# Airfoil Circumference and Area

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#### Aerowerx

##### Well-Known Member
I have created an Excel spread sheet for calculating the circumference and sectional area of an airfoil.

It is useful for getting a reasonable estimate of the surface area and volume of the wing. From these you can make a reasonable first estimate of the weight of the wing.

The airfoil data is entered in the first two columns (max 140 data points) in the DAT file format. Then enter the desired chord length (in feet, inches, meters, parsecs, etc) and the chord length of the D-tube section (as a fraction of the total chord). The circumference is given in the same units, and the area in the units squared.

I am quite tired :tired:as I type this, and my brain is too fuzzy to give more detailed instructions. If you have any questions, please ask and I will try to answer when I am more awake.

View attachment Airfoil Calculations.xls

#### pictsidhe

##### Well-Known Member
You read my mind! I was going to add an aerofoil area calculator to my spreadsheet tomorrow!
My wing warping scheme means I've been maximising lift to aerofoil area.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
I have created an Excel spread sheet for calculating the circumference and sectional area of an airfoil.

It is useful for getting a reasonable estimate of the surface area and volume of the wing. From these you can make a reasonable first estimate of the weight of the wing.

The airfoil data is entered in the first two columns (max 140 data points) in the DAT file format. Then enter the desired chord length (in feet, inches, meters, parsecs, etc) and the chord length of the D-tube section (as a fraction of the total chord). The circumference is given in the same units, and the area in the units squared.

I am quite tired :tired:as I type this, and my brain is too fuzzy to give more detailed instructions. If you have any questions, please ask and I will try to answer when I am more awake.

View attachment 61769
You can also calculate EI on both axes and GJ, and then be able to size the spar.... Cool.

#### Aerowerx

##### Well-Known Member
You can also calculate EI on both axes and GJ, and then be able to size the spar.... Cool.
Please explain. I do not see how there is enough information in the spreadsheet to size the spar.

#### plncraze

##### Well-Known Member
HBA Supporter
This book has a few pages devoted to what Billski is talking about http://www.flyingonyourownwings.com/. As I understand wing design, and I am still learning, the leading edge (D-section) provides a great deal of the stiffness to the wing. The area of what ends up being the nose rib and the perimeter of this same section let you know how stiff your wing will be in torsion. EI is the stiffness of something so once you know what proportion of the stiffness the leading edge tube will provide you will know what is left for the spar to carry.

#### Aerowerx

##### Well-Known Member
This book has a few pages devoted to what Billski is talking about http://www.flyingonyourownwings.com/. As I understand wing design, and I am still learning, the leading edge (D-section) provides a great deal of the stiffness to the wing. The area of what ends up being the nose rib and the perimeter of this same section let you know how stiff your wing will be in torsion. EI is the stiffness of something so once you know what proportion of the stiffness the leading edge tube will provide you will know what is left for the spar to carry.

But there is nothing in the spreadsheet about material properties, so how do you know the stiffness?

And how do you get EI out of circumference and area?

#### Behemot_86

##### New Member
Greetings,

I would like to propose a reviewed version of the tool. It seems that the formula used to compute the airfoil area is not correct (or I may have misinterpreted the definition of airfoil area...). The formula, in fact, returns areas that are too small.

Essentially you must change the formula of column D with this one:

=IF(D5<>"";ABS(D5-D4)*AVERAGE(ABS(E5);ABS(E4));"")

Which is the trapezoidal area calculation: (x2 - x1)*(y2+y1)/2

Hope it could help ;-)

#### BJC

##### Well-Known Member
HBA Supporter
The old-timers (they know who they are) used a mechanical integrator to measure the enclosed area of an airfoil.

BJC

#### Aerowerx

##### Well-Known Member
Greetings,

I would like to propose a reviewed version of the tool. It seems that the formula used to compute the airfoil area is not correct (or I may have misinterpreted the definition of airfoil area...). The formula, in fact, returns areas that are too small.

Essentially you must change the formula of column D with this one:

=IF(D5<>"";ABS(D5-D4)*AVERAGE(ABS(E5);ABS(E4));"")

Which is the trapezoidal area calculation: (x2 - x1)*(y2+y1)/2

Hope it could help ;-)
That was 4 years ago, but let me wake up those dormant brain cells....

Column D is the raw input data. There is no formula there. So I assume that is a typo in your post? The formula you are referring to is in column G.

I can see where your change might give more accurate results in some cases. But keep in mind that the values for Y can be either positive or negative and the formula has to handle the case of one Y being positive and the other negative. Your proposed change I think will give an error by taking the absolute value of each Y individually.

Keep in mind that my original post said it gives a "reasonable estimate" of the area and circumference. In other words, I acknowledge that it is not exact.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
Please explain. I do not see how there is enough information in the spreadsheet to size the spar.
No, but the calculation tool is now set up for a straightforward expansion to do I and J of the section, convert the section to a skin, compute volume of the skin, add E and G for each material and so on. The big step is getting it all started...

#### wsimpso1

##### Super Moderator
Staff member
Log Member
As I understand wing design, and I am still learning, the leading edge (D-section) provides a great deal of the stiffness to the wing.
The D-tube, when added as aircraft plywood, sheet metal, or composite, to a hollow wing of spars and ribs, does a couple things:
• It allows a fabric covering to wrap around the leading edge with a decent approximation of the intended wing shape (even with false ribs it would never be very good) which is important to stall behavior;
• It adds a bunch of torsional stiffness and strength at about the lowest weight. Getting that much torsional stiffness and strength by other means gets difficult and heavy
The area of what ends up being the nose rib and the perimeter of this same section let you know how stiff your wing will be in torsion. EI is the stiffness of something so once you know what proportion of the stiffness the leading edge tube will provide you will know what is left for the spar to carry.
EI is bending stiffness with bending moment applied in a particular axis. Typically we are talking about bending around a horizontal line, as when lift pulls the wing tip up or down. If that is one axis, the other of interest is perpendicular to it, with bending around a vertical line, as when drag pulls the wingtip aft.

Adding a D-tube does add some EI, and may decrease the amount of main spar you need, but the D-tube is typically pretty low stiffness compared to the main spar.

GJ is torsional stiffness and the D-tube adds quite a bit to bare spars and ribs. Sheeting the entire wing, further increases both of the EI's and GJ. Structural full skins generally remove the need for the aft strut and can allow the drag spar to be much lighter as well. Many single strut structural skinned wing examples exist, including C150's-C182's (aluminum skin and structure), Wittman Tailwind (wooden wing and stucture), and others.

Billski

#### Aerowerx

##### Well-Known Member
Interesting that I got a response from a post I made 4 years ago.

#### plncraze

##### Well-Known Member
HBA Supporter
It took a lot of thought. LOL

#### wsimpso1

##### Super Moderator
Staff member
Log Member
It took a lot of thought. LOL
I just never came back to the thread back when, and then it became active again, and I took another look.

#### atypicalguy

##### Active Member
HBA Supporter
Interesting that I got a response from a post I made 4 years ago.
Pretty timeless topic. Forums are really cool for that - the people that most need the information don't always know they need it when you post it. Sometimes not for years.

#### Retiree

##### Well-Known Member
Greetings,

Which is the trapezoidal area calculation: (x2 - x1)*(y2+y1)/2

Hope it could help ;-)
This is the correct formula to calculate the approximate area under the airfoil coordinates, not the formula in the spreadsheet. The formula should be in column G.

#### Aerowerx

##### Well-Known Member
This is the correct formula to calculate the approximate area under the airfoil coordinates, not the formula in the spreadsheet. The formula should be in column G.
See post #9 for more problems with the revised formula.

#### rtfm

##### Well-Known Member
Hi,
Grab a copy of DevWing CAM (free, except you can't save, I think). Work through the various pages, until you get this sort of thing:

#### Retiree

##### Well-Known Member
Hi,
Grab a copy of DevWing CAM (free, except you can't save, I think). Work through the various pages, until you get this sort of thing:
Hi rtfm,
Do you know how the weight is calculated in the program?
Also, how are the areas calculated, planform or surface?
Thanks, Doug

Last edited:

#### rtfm

##### Well-Known Member
Every part of the wing is specified on the specification pages. At the end, there is an option to calculate the area, volume and weight of the wing. Each element is listed any then tell the app what material is used for each element from their comprehensive database. If your chosen material isn't there, you can add it.