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Aerodynamic center, aka the Center of Lift or Center of Pressure. I would like to know where this is for an A320 airplane.

Sadly I don't know how to estimate aerodynamic things. I can do it for the center of mass, but when it comes to aerodynamics, I cannot simply find the geometric center of multiple arranged bodies, each one assumed to be uniform density. If anyone knows a trick or method of estimating the aerodynamic center, please let me know.

enter image description here

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The location of the aerodynamic centre can be tricky to find in an existing aeroplane, it will shift as a function of speed, Angle of Attack, flap deflection etc. In the pre-design phase the aerodynamic centre is often taken at 25% of Mean Aerodynamic Chord, and since you draw a plan view of the aircraft, we can use this to get an approximation.

If the wing has straight taper over the planform, the MAC can be constructed like in the picture below. Then take the point at 25%: this approximates the location of the aerodynamic centre for one wing, the other side is identical of course, and aerodynamic centre of both wings is halfway the connection line of the two. enter image description here However, like many transport jets, the A320 has a trailing edge sweep of zero next to the fuselage to accommodate the main gear. So the aerodynamic centre shifts a bit aft. You can construct it or estimate it, aerodynamicists may frown upon this. There are many sites that show the graphical method of the picture above (here's mine), because it is nice and simple. To illustrate the complexity of finding the MAC in other cases, here is a graph from the same source.

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Update

The above method gets us the MAC, which is the first step in determining the AC of the aircraft. A further method for finding AC in the pre-design phase is presented in Appendix E of Torenbeek:

  1. Find wing AC as above.
  2. Wing/Fuselage pitching moment, Appendix E.7 This is sensitive to the pressure distribution and is therefore hard to predict, except for:
    • Forward shift due to fuselage sections fwd & aft of the wing, particularly the nose. Based on the ratio of fuselage lengths.
    • Correction for lift loss in the wing/fuselage lift carry-over according to DATCOM.
  3. Fuselage pitching moment. Equation obtained from Munk's theory for near circular cross sections.
  4. Nacelle contributions. Appendix E.8, cannot be predicted reliably other than by wind tunnel tests, only a statistical correction is given.

The above is used for determining the AC of the aircraft. The contribution of the tailplane is included in the lift equations since it is dependent upon the Angle of Attack of the aircraft.

The complete method including graphs and equations is too lengthy to present in this forum, and can be consulted directly in the referenced Appendix.

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  • $\begingroup$ Thanks but this seems to only be for the wing. The AC of the whole airplane has to take into account the 3 tail surfaces too. Also, I'm not sure I understand the first picture.There's a circle marking the quarter chord point in the middle of the span, but it also constructs a big X that intersects lower. Where is the AC for the wing? Is it the circle or the X? $\endgroup$
    – DrZ214
    Commented Sep 13, 2017 at 1:02
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    $\begingroup$ The big X is for constructing the mid point of the Mean Aerodynamic Chord, the AC of the wing is then taken at 25% of the MAC. Yes the wing/body blended area and the fuselage have influence on the MAC as well. The tail surfaces can be trimmed, horizontal tail deflection is used to balance shifts in CoG. The wing cannot be trimmed, so in the pre-design stage the AC of the plane uses wing & fuselage geometry for determining the dimensions of the aircraft. But of course you're right, the rest of the aeroplane must be considered as well. $\endgroup$
    – Koyovis
    Commented Sep 13, 2017 at 2:14

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