What is the physical meaning of Mean Aerodynamic Chord?

Question

I have not been able to find a consistent definition of what it really is.

I have come across definitions such as: "Physically, MAC is the chord of a rectangular wing, which has the same area, full aerodynamic force and position of the center of pressure at a given angle of attack as the given wing has." which is contradictory with this one "The mean aerodynamic chord is (loosely) the chord of a rectangular wing with the span, (not area) that has the same aerodynamic properties with regarding the pitch-moment characteristics as the original wing."

I am very confused and I wonder if you could please give me a precise definition (maybe in relation to an equivalent rectangular wing, as those two definitions I found), that shows intuitively what it is

Answer 1

The mean aerodynamic chord is only identical to the mean chord for rectangular wings. For tapered wings it is slightly longer.

Why? Because the mean aerodynamic chord is the mean chord of a rectangular wing that has the same pitch characteristics as the "real" wing. Pitch characteristics need to include pitch damping, and pitch damping grows with the square of the local chord. That is why the formula for the mean aerodynamic chord divides the square of the local chord by the wing area: $$\text{MAC} = \int_{y=-\frac{b}{2}}^{y=\frac{b}{2}}{\frac{c^2}{S}}dy$$ Here $b$ denotes wing span, $y$ the spanwise coordinate and $S$ the wing area. Since the chord is squared, deeper sections of the wing are overrepresented in the result. The resulting rectangular wing will have a larger area than the original, tapered wing but the same pitch damping! In case of a delta wing, MAC will grow to be ⅔ of the root chord, and for an elliptical wing it will be 90.5% of the root chord.

The MAC has been invented to convert arbitrary wing planforms into much easier to calculate rectangular wings. By doing all calculations on the correctly sized rectangular version, the more complicated calculations on the real one could be avoided. However, this works only up to a point:

• if you want to calculate lift, you need a wing of equal area.
• if you want to calculate induced drag, you need a wing of equal span.
• if you wand to calculate pitch motion, you need a wing of the correct MAC. This rectangular wing can either have the same area or the same span as the real wing, but not both together, unless the real wing is rectangular, too.

You are right, the two definitions you quote are not compatible. The rectangular wing cannot have the same span than the real one, or its area and all associated forces and moments would be higher.

Answer 2

On transport aircraft, as you have already gathered the position of its centre of gravity is expressed in relation to the MAC. The definition of MAC, that I will provide is I hope a little clearer. If you were to take a plan view of the wing and draw any number of chord lines over the surface you would notice they're of various lengths, usually longer at the end closest the fuselage (wing root) and shorter at the end farthest the fuselage (wing tip) with different distances from the nose of the aircraft, the shortest distance being again at the root and farthest at the tip. Applying mathematics to find the mean of all those chord lines you have the MAC. This is shown as a single length beginning at the 'reference datum'. For example, an aircrafts MAC may be 520cm in length extending from 2006cm to 2526cm aft of the reference datum.

Answer 3

Mean aerodynamic chord is the chord drawn through the centroid (geographical center ) of the plan area.remember it is not the average chord but it ia the chord through the centroid of the wing area..