Aerodynamic center

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The aerodynamic center of an airfoil moving through a fluid is the point at which the pitching moment generated by the airfoil is constant regardless of the angle of attack^[1], ^[2]. This is an aspect of aerodynamics. For symmetric airfoils the aerodynamic center is located at a distance equal to 1/4 of the chord from the leading edge of the airfoil. Thus, this point is referred to as the quarter-chord. This result also holds true for 'thin-airfoils '. For non-symmetric airfoils the quarter-chord is only an approximation for the aerodynamic center.

Similarly, the Aerodynamic center is also defined for an entire vehicle.^{[citation needed]} This is used as a sanity check to make sure the moments and forces are reasonable. Note that the reference point should be chosen as the CG if it is known. If it is not, any value will work, but intuitive analysis will be more difficult.^{[citation needed]} Also note that the Lift direction differs from the Z direction by a small angle and may be neglected. Derivation was performed assuming small angles, but the final equations do not make that assumption.

For

β = 0

and

γ = 0

^{[citation needed]}

L = q S C L

M = q S C m c

$L \left( X_{AC} - X_{CG} \right) = M$

$C_L \left( X_{AC} - X_{CG} \right) = C_m c$

$X_{AC} = X_{ref} + c{dC_m\over dC_z}$

Y A C = Y r e f

$Z_{AC} = Z_{ref} + c{dC_m\over dC_x}$

General Case: From the definition of the AC it follows that

$X_{AC} = X_{ref} + c{dC_m\over dC_z} + c{dC_n\over dC_y}$

$Y_{AC} = Y_{ref} + c{dC_l\over dC_z} + c{dC_n\over dC_x}$

$Z_{AC} = Z_{ref} + c{dC_l\over dC_y} + c{dC_m\over dC_x}$

where:

C_n = yawing moment coefficient

C_m = pitching moment coefficient

C_l = rolling moment coefficient

C_x = X-force ~= Drag

C_y = Y-force ~= Side Force

C_z = Z-force ~= Lift

ref = reference point where moments were sum about

c = reference length

S = reference area

q = dynamic pressure

[edit] References

^ Benson, Tom (2006). Aerodynamic Center (ac). The Beginner's Guide to Aeronautics. NASA Glenn Research Center. Retrieved on April 1, 2006.
^ Preston, Ray (2006). Aerodynamic Center. Aerodynamics Text. Selkirk College. Retrieved on April 1, 2006.