Root Mean Chord by Graphic Analysis
by Michael A. Morrow

Calculating the Root Mean Chord Using Graphic Analysis

Yeah. I saw what you did there. You clicked on the Quadratic Formula method for finding the Root Mean Chord, scrolled down, took one look at the quadratic formula, and your brain screamed "Aaaiiiiiiiieeeeee!!!! It's 'THE MATH'!!!!", and back-clicked so fast that there was a pop from the air rushing into the vacuum you created when you disappeared. Don't try to tell me you didn't.

Sooo. This is the "easy" way to find the root mean chord. All you need is the plan form of the wing section, a good ruler (preferably a machinists ruler that measures hundredths of an inch), a sharp pencil, and a calculator. And you don't really even need a calculator if you can draw a straight line, measure the length of that line, and multiply that length by 0.25 (for a 25% chord balance point).

So here's how to do it. You start with a full-size drawing of the wing planform like this (ignore rounded wingtips - square them off):



Draw the lines in red as shown below to determine the measurements of the leading edge sweep-back (a), and trailing edge sweep-forward (b) like this:



Draw a line in for 'a' and 'b' as shown here. I've drawn in the 'a' line, (leading edge sweep-back) in red, and the 'b' line (trailing edge sweep-forward) in green, like this:



Now measure the 'a' line (the top red line), and add a line that long to the bottom end of the 'b' line (the green line), like this:



Now measure the 'b' line (the bottom green line), and add a line that long to the end of the 'a' line (the top red line), like this.



Now draw a diagonal line from the end of the top of the top green line, to the bottom of the root rib of the wing, like this (the thin blue line):



Now draw a diagonal line from the bottom of the bottom red line to the top of the root rib of the wing, like this (the thin purple line):



Draw a vertical line through the point where the thin blue and purple lines cross, like this (the vertical red chord line):



Congratulations! You have just drawn the Root Mean Chord!

Measure the length of the Root Mean Chord, and multiply that length by 0.25.




Mark a point 25% of the Root Mean Chord from the leading edge of the wing:




At the point you just marked, draw a horizontal line across to the Root Rib like this:




Where the line intersects the root rib is the 25% Center of Gravity (CG) as shown here:




The CG target ----> is where you will balance the model.

Congratulations! You have just found the Center of Gravity using the graphical analysis method!

That wasn't so hard was it?

Now back to your flight-trimming process in progress!
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