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CM, CMsub0, CMsub0.25 ad infinitum

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Norman

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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 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.
 
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Topaz

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I guess I'm a little confused about the terminology here. Cm0 is usually the airfoil's pitching moment coeff. at the zero lift angle, referenced to the aerodynamic center - or 0.25c, depending upon the airfoil designer. What's Cm0.25? The pitching moment coefficient at some "0.25" angle or lift coefficient, or is it simply another way of notating that the pitching moment coefficient is usually assumed to be around the quarter-chord point?

I've got a spreadsheet (attached*) that calculates the true aerodynamic center rather than the 0.25c 'assumption', but I suspect that may not be what you're looking for. I have a hard time comprehending how the very slight 'error' in the position of the aero center versus the 0.25c assumed position could generate an eight-fold change in your output number - I'm assuming that's geometric twist to trim since you're using Panknin's routine?

*This is an excerpt from the #7 spreadsheet in John Roncz's old "Designing Your Homebuilt" series of articles in Sport Aviation. All credit goes to him.
 

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Norman

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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 a fixed value of 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:nervous:


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


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


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.:think:


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.:emb:


So here's my conclusion (and I'm stick'n 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 :beer:, see attached spreadsheet.


I'm satisfied... for now


Just for fun I've included a comparison polar of the sections that Northrop used on these planes and the one I gave you the other day
 

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Norman

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*This is an excerpt from the #7 spreadsheet in John Roncz's old "Designing Your Homebuilt" series of articles in Sport Aviation. All credit goes to him.
Topaz, I downloaded that aerodynamic center calculator but all I got was what looked like results but no math.

I added formulas to mine 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. :) 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
 
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Topaz

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...So here's my conclusion (and I'm stick'n 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....
As far as I know, that's exactly the case, on both counts. The N-9M was definitely a demonstrator for the XB-35/YB-49 designs, and that's about the cruise altitudes they used back in the late-forties for design of new bombers.
 

Norman

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It works

The Reynolds number calculation is dead on at sea level now and within 3% of true up to 12,000ft. By 40,000 the error is up to 8%. Compared to the usual L*V*(some constant) form it's surprisingly accurate. But of course there are computer programs now that compute it EXACTLY although I fail to see the need to compute an approximation to a high degree of accuracy. Anyway if you want to follow my babes in the woods spreadsheet design proses it's at RCGroups. Why?:think: Because there are more of them than you
 
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Norman

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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 distance from the center of earth plus hight above sea level). Even though it's only a 7 ft difference 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.:tired:


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.



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

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Re: Flying wing spreadsheet

I've updated my flying wing spreadsheet (hopefully for the last time). I've checked to see that all the elements for the acceleration of gravity are in there and correct, apparently they are (the only thing I changed in that part is a more refined number "big G", it really doesn't affect "little g" much).

The one thing I did change from the version of a few days ago that's significant is the span efficiency correction factor. The old one worked ok as long as the taper ratio was ~0.25 but went all wonky at anything else, especially un-tapered 'wings. This one dose a better job but still gives stupid numbers if you put in really large numbers for static margin and the design CL combined with chambered airfoil. There's now a % next to the span efficiency as a sanity check. If that percentage is more than 30 there's something wrong.


Here's the workflow:

You type in the geometry of your flying wing and the speed and altitude you want data for. (that's 14 veriables)

So, what's it do?

First it converts your altitude to geopotential

then figures out the Reynolds numbers at the root and tip so you'll know how efficient the tip airfoil will be at that altitude and speed and you can calculate what the local CLmax will be so you can see if tip stall from low Re will be a problem.

Then it calculates lift based only on speed, density and area.

Then it estimates the non-lifting, pitch-trimming, area at the tip and subtracts that from the total area to estimate actual weight. <<< Doesn't even try to do this anymore, too many variables

Mach number is in there because it's a speed factor in airfoil Analysis programs like Xfoil.

[EDIT] BTW the spreadsheet is protected to prevent a formula from being accidentally overwritten. The password is "penguin" [/EDIT]

[EDIT 2] This .ZIP file contains separate metric and imperial versions [/EDIT 2]
 

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Topaz

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Re: Flying wing spreadsheet

I've updated my flying wing spreadsheet (hopefully for the last time). I've checked to see that all the elements for the acceleration of gravity are in there and correct, apparently they are (the only thing I changed in that part is a more refined number "big G", it really doesn't affect "little g" much)....
Wow. Sounds pretty impressive, Norman! I've downloaded it and will try and take a look over the next couple of days.
 

Norman

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Have fun, Mark--

I'm sure you realize it isn't intended to work for planke. In fact very small sweep angles+high CLd are one of the things that make it return stupid looking numbers. The Panknin formula had that problem even before I added my area adjustment so I don't take all the blame for that. Of course the solution is to design to the high speed end of the performance envelope and use the pitch trim to slow down (whether that be elevons or inboard elevators, or both).

ps if you happen to see where that high altitude discrepancy is coming from pleas don't hesitate to tell me.
 
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