To Locate the Mean Aerodynamic Chord on a Tapered or Delta Wing
Measure the root and tip
chord. Then draw the following lines on the plans:
At the root of the wing, draw a line parallel to
the centerline of the fuselage extending forward from the leading edge and
rearward from the trailing edge. Both lines should be the length of the tip chord.
Do the same thing at the tip but drawing the
lines the length of the root chord.
Connect the ends of the lines so that they create
an "X" over the wing panel. Where the two lines intersect is the
spanwise location of the Mean
If the plan indicates that the CG should be
located at some percentage of the MAC, then measure the MAC and put the CG the
given percentage back from the leading edge along the MAC. For example, if
the MAC is 10" and the plan indicates the CG should be 25% back from the leading
edge, then the CG is 2-1/2" back from the leading edge at the MAC.
This drawing should help you
visualize what you need to do:
Note: The lines cross at the spanwise
location of the MAC. It is not the fore/aft CG location (unless the
CG happens to be located at 50% MAC).
The following formula will give the measurement
(chord) of the MAC. It does not give the span wise location of the MAC.
rc = Root Chord
t = Taper Ratio = (Tip Chord ÷ Root Chord)
MAC = rc x 2/3 x (( 1 + t + t2 ) ÷ (
1 + t ))
Using the drawing above, let's say
the root chord is 11" and the tip chord is 6"
t = 6 ÷ 11 = .5455
Now plug t into the formula to find
the MAC. Note that the wingspan and sweep do not matter. No matter what
the span or how much the wing is swept, the MAC will always be the same length.
MAC = 11 x 2/3 x (( 1 + .5455 +
.54552 ) ÷ ( 1 + .5455 ))
MAC = 22/3 x ( 1.8431 ÷ 1.5455 )
MAC = 7.3333 x ( 1.8431 ÷ 1.5455)
MAC = 7.3333 x 1.19254
MAC = 8.7453"