Cm, CMsub0, CMsub0.25 ad infinitum

[nmasters]

I've been working on a spreadsheet to calculate some numbers that I'm interested in. One formula I'm using requires CM and assumes that it will be CMsub0.25

This is fine as long as I'm using section data generated by the Eppler code. Since I don't have access to much of that I'd like to include a conversion factor so the spreadsheet can work with data from a variety of sources. Anyone know what such a conversion formula might look like?

I've attached the spreadsheet with the example data from the B² web site where I got that part of the formula. If I used this as the test data I would not have noticed the error. Fortunately I used the N-9M and section data that was generated by Xfoil/profili. Using that data the twist prediction was off by a factor of 8.

--Norm

[HerkS]

Norm, The N9M must have had a symmetrical airfoil - I think Jack Northrop was fixated on symmetrical airfoils for his flying wings. That would have a CM of about zero wouldn't it? Am I missing something????

[nmasters]

Yep, they were symmetrical and really thick (see attachment). Cm0=0 as you'd expect. I've been using data from two dimensioned drawings and Charles Tucker's description of the stall tests in “Northrop Flying Wings”. The drawing shows the mean chord to be 110” and the AC at 30%. Tucker mentions that they usually flew the YB-49 at 24% so I put the SM at 6% in the spreadsheet. Originally my weight calculation used 0.00238 for density. Now there's a table to pick density and I found a formula to calculate it so a future version will have an input cell for altitude :cool: . So anyway the first time I ran this spreadsheet I couldn't get a mix of inputs that would produce 5,800 lb of lift with 4 degrees of twist. The only way the get 58 hundred pounds of lift with that static margin was to set the CL at 0.1 but then the twist came out 0.51 degrees. To get the target twist required CL=0.4 but then the lift was several times the weight of the aircraft. It looks like I made four errors.

The first was using a constant for density. Airplanes don't fly at sea level. :p

The second one was a typo in the twist calculation that caused it to come out half of what it should be.

The third one was not realizing that the design was actually for a 100,000 lb high altitude bomber, not a 5,800 lb sport plane that barely had enough power to get over the Sierra Nevada.

The forth was Panicking and looking for some esoteric problem that probably doesn't exist anymore, if it was ever anything more than a notation difference for identical numbers. Then bleating my distress over trifles to the entire world. :o

So here's my conclusion (and I'm stickn' to it, unless somebody tells me otherwise):
The N-9M was a scale model of a long range bomber that would have cruised between 30,000 and 40,000 ft. Those airfoil sections' low drag bucket extended up to CL ~ 0.5. So I set the altitude to ~40,000ft and the design CL to 0.425 and the results shake out to be pretty close to the real plane.

--Norm... satisfied, for now

PS the other section in the comparison polar is one of mine. It's just for reference.

[nmasters]

I added formulas so now it has cells to input altitude and temperature so the Reynolds number and lift are more accurate. Although the temp calculation only works in the troposphere and the lift calculator still doesn't account for span. I also added an altitude corrected Mach number calculator, but it doesn't account for temperature so it'll be a bit off on hot days :D

-- Norm, a bit more satisfied

[HerkS]

Norm -- neat project -- What prompted you to undertake it?

[nmasters]

Why?... Well I guess the immediate reason for this spreadsheet is that a couple of people on mailing lists I read have been asking questions that suggest they're going to need this kind of information. One has drawings for a Mitchel U-2 that he plans to use as a jumping off point to a new design. The other restored the Horten H-1b to flying condition last summer and now wants to design his own flying wing. There are videos of him flying the H-1b on youtube.

[chispas2]

Hi, Norm.

I too am on a mailing list of flying wings and build some small RC flying wings of my own design:
http://fotos.sapo.pt/chispas/playview/4
videos on youtube: http://www.youtube.com/watch?v=boCL99MrQwc
and http://www.youtube.com/watch?v=S1SY7iCpCyo

Thanks for your efforts and work on this spreadsheet.
It will going to help me in designing my next ones :)

Happy New Year
Paulo "Chispas"

[nmasters]

Beautiful flight, Paulo--

I love those delicate little planes but I'm such a clumsy old bull that I don't dare touch them. It looks like you don't need much help designing your wings.

--Norm

[chispas2]

Hi, Norm.

Thanks for your kind words :)
I have got into the indoor scene about two years ago but was lacking a form to calculate the Reynolds number for my flying wings in order to achieve a slower flight, like my other indoor planes do.

Thanks again, Norm.
Paulo "Chispas"

[nmasters]

Hi, Chispas--

Yeah, that pesky Mr. Reynolds :) I tried to get the best formula I could find but it still comes out a bit different than this one on the NASA K-12 site: http://www.grc.nasa.gov/WWW/K-12/airplane/airsim.html

I'll see what I can change to make it more accurate. I also want to add a correction for span efficiency but I haven't figured out how to make it versatile. I may just stick a crude factor in.

--Norm

[HerkS]

Hi Norm

I did a little spreadsheet for myself some time ago.

I'm not sure that it's extremely accurate but it is ballpark I think.

[nmasters]

Thanks, Herk--

I'm on a search right not for why the formulas I pieced together from books and other people's spreadsheets are not matching the above NASA K-12 site or the one in your prop calculator. Right now I'm thinking my viscosity constant ma need to either be changed or replaced with a formula that adjusts it according to temperature like the density dose.

Nothing that solves that problem so far but I did find a neat standard atmosphere calculator here: www.people.virginia.edu/~rjr/modules/xls

--Norm

[HerkS]

Hi Norm, This is good, when you reach your conclusions, please let us know.

RN is a pretty simple equation, but keeping the dimensions consistent; and finding a consistent source for the viscosity and density parameters can be challenging.

[HerkS]

I don't know if this will be of any help to you, but it's what I use.

[nmasters]

Thanks, Herk--

I'll look at that later, I have to go out and act like a grownup for a few days. :( :confused:

As it is right now my spreadsheet seems to be starting out about 1,000 ft high with an error that increases by ~ 2/3 per 1,000 ft. Not really bad below 12,000 ft but at 40,000 it kind of throws off the lift prediction.

--Norm

[nmasters]

Found a neat atmospheric properties calculator:
http://www.aerospaceweb.org/design/scripts/atmosphere/
Looks like my equation for density is over predicting. Viscosity is supposed to be negligible but I'll check this evening. If it's significant I'm not sure how to work it in as a variable. I've already got the lapse rate in there for the pressure variation so once I know how viscosity of air varies with temperature it should be easy, or at least simple (surprising how they're not the same).

Well lunch is over. Back to the act

[nmasters]

Ok, this is it--

Now it calculates Reynolds number with an error of less than 3% up to 12,000 ft then the error increases to 8% at 40,000 ft. Oh well when Re>8,000,000 what's 700,000 ;)

Anyway it looked like the only really accurate way to get the viscosity variation with altitude would have been to use Sutherland's formula and that would have been more work than all the rest of this little spreadsheet, if I could have figured it out at all. So I dissected the equation that dose the same thing for density and threw out all the stuff that wasn't relevant to viscosity. Whad'ya know... it sort of worked :D

I also want to put a correction into the lift equation for span efficiency but that could also be pretty complex to do accurately. I will probably end up doing what Curtis dose, just to subtract 30% from the lift estimate. Actually though that's a bit too conservative. That number is 30% of the span not the area. I need to brush up on my geometry and figure out how to take 30% off of the skinny end of a trapezoid.

--Norm

[nmasters]

BTW I protected that spreadsheet so that users couldn't accidentally wipe out a formula not to keep anything to my self. anybody who wants to examine the math to make changes or reuse some of it is certainly welcome to. The password is "penguin" same as the file.

--Norm

[Brandano]

Maybe a silly idea, since the error is so small, but perhaps you could just work out viscosity values at 1000 feet intervals using a table of values and interpolating linearly for the values in between? Well, I'd use 100-200 meter steps, but just because I am very fond of the SI system

[nmasters]

Maybe a silly idea, since the error is so small, but perhaps you could just work out viscosity values at 1000 feet intervals using a table of values and interpolating linearly for the values in between?
That's what Herk did in his propeller and speed spreadsheet and I started out with something similar but I didn't want a table. I wanted to be able to just type in the physical characteristics of the airplane and the flight regime and get out a certain set of numbers that would tell me if the plane is going to work. So far it's looking good but there are a few more numbers I'd like to get out

Well, I'd use 100-200 meter steps, but just because I am very fond of the SI system

I knew somebody would bring up the fact that I'm working with an archaic system of measurements. :rolleyes: I started off with a formula that uses degrees Rankine for the lapse rate and then was stuck with imperial units and didn't think to change until it was to late in my mind. As far as the accuracy thing goes. As it's applied to wings Re is an approximation anyway. If you set altitude to "0" my spreadsheet produces the same Reynolds number as the usual L*V*(some constant) within 0.01% depending on which book you got the constant (kinematic viscosity) from. The 3% error is hardly noticeable. For my second test case I used the XB-35 which was 91,000 pounds empty. The test pilot who survived the aft CG stall test said it was below 90 knots just before it went over backward so I set the speed=100 mph, and altitude= 0 and CL=0.9 to see if I'm getting enough lift for takeoff and viola it says 92,000 lb. So far so good. Although if if someone shows me a more accurate equation I'll try to use it.

--Norm

[HerkS]

Norm - RN

I think you are quite correct when you say that RN (as we use it anyway) is an approximation.

None of the systems of RN calculation that I've seen take into account the nature of the surface of the L component in the equations. As in -- are the surfaces curved or wavy, and what is the surface roughness like? Since much of what RN is about has to do with the transition of the flow from laminar to turbulent, these are important factors.

I'm sure that someone has developed a more complex way to calculate an "Effective Reynolds Number," but I've never taken time to look for it. What you've done does seem reasonably precise and quite practical actually. Congratulations

[nmasters]

None of the systems of RN calculation that I've seen take into account the nature of the surface of the L component in the equations. As in -- are the surfaces curved or wavy, and what is the surface roughness like? Since much of what RN is about has to do with the transition of the flow from laminar to turbulent, these are important factors.

I was actualy thinking of the way we use the chord for length. If you wanted to b anal retentive about accuracy the proper dimension is actual surface length from the leading edge stagnation point to the trailing edge. On the top that's longer than the chord. For instance I just now measured a Clark y. Starting from the LE stagnation point (which is about 30 degrees down from the center of the LE radius at the stall AoA) the top skin is 1.033 X the chord. So the chord is a reasonable approximation

[nmasters]

I don't know if this will be of any help to you, but it's what I use.
Here's that table already in ASCII format. Could save some lookup time and typing. Not to mention cutting down on transcription errors.

--Norm

[nmasters]

Oops :p :o ... Here's the link: http://www.pdas.com/e2.htm

[HerkS]

Norm - OOHh that is very handy -- thanks.

[nmasters]

Well... I thought I found the source of that small error that starts out zero at sea level and increases with altitude but it looks like I was wrong again. I thought maybe I was using a simplified version of geopotential altitude that doesn't account for the distance from the center of the Earth. So I checked my density formula includes

acceleration of gravity / the lapse rate * the gas constant

so I guess that's factoring in the distance from the center of the Earth. Why oh why did I go with geopotential altitude? Maybe I should factor in humidity or possibly a conversion formula for the altitude input since people think in terms of geometric altitude and the formula uses geopotential that may be all it is.

It's all explained on this page: Air Density and Density Altitude Calculations (http://wahiduddin.net/calc/density_altitude.htm) under the heading "Different Flavors of Altitude"

--Norm

[nmasters]

For anyone who may be interested I've added 2 corrections to my flying wing spreadsheet.

First I added a formula to the altitude that takes the input and converts it to geopotential (basically the average radius of earth plus hight above sea level). Even though it's only 7 ft at 12,000 feet it has reduced the error at 12,000 ft from the previous 3% to less than 1%. However the error still grows with altitude so something could still stand to be tweaked. My first guess is that the geopotentail correction should be working on the acceleration of gravity instead of the actual altitude but for now I'm satisfied that <1% is close enough.

The other thing is an approximate correction for span efficiency. Basically it lops off about 30% of the span at the skinny end of the wing (for the test case N-9M that's a 23% area reduction). 30% is pessimistic for most 'wings so I have tried to make it sensitive to the aspect ratio and design CL.

So far I have only tested it with the N-9M. I'll check it against other data sets as I find them. If anybody reading this could fill in column C with their airplane's data and send it back to me I'd appreciate it.

--Norm

Oh yeah... if you find it useful or enlightening, you're welcome

[chispas2]

Hi, Norman.

I downloaded your spreadsheet, thanks :) and inserted the numbers of my indoor flying wing.

It is good to know that i was not very far on the washout, i use 0,5 more degrees, and to know the Re numbers for my designs.
I dont remember the Moment coefficient at zero lift or the Angle of attack for zero lift of airfoil used, HS 520 a root and NACA0009 at tip.

I saved the spreadsheet and here it is.

Thank for your work.
Paulo "Chispas"

[nmasters]

Thanks, Chispas--

Is your plane 4.73 ounces?

Hmmm most of the HS sections aren't in the UIUC database. But I did find them here (http://tracfoil.free.fr/airfoils/h.htm) I ran the HS 520 through Profili at Re=100,000. The zero lift angle is -2.2 and CM0 is -0.04

it's AoA for best lift to drag is 7 degrees and it is efficient up to a cl of 0.9

There's a separation bubble that is probably responsible for some of the pitching moment. If you're wing is smooth you might get better performance with a trip at 20% on top

--Norm

[nmasters]

Paulo--

I love this software :) This is a type 4 polar from Xfoil/Profili. Look at how much a trip strip at 20% reduces the pitching moment of both of the airfoils on your 'wing.

--Norm

[chispas2]

Hi, Norman.
Thanks, Chispas--

Is your plane 4.73 ounces?

Hmmm most of the HS sections aren't in the UIUC database. But I did find them here (http://tracfoil.free.fr/airfoils/h.htm) I ran the HS 520 through Profili at Re=100,000. The zero lift angle is -2.2 and CM0 is -0.04

it's AoA for best lift to drag is 7 degrees and it is efficient up to a cl of 0.9

There's a separation bubble that is probably responsible for some of the pitching moment. If you're wing is smooth you might get better performance with a trip at 20% on top

--Norm
After changing for a lighter Lipo the actual weight is 3,73 ounces.

My results show Re to be around 60.000 to 90.000 in order to fly slow on indoor.
I was suspicious about the best AoA to fly slow will be high, i was pitching up to get an higher Aoa and the wing was flying slower without signs of instability, you confirmed that, thanks.

About the trip a 20% cord, i have the principal spar around that place.
I suspect i get it right without knowing :)

Thanks for getting the numbers for my airfoils.
Paulo "Chispas"

[chispas2]

Hi, Norman.

About the HS 520 airfoil, i am working on a version of mine built from Depron of 6mm.
It will have the top part of the HS520 airfiol, 5% camber and a 7 inchs of chord the thickness will be 6mm, around 3%.
Just waiting to have some spare money to get the micro servos that will fit on that tickness, the Toki bio-metal.
Here is an early drawing.

Thanks again, Norm.
Paulo "Chispas"

[nmasters]

Paulo--

I haven't had any luck analyzing 3% sections with profili. When I try to get a pressure plot it flashes "NOT CONVERGED" a bunch of times then draws a plot with crazy spiky lines. But I do know this much about the pitching moment. The pitching moment is do to the curvature of the mean line, not the upper surface. So if pitching moment is important to your design (it is, right?) you should pick a thick airfoil that has the moment characteristics you want and use its mean line for your camber.

--Norm

[rpage53]

I managed to analyze some Depron sections in Profili but it took a lot of messing about. You need a lot of points at the leading edge and if you want a thick trailing edge, it helps to leave it open. You should also use a turbulent flow.
However, the results don't mean a heck of a lot and some Re converge but others don't.

Rick.

[chispas2]

Hi, Norm and Rick.

Thanks for your responses :)

I am aware of the problems with thin airfoil sections like the one i designed.
As i am not well versed on theory and analyses of aerodinamics predictions, dont have a formal education on the area, i tend to test my ideas on the "real wolrd". From there i proceed to prediction programs and spreadsheets to develop and improve the concept.

This airfoil comes from some tests with a Walkalong glider that went througt some modifications.
With the information that it works i compared its section with existing airfoils and the result is the one i presented.
I hope to get a new flying wing with this airfoil, and low wheigt and low speed too, to fly on indoors this season.

Thanks again.
Chispas

[nmasters]

As i am not well versed on theory and analyses of aerodinamics predictions, dont have a formal education on the area, i tend to test my ideas on the "real world". From there i proceed to prediction programs and spreadsheets to develop and improve the concept.
Well it is a Hobby after all. The main thing is that you enjoy the proses. I used to enjoy building too. There's a lot of satisfaction in taking a pile of wood and a bottle of glue and turning it into something magical.

BTW I've been fiddling with the span efficiency correction factor because I wasn't satisfied with the way it scaled for taper and aspect ratio (it didn't work at all for anything much different than t/r=0.25). This one works better although you can get out of bounds with certain extreme combinations. For your plane it predicts that its ideal weight is 7 grams heavier than the old formula. Oh yeah, speaking of grams, I added cells to convert pounds to onces and grams because most people who might use this aren't going to build a 6,000 lb airplane. And now there's a percentage by the span adjustment as kind of a sanity check. If it's more than 36% check the design CL and static margin, or just ignore it :D


--Norm

[chispas2]

Hi, Norm.

Thanks for the new spreadsheet.
It have the numbers of my indoor flying wing and the wheigt too.
Now i understand why i have to chose a more capable of wheigt lifting airfoil or build a lighter wing :)

Your spreadsheet is going to be very useful on my next flying wing as it can predict very acurately what is going to happen. I introduced the numbers of others flying wings i built before and the results are most correct.

Thanks again for your work.
Paulo "Chsiaps"

[nmasters]

I've added columns with metric conversions. I colored the metric columns dark turquoise and the imperial columns pale yellow. The conversion formulae are in the imperial columns. careful not to save it if you put real numbers in the yellow imperial column or it won't work for metric anymore

--Norm

[nmasters]

No real updates just removed my lame attempt at a span efficiency adjustment and replaced it with a note to get Andy Lennon's book.