Rule of thumb · PhysicsNº 106 / 238

A tenth of lift coefficient per degree

How much lift does a wing gain for each degree of angle of attack?

A thin wing gains about 0.1 of lift coefficient for every degree of angle of attack, until it stalls.

Why it works

Thin-airfoil theory gives a lift slope of exactly 2π per radian, which is 0.1097 per degree, whatever the shape of the section. A flat plate and a 12% thick wing agree at low angles, because the lift comes from the air being turned, not from the thickness.

When it fails

It holds only below the stall, which for a real wing is roughly 12 to 18 degrees, and it assumes the air is slow: by Mach 0.8 the slope is 1.67 times larger, and above Mach 1 it falls to 4 divided by the square root of (M squared minus 1). A short, low-aspect-ratio wing has a smaller slope than a long one, and at the Reynolds numbers of a model aircraft the slope is lower still.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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