<< Page 3 Page 4: Page 5 >>   Lift This is probably the most misunderstood of the four forces. So, as you read this, try to forget all you have heard about lift. Lift is generated because the wing moves air downwards, so that air pushes upwards on the wing, so the plane is pushed up. This much, a simple conclusion based on Newton’s Third Law, everyone can agree on. But HOW does a wing get the air to move down? THAT is the question, often misunderstood, cloaked with an apparent impenetrability and vagueness. It’s the question everyone wonders about: “Why does an airplane fly”? Ok, let’s get to it. A wing generates lift (pushes/pulls air downwards) because its curvature generates low air pressure over the top of the wing and high air pressure under the bottom of the wing. (This much everyone seems to agree on, as well). Why does a wing’s shape cause these pressure differences? Here’s where a lot of people think they know an answer, but don’t. They say this: The top is more curved than the bottom, so the air has a longer path to take over the top than over the bottom. Because the air on top has a longer path to take in a given amount of time, it goes faster than the air on the bottom. Because Bernoulli’s Law says that air pressure falls when air is accelerated, then this means the faster air on the top is at a lower pressure, sucking the wing up. The preceding paragraph is NOT TRUE. Well, it is true that the air on top of a wing is at a lower pressure than the air at the bottom, and so it sucks the wing up. However, the air under a wing has a pressure higher than atmospheric. How do you explain that? It is also true that air that is accelerated will drop in pressure, under certain conditions. In fact, this does happen on most wings. But the air over a wing is NOT accelerated “because it has a longer path to take”. There is no reason why the air going over a wing has to get to the back of the wing taking the same time as air going under the bottom. In fact, air going over the top of the wing often gets to the back faster than air going under the bottom, despite the longer path. How do you explain that? What really happens – the air on top “beats” the air on the bottom to the back of the wing Imagine a flat plate (like, say, a piece of cardboard or thin piece of foam) moving through the air at a slight angle. It will generate lift, as we will see in class. But because it’s flat and thin, the path the air takes at the top is the same length as the path at the bottom, just about. But lift is still generated, without the typical airfoil curvature. How do you explain that? All right, enough myth-busting. By now you see the myth is not true. So let’s have some real explanations. There are two important mechanisms wings use to generate those pressure differences. 1) The wing accelerates the air over it and decelerates the air under it (but NOT due to path length differences). The faster air on top is at a lower pressure, sucking the wing up, and the air under the bottom is at a higher pressure, pushing the wing up. 2) The shape of the surface of the wing causes the air on top to make a turn, and the air on the bottom to go straight (or to turn slightly), and the centrifugal force of the air making a turn pulls/pushes the wing up. (or, more strictly, the wing must supply a downwards centripetal force) Let’s look at how these effects happen: 1) Air flowing past an object at subsonic speeds is effectively incompressible, like water. If the channel through which the air flows constricts the air, the air will not be compressed. It will accelerate, so that the same amount of air gets by, per second. If the channel widens, the air will not expand. It will slow down, so that the same amount of air gets by, per second. Here’s a good analogy, showing the exact same phenomenon: Where a river is very wide and/or very deep (i.e. large cross-sectional area), water flows slowly. Where a river is shallow and/or narrow, water flows quickly. This is so that at each spot, the same amount of water (in gallons, say) gets by per second. In a wide place, there’s more water going by more slowly, and in the narrow place, there is less water going by more quickly, so it evens out. So the air on top is going faster because a bump at the top is constricting the airflow (like river rapids). The air on the bottom is slower because the bottom of the wing curves inwards slightly (this is called camber). There is an equation in Fluid Mechanics that tells you that air flowing along a certain path will drop its air pressure if it accelerates, and raise it if it slows down. This is called Bernoulli’s Equation. It’s not true for turbulent air, and it’s not true across different paths, just along one path (so it would not allow you to say “the air over the wing is faster than the air under the wing so it has lower pressure” as the myth says), but it shows how the bump on top of the wing decreases air pressure. This can be non-intuitive. The air is “pinched” by the wing so its pressure drops? Yes. Air in a container will increase its pressure when squeezed, true, but air that is moving will decrease in pressure when its path narrows. This is a well-observed phenomenon. Water or air moving through a pipe of varying diameter will be at lower pressures where the pipe is narrower. You’re going to have to take my word on this one. 2) Now, if the path taken by a fluid makes a turn, then in order for the fluid to be made to turn, the pressure on the inside of the turn must be low (in order to suck the fluid inwards, a centripetal force) and the pressure on the outside of the turn must be high (in order to push the fluid inwards, another centripetal force). This is described by the Euler N equation. It says that if fluid is making a turn (not flowing in a straight line), that the outside of the turn is at a higher pressure than the inside of the turn. Above, the airfoil cross-section from the Wright Flyer. Because air making a downwards turn will generate lift, all one really needs is a curved thin airfoil that will cause air following it to turn that way. Imagine an airfoil which is just an arc of a circle (like the Wright airfoil above). The air going over the top is turning downwards, and the top of the airfoil is in the inside of the turn (under the air), so the air turning over the airfoil has a pressure drop at the top surface of the airfoil. The air going under the bottom is also turning downwards, and the bottom of the airfoil is in the outside of the turn (over the air), so the air turning under the airfoil sees a pressure increase at the bottom surface of the airfoil. This means the pressure over the airfoil drops, and the pressure under it increases. Even a flat plate, if tilted in relation to the incoming air, will cause the air to turn, and hence generate lift. That’s how airplanes fly. Well, that’s how wings generate lift, anyways.   - - - - - - - - - - - - - - - - - -   Summary so far: -Wings do NOT generate lift “because the air going over the wing must get to the back of the wing at the same time as the air going under the wing, but has a longer path to take, so it speeds up” -Wings generate lift because they move air down. They do this because they generate low-pressure air over them and high-pressure air under them. -Wings generate lift because the air going over the top has a narrower path to take, so it must speed up, while air going under the bottom has a wider path to take, so it slows down. Because of Bernoulli’s Equation, air that speeds up drops in pressure (sucking the wing up) and air that slows down increases in pressure (pushing the wing up) -Wings generate lift because the air following their shape curves downwards. The Euler-N Equation says a fluid turning has a smaller pressure on the inside of the turn than the outside, so air turning down over the top of the wing has a lower pressure near the wing (on the inside of the turn it makes), and air turning downwards under the bottom has higher pressure near the wing (on the outside of the turn it makes).   - - - - - - - - - - - - - - - - - -   Above: The pressure drop over the wing of an airplane often causes a slight drop in temperature there. If the air is at a very high relative humidity, this drop in temperature might bring the humid air below its dew point, causing water to condense over the wings. So when an airplane is near a cloud (water on the verge of condensing), or just flying during a humid day, or turning steeply (air pressure drop over the wings becomes larger, temperature drops more), sometimes water condenses into droplets just over the wings, i.e. a small cloud forms just over the wings. This is evidence of the pressure drop that causes lift (then again, so is the simple fact that the airplane is off the ground). Below, a Blue Angels F/A-18, an F-4, a C-17 (with condensation over the wings), a Super Hornet, an F-14 (with a huge round cloud of condensation over itself) and an F-15 (with clearly-condensed wingtip vortices – see pages 45-46 & 48 – as its afterburners glow orange) show lift-induced condensation, representative of their high wing loadings (see pages 116) at the time. Now, there are many things that affect how a wing generates lift. Lift is a force caused by accelerating a lot of incoming air downwards, continuously, though a pressure difference. So if the incoming air is deflected downwards more, more lift is generated. If more air is deflected downwards, more lift is generated. How do you deflect air downwards more? Through increasing the angle of attack, by adding camber, and by increasing wing cord length (distance from the front of the wing to the back of the wing). How do you deflect more air downwards? By flying faster or though denser air (more air goes by the wing per second), or by having a larger wingspan. To keep things clear, here it is in table form: More lift by moving the air more: -higher angle of attack -more camber -longer cord length More lift by moving more air: -flying faster -flying through denser air (lower altitude) -wider wingspan Let’s look at these variables and terms one at a time. 1) Angle of attack: Also called the angle of incidence and often nicknamed “alpha” or AOA, this is the angle between the airflow and an imaginary line from the front to the back of the airplane or of the wing. You have probably noticed that when an airplane lands, its nose is tilted upwards even though it is flying slightly downwards (so it is in part flying onto its belly). This means it is at a higher angle of attack than when it is flying fast, with its nose pointed forwards. Wings at higher angles of attack deflect air downwards more, so when a plane slows down (less air going by the wing per second, less lift), the pilot will increase the angle of attack to compensate, to keep generating enough lift to keep the plane in the air. Because these are the only two variables that can be easily and quickly adjusted, alpha and airspeed are closely linked: when one goes up, the other usually goes down, and vice-versa. This game does have boundaries: If the angle of attack goes up past 15 degrees or so (this varies with different planes), the wing stalls. The air no longer follows the contour of the wing, but instead flies straight back. Because of this, the wing generates much less lift and a heck of a lot of drag, which in turn slows the plane down more. The only way to fix this is to dive to gain more speed by descending. Remember, high angle of attack means low speed, so the faster you fly, the lower the angle of attack, the least likely the stall. Most airplanes have a certain stall speed. If you go any slower, you fall until you pick up speed again. If you stall just before a landing or right after a takeoff (when you are flying low and slow, and need all the lift you can get), it is pretty much certain you will crash. This is why landings and takeoffs are so tricky – the pilot is going as slowly as the plane can go, but if he goes any more slowly, the plane stalls and falls. 2)Camber: A wing that is curved on top and flat on the bottom is constricting and turning the air going over it, but not the air flowing under it. So the pressure over the top goes down but the pressure under the bottom does not go up: A cambered airfoil generates more lift, because not only is it turning and constricting the air at the top, it is also turning and widening the air at the bottom, so the pressure under it is higher: As you have read, less lift is generated at slower speeds. Many airplane wings have flaps and slats, which extend during takeoff and landing in order to increase wing camber when the airplane is flying slowly. 3) Longer cord length: This is a no-brainer: This airfoil: must deflect air downwards more than this airfoil: As the air flows over it, it just has more time to move the air down more. This is something else that flaps and slats do. When they are deployed, they extend outwards (the flaps, at the back, extend out to the back, and the slats, in the front, extend out to the front), thus increasing cord length. It is easy to see that a 737 wing with flaps retracted has a smaller cord length than the same wing with flaps deployed: 4) Speed: The more air molecules are being blown down by the wing per second – and there will be more of them per second if the wing is flying faster – then the more of a downwards force the wing must exert on the air, and the more of an upwards force the air is exerting on the wing. In fact, when airplanes are flying very fast, they try to generate LESS lift, because the wing simply generates too much. Very fast airplanes have wings that are essentially flat plates, when the flaps and slats are up. The Concorde, SR-71 and F-104 – three exceptionally fast airplanes – have a wing that is one twentieth (or less) as thick as they are long, at the thickest point. An airliner wing is designed to be fairly flat, so that it generates just enough lift at cruise speeds, and then it deploys flaps and slats at low speeds so as to then be more curvy and still keep generating just enough lift. 5) Density: Like before, the more air molecules are being blown down by the wing per second – and there will be more of them per second if the wing is flying through denser air – then the more of a downwards force the wing must exert on the air, and the more of an upwards force the air is exerting on the wing. Air is denser at lower altitudes and thinner at higher altitudes. This means an airplane has less trouble generating lift during takeoff and landing when at New York or San Francisco than while at Denver or La Paz. Air is also denser on colder days than on hotter days. Again, faster speeds are used to make up for this. Landing speeds and take-off speeds are higher at higher-altitude airports than at sea-level airports, and higher on hot days than on cold days. This means the airplane needs more room (and more time) to accelerate during takeoff and to slow down during landing. The very same airplane, carrying the same load, will need a longer runway to operate from Denver than it needs at LA. Also, the same airplane carrying the same load on the same airport (especially one that sees very different temperatures over the year, like, say Phoenix, AZ) will need more of the runway to take off and land on a hotter day than on a colder day. Before, I said that when an airplane is flying fast, its wing should not generate too much lift. The low density at high altitudes helps here. Airplanes usually fly the fastest when they fly high (we will see why later), and so the drop in air density makes it easier for the wings to generate the right amount of lift by somewhat making up for the high speed. 6) Wider wingspan: This too is a no-brainer: These wings affect only the air right by the airplane, so they move less air than these wings: Because both wing cord length and wingspan increase lift when they increase, simply by making the wing bigger, the two variables may be simplified into one (their product), so lift varies approximately with wing area.   - - - - - - - - - - - - - - - - - -   Summary of how more, or less, lift is generated: More lift by moving the air more: -higher angle of attack -more camber -longer cord length More lift by moving more air: -flying faster -flying through denser air (lower altitudes, colder temperatures) -wider wingspan -wingspan and cord may be combined to define the overall “size” of the wing, measured by the wing area.