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Aerofoils and Wings

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= What does the lift force depend on =
=== In two dimensions (aerofoils) ===
In 2D, the lift force produced by an aerofoil depends only on two factors: the angle of attack, and the geometry of the aerofoil. To be specific, the only factor about an aerofoil that matters is the '''camber''' of the aerofoil, i.e. how bent it is (the mathematical definition will not be introduced in this elementary article). The thickness of the aerofoil has zero (in theory, and very little in practice) effect on lift, which is not easy to understand without working through the continuum mechanics. However, thickness is a useful design tool to modify the pressure distribution around the aerofoil, thereby improving the stalling characteristics.
Any symmetric aerofoil has a lift coefficient (lift force per unit chord and unit depth) of 2πα, where α is the angle of attack. A cambered aerofoil has an additional lift coefficient at zero angle of attack added to this value.
=== In three dimensions (wings) ===
In 3D things are more complicated. Consider the tip of a wing: little pressure difference on the upper and lower surfaces can be sustained at the tip, otherwise the flow will accelerate to very high speeds because an escape from the lower to the upper surface is possible. Therefore, it is necessary that the flow around a 3D wing has a '''spanwise variation''', despite the wing might have the geometry of a uniform extrusion. As a result, it is expected that the '''aspect ratio''' of the wing (how slender or stubby it is) to have an effect on aerodynamic performance.
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