# Aerodynamic center

The aerodynamic center of an airfoil moving through a fluid is the point at which the pitching moment coefficient for the airfoil does not vary with lift coefficient i.e. angle of attackcite web
last = Benson
first = Tom
coauthors =
year = 2006
url = http://www.grc.nasa.gov/WWW/K-12/airplane/ac.html
title = Aerodynamic Center (ac)
work = The Beginner's Guide to Aeronautics
publisher = NASA Glenn Research Center
accessdate = 2006-04-01
] , cite web
last = Preston
first = Ray
year = 2006
url = http://selair.selkirk.bc.ca/aerodynamics1/Stability/Page7.html
title = Aerodynamic Center
work = Aerodynamics Text
publisher = Selkirk College
accessdate = 2006-04-01
] .

:$\left\{dC_mover dC_L\right\} =0$ where $C_L$ is the aircraft lift coefficient.

The concept of the aerodynamic center (AC) is important in aerodynamics. It is fundamental in the science of stability of aircraft in flight.

For symmetric airfoils in subsonic flight the aerodynamic center is located approximately 25% of the chord from the leading edge of the airfoil. This point is described as the quarter-chord point. This result also holds true for 'thin-airfoils '. For non-symmetric (cambered) airfoils the quarter-chord is only an approximation for the aerodynamic center.

A similar concept is that of center of pressure. The location of the center of pressure varies with changes of lift coefficient and angle of attack. This makes the center of pressure unsuitable for use in analysis of longitudinal static stability. Read about movement of centre of pressure.

Role of aerodynamic center in aircraft stability

For longitudinal static stability::$\left\{dC_mover dalpha\right\} <0$:$\left\{dC_zover dalpha\right\} >0$

For directional static stability:::

Where::$\left\{C_z = C_L*cos\left(alpha\right)+C_d*sin\left(alpha\right)\right\}$:$\left\{C_x = C_L*sin\left(alpha\right)-C_d*cos\left(alpha\right)\right\}$

For A Force Acting Away at the Aerodynamic Center, which is away from the reference point::$X_\left\{AC\right\} = X_\left\{ref\right\} + c\left\{dC_mover dC_z\right\}$

Which for Small Angles $cos\left(\left\{alpha\right\}\right)=1$ and $sin\left(\left\{alpha\right\}\right)=0$, simpifies to::$X_\left\{AC\right\} = X_\left\{ref\right\} + c\left\{dC_mover dC_L\right\}$:$Y_\left\{AC\right\} = Y_\left\{ref\right\}$:$Z_\left\{AC\right\} = Z_\left\{ref\right\}$

General Case: From the definition of the AC it follows that:$X_\left\{AC\right\} = X_\left\{ref\right\} + c\left\{dC_mover dC_z\right\} + c\left\{dC_nover dC_y\right\}$: .:$Y_\left\{AC\right\} = Y_\left\{ref\right\} + c\left\{dC_lover dC_z\right\} + c\left\{dC_nover dC_x\right\}$: .:$Z_\left\{AC\right\} = Z_\left\{ref\right\} + c\left\{dC_lover dC_y\right\} + c\left\{dC_mover dC_x\right\}$

The Static Margin can then be used to quantify the AC::$SM = \left\{X_\left\{AC\right\} - X_\left\{CG\right\}over c\right\}$

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 (about which moments were taken):c = reference length:S = reference area:q = dynamic pressure:$alpha$ = angle of attack: = sideslip angleSM = Static Margin

References

ee also

* Aircraft flight mechanics
* Center of pressure
* Flight dynamics
* Longitudinal static stability
* Thin-airfoil theory
* Joukowsky transform

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