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| The [[torques]] or moments acting on an [[airfoil]] moving through a [[fluid]] can be accounted for by the net [[lift (force)|lift]] applied at some point on the airfoil, and a separate net pitching moment about that point whose magnitude varies with the choice of where the lift is chosen to be applied. The '''aerodynamic center''' is the point at which the [[pitching moment]] coefficient for the airfoil does not vary with [[lift coefficient]] (i.e. [[angle of attack]]), so this choice makes analysis simpler | | Jayson Berryhill is how I'm called and my spouse doesn't like it at all. The favorite hobby for him and his children is fashion and he'll be beginning some thing else along with tarot [http://c045.danah.co.kr/home/index.php?document_srl=1356970&mid=qna psychic readings] ([http://conniecolin.com/xe/community/24580 http://conniecolin.com]) it. Office supervising is where my primary earnings arrives from but I've always wanted my own business. Her family lives in Ohio but her spouse wants them to transfer.<br><br>Here is my webpage; [http://www.herandkingscounty.com/content/information-and-facts-you-must-know-about-hobbies tarot readings] |
| .<ref name="NASA GRC 2006">{{cite web | |
| | last = Benson
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| | first = Tom
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| | coauthors =
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| | year = 2006
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| | url = http://www.grc.nasa.gov/WWW/K-12/airplane/ac.html
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| | title = Aerodynamic Center (ac)
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| | work = The Beginner's Guide to Aeronautics
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| | publisher = NASA Glenn Research Center
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| | accessdate = 2006-04-01
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| }}</ref>
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| :<math>{dC_m\over dC_L} =0</math> where <math>C_L</math> is the aircraft [[lift coefficient]]. | |
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| The concept of the aerodynamic center (AC) is important in [[aerodynamics]]. It is fundamental in the science of stability of aircraft in flight.
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| For symmetric airfoils in subsonic flight the aerodynamic center is located approximately 25% of the [[Chord (aircraft)|chord]] from the leading edge of the airfoil. This point is described as the quarter-chord point. This result also holds true for '[[thin-airfoil theory|thin-airfoils]]'. For non-symmetric ([[Camber (aerodynamics)|cambered]]) airfoils the quarter-chord is only an approximation for the aerodynamic center.
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| A similar concept is that of [[center of pressure (fluid mechanics)|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 [[Center of pressure (fluid mechanics)#Movement of center of pressure|movement of centre of pressure]].
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| == Role of aerodynamic center in aircraft stability ==
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| For [[longitudinal static stability]]: <math>{dC_m\over d\alpha} <0</math> and <math>{dC_z\over d\alpha} >0</math>
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| For directional static stability: <math>{dC_n\over d\beta} >0</math> and <math>{dC_y\over d\beta} >0</math>
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| Where:
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| :<math>{C_z = C_Lcos(\alpha)+C_dsin(\alpha)}</math>
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| :<math>{C_x = C_Lsin(\alpha)-C_dcos(\alpha)}</math>
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| For A Force Acting Away at the Aerodynamic Center, which is away from the reference point:
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| :<math>X_{AC} = X_{ref} + c{dC_m\over dC_z}</math>
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| Which for Small Angles <math>cos({\alpha})=1</math> and <math>sin({\alpha})</math>=<math>\alpha</math>, <math>{\beta}=0</math>, <math>C_z=C_L-C_d*\alpha</math>, <math>C_z=C_L </math> simplifies to:
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| :<math>X_{AC} = X_{ref} + c{dC_m\over dC_L}</math>
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| :<math>Y_{AC} = Y_{ref}</math>
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| :<math>Z_{AC} = Z_{ref}</math>
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| General Case: From the definition of the AC it follows that
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| :<math>X_{AC} = X_{ref} + c{dC_m\over dC_z} + c{dC_n\over dC_y}</math>
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| : .
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| :<math>Y_{AC} = Y_{ref} + c{dC_l\over dC_z} + c{dC_n\over dC_x}</math>
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| : .
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| :<math>Z_{AC} = Z_{ref} + c{dC_l\over dC_y} + c{dC_m\over dC_x}</math>
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| The Static Margin can then be used to quantify the AC:
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| :<math>SM = {X_{AC} - X_{CG}\over c}</math>
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| where:
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| :<math>C_n</math> = yawing moment coefficient
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| :<math>C_m</math> = [[pitching moment]] coefficient
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| :<math>C_l</math> = rolling moment coefficient
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| :<math>C_x</math> = X-force ~= Drag
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| :<math>C_y</math> = Y-force ~= Side Force
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| :<math>C_z</math> = Z-force ~= Lift
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| :ref = reference point (about which moments were taken)
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| :c = reference length
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| :S = reference area
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| :q = [[dynamic pressure]]
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| :<math>\alpha</math> = [[angle of attack]]
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| :<math>\beta</math> = sideslip angle
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| SM = Static Margin
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| ==References==
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| <references />
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| ==See also==
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| * [[Aircraft flight mechanics]]
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| * [[Flight dynamics]]
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| * [[Longitudinal static stability]]
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| * [[Thin-airfoil theory]]
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| * [[Joukowsky transform]]
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| {{DEFAULTSORT:Aerodynamic Center}}
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| [[Category:Aerodynamics]]
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| [[Category:Geometric centers]]
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