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Old Nov 26, 2008, 11:31 PM
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Fredriksson's Avatar
United States, KY, Hopkinsville
Joined Feb 2008
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Wing Dihedral Table

The other day I was reading in the threads here at RCG and saw some posts concerning dihedral of model aircraft wings. Some people wanted distance out on wing to measure to level to get correct dihedral while others wanted the angle itself. So I thought I would try to find a way to help these people out. What I ended up with is a table that I attached in JPG format. The original document is an Excel spreadsheet. If anyone wants the document in its Excel format or a higher resolution JPG file, send me a message with your e-mail address and I can send either or both to you.

The document itself has a diagram below the table showing the 3 pieces of information - Length down the wing, Height of wing from level at that spot, and Angle of dihedral. The table shows lengths to be measured out on one wing across the top row. Down the left column are distances that the wing is above level at that length distance. All of the numbers in the body of the table are degrees of dihedral.

To use the table to convert length out the wing and height from level to dihedral angle, simply go across the top row to the length you need across the wing. Then follow the column down to the height from level in the left column. Where these 2 meet is the angle of dihedral. For example on a GWS slow stick some will say that when you hold one wing down on a table, the end of the other wing is 6 inches above the table. I know that the SS wing is 46.3 inches. Half of this, one side of the wing, is roughly 23 inches. Using the dihedral table and finding 23 on the top row you can follow that down to the 6 inches on the left column. The intersecting block shows 15.1 of dihedral.

You can use this chart the other way around too. You can follow the length out the wing column down to the angle you desire. Then follow that across to the left column and it will tell you the height of the wing from level for the angle. For example if you wanted that same SS wing to have 10 of dihedral you would just follow the 23 inch line down until you find the angle closest to 10. It just so happens that 10 is on the table. So from the 10 box follow that row across to the far left column and you will find that the height from level to get 10 of dihedral is 4 inches.

Finally, the distance numbers are just units. They can be inches, mm, cm, whatever you want as long as both the top row and the left column are the same units. Just move the decimal either direction as far as you want to make the chart work for you. Just remember that whatever you do across the top row has to be done to the left column in the same way. for example we could multiply each of the values on the top row to make them work better as millimeters. the numbers would be 200, 300, 400, etc. Then doing the same to the left column the numbers would be 25, 50, 75, 100, etc.

If you want to be more accurate you can do the math with any scientific calculator. To convert the length and height to an angle the formula is:

Arcsine (H/L) = Angle

Or, if you know the length and the desired angle and need the height the formula is:

Sine(Angle) x L = H

I hope this helps some of you.

Freddy
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Old Nov 27, 2008, 07:01 AM
Jack
USA, ME, Ellsworth
Joined May 2008
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That's a handy table to have. Thanks for posting it, Freddy.

Now we only have to resolve what people really mean when they describe a plane as having "x" degrees or inches of dihedral.

I always think of the height or angle as being the measurement that would be obtained with the plane in level flight. So, to me, a wing described as having 2" or dihedral would be 4" when looked it was up on the table above. And expressed as an angle, the dihedral would be half of the value seen in the table.

I wonder what the consensus is as far as most people thinking in terms of dihedral as being a total value or the amount that measured on each wing tip?

Jack
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Old Nov 27, 2008, 08:04 AM
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Very nice Freddy, thanks for sharing.

Happy Thanksgiving from Frankfort, KY.

Rick
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Old Nov 27, 2008, 08:08 AM
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Quote:
Originally Posted by jackerbes
That's a handy table to have. Thanks for posting it, Freddy.

Now we only have to resolve what people really mean when they describe a plane as having "x" degrees or inches of dihedral.

I always think of the height or angle as being the measurement that would be obtained with the plane in level flight. So, to me, a wing described as having 2" or dihedral would be 4" when looked it was up on the table above. And expressed as an angle, the dihedral would be half of the value seen in the table.

I wonder what the consensus is as far as most people thinking in terms of dihedral as being a total value or the amount that measured on each wing tip?

Jack

From Wikipedia:
Quote:
Dihedral is the upward angle from horizontal of the wings or tailplane of a fixed wing aircraft or the wing of a bird.
I think it is easier for most to measure from the table top to the wingtip. Most do not have a gauge to measure an angle accurately.

Freddy's table is very helpful figuring tip height for a specific wing design. I am thinking about a polyhedral wing with 12" outer sections set at 20 from the wing center section. Freddy's table tells the wing tip will be about 4 1/8" from the table.

Rick
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Old Nov 27, 2008, 12:47 PM
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United States, KY, Hopkinsville
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Quote:
Originally Posted by jackerbes
I wonder what the consensus is as far as most people thinking in terms of dihedral as being a total value or the amount that measured on each wing tip?

Jack
I was thinking of that when I posted and chose to show it as it was described in the thread that gave me the idea. In addition, often on a model dihedral is the difference between 2 flat wings joined in the middle and the original description works well for that.

Looking around on the web I have found that dihedral is given as the amount of angle for each wing with the fuselage level. There is also the consideration of wing tips with dihedral on level wings or even polyhedral where there is initial dihedral at the wing root and then wing tips with additional dihedral.

But that is not a problem. The chart still works. I have attached an additional diagram showing the above configurations with the fuselage level. Also, if the dihedral is given per wing, they can be added together for a total dihedral. So if a model with 2 flat wings calls for 8 of dihedral on each wing these can be added together for a total of 16 and then the chart used with a build configuration of laying one wing flat on the workbench and setting the other wing to 16. When the wings are finished and leveled on the plane there will be 8 of dihedral on each wing.

In reality, the chart just shows rise over distance. For any given rise of a line over a given distance there is an associated angle to the reference line. Normally in math the distance is measured on the reference line (the distance under the wing that follows the reference line). On my chart I made it to follow the object line (the solid wing itself). That is because it is easier to measure along a solid object than it is to measure into open space along an imaginary line.

Keep in mind that the formulas in the original post can be used for more accurate angles and distances. And you do not have to have a scientific calculator. Here is a link to a sine table that can be used. It can be used to find the sine of any angle for use in the formula where you know the desired angle and the length or can be used in reverse to find the angle when all you have is length and height.

I hope all this helps. I am a math nerd and this stuff is fun to me. But I am sure there are many more nerds out there that get into this stuff too. And perhaps some non-nerds that find this as an easy way to set dihedral on their models.

Freddy
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Old Nov 27, 2008, 01:10 PM
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I have been thinking about this as well and trying to use a formula to get the correct height rather than rely on my measurements of the the angle. This is exactly what I was looking for. Thanks!
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Old Nov 27, 2008, 06:29 PM
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Wow thanks, I just started building from plans and this helps so much for a late bloomer.
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Old Nov 29, 2008, 09:41 PM
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Freddy: Thank you for the table above, I need all the help I can get and I am sure all of us appreciate all the good tips shared by this "family".
Keith
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Old Nov 30, 2008, 06:17 AM
Jack
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Joined May 2008
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"..I am a math nerd and this stuff is fun to me..."

LOL! It is hard to get through life without math. I have always struggled with the theory and concepts but had to learn how to do it by rote when I was working as a machinist. I did not fully understand it all but I knew how to do it. Thank heavens for the hand held calculator!

When I was trying to figure out what amount of right thrust and down thrust I had a motor set to, I just went to this link:

http://www.carbidedepot.com/formulas-trigright.asp

and entered the thickness of the washer (.065") and the mounting hole spacing (.748") and was able to see that my side thrust angle was 4.966435329503548 degrees.

Of course I had to convert the metric spacing on the mounting holes to inches to get a common math base. But this handy little units converter got me through that nicely:

http://joshmadison.com/article/convert-for-windows

I have been using that piece of software for ten years of so, it is one of the all time great freewares as far as I am concerned. Thank you again, Josh Madison!

Jack
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Old Dec 01, 2008, 07:55 PM
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Fredriksson's Avatar
United States, KY, Hopkinsville
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Quote:
Originally Posted by jackerbes
"..I am a math nerd and this stuff is fun to me..."

LOL! It is hard to get through life without math. I have always struggled with the theory and concepts but had to learn how to do it by rote when I was working as a machinist. I did not fully understand it all but I knew how to do it. Thank heavens for the hand held calculator!

When I was trying to figure out what amount of right thrust and down thrust I had a motor set to, I just went to this link:

http://www.carbidedepot.com/formulas-trigright.asp

and entered the thickness of the washer (.065") and the mounting hole spacing (.748") and was able to see that my side thrust angle was 4.966435329503548 degrees.

Of course I had to convert the metric spacing on the mounting holes to inches to get a common math base. But this handy little units converter got me through that nicely:

http://joshmadison.com/article/convert-for-windows

I have been using that piece of software for ten years of so, it is one of the all time great freewares as far as I am concerned. Thank you again, Josh Madison!

Jack
Thanks Jack. That first link is really sweet. I bookmarked it for future use. And the conversion program is pretty nice. It is missing several different units of measure but has the most common ones. For conversions I use http://www.onlineconversion.com/. It has pretty much every unit of measure.

Freddy
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Old Dec 02, 2008, 12:44 PM
Jack
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That page has some seriously obscure conversions on it. I'll bet you could build Noah's Ark from the original specs with that...

One of the things I like about his app is that you just unzip it and run it, it does not need any dll's or installation or uninstallation. and I've never found a version of windows that it will not run on either. But I've not tried Vista yet...

And you can run multiple instances of Convert too, that is handy when your are going back and forth between two standards, you can just copy the output from one and past it into the other.

Jack
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Old Dec 02, 2008, 04:46 PM
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Laveen, AZ
Joined Sep 2007
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Quote:
Originally Posted by jackerbes
One of the things I like about his app is that you just unzip it and run it, it does not need any dll's or installation or uninstallation. and I've never found a version of windows that it will not run on either. But I've not tried Vista yet...
I've been using Josh Madison's Convert program for many years as well. And I can confirm that it does work on Windows Vista.

The table shown in the original post of this thread is the result of Trigonometry. If you've never taken Trigonometry before, you can skip the semester long community college course and read the following Wikipedia article:

http://en.wikipedia.org/wiki/Trigonometry

And if you've never heard it before, the secret to remembering Trig is "SOH CAH TOA" (pronounced like "Soak a toe -ah"). Which basically means:

Sine of an angle = Opposite / Hypotenuse
Cosine of an angle = Adjacent / Hypotenuse
Tangent of an angle = Opposite / Adjacent

- Matt
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Old Feb 17, 2014, 06:03 PM
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I use right angled triangle calculator:
http://www.hackmath.net/en/calculato...ulator?what=rt

In our case .065" x .748" calculate:

http://www.hackmath.net/en/calculato...8&submit=Solve

It's calculate: Angle ∠ A = α = 4.9664353295 = 457'59″
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Old Feb 18, 2014, 07:48 AM
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And we were certain there was no use for trig in high school......
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Old Feb 21, 2014, 07:48 PM
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United States, KY, Hopkinsville
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Quote:
Originally Posted by clipper453 View Post
And if you've never heard it before, the secret to remembering Trig is "SOH CAH TOA" (pronounced like "Soak a toe -ah"). Which basically means:

Sine of an angle = Opposite / Hypotenuse
Cosine of an angle = Adjacent / Hypotenuse
Tangent of an angle = Opposite / Adjacent

- Matt
Yup, I have called to SOH CAH TOA many times in my career in engineering. If you know the math, you do not need any tables.

Fredy
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