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 Multi-Wing 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.

• Calculating the Area of a True Ellipse
• Calculating the Area of a Shape that is not a True Ellipse

How to Plot the Outline of an Ellipse

If you want to plot an ellipse, then the formula is:

(x² ÷ a²) + (y² ÷ b²) = 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.

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Copyright © 2003 Paul K. Johnson