Center of pressure vs. aerodynamic center

[Daniel Hofer]

Hello

I have a small problem to understand the difference of center of pressure
and aerodynamic center.

I've read in several books, but I don't really understand.
Does anybody have an easy explanation?

Thanks a lot!

Daniel

[Aeroengineer]

There is a pressure distribution around an airfoil. Summation of this
pressure distribution over entire surface of the airfoil results in the
aerodynamic force. However, this pressure distribution also generates
aerodynamic moment around any arbitrary point on the chordline. But
there is a single point on the chordline where sum of the moments of
distributed pressure forces is equal to zero. This point is called the
center of pressure. Location of the center of pressure changes with the
angle of attack.

There is also another point on the chordline, where sum of the moments
of distributed pressure forces is not zero, but stays constant even if
the angle of attack is changed. This pointy is called the aerodynamic
center. The distance of the aerodynamic center from the leading edge is
about 25% of the chord for almost all subsonic airfoils. For supersonic
airfoils, this distance is about 50% of the chord.

Hope this explanation helps you.

[Ron Freimuth]

> I have a small problem to understand the difference of center of pressure
> and aerodynamic center.
> I've read in several books, but I don't really understand.
> Does anybody have an easy explanation?

I'd say the Aerodynamic Center is a defined reference point near, but
not necessarily at, the Center of Pressure. I'm also assuming the Center of
Pressure is the same as the "Center of Lift".

The "Aerodynamic Center" is usually taken as 25%* of the Wing's MAC,
and it's "Waterline". Which is near the Center of Lift for typical wings
before compressibility has an effect.

* Supersonic wings may be based on 50% MAC since the actual Center of
Lift is often near that location in the Supersonic realm.

The Actual Center of Lift of a wing varies a bit from 25% MAC, depending
on camber, etc.. However, that variation is taken care of by adding a "Zero
Lift Pitching Moment": Cmo. Note a moment moves the Center of Lift
forward/aft without changing its magnitude.

Further, The Center of Lift varies with Angle of Attack. That is
conventionally handled by extending the Pitching Moment to cover a range of
AoA, Alpha.

The "Center of Lift" above is relative to the complete AC, not an
isolated wing. However, 25% of the wing's Mean Aerodynamic Chord is still
used for this reference.

Further, the horizontal stabilizer may have positive or negative life,
and that moves the effective Center of Lift. I'm a bit confused on
details on the nomenclature, though I understand the effect. ;)

Now AC longitudinal stations (distances) in real AC are based on a
somewhat arbitrary "Reference Datum". That is rarely at the Aerodynamic
Center, rather it may be at or near the tip of the nose. Basic analysis is
best done relative to the 'Aerodynamic Center'.

Regardless, for a wing alone, 25% MAC is commonly assumed to be the
Center of Lift, and small variations from that reference are accounted for
by adding a Pitching moment. Airfoil polars in "Theory of Wing Sections"
are based on that longitudinal reference and any variation from that point
is accounted for by the corresponding Pitching Moment curve.

RAF

[Dennis Straussfogel]

> I have a small problem to understand the difference of center of pressure
> and aerodynamic center.
>
> I've read in several books, but I don't really understand.
> Does anybody have an easy explanation?
>

"Center of pressure (c.p)" is exactly what you'd think it is: the point
at which the pressure distribution can be considered to act--analogous
to the "center of gravity" as the point at which the force of gravity
can be considered to act.

The concept of the "aerodynamic center (a.c.)," on the other hand, is
not very intuitive, and is often misused and misunderstood. Because the
lift and location of the c.p. on an airfoil both vary linearly (more of
less) with angle of attack (AOA), at least within the unstalled range of
AOA, it works out that you can define a point on the chord of the
airfoil at which the pitching moment remains *constant*, regardless of
the AOA. That point is usually near the quarter-chord point (.25c) and
for a symmetric airfoil the constant pitching moment would be zero. For
a cambered airfoil the pitching moment about the a.c. would be non-zero,
but constant. The usefulness of the a.c. is in stability and control
work where the aircraft can be defined in terms of the wing and tail
a.c.'s and the required lift and moments calculated without worrying
about the shift in c.p. with AOA.

Hope that explanation is "easy" enough, though a.c. doesn't really lend
itself to one.

Dennis M. Straussfogel, Ph.D.
Aerospace Engineering Consultant

[Don Stauffer]

I am not sure how easy this is, but here is a try. The CP is pretty
easy- it is an aerodynamic pressure equivalent to the center of
gravity. That is, it is the effective point where the force could be
considered as acting at.

The aerodynamic center is something else. With many airfoils at normal
angles of attack, the actual lifting force and the center of pressure
act in a funny way. They act in such a way that the moment, or
twisting force, appears to be a constant if we pick the right point to
consider it acting at.

That is, if we are at the aerodynamic center, then when the lift force
increases, the cp moves closer to the ac, so that the product is a
constant. If the lift force decreases, the cp moves away from the ac by
a corresponding fractional amount.