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Lift is an upward force generated when air flows around a curved surface, like an airplane wing. It matters because it's what allows aircraft to stay in the air and fly.
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The 1902 Wright Glider shows its lift by pulling up
When a fluid flows around an object, the fluid exerts a force on the object. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it may act in any direction perpendicular to the flow.