Visitor comments regarding How to Find the Mean Aerodynamic Chord

November 08, 2007

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GBrichan
Michigan, USA
Posted:February 8th, 2013
11.37 PM

I find your web site very interesting and full of handy information regarding model airplanes and their design. I have tried using the information on the page entitled 'Mean Aerodynamic Chord' and met with errors. After further research and some trial and error on my part, I found that a more precise formula would be as follows.
M.A.C. = SquareRoot( ( TipChord2 + RootChord2 ) ÷ 2 )

Since the Mean Aerodynamic Chord would divide the wing area in half, I squared each of the chords, tip and root, added the products and divided by two in order to find the mean average area. Then, taking the square root yields the Mean Aerodynamic Chord.

Using a tip chord of six inches and a root chord of eleven inches we find the following:
M.A.C. = Sqrt(( 62+112)÷2)
M.A.C. = Sqrt((36+121)÷2)
M.A.C. = Sqrt(157÷2)
M.A.C. = Sqrt(78.5)
M.A.C. = 8.8600

To find the span-wise location of the M.A.C., first we calculate a 'taper factor' based on the amount of taper along the span of the wing panel. We can calculate the taper factor by taking the difference in chord lengths and divide by the wing panel span. Continuing the example above with a wing panel span of twenty-four inches we get the following:
Taper Factor = ( RootChord – TipChord ) ÷ Span
Taper Factor = (11 – 6) ÷24
Taper Factor = 5 ÷ 24
Taper Factor = 0.2083

Using this 'taper factor' we can then calculate the span-wise location of the M.A.C. To calculate, we take the difference between the root chord and the mean aerodynamic chord and divide by the taper factor.
Location = ( RootChord – MAC ) ÷ TaperFactor
Location = (11 – 8.8600 ) ÷ 0.2083
Location = 2.1400 ÷ 0.2083
Location = 10.2736*

This is the distance from the wing root to the M.A.C.

*Note: These numbers were derived by rounding off to the fourth decimal. More accuracy can be found using the 'un-rounded' numbers on a computer spreadsheet for example. The true location works out to be 10.2718916479936 (it goes on).

We can confirm our results by finding the area of the wing panel using the numbers above.
The total area of the wing panel:
Area = ( TipChord + RootChord ) x Span ÷ 2
Area = ( 6 + 11 ) x 24 ÷ 2
Area = 17 x 24 ÷ 2
Area = 204

The area of the root-half of the wing panel would be:
Area = (8.8600 + 11) x 10.2719 ÷ 2
Area = 19.8600 x 10.2719 ÷ 2
Area = 102

Again, using the actual (non-rounded) number yields the more accurate numbers.

kcaldwel
Canada
Posted:February 8th, 2013
11.15 AM

The formulas presented for the elliptical wing MAC and it's spanwise location are incorrect. The spanwise location must be less than 50% of the span, given the taper in an elliptical wing.

The correct numbers are:

MAC = 0.9055 * root chord

y = 0.4244 * b/2

http://www.paracreo.com/articles/Paracreo%20Aerodynamics%20Article%203%20-%20Mean%20Aerodynamic%20Chord.pdf

kcaldwel
Canada
Posted:February 8th, 2013
11.15 AM

Charles V
FRANCE
Posted:February 14th, 2011
2.25 PM

Please , I am looking for the basic genuin and exact physical definition of the MAC .
I try doing the calculation including the Reynold :( Re), in the air dynamic formula :

CAM= Sum [(Wing Chord )². dx ]{0 to "b"} / Sum [(Wing Chord )dx ]{0 to "b"}

Which drives me to common : CAM = (2/3).(r²+rt+t²)/(r+t)
r= Root chord , t = Wing tip chord
But I would like a confirmation ...
Could someone tell me the true definition of this thing ?

wim

Posted:April 2nd, 2005
8.11 AM

Hi,
In addition to Alasdair Sutherland's information about the mean aerodynamic chord of an elliptical wing:

The formula to find the mean aerodynamic chord of an elliptical wing is as follows:

Mean Aerodynamic Chord:
mac = (8*rootchord) / (3 * pi)

Location of mac
locmac = sqrt(1-64/(9*pi*pi))

which gives the figures as presented by Alasdair Sutherland

And to be complete:
Wing Surface
S = pi*span*rootchord/4

Greetings,

Wim

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