Can someone tell me the proper way and or formula for calculating the area of an elipticaly shaped wing???? Thanks
HOW DO YOU ....
Stuka Stunt Main Forum · 14 of 14 known posts recovered
Pat Mackenzie · Jan 18, 2004 05:12 PM
#1 source (pi*span*root chord)/4
Pat MacKenzie
Pat MacKenzie
Steve Helmick · Jan 19, 2004 07:49 AM
#2 sourceIf you are designing a true eliptical wing, math works. However, if you are trying to measure a wing that somebody else designed, there may be some doubt as to whether it is a true elipse. For that case, or any other really strange shape, you might cut it out of butcher paper, wrapping paper, etc, & weigh it on a gram scale. Then, recut the same piece to a rectangular or tapered shape that you can easily measure and calculate the area. Reweigh, divide the weight by the area, and you get the grams/sq. inch. Divide the weight of the eliptical shape by this figure. The result will be the area. Steve
As suggested by Steve, there may be some question that the wing planform is a true ellipse. Another way to determine the area is to lay out on the plan (or a tracing of the planform) and draw in a trapezoid or series of trapazoids that can be fit inside the planform. Then you have spaces between the sides of the trapezoid and the curved planform of the wing. Draw in triangles to start filling these spaces until you have essentially filled in all of the spaces. When those triangles get very narrow and long, you can approximate the area that is left with another triangle. Then calculate and sum the areas of the trapezoids and triagles. This should get you within less than a 1% error of the total area.
Keith
Of course if you have Autocad, import the plan to ACAD, and use the area function to trace over the outline. Fast, accurate, and able to handle any shape. I suspect other CAD programs can do the same.
Larry Renger
think S.M.A.L.L.
There is a long and detailed discussion of this on the Aerodynamics fourm in RC Universe. I havn't' gone back and looked at it, but I think 85% of the base chord x span comes pretty close.
Jim Thomerson
Larry Cunningham · Jan 19, 2004 07:22 PM
#6 sourceThe correct equation is (Pi/4) * Root Chord * Total Span. I believe you'll find it correct even for compound elliptical shapes, where the leading edge and trailing edge are different ellipses. That's closer to 78.5% * Root Chord * Total Span..
[photo not recovered: 3e69bb3870f12ad5.jpg]
"The reason so little is done, is generally because so little is attempted." -Samuel Smiles
>The correct equation is (Pi/4) * Root Chord * Total Span. I
>believe you'll find it correct even for compound elliptical
>shapes, where the leading edge and trailing edge are
>different ellipses. That's closer to 78.5% * Root Chord *
>Total Span..
>
>[photo not recovered: 3e69bb3870f12ad5.jpg]
>believe you'll find it correct even for compound elliptical
>shapes, where the leading edge and trailing edge are
>different ellipses. That's closer to 78.5% * Root Chord *
>Total Span..
>
>[photo not recovered: 3e69bb3870f12ad5.jpg]
As has been mentioned before, if the planform is a true ellipse the equation is as you and others have submitted. That is the same equation for a circle: (pi/4) * "width" * "height" of the circle where the width and height are equal to the diameter of the circle which are the same as the root chord and total span of a circular flying saucer.
Keith
BillLee20018 · Jan 19, 2004 09:03 PM
#8 sourceLAST EDITED ON Jan-19-04 AT 09:13 PM (CDT)
>Can someone tell me the proper way and or formula for
>calculating the area of an elipticaly shaped wing????
>Thanks
>Can someone tell me the proper way and or formula for
>calculating the area of an elipticaly shaped wing????
>Thanks
Plot the planform on a piece of paper (i.e., the outline of the wing).
Approximate the outline by as many short (or long if it works) straight line segments. The closer the approximation, the better the answer.
Place an arbitrary x-y coordinate system (i.e., do this all on a big sheet of x-y graph paper).
Write down the x-y coordinates of the endpoints of every line segment.
Then the area will be very closely approximated by the formula:
A= 1/2 * {X1 (Yn - Y2) + X2 (Y1 - Y3) + . . . + Xn (Yn-1 - Y1)}
This is called "Area by Coordinates" and you can find a number of references to it in a Google search. It is a tool used commonly in surveying where the outlines of a plot of land are defined by straight line segments.
In 1990 at the CL World Champs in France, the French had a large digitizing table. To measure the wing area of the F2C models, they projected the outline onto the table and recorded the x-y values where the straight line portions of the wing changed. Then a simple program inside the digitizing computer calculated the wing area and allowed for a check on the minimum required area. Really a neat set up. Probably anal. 
And it worked just fine on everybody's models until they came to Timmy Gillott's: his were conventional models and their software was only prepared to measure a single wing! Much confusion and concern until I suggested that they do it twice, once for the wing and again for the stab/elevator, and add the two numbers with a paper and pencil! Great fun!
Well, you wanted to know!
Regards,
Bill Lee
>Can someone tell me the proper way and or formula for
>calculating the area of an elipticaly shaped wing????
>Thanks
>calculating the area of an elipticaly shaped wing????
>Thanks
I have a 1962 publication of Flying Models Magazine which gives the following formula:
Area of Elliptical wing = Length X width X .7854
I can't vouch for this but I suppose that someone who knew what they were doing devised it. Hope so anyway!!! I would hope the publication would not have printed it if not substatially correct.
Mel Peeples
>I have a 1962 publication of Flying Models Magazine which
>gives the following formula:
>
>Area of Elliptical wing = Length X width X .7854
>
>Mel Peeples
Just for informational purposes this same publication gives the following formula for a parabolic shaped wing:
Area = Length X width X .666
Same qualifications apply.
Mel Peeples
LAST EDITED ON Jan-20-04 AT 02:03 AM (CDT)
Deleted. I just repeated Serge calculation before I read his post.
Deleted. I just repeated Serge calculation before I read his post.
Keith
BillLee20018 · Jan 20, 2004 10:01 AM
#13 sourceAnd, of course, all the wonderful formulas are only worth anything if the wing is REALLY an elliptical planform and not just something that looks good.
As awful as it looks, that's why the "Area by Coordinates" is a valuable tool: it works for ANY planform, and is as accurate as you want to make it.
Bill