The Wright brothers approached aerodynamics in a thorough, practical, experimental
way. From their writings, it is evident that they were very concerned about
accurately determining the aerodynamic forces on their aircraft.
But they were more practical engineers than theoreticians and many of the
factors which affect lift and drag are better understood today
than they were by the Wright brothers. For your more complete understanding,
we present here a page which describes the modern method for
accounting for the movement of the center of pressure (cp) with angle of attack.
The brothers understood the theory of their day, which incorrectly
described a steady movement of the cp from the center of
a flat plate forward to the leading edge of the plate as the angle of
attack decreases from 90 degrees to zero. With the wing of the 1901 glider,
the brothers cleverly mapped out the motion of the cp which showed a motion
initially forward with decreasing angle, then a reversal to the trailing edge.
The brothers determined that the theory, as presented to them in textbooks,
was incorrect. The modern use of the aerodynamic center to perform design
and analysis, instead of the center of pressure, began several years after
the brothers had successfully flown.
As an object moves through a fluid, the velocity
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 which we call 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 constrained in some way
it will flip 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 also change.
Since the pressure distribution changes with angle of attack, the torque
created by this force also changes.
So determining the aerodynamic behavior of an airfoil
is very complicated if we use the center of pressure
to analyze the forces.
For a single angle of attack,
we can compute the moment about any point on the
airfoil. 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 moment is always the same,
regardless of the angle of attack.
Engineers call the location where the 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. This set of conditions is used experimentally to
determine the aerodynamic moment which is then applied for all other flight
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.
- Re-Living the Wright Way
- Beginner's Guide to Aeronautics
- NASA Home Page