A Fly in the Ointment
I was flying last month to attend a graduation and it occurred to me that I was, in fact, flying in a large metal tub with metal flappy bits bolted on. How do airplanes fly? Well, they have wings. Duh! But why do wings fly? What makes a wing a wing? Can any flat sheet of metal be used? Why do planes only fly when moving? This is quite an interesting question indeed. The answer is quite subtle – subtler than you may think. It is in fact confusing enough that a lot of high school text books and a good chunk of introductory university physics textbooks explain it incorrectly. You may have been taught the answer in high school and you have just accepted it without thinking too hard about it. Read on if you wish to check if you were indeed taught correctly.
An airfoil is a visualization of a wing across its cross-section. It is useful to think of wings in terms of slices of wing with air flowing around it (for simplicity). The purpose of an airfoil is to generate lift. Lift is the force that is exerted on an airfoil when air moves around it. Usually, it is the airfoil that is being pushed through the air through the use of powerful aircraft engines, but we can pretend for the moment that the airfoil is stationary and that it is the air that moves around it backwards at the same speed. While this backwards view of the world may seem weird at first, it’s a useful transformation to help us better reason about how airfoils work. There are two common explanations that are presented in school and introductory college text books for why airfoils generate lift. They both contain some truth but mess up the details in a subtle but highly misleading manner. Let us look at them. I’ll call the two explanations the Bernoulli explanation and the Newton explanation respectively, named after the primary principle from which they each begin their reasoning.
This is the most common explanation seen in text books. This was how I was taught about wings. Airfoils come in an asymmetric tear drop shape. The bottom of the wing is usually flatter and the top of the wing is more curved, as seen in this picture. When this wing moves through air, it needs to push the air around it. When it does this, the air on the top needs to move a longer distance to get to the rear of the wing. Bernoulli’s principle roughly states that when a non-viscous fluid flows smoothly, a speed up of the fluid should be accompanied by a corresponding decrease in its pressure. Air can be considered a rare (i.e. not dense) fluid.
You can see common demonstrations of Bernoulli’s effect here:
Since the air moving over the top of the wing needs to move further, it also needs to move faster to cover that distance. This causes it to have a lower pressure than the air moving along the bottom of the wing, generating lift. The lower pressure above the wing causes the wing to be “pulled up” by the air flow, generating lift.
This seems like a pretty good explanation and is the one commonly presented in high school textbooks. There is one slight issue – we all have seen aircrafts fly upside down. If a wing’s shape is the only determining factor when it comes to lift, an upside down wing would cause an aircraft to fall like a rock. There would be no way to generate lift through an inverted wing. And yet, air shows feature fighter jets and aerobatic aircrafts demonstrating their inverted flight capabilities all the time. Furthermore, there is no particular reason for the air above the wing to join up with air below the wing. Why do the two air streams need to change speeds anyway? Something seems amiss…
Newton’s Third Law of Motion
This is another explanation less commonly given, and it uses a law you may remember from school – every action has an equal and opposite reaction. What this means is that forces occur in pairs. They may affect distinct objects, but they do occur in pairs and oppose each other. Using this simple law, one has to reason that if a airplane is taking-off, presumably by pushing against air underneath it, an equal and opposite force applies on the air under it, pushing the air away from the airplane. This must hold because the airplane has nothing else to push against and we know that there is a force holding a flying plane up against gravity. Yay! Problem solved, everyone go home… or is that it? We still haven’t demonstrated anything about why the air was pushed down. What causes this force that pushes the aircraft up and the air downwards? Clearly the wing is causing air flowing around it to be pushed down. How can we push air downwards? A simple way is to simply deflect it. The airfoil is not really pointed parallel to the incoming stream of air. It is gently tilted “downwards”. This deflection is known as the angle of attack of the airfoil. This gentle angle of attack causes the air that hits it to bounce downwards to the angle of the wing. The resultant air stream looks like the diagram shown, with the incoming air being systematically pushed downwards. The faster a wing moves through air, the larger the volume of air that is deflected downwards and hence, the larger the force on the wing. Once the wing is moving fast enough, it has enough force applied on it to carry the airplane. This is similar to skipping a stone off of the surface of a pond.
This explanation also seems pretty reasonable. We have all seen fluids being deflected and can image air being deflected by a wing much like a rudder deflecting water. Yet, this explanation seems to be a bit inadequate. Why do we need the tear drop shape for the wing? Why don’t we just use thick sheets to deflect air? Almost all airfoils have the sleek tear-drop like profiles, and this can’t be a coincidence. Nevertheless, there must be some truth to this explanation because model airplanes and paper airplanes frequently have flat wings and they manage to fly.
So Which One Is It?
As with a lot of explanations, there is a kernel of truth in both of the above models, but for the sake of simplicity they exclude some critical details or fudge them. First off, we need to acknowledge that there is nothing wrong with Bernoulli’s effect or with Newton’s laws of motion. The first is a statement of the conservation of energy in a fluid (for those curious – “an increase in velocity and dynamic pressure must be accompanied by a corresponding decrease in potential energy and static pressure in a closed system”). The second is a statement of the conservation of momentum. Both of these conditions must hold! And it isn’t just the upper or lower wing surfaces that produce lift. Both surfaces work together to turn air flowing around it. In our original explanation of the wing using Bernoulli’s effect, we used a sleight of hands to just assume that the air above and below the wing will meet up at the other end. This is commonly known as the equal transit time assumption. This assumption is false. The surprising fact is that the air above an airfoil actually moves faster than predicted by the equal transit time assumption. When the two steams combine aft of the airfoil, the air is actually moving downwards. The lower surface isn’t the only surface pushing the air downwards. The upper surface also “pulls” the air downwards and, in fact, produces the majority of the lift. This is all very confusing and doesn’t fit into a nice framework; so let’s take a step back and look at some other phenomena to help us understand this one.
When fluids flow past a surface, it tends to deflect to stick to the surface. This weird phenomenon is known as the Coanda effect. You can demonstrate this quite conclusively by holding a spoon under a running tap – the spoon will tend to be drawn towards the stream of water, and the water will stick to the stream. Here is a very methodically performed demonstration of this effect:
This effect is also seen during fires near tall buildings or structures. The flames tend to go up vertically or be attracted to vertical structures and even bends around corners because the rushing hot gases tend to stick to surfaces. This effect is simply a special case of the Bernoulli effect – a fluid moving at a high speed has lower static pressure. The lower pressure causes it be “sucked towards” surfaces and also causes the surface to be sucked towards it. At the same time, the fluid doesn’t keep travelling in the same direction – it deflects to get closer to the surface. I say “sucked towards” in air quotes because the one must be careful when reasoning with pressures and pressure differentials. The fluid flow that has been entrained along a surface has a lower pressure causing the fluids even further away it to rush in to equalize the pressure. This runshing movement causes a deflection. This phenomenon is known as circulation and causes a change in the direction of fluid flow in the presence of obstacles. The hardest thing to explain about this phenomenon is the reason for why the fluid accelerates. A full explanation of this would require knowledge of differential equations and physics and would involve us solving the Navier-Stokes equation. Mathematicians do not currently know how to solve this equation except for very constrained situations. For most real-world situations, the solution is derived numerically by throwing lots of computers at the equation rather than analytically deriving a closed form. Nevertheless, we now at least have an empirical understanding of circulation and the Coanda effect. Let’s apply this to wings.
When we think of an airfoil as a device that should deflect air downwards by getting air to stick to it, accelerate, and leave the trailing edge flowing downwards, we get a far better understanding as to why wings are shaped the way they are. To start off, a wing must absolutely have a positive angle of attack to be able to generate lift. A simple teardrop shape parallel to the airflow would neither deflect the air up nor down and hence would generate no lift. A teardrop that is angled “upwards” on the other hand, would cause air to leave the wing in a downwards direction. This downward flowing air is known as the downwash. If we increase the speed of the air moving over the airfoil, we roughly increase the speed of the downwash, leading to increased lift. If we increase the angle of attack, we increase the amount of deflection and hence increase lift albeit at the cost of increased drag on the wing. We now also have an understanding as to what a stall is. When an airfoil is at a high enough angle of attack (known as the critical angle of attack) that the air flowing over the top of it doesn’t adhere to the surface and follow the airfoil. Instead, the streamlines separate from the airfoil and simply travel straight aft-ward. This condition is known as an aerodynamic stall. Since air is only accelerated when it is following the contour of the wing, the air flowing above the wing that is stalled does not deflect and produce a lower pressure. A wing that is stalled suddenly looses a majority of its lift and can no longer sustain its weight and generates vastly more drag due to turbulent buffets in the region between the wing and the separated flow. This is an extremely dangerous condition and is remedied by reducing the angle of attack of the wing (usually done by pitching down). Here is an excellent video showing an airfoil performing at various angles of attack and also stalling:
The video is very realistic and shows smoke trails across an airfoil in a wind tunnel. Note that this picture is slightly deceptive due to the fact that when an airfoil is close to the ground, an effect known as ground effect kicks in. This is because the airfoil is now able to directly exert forces on the ground and the air doesn’t have room to move downwards due to it being blocked by the ground. Hence, the streamlines leave the wing more parallel to the ground (in this case, the floor of the wind tunnel) than they would have had the airfoil been in operation at altitude. Nevertheless, it demonstrates angle-of-attack, the Bernoulli effect, the Coanda effect, attached flow and separated flow with a stalled wing extremely well.
Rock and Roll
Now you can see how an airplane can fly upside down – it just needs to point its nose up to reestablish a positive angle of attack. The airfoil may be less suitable for this due to its shape and excess drag may be incurred. But as we know, planes don’t fly upside down all the time and not all planes can do it – only high performance planes with the correct symmetric wing structures and powerful engines that can generate extra thrust fly upside down. Our understanding of airfoils now lets us better understand and predict the behaviour of wings on airplanes. Let us try to investigate how various flight control surfaces work. Control surfaces are panels or protrusions from the wing of an airplane that allow the pilot to change the behavior of the airflow over the wing. This allows the pilot to control and direct the airplane. If you have looked out of an aircraft as it flies, you can see a number of panels in the wing. Here is a sample of an aircraft landing:
As you may see, the wing looks like what you might expect to see during a flight but as the plane starts descending, panels drop down from the trailing edge of the wing. These are called flaps. Think of them as extensions to the airfoil. What do you think their effect is? They cause the air to continue sticking to the wing and curve down further. This produces additional lift on the wing at lower speeds allowing the plane to descend without stalling. As the plane is ready to land, the flaps are fully extending, producing maximal lift and also, maximal drag, simultaneously slowing the plane down while producing the lift needed. After the plane touches down, you see another set of panels push up from the middle of the wing. These pop up vertically and stand perpendicular to the wing in the path of the airflow. These panels are called spoilers. Their purpose is to ruin/spoil the airflow over a wing, causing it to stall. As airflow encounters a spoiler, it diverts up to go around it, and then separates. This instantaneously cuts out the lift of a wing, transferring the weight of the airplane onto its tires letting them effectively grip the runway. This is done to increase the efficiency of the wheel brakes.
Some other flight surfaces include the ailerons, which are flappy bits at the trailing outer edges of a wing. They are hinged surfaces and act to deflect air passing over them. They usually move in opposite directions when used, one wing surface curving up while the other curves down. The surface that curves up deflects airflow up wards, reducing the effective angle of attack of that wing. The other surface acts like a flap, increasing the angle of attack on that wing. The net effect is that one wing lifts harder than the other, causing the plane to rotate. This motion is known as a bank or a roll. Similar flight control surfaces mounted on the tail lets the pilot pitch the aircraft down or up using its elevators or yaw the aircraft left or right using the rudder.
Take Home Lesson
Through this article, I hope I’ve imparted an elementary understanding on how wings work. We have learned that predicting aerodynamics properties of airfoils is hard and subtle. We also learned that most common explanations of why wings work are subtly wrong and produce an incorrect understanding as to how wings work and react. We also learned how to think of airfoils in terms of the Coanda effect, circulation and Bernoulli’s effect. And finally, we saw how a pilot can control an airplane by using surfaces extruding from the wing that work like mini-wings themselves. Next time you fly, I hope you remember that you are being held up in the air due to air’s tendency to stick and follow wing surfaces.