Aerodynamic center: Definition from Answers.com

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].

${dC_m\over dC_L} =0$ 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 of longitudinal static stability. Read about movement of centre of pressure.

Role of aerodynamic center in aircraft stability

For longitudinal static stability: ${dC_m\over d\alpha} <0$ and ${dC_z\over d\alpha} >0$

For directional static stability: ${dC_n\over d\beta} >0$ and ${dC_y\over d\beta} >0$

Where:

C z = C L * c o s (α) + C d * s i n (α)

C x = C L * s i n (α) - C d * c o s (α)

For A Force Acting Away at the Aerodynamic Center, which is away from the reference point:

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

Which for Small Angles $c o s (α) = 1$ and $s i n (α) = 0$ , $β = 0$ simpifies to:

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

Y A C = Y r e f

Z A C = Z r e f

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

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

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

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

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

α

= angle of attack

β

= sideslip angle

SM = Static Margin

References

^ Benson, Tom (2006). "Aerodynamic Center (ac)". The Beginner's Guide to Aeronautics. NASA Glenn Research Center. http://www.grc.nasa.gov/WWW/K-12/airplane/ac.html. Retrieved 2006-04-01.
^ Preston, Ray (2006). "Aerodynamic Center". Aerodynamics Text. Selkirk College. http://selair.selkirk.bc.ca/aerodynamics1/Stability/Page7.html. Retrieved 2006-04-01.

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Aerodynamic center

Role of aerodynamic center in aircraft stability

References

See also