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Finding the area and center of mass of NACA 4 number symmetric airfoil
The equation for NACA 4 digit symmetric airfoils isref
where rxc is x/c or the ratio of position x to chord c and Nn is the NACA number or thickness ratio; by multiplying by two and integrating with respect to rxc going from 0 to 1 we obtain its area
and integrating the same equation from 0 to xcg and making it equal to the area divided by two we obtain the equation for the center of mass along the chord
from which Nn and c can be factored out
and xcg can be found numerically to give 0.3994c for a closed trailing edge, as on the equation shown, and 0.4015c for an open trailing edge
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