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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 attack[1], [2].
- Failed to parse (Missing texvc executable; please see math/README to configure.): {dC_m\over dC_L} =0
where Failed to parse (Missing texvc executable; please see math/README to configure.): 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:
- Failed to parse (Missing texvc executable; please see math/README to configure.): {dC_m\over d\alpha} <0
- Failed to parse (Missing texvc executable; please see math/README to configure.): {dC_z\over d\alpha} >0
For directional static stability:
- Failed to parse (Missing texvc executable; please see math/README to configure.): {dC_n\over d\beta} >0
- Failed to parse (Missing texvc executable; please see math/README to configure.): {dC_y\over d\beta} >0
Where:
- Failed to parse (Missing texvc executable; please see math/README to configure.): {C_z = C_L*cos(\alpha)+C_d*sin(\alpha)}
- Failed to parse (Missing texvc executable; please see math/README to configure.): {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:
- Failed to parse (Missing texvc executable; please see math/README to configure.): X_{AC} = X_{ref} + c{dC_m\over dC_z}
Which for Small Angles Failed to parse (Missing texvc executable; please see math/README to configure.): cos({\alpha})=1
and Failed to parse (Missing texvc executable; please see math/README to configure.): sin({\alpha})=0
, Failed to parse (Missing texvc executable; please see math/README to configure.): {\beta}=0
simpifies to:
- Failed to parse (Missing texvc executable; please see math/README to configure.): X_{AC} = X_{ref} + c{dC_m\over dC_L}
- Failed to parse (Missing texvc executable; please see math/README to configure.): Y_{AC} = Y_{ref}
- Failed to parse (Missing texvc executable; please see math/README to configure.): Z_{AC} = Z_{ref}
General Case: From the definition of the AC it follows that
- Failed to parse (Missing texvc executable; please see math/README to configure.): X_{AC} = X_{ref} + c{dC_m\over dC_z} + c{dC_n\over dC_y}
- .
- Failed to parse (Missing texvc executable; please see math/README to configure.): Y_{AC} = Y_{ref} + c{dC_l\over dC_z} + c{dC_n\over dC_x}
- .
- Failed to parse (Missing texvc executable; please see math/README to configure.): Z_{AC} = Z_{ref} + c{dC_l\over dC_y} + c{dC_m\over dC_x}
The Static Margin can then be used to quantify the AC:
- Failed to parse (Missing texvc executable; please see math/README to configure.): SM = {X_{AC} - X_{CG}\over c}
where:
- Failed to parse (Missing texvc executable; please see math/README to configure.): C_n
= yawing moment coefficient
- Failed to parse (Missing texvc executable; please see math/README to configure.): C_m
= pitching moment coefficient
- Failed to parse (Missing texvc executable; please see math/README to configure.): C_l
= rolling moment coefficient
- Failed to parse (Missing texvc executable; please see math/README to configure.): C_x
= X-force ~= Drag
- Failed to parse (Missing texvc executable; please see math/README to configure.): C_y
= Y-force ~= Side Force
- Failed to parse (Missing texvc executable; please see math/README to configure.): C_z
= Z-force ~= Lift
- ref = reference point (about which moments were taken)
- c = reference length
- S = reference area
- q = dynamic pressure
- Failed to parse (Missing texvc executable; please see math/README to configure.): \alpha
= angle of attack
- Failed to parse (Missing texvc executable; please see math/README to configure.): \beta
= sideslip angle
SM = Static Margin
References
- ^ Benson, Tom (2006). Aerodynamic Center (ac). The Beginner's Guide to Aeronautics. NASA Glenn Research Center. Retrieved on 2006-04-01.
- ^ Preston, Ray (2006). Aerodynamic Center. Aerodynamics Text. Selkirk College. Retrieved on 2006-04-01.
See also
sv:Aerodynamiskt centrum
tr:Aerodinamik merkez
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