- Aerodynamic center
The

**aerodynamic center**of anairfoil moving through afluid is the point at which thepitching moment coefficient for the airfoil does not vary withlift coefficient i.e.angle of attack cite 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] .:$\{dC\_mover\; dC\_L\}\; =0$ 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 oflongitudinal static stability . Read about movement of centre of pressure.**Role of aerodynamic center in aircraft stability**For

longitudinal static stability ::$\{dC\_mover\; dalpha\}\; <0$:$\{dC\_zover\; dalpha\}\; >0$For directional static stability::$\{dC\_nover\; deta\}\; 0$:$\{dC\_yover\; deta\}\; 0$

Where::$\{C\_z\; =\; C\_L*cos(alpha)+C\_d*sin(alpha)\}$:$\{C\_x\; =\; C\_L*sin(alpha)-C\_d*cos(alpha)\}$

For A Force Acting Away at the Aerodynamic Center, which is away from the reference point::$X\_\{AC\}\; =\; X\_\{ref\}\; +\; c\{dC\_mover\; dC\_z\}$

Which for Small Angles $cos(\{alpha\})=1$ and $sin(\{alpha\})=0$, $\{eta\}=0$ simpifies to::$X\_\{AC\}\; =\; X\_\{ref\}\; +\; c\{dC\_mover\; dC\_L\}$:$Y\_\{AC\}\; =\; Y\_\{ref\}$:$Z\_\{AC\}\; =\; Z\_\{ref\}$

General Case: From the definition of the AC it follows that:$X\_\{AC\}\; =\; X\_\{ref\}\; +\; c\{dC\_mover\; dC\_z\}\; +\; c\{dC\_nover\; dC\_y\}$: .:$Y\_\{AC\}\; =\; Y\_\{ref\}\; +\; c\{dC\_lover\; dC\_z\}\; +\; c\{dC\_nover\; dC\_x\}$: .:$Z\_\{AC\}\; =\; Z\_\{ref\}\; +\; c\{dC\_lover\; dC\_y\}\; +\; c\{dC\_mover\; dC\_x\}$

The Static Margin can then be used to quantify the AC::$SM\; =\; \{X\_\{AC\}\; -\; X\_\{CG\}over\; c\}$

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 :$eta$ = 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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