As an object moves through a fluid, the
of the fluid varies around the
surface of the object. The variation of velocity produces a variation of
pressure on the surface of the object.
Integrating the pressure times the surface area around the body
on the object.
We can consider this force to act through the average location of
the pressure on the surface of the object. We call the
average location of the pressure variation the
center of pressure
in the same way that we call the
average location of the
of an object the
center of gravity.
In general, the pressure distribution around the object
also imparts a
torque, or moment,
on the object.
If a flying airfoil is not controlled in some way
it will tumble as it moves through the air.
If we consider an airfoil at angle of attack, we can (theoretically) determine
the pressure variation around the airfoil, and calculate the aerodynamic force
and the center of pressure. But if we change the angle of attack, the
pressure distribution changes and therefore the aerodynamic force and the
location of the center of pressure and the moment all change.
So determining the aerodynamic behavior of an airfoil
is very complicated if we use the center of pressure
to analyze the forces. We can compute the moment about any point on the
airfoil if we know the pressure distribution. The aerodynamic force will be the
same, but the value of the moment depends on the point where that force is
applied. It has been found both experimentally and theoretically that,
if the aerodynamic force is applied at a location 1/4
back from the leading edge on most low speed airfoils,
the magnitude of the aerodynamic moment remains nearly constant
with angle of attack.
Engineers call the location where the aerodynamic moment remains constant the
aerodynamic center (ac)
of the airfoil. Using the aerodynamic center as the location where the aerodynamic
force is applied eliminates the problem of the movement of the center of pressure
with angle of attack in aerodynamic analysis.
(For supersonic airfoils, the aerodynamic center is nearer the 1/2 chord
For symmetric airfoils, the aerodynamic moment about the ac is zero
for all angles of attack. With camber, the moment is non-zero
and constant for thin airfoils.
For a positive
the moment is negative and results in a counter-clockwise rotation
of the airfoil.
With camber, an
angle of attack can be determined for which the airfoil produces no lift, but
the moment is still present.
For rectangular wings, the wing ac is the same as the airfoil ac. But for wings
with some other planform (triangular, trapezoidal, compound, etc.) we have to
find a mean aerodynamic center (mac) which is the average for the whole wing.
The computation of the mac depends on the shape of the planform.
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