Thickness Effects
The same ideas used in predicting the characteristics of very thin airfoils
with camber can be applied to study airfoils with some thickness.
Just as we placed vortices on the airfoil chord line to model a camber line,
we can place sources on the x axis to model a thick symmetric airfoil.
The source strengths can be computed much more simply than the vortex strengths,
however.
To satisfy continuity in the region ABCD:
where σ dx is the source strength contained in the box.
To first order then:
The induced velocity on the chord line is:
Note that the condition for tangent flow,
is automatically satisfied by the given solution for source strength in
(2).
The total x component of velocity is then:
Near the nose of the airfoil our approximation of small angles is no longer
valid and the answers given by the previous expression are not accurate.
In the 1950's Riegels introduced a correction to thin airfoil theory that
greatly improves the accuracy. In fact, the Riegels correction produces
results that work for ellipses up to and exceeding 100% thick, while the
previous theory only works well up to 10 or 15%. The velocity on the surface
of the airfoil with Riegels modification is:
