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→In two dimensions (aerofoils): Use MathJax for formulas.
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 2π*\(2\pi\sin(α\alpha)\), usually simplified into 2πα\(2\pi\alpha\), where α \(\alpha\) is the angle of attack (measured in radians). A cambered aerofoil has an additional lift coefficient at zero angle of attack added to this value. Therefore, the lift-AOA charts all look very much similar for different aerofoil shapes: the gradient is invariant.
=== In three dimensions (wings) ===
