Air contains millions of little particles, known as molecules. These molecules move around in a roughly random fashion, bouncing off each other and other objects. When they bounce off an object, they push it ever so slightly. When millions push, it creates a force known as pressure.
If you hold your arm out, the air is creating air pressure on all sides of your arm, so there is no apparent force. However, if you were to reduce the pressure on one side, you would feel a definite force from the other side, pushing your arm towards the lower pressure. This force is known as suction, since it seems like the low pressure is "sucking" on your arm.
Another way to observe the "suction" is to take a jar with a rubber lid, and reduce the pressure of the air inside, either by sucking it out with a pump, or by cooling it. When you cool the air, it loses energy, and so the molecules are unable to travel as far so the air effectively has less volume, and cannot exert as much pressure. Thus, inside your jar, you have depressurised air. Since there is less pressure on the inside than the outside, there is a suction force trying to pull the jar in on itself. The jar itself is made of glass, which requires a lot of force to cause it to collapse, so nothing happens. However, the lid is made of rubber, which requires very little force to bend, and so it collapses inwards until the pressure is equalised.
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How does an aeroplane's wing create lift? Well, here's a basic fact: when air moves fast, it has less time to hit a surface, and so creates less pressure. So, if you can make air move faster over the top of a wing, it will reduce the pressure, and so suck it up into the air. To prove this, get a strip of paper. Hold one end just underneath your mouth, and blow across it. The air moving across the top is much faster than that on the bottom, and so the piece of paper will rise and flutter a bit. It will not rise up past the flat, since after that point you will just be blowing straight onto the paper. But as soon as you stop the air moving (by not blowing), the piece of paper drops down again.
It would be very impractical to put a fan on top of an aeroplane wing, and you would not be able to get a nice, steady stream of air over the entire wing (besides, a flat wing creates other problems - see below). So, the trick with any wing is to force the air to move faster on top in another way.
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So what shape best does this? It is in the nature of man to make things rectangular. This is the dumbest thing to do with a wing, as can be seen in the diagram below. Firstly, the air has no incentive to move around the wing. The flat surface in front just means that the air hits the wing and causes heavy drag. Secondly, there is no inclination for the air to move faster over the top than the bottom, or the other way around. Thirdly, when the air finally makes its way over to the other side of the wing, it finds it has to rush in to fill the gap left by the wing, and this causes little eddies, which reduce the pressure on the back of wing, forcing more drag.
It was mentioned above that one of the problems with a rectangular wing is drag. So why is drag so bad? Well, take a look at the picture below. There are four basic forces which act on a wing, and thus a plane: Thrust, Lift, Drag and Gravity. When Thrust is greater than Drag, the plane moves forwards. When the plane move forwards, wind moves over the wings. Depending on their shape, this could well create lift. When lift exceeds gravity, the plane flies. It's as simple as that. Drag and Gravity are enemies to flight. You can change gravity slightly by making the plane lighter, but on a jumbo you have to change drag - by changing the shape of the wing. The less drag, the more efficient the wing.
What other shapes can we try? How about a circle? Well, a circle definitely doesn't create those flat surfaces that a rectangle does, so there will be less drag (it's impossible to remove drag entirely, unless you can make a wing which tapers to a point smaller than a single atom). But there are still problems - the rear end still disappears a little too quickly for the air to settle back in easily - it will overshoot the mark and make more little whirlwinds: drag. Also, both faces of the wing have the same length - no change in wind speed, so no lift.
So what shape is going to work? Let's have a little think about this: what is needed is something where the top is longer than the base. The front should be curved, and the rear should taper to a point, so that the air can saunter back into place, instead of racing. There is no official name for this (that we know of), so we shall refer to this as a classic wing shape. As shown on the diagram, this shape is almost optimal. There are various tweaks that can be made, based on the conditions, but these can only be done well by special "smart" materials, which adapt depending on circumstances. For general conditions, though, the classic wing shape is just about the best.
Paper Planes
Surface Area to Mass Ratio. This is vital. The plane must have a large surface area on its wings, to compensate for its mass - the big suface area creates more lift, so that it can fight gravity (affected by the mass). The optimum state for this is when you take the piece of paper and do nothing to it - large SA, small mass. But try throwing a piece of paper, and you find that it isn't a good flyer. Not only doesn't it go far, but it also keeps trying to curl up. So there's obviously something else...
Rigidity. This ridiculous word with a lack of originality in vowels basically means how difficult it is to bend the piece of paper. If the piece of paper can't bend, it will keep its surface area. So why not try a piece of cardboard? Unfortuantely, cardboard has a bit more mass, so it causes problems with the SA:M ratio (see above). Also, cardboard is hard to fold, and the conditions below require some folding. What other options do you have then, to make the paper rigid? Try folding it. By folding just enough of the paper over, you can make it rigid without sacrificing too much Surface Area. We have solved the rigidity problem. But throwing the paper accurately is still near impossible - we are still at the mercy of wind currents.
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Flying Directions. Before we look at the effects of the wind on the plane, it is important we learn about the different way pilots look at directions. Most mathematicians prefer a 3D view of the world - up/down, left/right, forwards/backwards. These are measured along three axes - x, y and z. Pilots can accept these, but when talking about how their plane is moving, it's much easier to talk in terms of yaw, roll and pitch. Imagine drawing three lines through a plane - one through the nose and the centre of the plane's body, one from one wingtip to the other, and the third through the plane down to the ground (assuming the plane is flying flat). These are the axes mentioned above - Through the wings is x, through the plane is y, and straight down is z. Now, imagine how the plane spins on each of these three axes. When the plane spins on the z axis, it turns left and right, and this is called the yaw. When it spins on the y axis, it looks like it is rolling over, so this is logically called roll. And when the plane rotates on the x axis, the nose goes up and down, and this is called the pitch. You will find that your piece of paper tends to do all three, and the addition of three simple little things can fix this: a fuselage, a nose and changing the distribution of mass.
Addition of a fuselage can help stabilise the roll. The fuselage is a small section in the middle which juts out vertically. On a plane, the fuselage is not so much the body of the plane than the tail. The air is forced to move equally around both sides of the fuselage/tail, and so it will move in a roughly forward motion. However, you need only make a small fuselage, since if it is too large, the plane will tend to flip on its side, and use the fuselage as a wing, and the wings as fuselage! And since this is not balanced, the plane is very unstable. The fuselage must also be on the base, as otherwise the plane will roll to lower its centre of gravity. Another way to reduce the roll is to make small snips in the backs of the wings and add stabilisers.
Congratulations! With folds to make it rigid, definite wings and fuselage, you have a piece of paper no longer - you have a glider! It's not a good glider, though. There's still more to add before you can think of long distance flights or stunts. Read on...
Shape of the Nose: You should no longer have many problems with the roll of the plane (bad folding and the impossiblity of throwing straight might cause some difficulties). But what about the yaw? To fix this, you have to change the nose, so that the air hitting it doesn't hit it where it's most sensitive - at the front-most point. A nice, sheer point is ideal, since it forces the air to flow, rather than hit. Either cut the nose into a point, or fold the paper down. Once again, folding is ideal, since it adds mass to the nose (see below).
Distribution of mass. Where you put the mass on the plane seriously affects the way it flies. Obviously the mass has to be evenly distributed on the left and right, or else you suffer from roll (just after it had been cured by the fuselage). But it may not occur to you that perhaps it is not so good an idea to distribute the mass evenly front and back! Experiment by putting some mass on the back of the plane. Try folding it over a couple of times, then launch it. The plane will probably go forward at an incline, until it points striahgt up, at which point it drops. The plane has lost all of its lift as the wings are no longer facing downwards. And since they're pointing forwards, there is so much drag that all of the forward momentum that you put into it is lost - No up, no forward, only one other way to go - down. This movement can be utilised in a well-made plane to cause it to loop-the-loop, or just go almost straight up, then into a glide. However, yours is not a well-made glider just yet, and these planes usually have some method of gradually changing forwards momentum into momentum in another direction, to keep it going (if you make a standard glider, and twist the back ends of the wings up you should get something similar to this effect). Logic then dictates that since the mass can't go to the back, it must go to the front. To do this, fold the nose over. But wait! If you have been reading carefully, you would have already folded the nose to make it pointy! You've just solved to problems with the one fold.
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The first design is one arrived at by the steps above. This is considered the standard glider shape. This works best in a large area with little wind or other interference - e.g. a school hall.
The second design occurs when you fold the nose point several times. The result is a very sharp nose and small wings. This is referred to as a dart, and will travel very fast over a reasonable distance in most conditions - Since there is such a little nose, and small wings, the wind barely touches it.
You may find when throwing these planes though, that if you throw them at a wall the nose crimples and loses its efficiency. The way to fix this is to fold the nose back on itself a few times. Here, the nose does lose some efficiency, but much less than if the nose is decimated. If you do this to a glider, the result is a stunt plane, so called because it can be thrown at walls and other objects (yes, including people, although I don't condone it) without any damage. Also, if thrown a bit more upwards, since it has a heavy nose, it will tend to either loop-the-loop, or else stall and then right itself - in effect performing "stunts". However, do this to a dart and you effectively end up with recycling.