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I'm interested in what kind of mathematics gets used in basic airfoil design. I suspect the calculus of variations must be involved, but I know nothing about deriving the shape of a plane wing.

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- Thread starter dydxforsn
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- #1

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I'm interested in what kind of mathematics gets used in basic airfoil design. I suspect the calculus of variations must be involved, but I know nothing about deriving the shape of a plane wing.

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It depends on how you define "design" and where you're looking for the calculus. For example, a very rudimentary aspect of airfoil design, which is very limited but useful for a basic understanding of airfoil properties is Thin Airfoil Theory.

Also, very important to designing an airfoil or wing is determining the rate of change of various coefficients with respect to flow properties, say lift coefficient vs. aoa or moment coefficient vs. aoa:

[itex]\frac{dC_l}{d\alpha} ; \frac{dC_m}{d\alpha}[/itex]

There's also the new theory of stall, which is useful in the same respect that T.A.T is.

In the more rigorous design of airfoils, the calculus is maybe more obscure. Airfoils are designed nearly exclusively via CFD (the exceptions being cases like an R/C maker). CFD involves the solution of PDE's such as the Navier-Stokes equation.

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