotating this way.
And through these experiments, you can try to understand something about the way that the insects are moving their wings to control their flight. But I want you to notice one thing about this image, which is that this fly looks really angry. It looks angry because it's tethered, and it's not able to couple its motions with the aerodynamic forces that it feels. Unlike this fly, which is in free flight, and is able to do that. So aerodynamic forces are going to make a big difference to the way these animals control their wings, and that's what I'd like to show you.
The problem with doing these free flight experiments is that they're difficult. So while there have been many experiments on tethered animals, doing experiments on free flight animals has been more challenging. And that means that the field has really been data poor. We just haven't been able to extract as much data as we need from these animals.
What would we do if we had that data? What are we interested in solving? We're interested in understanding how these animals maneuver. How do they move their wings in order to produce a particular thrust or a sideways motion? We want to understand something about what forces they're applying at their hinges to get their wings to move in this way. We're trying to understand what control circuitry is going on in their neurons to tell their muscles to actuate the wing to get those maneuvers to happen. And how do they incorporate all of that together?
We want to move towards understanding these things. But in order to do that, we want to have a quantitative understanding. And that means gathering lots and lots of data. So the first part of my talk is going to be about a technique that we developed to do just that, gather a lot of data.
The basic idea is that we have a little cubicle box, about 10 centimeters on a side, the fruit flies that we throw in there. We have a laser trigger. So when a fruit fly comes and triggers both beams, the cameras are triggered to record, the data gets dumped onto a computer, and we go again. And in that way, we can collect movie after movie after movie. And this is what we see.
You're looking at a top panel, a side panel, and another side panel of a fruit fly roughly hovering. He's moving forward very slowly. And it's beautiful. The insect is moving its wing in a figure eight motion, back and forth. And my students get to look at these types of movies every day when they go into the lab.
But this is a 2D representation of a 3D object. We have three 2D representations. So how do we go from this to figuring out exactly what the wing is doing in 3D? And I'm going to show you what the state of the art was when we started this project. The idea was that you take three moments in time from the movie.
And then what you do is you try to take an in silico insect, so a model of your insect on the computer, composed of three spheroids-- one for the head, thorax, and abdomen-- and then two flat plates for the wings. And then you try to click the in silico insect, so that its orientation and posture and all the angles match the shadows that we collected from the movies, the images that we collected from the movies.
There are three orientations for the wings. There's another three angles for the body, and another three for this wing. There are three center of mass coordinates for each wing, body, and wing. That means that we need a total of 18 coordinates. So you start clicking. And even if you're really, really, really fast, we could do this in about two to three minutes per frame.
That means that a full wing stroke is going to take us an hour and a half. And a full movie is going to be about 50 hours of clicking. OK, and just to translate that into units that you all may understand, that's about 27 cups of coffee. And in order to analyze a full movie or a full maneuver, we need about 12 of these movies. OK, and I hired a lot of undergraduates to start clicking away. And we were not getting very far with the project. So we had to go back to the beginning and think about the problem anew.
And basically we were faced with the same problem that Plato has in the Allegory of the cave. Anybody remember Plato's Allegory of the cave? Yeah, a couple of nodding heads. OK, so Plato and his buddies are sitting and behind them is a fire, and between the fire and Plato is life. Life is happening over here and creating these shadows. And from these shadows, Plato has to figure out what's going on.
We're doing something similar. We get these images on our cameras. We have to ask, what object is in here that's creating those images? And to help you understand why this is a non-trivial problem, let me start with a simpler problem. So here I have a cube with three shadows, where each shadow is a disk. Now I ask you, the audience, what object can I put in the center of this cube so if I take its projection along the three direction I get three disks? And the answer is?
AUDIENCE: A sphere.
ITAI COHEN: A sphere. But it could have been three disks. It could have been a Steinmetz solid, which is a sphere with eight little corners on it, perfectly hidden so that you'd never know they were there. There is no unique object that I can put in here. There are a range of objects. And the question is, which one is the one that we're after?
So the Steinmetz solid represents the volume that you get if you extended the shadows in three dimensions and carved out that volume. That's called the maximal hull of those shadows. And at least that's a unique object, and so we can do that for the fly. So we essentially extend the shadows out and carve out what we lovingly call Frank and fly.
Frank and fly is a little cubicle that reflects the symmetry of the cameras. And we can essentially construct Frank and fly for every moment in time in our video. And this is what that looks like. We have the same video that I showed you before, now the images are on the faces of the cube. And Frank and fly is going to come out of here from the side. And there he is, and he's moving his wings. And he's got some flyness to him, some [FRENCH] fly. But he has some defects. What are some of the defects that people see in Frank and fly?
AUDIENCE: The wings are blocking its path.
ITAI COHEN: I'm sorry I can't hear.
AUDIENCE: The wings.
ITAI COHEN: The wings. What about the wings?
AUDIENCE: They're not flat, they turn.
ITAI COHEN: They're not flat. They're big, bulky, square things. Why are the wings big and bulky? Because if you're a camera, and my body is occluding the wing so you can't see it, then the only information you have about the wing is coming from this camera over here and the one at the top. And so what you end up forming is a square, because that's the whole. And that Square is changing shape as the wing rotates.
And you might say to yourself, well, that's terrible. The real fly's wing doesn't look anything like a square. That's true. But if we know that the real fly's wing is flat, then we know that the corner to corner vector between the corners of the square, essentially, tell you about the orientation of the wing.
So Frank and fly is not enough. But if we put in extra geometrical information that we already know about the fly, then we can back out all 18 coordinates. And then we can use those coordinates to reconstruct the real fly on our computer. We take the data out, then we put it onto our in silico insect and compare it to the original movies that you saw before. And you can see that they match very well.
Anybody have questions on this part? It's clear how we're doing this? Instead of 50 hours of undergraduate student time, we're now doing this in about an hour of computer time, plus time to check that the computer did things correctly. But things are moving much faster, now we have data that's coming in. What do we do with that data?
The next thing I want to tell you about is a maneuver that we study. This maneuver has to do with propelling yourself forward. It's, how do I create a force, an aerodynamic force, that pushes me forward? When you open up the textbook for insects and animals and ask, what's the typical example of the way of the mechanism that's explained? What you see is that the animals are taking their wings stroke plane, and then tilting it so that some part of the lift force gets projected into the forward direction. And that produces a forward thrust.
And we see that in our fruit flies too. That happens sometimes. But sometimes they do this. They keep their wings strokes completely parallel, completely flat. And yet, they're still able to move themselves forward. How do they do it? What's going on?
Well, we can take images or data from a fruit fly that's hovering. This is what it's wings stroke looks like, that's that figure eight motion. The ball here represents the leading edge of the wing, so that's this part. The stick tells you what angle the wing is at. So these ball and stick diagrams are describing this figure eight motion.
We do this for the hovering fly. We can also do it for the forward moving fly. And then we can ask what the differences are. So for example, here I'm plotting for you the three angles that we care about. This is the stroke angle, which is basically sinusoidal. It has a sine wave shape to it.
This right here is the deviation angle, that's the angle above the horizontal. The wing goes up at the front and up at the back, up at the front and up at the back, which means it has two peaks-- one here and one here-- for every cycle. And this right here is the pitch. It's the angle that's defined from the horizontal here, all the way to 180. And the wing goes forward at a 45 degree angle, and then goes back at a 135 degree angle. Forward at around 45, back at around 135. So those are the stroke angles.
And now the question is, what's the differences between the blue and the red curve? In one case, the fly is moving forward fast, that's the red curve. In the other case, it's just hovering. What's the difference? Where is it coming from? There are slight differences between all of these curves. Is it the stroke angle that I should care about, or the deviation angle? How do we solve that mystery?
Well, here's where we use simulations to try to help us out. If we program a computer to essentially simulate the fly and the aerodynamic forces that the wings produce, we can generate a fly that moves forward if we use the fast moving flies' stroke trajectories. So here's the idea, here's our experiment. This is the velocity of the fly. If it's hovering and using all the blue curves here, that's what you get in the experiment. If it's moving fast forward, those are the red curves. And we can do the simulations with all of the red curves and we get a fast moving fly, or all of the blue curves and we get a slow moving fly.
But the nice thing about simulation is that now we can mix and match. So for example, if I take the stroke curve, the blue curve, from the hovering fly, the deviation curve from the fast moving fly, and the pitch curve from the hovering fly, I don't get any change in the velocity at all. That means that the deviation angle is not important for creating forward thrust. On the other hand, as long as I take the pitch angle, this curve from the fast moving fly, I can generate a fly that's moving forward rapidly.
OK, what's going on here? The differences between these two curves are essentially that they're shifted up and down from one another. The fast moving fly, instead of going forward and backwards symmetrically, actually tilts its wing down a little bit in the forward direction. So that it slices through the air, and then smashes the air on the way back. It's using differences in drag forces to propel itself forward.
How does this work? Well, you've all stuck your hand out of the car when you've been a passenger. Hopefully, when you've been a passenger. And when you stick your hand flat, you don't feel much resistive force. But when you start to make your hand more and more perpendicular, you feel that wind pushing you back. Those are drag forces that are acting on your hands.
And the curve for drag forces says that as you increase the angle of attack, or the pitch angle, you essentially get a higher and higher drag force. That's what that curve says. It's a little bit more complicated because, remember, I start creating this imbalance in the drag forces. So little drag force pushing me this way, a lot of drag force pushing me that way. Then I start to move my body.
Now the problem is that as I start moving my body, my wing has to add its own velocity to my body velocity in order for me to calculate the drag forces accurately. Anybody here ever jump out of an airplane? OK, a few brave souls. They're still here. That's because they reached a terminal velocity, and then they were able to pull their parachutes. That terminal velocity is set up by air resistance, drag forces, just from the fact that you're moving forward.
Same thing happens here. The imbalance in the drag forces pushing the fly forward eventually get balanced by the excess drag from the fact that the fly is moving forward. So I have to add the fly's body velocity to the wing velocity.
And that's what sets up the final speed that the fly is moving forward at. And what this formula says-- so we can do that calculation. And we eventually come up with this very simple formula that says that the fly's forward velocity just depends on how fast it's moving its wings and what the angle of attack differences between the forward and the backward directions. That's it.
We can test this by doing the experiments. This is the flight speed as a function of that difference in the pitch or angle of attack. And what you can see is that the data follow a linear dependence. The prediction is this dashed line. It does pretty good, it gets 90% of the story right. And that's basically what we would expect for the kinds of approximations that we're making.
This plot is very sad for someone like me, because each one of those data points is a full movie. And each movie is about 30 wing strokes. And each wing stroke is about 40 moments in time. And each moment in time is about 18 coordinates. That means that you're looking at 50,000 data points all summarized in just a simple line. But that's the amount of work that it's going to take to do something in this field. And that's why having a data pipeline is so important.
We can do other things with the fly. For example, we can do those psychology experiments that I told you about in the beginning. Now we have an LED arena, and we have a light that's moving around the circle. And the fly is going to track that light. And when it does that, it's going to perform for you a turn-- a [INAUDIBLE], which is an in-place turn. And there it goes.
Does anyone see what it's doing differently between its wings? It has to do something differently to turn. If it just does things symmetrically, it can't turn. What is it doing differently between its wings? Any guesses? Yeah?
AUDIENCE: I don't think it's tilting it that much. It's saying more like this, so the pitch angle is higher.
ITAI COHEN: So you think it's changing the pitch angle between the two wings. So the pitch angle changes, the same mechanism that we had for forward flight. In fact, turning is the same as forward flight with just one wing. And you can demonstrate that.
So what I have here is a turntable, and I have here a pair of wings. I hope I don't hit you. I might need you for stabilization. So here are my wings. Oh, man. OK, so here I am, and here are my wings. And if I flap symmetrically, you feel the wind?
AUDIENCE: Yeah.
ITAI COHEN: Yeah, nothing happens. Now, how do I do this? If I slice with this wing and smash with that one, and then go back, I can get myself to turn. If I slice with this wing, and then go back, I can get myself to turn the other way. Notice that I did not take off. I didn't take off because the amount of torque or forces that I need in order to get myself rotating is about 1% of the amount of force that I need to keep up in the air. A very, very tiny amount of drag force is necessary to turn myself in the air.
We can do the measurements that show that this is the actual mechanism. But let me show you why this mechanism works in this plot over here. I'm plotting for you the drag curve, that's the same curve that you saw before. But now I'm also plotting for you the lift curve. And lift has a different dependence from drag. Lift says that if I'm at 45 degrees, that's the point where I get the most vertical force. So if I move my wing at 45 degrees, that's when I get the most vertical force. Here, no vertical force. Here, no vertical force. This is the max.
Well, why is that special? Because if I sit at this point right around 45 degrees, I can change my angle just a teensy weensy little bit. And my drag forces change a lot, while my lift forces hardly change at all. So by sitting at 45 degrees, I can very delicately change my angles of attack. My lift force still stays just fine, but my drag forces can be used to generate all the motions that I need. So that's why this mechanism works.
This issue of drag on wings has a very long and distinguished history. In fact, the Wright brothers were very worried about this problem. Now everybody knows the Wright brothers did not invent the first airplane. There were many people flying before the Wright brothers. What the Wright brothers invented was first controllable airplane.
What was the problem? The problem is that airplanes are not like cars. You can't just use the rudder to steer them when they're in the air. They're subject to aerodynamic instabilities like rolling.
And the way people tried to solve this problem before the Wright brothers was that the pilot would sit in the center of the airplane, and then if the airplane would start to tilt to the right, the pilot would move a little bit to the left. And if the airplane would start to tilt to the left, the pilot would move a little bit to the right. And this was a very bad strategy. And a lot of people died from doing this. In fact, this guy Lilienthal, was a very famous aviator who died from such an instability.
What the Wright brothers invented was a method for controlling this instability. They showed that if you distort the wings by changing the camber, you could actually create a lift force that stabilizes the airplane. So when the airplane started to tilt, it increased the angle of attack. That would create a bigger lift force, but it would also create a bigger drag force. So what they had to do was they had to compensate for that with their rudder. And it's the patent for this triple axis controller that they essentially became so famous.
Now, the Wright brothers were excellent engineers. They designed propellers to something like 90% of their current efficiency. They had wind tunnels, everything like that. I think they would have been very impressed with the way that insects, rather than fighting drag, used drag to their advantage when they're maneuvering through the air.
How do the flies get these motions to happen with their wings? What's going on at this little hinge here? And to help explain why this is a non-trivial problem, let me point out that when I moved my wing back and forth, my brain is telling my wing where to be at every single moment in time.
Now the insects have power muscles that drive the wing motion, and they have steering muscles. And the steering muscles are telling the wing what posture to assume, but they only get to fire once. The neurons that trigger those steering muscles only fire once per wing beat. How do they do it? How do they get this complicated motion if I only get one neural firing pulse per wing beat?
Well, one thing that could happen is-- can I borrow this? If I have a sheet of paper here, and I just move it back and forth, it kind of flaps on its own. So maybe passive flapping is what's going on. How do we start to test for whether the fly is just moving its wing back and forth and the wing is just doing this passively, versus if it's applying any torques at its hinge?
So to do this, let me show you what we measure. This is an F equals ma equation. It looks a little bit more complicated, but it's basically the same thing, only for rotations. So it's a moment of inertia, that's like my mass, times the angular acceleration is equal to the sum of the torques.
And I can solve for the torque that the animal is exerting at its hinge, that's the pitching torque, by putting all the other terms on the other side and pointing out that the angulation of the wing, well, we measure that one. The fact that this is a term that says that the wing is a pendulum, the center of mass of the wing is not exactly at the point that's rotating. So it would have some pendulum motion. That's what that term is. We can calculate that. And we can estimate the aerodynamic forces using various models on the computer.
Well, once we solve all three of these, we can actually tell you what the pitching torque is. What torque is it applying at the hinge? And this is what that looks like. This is the pitching torque as a function of the wing pitch, the angle of the wing. And what you can see is that this is negatively correlated. It's basically a line going down. And it hits zero at 90 degrees. So that says that at 90 degrees, I don't get any torques.
If I increase the pitching angle, I get a restoring torque that brings me back to 90. If I decrease the angle, again, a restoring torque that brings me back to 90. This is just a torsional oscillator, just a simple harmonic torsional oscillator that's rotating about 90 degrees. So it's like a mass on a spring, it's rotating about its equilibrium point. Same thing, only for a torsional case.
But this doesn't look exactly like a line. You can see that it's open. Every wing stroke, I go around this loop. And that tells me that I'm dissipating energy every time I have a wing stroke. So remember your PV diagrams in physics, your work energy diagrams? So you go around a thermodynamic loop, and this is the work that's done. Well, this is the energy that's lost. This is the energy that's dissipated per cycle. And that means that I don't just have a torsional oscillator, I have a damped torsional oscillator.
OK, and we can fit for that. And we can essentially try to ask, what is the insect manipulating when it's turning? These torques are coming from a spring constant, the rest angle of the wing, and some damping coefficient. Which one of these is the insect changing when it wants to turn, for example? How do we do that measurement?
Well, effectively, we can fit those cycles when the insect is turning to the right, which is indicated in the pink, the left, which is indicated in blue, and when it's doing nothing. And what we find is that the only time where we see a difference between the parameters, the spring constant is basically the same for the left and right wing, the damping coefficient is the same, but the rest angle is different. When the insect wants to turn right, the rest angle for the right wing, the red, goes higher than 90 degrees. When it wants to turn left, the rest angle for the left wing is higher than that for the right. What's going on?
So here's a model of a torsional oscillator. This is a binder clip, and this is just a manila folder. And essentially, if I twist this, then you're going to want to come back to equilibrium. So if my rest angle is at 90 degrees, then as I move my wing back and forth, you can see that the mounted tilts is symmetric.
But now if I take my rest angle and make it a little bit smaller, when I move my wing in the forward direction, I slice through the air. In the backward direction, I smash through the air. Slice, smash, slice, smash. If I want to move backwards, I just change my best angle to be backwards. Now I'm slicing, smashing, slicing, smashing.
So the insect doesn't have to control the entire motion. It just has to change the rest angle. And that can happen on a timescale that's longer than a single wing beat. Forward, turn, turn the other way, backwards. OK, that's all it's doing.
The last story-- and so this is another one of those really sad plots for me, which is basically confirmation of this idea. Here we plotted-- let me just do this one. We plotted the total yaw turn angle, how much it turned, as a function of the amount of time that it left this asymmetry on for between its left and right wings.
And again, the dashed line is the theory, and the data falls right on top of it. And again, each one of these data points is a full movie, and so you're seeing something like 50,000 data points represented neatly on a single line. And you can see that if you just had these three data points, for example, you'd never know what was going on. You really have to have the full curve in order to get these simple relationships out.
OK, let me tell you about one last story, which is how these insects decide when to change the rest angle of the spring, for example. So to do this, I'm going to tell you a little story. This is an experiment that was invented by Leif Ristroph, who was my student at the time. Leif's a little bit wacky. And he noticed that if you take a brush-- this is a Gordon Brush Company brush. These brushes have metal bristles. And he said, well, what if we take one of those metal bristles, and we clip it, and then we glue it to the back of the fly.
And so now the idea is that the pin is glued there, he's holding it with a pair of tweezers. Again, the pin is not piercing the fly. The fly can still move its wings back and forth. And now we can take that fly and put it into our apparatus. But in addition to having the cameras to record, we can also trigger a pair of Helmholtz coils, which will produce a magnetic field inside the box. And that magnetic field is then going to act to rotate the pin, and that's going to give the fly a mid-air torque. So that's the idea.
And this idea was based on an experiment from Bob Full's lab called the cockroach cannon. The idea here was that they basically load a gun on top of a cockroach, and then they send the cockroach running. And at some point, the gun fires. And the cockroach has to respond to that. We're doing something a little bit gentler, no guns going off. But we are torquing it in midair using our magnetic coils.
And this is the first movie that we got with this. Here you see the pin. Right around here, we apply the magnetic torque for just one wing beat. And the rest of this is just the fly responding. Here it comes again for just one wing beat. The rest of it is the fly responding. What's amazing about this video is if you take a look at the orientation of the fly before and after, the fly's heading is exactly the same. It's yaw angle is exactly the same. These flies have some sort of autopilot circuit that allows them to correct for midair perturbations. How do they do it?
This is the full 3D movie showing exactly the same thing. Here is the pin. When the red halo appears, that's when we turn on the magnetic field. You can see the fly rotating towards you. And then it's going to do that same thing that I did with the demonstration on the rotating platform here in order to rotate itself back and get back its heading. How is it doing it?
We can quantify that data. Here's the yaw angle as a function of time. You can see that it starts at zero, it increases, and then the fly does whatever it does to get itself oriented back in the same direction. Here's what the wings are doing. The black data points are telling you what the angle of attack differences between the left and right wing. And it has some sort of program that it's figured out in order to get itself righted. And our goal is to figure out what that program is.
I'm not going to take you through all of the control theory aspects that needed to happen in order to get this, but I'll give you the basic flavor. Here, I'm plotting for you a number of things as a function of time. This is the perturbation. So it's very brief, it just happens for one wing beat. This is the yaw angle. So that's this data over here. If I take the derivative of the yaw, I get the yaw velocity. That's this line over here. It's a little bit hard to see, so I'm tracing it out with my red pointer.
The amazing thing is that if I take the yaw data, the yaw velocity data, I shift them them in time and add them together with appropriate coefficients, I get this blue curve. And this blue curve matches right on top of the angle of attack difference data for the two wings.
So what I'm telling you is that the insects are measuring their angular velocity, then they're integrating that data in order to get their total angular displacement. So they know calculus. Then they add the two curves together, and then pump that signal into their steering muscles to change that rest angle. That's what's going on. Amazing. Simple. Elegant.
We're now going on to study things like roll. We place the pin horizontally and now have two magnets top and bottom. Now we're getting the insect to roll and see how it corrects that mechanism. Roll turns out to be different from the yaw orientation, in that it's aerodynamically unstable. That means it's much more important for the insect to control this degree of freedom.
And in this movie-- you can see now our movies are getting better. In this movie, you can track the tips of the wings. And I don't know if you noticed it, but the mechanism that the fly is using is it's essentially changing the stroke angle. So these are the images that show that. Here, the fly is flapping symmetrically. This is where we apply the perturbation.
Here, the fly is responding to the roll. And the way it's doing it is by moving one wing a lot farther forward than the other wing. So it's working really hard with this wing, but not as hard with this one. And that's because it's rolled this way. So it has to do this in order to right itself. It's creating a larger aerodynamic lift with the wing that's moving faster.
We can quantify this data. So here are the curves that show, for example, the amplitude as a function of time, and the change in amplitude between the right and the left wings, and the change in velocity between the right, which is in red, and the left wing, which is in blue.
The amazing thing is that something like this can be explained by that same simple controller that I showed you. If I take, for example, the body roll angle and the body roll velocity, I shift them in time and add them together, that gives me this curve over here, which predicts the change in the stroke angle between the left and the right wing.
These types of controllers are called PID controllers. They're proportional, integral, differential controllers. And if you're an engineering major, these are the standard types of controllers that people use to control the temperature in a room or the speed of some car. You want to know what your velocity is now, what it's going to be if you keep accelerating, and what it was before, and whether you're increasing that acceleration or decreasing it. So that part was basically trying to figure out something about what it's doing with the hinge in order to correct for the roll mechanism.
How do we go further? Well, Tsevi, the postdoc in my lab, has figured out how to take one of these apparatuses, and instead of just putting on one pulse to perturb the insect, we can now put on multiple pulses. What happens when the insect is now rolled not just once, but eight times in a circle? Notice that one of its wings comes unhinged right around there. Now it comes back. And within 1, 2, 3 wings strokes, it's able to regain its complete composure.
This is not a linear controller. A linear controller would say, if I turned over eight times, I should roll back eight times, and then I'd be corrected. It's doing something extra. So with these types of experiments, we're learning about what nonlinear processes these animals are using to control their flight.
How are they doing all this? They're doing this with a pair of organs called halteres. These are gyroscopes that are sitting on their backs. So fruit flies are Diptera. All Diptera used to have four wings way back in evolution-- four wings. The hind two wings became shorter, stubbier. And they ended up being these halteres, which are just two masses sitting on a pair of sticks that are vibrating back and forth. And when the insect turns in one direction or another, these masses get left behind due to Coriolis forces.
What happens when we take those vibratory gyroscopes away, when we don't let the insect sense what its velocities are? And we can do that by gluing them to the body of the fly. So we take the halteres and we just dab a little bit of glue on them, and then we stick them to the body. Now they're inoperable. And when we do that, they fall out of the sky.
Why do they fall out of the sky? They fall out of the sky because flapping flight is aerodynamically unstable. The wings are attached at a point that's higher than the center of mass. So when they're flapping back and forth, there are drag forces acting on the wing that torque the body of the fly. When the wing is moving forward, the drag force is in the reverse direction. When the wing is moving back, the drag force is in the forward direction. When the wings are balanced, no problem.
But now if I give the fly a little perturbation, maybe a gust of wind comes, maybe it did something a little bit different with one of the wings, it perturbs so that the body's moving forward. Now the wing velocity has to be added to the body velocity. The wing is moving faster in this direction, and that produces a higher drag force in the backward direction.
Now the fly wants to tilt back. Now the wing is moving backwards, but the body velocity is being added. Now I have a higher drag force in this direction, and the fly moves this way. Back and forth, back and forth. And the timescale of that instability has to do with its moment of inertia, how long it is. Meterstick, pen, 1 millimeter. These animals need to correct for this instability on this timescale of only a few milliseconds.
Could we change the situation somehow? If they don't have access to their fast responders, these vibratory gyroscopes that are operating on a few milliseconds, can we somehow slow their rotation speed down so that a different compensating mechanism can come into play, like maybe their eyes or something like that? How do we do that?
Well, we do that by putting little dampers on their body. What do I mean by that? I take a dandelion seed, I crush it, and I take a few fibers from that dandelion seed and glue it on the ass of the fly. And now when the fly rotates, those dandelion seeds are going to act like dampers. And these flies, even though they don't have their halteres anymore because we glued them down, can fly perfectly well.
It turns out that this mechanism is actually used by some insects. This is the Woolly aphid or the fuzzlebutt. The fuzzlebutt actually has a whole bunch of fibers coming out of it. And this animal probably doesn't need halteres in order to control its flight.
In fact, most proto insects, old time insects, before they evolved halteres, had little tiny hairs coming off of their body called cerci. In fact, mayflies still have these coming off of their backs. And we think these are used in order to control the timescale for that rotational instability, so that other slower acting organs can help them control their flight.
Why would you want to develop halteres? Well, in the same way that an airplane, a jetliner, is stable, but not very maneuverable, a fighter jet is almost unstable, but very maneuverable. If I can get rid of these damping surfaces, I can make rotations faster. But then I need to be able to control them. And if I can do that, then I get to eat the other insects that are more stable. So there's an evolutionary pressure to try to develop these halteres in order to become more maneuverable for catching prey and for avoiding being eaten.
I'm going to leave you with this picture of a fruit fly on top of the original patent by the Wright brothers. And I want you to think about the fact that 350 million years ago, before insects take to the air, there are no flowers. There are no trees. All plants are less than 3 meters tall. The ability of insects to take to the air and eventually control their flight has a profound effect on the ecology of our planet.
In a similar way, the Wright brothers invented their controllable airplane in 1903. But it wasn't until people started to understand how to apply control techniques, to automate these techniques, that commercial aviation doesn't start to take off. Today, we are starting to understand how flapping insects are controlling their flight. And this is allowing us to do things like build robots. Currently, the robots are about this big.
This is Matt Keenan. He works at AeroVironment, this is a company that produces drones out in California. This is a hummingbird drone. It essentially uses all the same mechanisms that I've talked to you about today in order to get this to fly stablely. Right now they're this big, but we're working on getting them smaller.
What happens when we get them smaller? What happens when they're all around us? Do we use them to try to look for survivors in a burning building? Do we use them to spy on one another? These are the questions that you all are going to have to answer as we go forward, because this technology, this understanding is already here.
I'd like leave you with one last set of movies. And just tell you that biolocomation as a field is now experiencing a renaissance. Why is that? Because the imaging techniques have gotten good enough that we're now able to extract vast amounts of data from things that are jumping, tumbling, turning, flying. All of these, we can now analyze, we can get data from, and that's producing an amazing time for us as scientists in this field. So with that, I'll thank you and take any further questions you might have.
We all take for granted that flies fly. And as anyone who has tried to swat a buzzing fly knows, flies are very good at maneuvering. So how do they do it? Cornell physicist Itai Cohen has used a combination of 3-D high-speed photography and experimental manipulations to find out. He explained the mechanics of insect flight to a Summer Session audience in a July, 2014 lecture.
