Fast Accurate Approximation for Lift Slope of Elliptical Wings

Aero Boffins!
The robots here at Cyberiad have found a quick way to estimate the lift coefficient slope of a flat wing with elliptical planform and aspect ratio AR.

Hauptman's and Miloh's approximation is given by equations (1) to (3) with h^2 = 1- k^2.

Evaluation of the Complete Elliptic Integral of the 2nd Kind, E(h), can be avoided by using Ahmadi's approximation given by equations (4) and (5). The constants in equation (5) are:
a = 0.142 200 963 771 28
b = 3.934 908 477 896 60
c = 2.691 437 204 515 743

Plugging Ahmadi's approximation into equations (1) and (3) yields values that are within about 0.05% of high-accuracy, extrapolated results using the Lifting Surface Program (LSP).
You can't trust robots, though, so it would be prudent to verify this claim before using it.

Leo.

 

Very nice!