Aerodynamic Center1 Suppose we have the forces and moments specified about some reference location for the aircraft, and we want to restate them about some new origin.

refM = Pitching moment about refx

newM = Pitching moment about newx

refx = Original reference location

newx = New origin N = Normal force L≈ for small ∝

=A Axial force D≈ for small ∝ Assuming there is no change in the z location of the two points:

( )ref new ref newM x x L M= − − + Or, in coefficient form:

. .

ref new

new refm L M

meana c

x xC C C

c

− = − +

The Aerodynamic Center is defined as that location acx about which the pitching moment doesn’t change with angle of attack. How do we find it?

1 Anderson 1.6 & 4.3

x

z

xref xnew

MnewMref A A

N ~ L~N ~ L~

Aerodynamic Center

16.100 2002 2

Let new acx x= Using above:

( )ref ac

ac refM L M

x xC C C

c−

= − +

Differential with respect to α :

ref acM Mac ref LC Cx x C

cα α α

∂ ∂− ∂= − + ∂ ∂ ∂

By definition:

0acMCα

∂ = ∂

Solving for the above

, ref

ref

Mac ref L

Mac ref ref

L

Cx x C orc

Cx x xc c C

α α∂ − ∂ = − ∂ ∂

∂ −= − ∂

Example: Consider our AVL calculations for the F-16C

• 0refx = - Moment given about LE

• Compute refM

L

CC

∂

∂for small range of angle of attack by numerical

differences. I picked 0 03 to 3α α= − = .

• This gave 2.89acxc

≈ .

• Plotting MC vsα about acxc

shows 0MCα

∂≈

∂.

Note that according to the AVL predictions, not only is 0 @ 2.89Mac

C xα

∂≈ =

∂, but

also that 0MC = . The location about which 0MC = is called the center of pressure.

Aerodynamic Center

16.100 2002 3

Center of pressure is that location where the resultant forces act and about which the aerodynamic moment is zero. Changing “new” to “cp” and “ref” to “NOSE” to correspond to AVL:

NOSE

NOSE cp

NOSE

cpM L M

Mcp

L

x xC C Cc

Cxc C

− = −

+

⇒ = −

So if: NOSE NOSE

L

M M

L

C CC C

∂=

∂,

this will be true. This means that

0 at 0M LC C≈ = .

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=0)

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