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Design => Engineering board => Topic started by: Motorman on June 21, 2015, 11:46:58 PM
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How do you calculate wing tip area? I have a wing with a 10" chord and the tips are 2" wide with the classic tear drop shape. Is there a way to figure the area of the tip? I have drawn it on 1" grid paper and cut and paste the partial squares 8)
MM
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I'd guess a little over half of the "box" dimensions.
But does it really matter that much?
Even if you are off a bit, it still amounts to only 10-20 square inches.
Tip shape and efficiency probably is more important than the area, I would guess.
R,
Chris
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4 x 10 x .7854 = 31.4 sq ins. This will be pretty close. If the shape were pure ellipse it would be exact. It is 4 x 10 as you have two of them.
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But does it really matter that much?
It does if the event requires a certain wing area.
That elliptical calc is dang close as one end is fatter and the other end is thinner. I got 16 each with my guesstimate technique.
MM
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Cut the outline of the tip out of a piece of cardboard and weigh it. Then cut out a known area of the same cardboard and weigh it also. Compare the weights and you have the area.
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Cut the outline of the tip out of a piece of cardboard and weigh it. Then cut out a known area of the same cardboard and weigh it also. Compare the weights and you have the area.
Awesome idea, but I would cut out the rectangle first, weigh it, then cut out the tip shape and weigh that, then use the ratio.
That should reduce any differences in cardboard densities.
Great idea!
R,
Chris
PS. Thanks MM for explaining why it mattered.
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How do you calculate wing tip area? I have a wing with a 10" chord and the tips are 2" wide with the classic tear drop shape. Is there a way to figure the area of the tip? I have drawn it on 1" grid paper and cut and paste the partial squares 8)
MM
I would be laying a length of string around the perimeter of the irregular shape, measuring the distance and then making the closest known regular shape out of that length - it won't be dead accurate as the more irregular it is the less area it contains but it should be workably close.
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I would be laying a length of string around the perimeter of the irregular shape, measuring the distance and then making the closest known regular shape out of that length - it won't be dead accurate as the more irregular it is the less area it contains but it should be workably close.
Trace around it with a plane polar planimiter.
Brett
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Trace around it with a plane polar planimiter.
Brett
Oh you mean a Plane Polar Planimeter!
Just googled it and never knew it existed ..... but I do now!
(Thanks for the accompanying maths.)
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Will they be teching with a planimeter at the nats?
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Will they be teching with a planimeter at the nats?
No, they probably won't even measure it, and if so, they will eyeball the curved parts, I expect.
Brett
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The planimeter is one of those wonderful inventions that simplified building complex shapes to a given area.
I used one back in the 1960's. Most things in life are done the hard way. Coming up with a simpler way that is accurate is the hard part.
Many moons ago I worked for the Friden company. Friden was the only company to ever go into production of a mechanical SQUARE ROOT MACHINE. I was one of less than 100 techs who were trained to repair them. Carl Friden was a brilliant engineer and though up a simpler way to do square root on a 10 key mechanical calculator. It used the odd integer method. If you knew all the machines that came before it they would send you to school for three months just for this one machine that had 10,000 moving parts. It was faster than all the early electronic square root machines,3-8 seconds to go 10 places. They were very reliable and would run for years with out service. I had the largest number of units in my territory of any place in the country. IBM-NASA,Cornell University,Link Aviation-NASA,GE-NASA. The funny part of all this is I was never very good at math. I have dyslexia so I need to see things as objects in my head to understand them. This gave me a great advantage on mechanical machines.
Life can be simple if you get rid of all the clutter.
Ed
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Here are a couple of other ways to get the area of something like a wing tip. These methods will get you probably within +/- 1 sq in or so. Some may have already been mentioned.
Make a full size outline of the wing tip shape. Depending on the shape, a triangle can be drawn inside that shape, like the base would be at the chord line where the curved tip shape starts and the legs of the triangle would go to the very end of the tip. Measure that triangle and calculate its area (1/2 the base times its height). Then you can draw two more triangles one at the LE and the other at the TE, using the two lines from your first triangle as their bases. These will probably be very slender triangles (long base and relatively short height). Calculate the areas. Then depending on how much accuracy you want, continue to draw successively smaller triangles until you have the entire tip described by triangles which will give you a fairly accurate area of that tip.
Another way and you have touched on this is to draw the full size shape of the tip on a paper that has a ruled grid showing 1" squares which is further subdivided into 1/4" or 1/8" or even 1/10" squares. (You can get these sheets in pads from drafting or art stores.) Then count the full one inch squares, and then go on and count the remaining smaller squares. Keep track of the smaller squares that are divided by tip outline to be only a fraction of a full square and add the ones that are say 1/2 inside the tip outline, or 1/3 inside the tip outline, and so on. You can get a total area measurement that will be within a fraction of a square inch of being accurate.
Either process does not take much time.
A planimeter works great if you have access to one.
Keith
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If you want to be awkward or scientific, S?P a PLANIMETER will do it for you .
(https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcRzaJlU2UadRJ4tjZO_nX7fO3vJBRomJviNeQk0hWxNHes5agvs)
We still have the one that was used for the Education Boards Site Level planing in the 50s . You just run it round the perimeter
and the little wheels do all the calculus .
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If it's still any help, almost all airfoil sections we use are about 60% of the area of a box that fits around them. So multiply the thickness by the chord by 0.6, and then divide by two for the area of a classic wing tip.
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Will they be teching with a planimeter at the nats?
You'll be going to the NATs? Wow! Great!
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FARO arm would get you within about .050" in^2. Scan it with the laser and import the point cloud into ProE, from there it's a piece of cake! n~
You can draw it in AutoCad and compute the area too.
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Intregrate it piecewise!
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Intregrate it piecewise!
That's what Kieth said -- only he didn't use scary words like "integrate".