Thin Airfoil Inverse Design
The basic thin airfoil theory formulation can be used to design airfoils
with a desired pressure distribution. This process is actually easier than
the direct analysis. The integral equation used to obtain the circulation
distribution given the airfoil shape:
can be evaluated directly if we know the circulation distribution.
We evaluate the integral at several values of x to find the surface slope
dz/dx along the airfoil.
which can be integrated to obtain:
C and a can be chosen to make z(0) = z(1) = 0.