How does airplane's wing generate lift?
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1) Billy Boy's answer is exactly not the right answer. It is a common misconception that lift is generated due to the rounded "airfoil" shape, forcing fluid to travel faster on top, and thus generating a pressure gradient through incompressible Bernoulli's equation. That is INCORRECT. A flat board can generate lift if you tilt it and swing it through the air.\n\n2) I don't think you really want a mathematical explanation. Because the mathematical explanation involves complex partial differential equations, or, if you prefer, integral equations. These are known as the Navier-Stokes equations, and they govern 3D fluid flow. A fully mathematical answer would be: the wings generate lift because the solution to the Navier-Stokes equations around the wings shows an upward momentum deficit in the flow, thus generating lift on the wings.\n\n3) But really, it's quite simple. When the plane is flying, the wing is pushing air down. Not straight down, but slightly down, and by Newton's 3rd law, the wing is pushed up. (Who's doing the work? The engines are pushing the plane forward, which forces the wings to push air down.)\n\nIn fact, if you actually follow the link Billy Boy gave, NASA would tell you the same - in different and probably more confusing terms.
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First, look at any typical airfoil shape. It is sort of teardrop shaped, with a round end and a pointy end, but not symmetrical--one side seems flatter than the other. Let's imagine that the pointy end points to the right, the round end point to the left, the flatter side is on the bottom and the rounder side is on top.\n\nLet air flow from the left to the right. Air flowing near the airfoil at speeds that are not too fast (less than the speed of sound) is not compressible. Let's follow two tiny blobs of air that start next to each other, but approach the round end of the airfoil in such a way that one blob goes up and over the airfoil, while the other slides over the bottom. These two blobs will arrive at the pointy end at approximately the same time. But, the one going up and over as a longer path to take and therefore must travel faster. All the air molecules in a blob are actually thrashing about randomly and can collide with other air blobs nearby as well as the upper surface of the airfoil. This is true of the upper blob and the lower blob. But, if the upper blobs average speed is faster, then its molecules collide with the upper surface of the airfoil less over the trip from round end to point end than do the molecules in the lower blob. Therefore the pressure caused by the collisions of the molecules in the upper air blob on the upper side of the airfoil is less than the pressure on the lower surface caused by collisions of the lower blob's molecules with the lower surface. This means there is a difference of pressure between the two surfaces--pressure drops as you go from upper to lower surface. If the airfoil is rigid, then this difference in pressure will become a force exerted on the airfoil from below, called lift. This lift is what makes an airplane rise on takeoff as it rushes through the air with its wings whose cross-sections are airfoil shaped, rounded end into the oncoming air and flatter side towards the ground.
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Forces Acting on An Airplane\nThere are four forces acting on the airplane all the time during airplane is flying.The four forces are\n(1) Lift, (2) Gravity force or Weight, (3) Thrust, and (4) Drag.\nLift and Drag are considered aerodynamics forces because they exist due to the movement of the Airplane through the Air.\nWeight: The weight acts vertically downward from the center of gravity (CG) of the airplane.\nThrust: is defined as the forward direction pushing or pulling force developed by aircraft engine . This includes reciprocating engines , turbojet engines, turboprop engines.
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Through Lift\n\n\nGeneral Concept: \nThe force of the air on the wings of a plane can be thought of as divided into two components: a component pushing the plane up and a component pushing the plane back. The upward force, the lift force, is what keeps the plane in the air. The sideways force that slows the plane down is called drag. So even though lift and drag are different words and are talked about differently, they both come from the same air hitting the plane... think about that! The pilot can change the lift force too: getting a lot of lift at takeoff (needed to accelerate the plane upward), and less lift during cruise (just need to overcome the weight of the plane).
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Lift, thrust, gravity, drag.
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The prop simply pushes the air behind it depending on the size of the surface area, pitch of the blade and the speed of rotation.\n\nIt DOES NOT have anything to do with the Burnelli affect, which a misconception of how an airplane has lift. The speed of the air over the wing creates a downward force, this is not the reason an airplane can fly. If true an airplane would not be able to fly upside down.
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According to the Bernelli principle it is because the ratio of high-speed wing over the TOP of the foil of the wing is not sufficient to generate lift.  Therefore gravity takes over and it falls back to earth.
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They dont "break through" gravity - there is no point it actually 'starts'.\n\nGravity is simply a negative force acting upon the aircraft ... in simple terms their weight.\n\nThe 'lift' from their wings (due to their shape and speed) counteracts the weight of the aircraft allowing it to leave the ground when enough has been generated.
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Technically, depending upon the type of airplane and speed of the head wind, a plane can "hover".  As long as air moves over the surface of the wing fast enough to create enough lift to make the airplane fly, it will fly--it just may not have very much forward speed.\nWhy does an airplane fly?  The Bernoulli principle.  Air flowing around the wing does so at two different speeds due to the shape of the airfoil.  It flows around and over the top more quickly than along the flat bottom of the wing.  This creates higher pressure on the bottom pushing up.  As long as there is enough push to overcome gravity (or weight), the plane will fly. You might ask, then without moving forward and in no wind, how does a helicopter fly?  Well, its airfoils are always moving through the air as long as it is running--the rotors are its wings.
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The airplane prop works just like the prop in a outboard motor in a boat. The prop has blades which have a pitch on them (angle) which in trun "paddles" through the air - the air is pulled over the blades and in turn pulls the motor through the air. (which of course, is attached to the wing which creates the lift required to get the plane off the ground)\n\nThe boat prop is a great example to use because you can see the water and how it flows over the blades.
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Everything you want to know....\n\nhttp://www.howstuffworks.com/airplane.htm
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The shape of a roof approximates the shape of an airplane wing. Air flowing rapidly over the roof generates lift, lifting the roof off the building.
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On the ground - there are power lines fed directly to the AEROPLANE, and also battery backup.\n\nWhen the AEROPLANE engines are running, they provide not only thrust for forward motion but also drive small alternators / generators.\n\nIn an absolute emergency a small wind turbine can be deployed from inside the fuselage for cabin power.\n\nAny AC power is NOT distributed directly, but converted to a stable DC system. It is then 'inverted' to a synthetic AC at the required voltage to feed any AC systems.
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More than Bernoulli's principle and wing shape (airfoil) are at work in keeping a plane in the air. The main criteria is the  "angle of attack" of the wing. That is, the angle at which the wing meets the air passing by it. When a plane is flying, its wing is always at a positive angle of attack; the leading edge of the wing is higher relative to the air going over it than the trailing edge. So the air pushes the wing up.  When the plane is inverted, the angle of attack must be great enough to overcome the "negative lift"  created by the airfoil. This is accomplished by adjusting the elevator. Inverted flight will always require the input of down elevator.
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By flapping. Air molecules have substance. When you push down on them they push back up with an equal and opposite force (See Newton's Laws of Physics). So when the bird flaps its wings, it pushes down, air pushes and up and this creates lift. The shape of a birds wing also helps create lift. Because a bird's wing is curved on the top, air must travel faster along the top than the bottom to meet at the end. This creates a pressure difference above and below the wing creating lift.
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An airplane's design helps it create and maintain lift and thrust. A needle's does not.
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On an airplanes wing, the top is curved in shape, and the bottom is straight.  When the plane gains speed, the air will be forced to move faster over the curved portion.  The faster moving air applies less pressure than over the straight portion therefore creating "lift"