
Calculating the Wing Area for Elliptical
Wings
Why Wing Area is Important
 Taken on its own, wing area is not important. However, the wing area
must be calculated to determine
wing loading which is very important.
Calculating Wing Area of MultiWing Aircraft
 Calculate the
wing area for each wing individually. Add these areas together to find
the total wing area.
Notes
 If you are building from a kit or a plan then the
wing area should be somewhere on the plan, in the instructions or on the kit box.
 When calculating the wing or
stabilizer area, the area that
crosses the fuselage is included even if that area does not provide lift.



Is it a True Elliptical Wing?
Finding the area of an ellipse is not difficult. Unfortunately,
determining if a shape actually is an ellipse is another story.
There is no
way to tell if a wing is a true ellipse just by looking at it. The only
way to know for sure is to actually use the Root Chord and Wing Span and plug
them into the formula to plot an ellipse and start plotting points.
If the points fall on the outline of the wing, then you have a true ellipse.
Otherwise you have to use other ways of determining the wing area.



How to Plot the Outline of an Ellipse
If you want to plot an ellipse, then the formula is:
(x^{2} ÷ a^{2}) + (y^{2} ÷ b^{2}) = 1
Where
a = Wing Span ÷ 2
b = Root chord ÷ 2
Basically what you do is determine the wing span and the root chord and then start plugging in numbers along the span to
find the chord at those locations.
There is also a method using two points (thumb tacks) and a string, but I
do not know it off the top of my head. It is fairly simple and I am sure you
can find it on the net someplace.



Finding the Area of a True Ellipse
You can use the
formula for an ellipse to calculate the area IF the wing is a true
ellipse (or close enough).
Area of an Ellipse = a x b x
PI
Where
a = Wing Span ÷ 2
b = Root chord ÷ 2
(In case you've forgotten, PI = 3.14)
Therefore (without showing all the steps that
got me here)...
Wing Area = ( 3.14 x Span x Chord )
÷ 4



Finding the Area of a Shape that is not a True Ellipse
There is a strong possibility that the
forward portion of the wing is not the same ellipse as the aft portion.
You can split the wing into two parts by drawing a spanwise line.
Calculate the elliptical area for
the forward portion and the elliptical area for the rearward portion and add
these areas together. Divide the result in half to find the
actual area.
The other option is to
draw the best fitting trapezoidal sections inside the ellipse, add all
their areas together and then make an attempt at counting how many
square inches did not get included.
This should get you close enough for practical purposes although the
figure should be as exact as possible if you plan to release plans or a
kit.






Back to
Formulas
Airfield Models Home 


Copyright © 2003 Paul K.
Johnson 
