Mean Aerodynamic Chord of a Wing
Finding the MAC (mean aerodynamic chord) of a wing, the easy way.
I am currently doing a lot of scratch building, mostly Depron profile models for indoor flying as well as Whip Control models for outdoors. Both of these types of models fly well with a Centre of Gravity of around 30-32% measured at the Mean Aerodyamic Chord. Most model plans and kit instructions show the CG as a point on the fuselage, or a dimension back from the Leading Edge at the root, not in relation to the wing's Mean Aerodynamic Chord. So for an own design model, or one of those pesky plans that doesn't show a Centre of Gravity, it means going back to basics.
Googling How to Find the Mean Aerodynamic Chord usually results in a drawing which looks like this (fig 1).
There is also the option of a mathematical formula, and I have used both methods. However, the problem really starts if you have a wing that looks like this (fig 2).
This was a genuine problem for me having recently built 4 indoor Spitfires and a Whip Control P-47 Thunderbolt. In the past I would draw in lines which fudged such a shape to straight lines, but I wasn't very happy about this solution (fig 3).
The clue to my simple solution is understanding that:
The Mean Aerodynamic Chord is a line on the wing parallel to the fuselage centre line where the wing area inboard of the line is the same as the wing area outboard of the line.
So here's what I have been doing on my last few models. My models are currently between 500 and 750mm wingspan, so it's possible to do this full size. For bigger models it would mean scaling down the wing plan to fit the paper or Depron. This is my Whip Control FW190 conversion from an RC foam kit.
Trace the wing outline onto printer paper or Depron and cut it out (fig 4).
Balance the template so that it's level over an edge like a see saw. I intend to find something better than the metal ruler I have, but it works well enough (fig 5).
If the template flops down like a Bloodhound's ears, put a crease in it (as shown). Make sure that you draw a line through the balance point which is parallel to the model centre line. This line is the Mean Aerodynamic Chord. If the paper is too short, don't glue a piece on as the template must be of constant thickness.
I usually scrawl notes on the template. The MAC for the FW190 measured 117mm with the 30% CG at 35,1mm back from the Leading Edge at the MAC. I then projected this line to the root and tip to be able to check the balance point on the model.
The FW190 kit instructions showed a balance point dimension back from the LE at the root, and the CG I had determined matched well with it. However, I have seen models where the CG information was out by a mile, so I'm cautious.
2nd March 2020
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