Lift Curve Slope 1

[Chickenhawk]

I'm designing, building, a strange low/slow single place fun cow pasture airplane of dubious proportions with dubious design skills. It is a wire braced triplane similar in configuration to the old Sopwith tripe of WWI.

An old NACA report by Munk has the Cl and Cd plots for a specific Gap/Chord ratio. I calculated that for my Gap/Chord ratio, Munk's data had lift curve slopes of .070 Cl/deg top wing, .050 mid wing and .049 bottom wing. The NACA tests were based on an individual wing aspect ratio of 6. Mine is 8.0 (small chord of 32&quot. I have arbitrarily adjusted Munk's lift curve slopes by multiplying them by the ratio of 0.079/.075 (or theoretical slopes for rectangular single wing of Aspect ratio of 8/Aspect ratio of 6) for a design lift curve slope of 0.073 top,.053 mid, and .052 bottom. I did this because I could find no better way. Triplane design references are pretty scarce.

Questions..1) Is this reasonable?
2) Is my assumption based on the early tests that airfoil profile shape should have little effect on the lift curve slopes other than where 0 lift happens correct?
3) Can I leave my Cd values attached to the AOA. I.E. if AOA changes from 5° to 10° (from sectional data to real wing data) for a Cl of 1.00, the sectional Cd for 10° would apply at a Cl of 1.00?

Any ideas would be appreciated. Surely someone out there can appreciate the bizarre enough to give this old Agricultural Engineer and first time airplane designer some pointers. I gave up on my last CG question. Must have gone completely over all yall's heads.

 

[buzz41]

It looks and feels to me that the ag engineer has things just about right.

I would say that data at AR = 6 can be extrapolated and used at AR = 8 with considerable confidence. Things are getting pretty linear at AR = 6 and higher, though I know that the wing as a group will operate down around AR =4.

Each foil of the triplane operates in the CURVED field of the others, so an assumptions that foil data will fit perfectly is not expected. But, guesstimating again, I expect the practical differences are quite small. I would make the same assumptions you have. If there is some blunder, you have company.

The small cord and lower reynolds numbers should invite some extra attention to this area. Check it out at those lower numbers to make sure all is well with the section used at these numbers and a bit lower and that you have what you need.

So, for the questions. I will say:

1) Yes
2) Yes
3) yes

Good luck, and make sure you watch out for that silo!

 

[Chickenhawk]

Thanks, Buzz, for the reply. I'm using a low RN of 700,000 and have ran the airfoil through a polar program I found and then made some comparisons to old NACA tests. The airfoil is very similar to the NACA 6412. I'm in the midst now of wrassling with induced drag concepts, trying to take old biplane formulas and make triplane formulas. Ever once in a while I have to go sit on the porch and eat a seedless grape to relieve the brain pressure. I get to wondering if I'm complicating things too much.
I hate to impose on ya'll too much but I've discovered/derived some hairy formulas for induced drag. They are based on some old biplane stuff and an experiment where I tied three chickens together and tossed them off the outhouse and measured the forward distance and rate of descent. I'd appreciate a knowledgable peer review...(said Orville, as he gazed across the sand flat..)

Lu=upper wing lift
Lm=middle wing lift
Lb=lower wing lift
Di(Top)=induced drag (Top Wing)
0.60=gap/span constant for gap span=.125
0.43=gap/span constant for gap/span=.250
b=span

Di(Top)=
((Lu squared) +(Lu*Lm*0.6)+(Lu*Lb*0.43))/(Pi*Q*bsquared)
Di(Mid)=
((Lm squared)+(Lm*Lu*0.6)+(Lm*Lb*0.6))/(@PI*Q*bsquared)
Di(Bot)=
((Lb squared)+(Lm*Lb*0.6)+(Lu*Lb*0.43))/(@PI*Q*bsquared)
0.60=gap/span constant for gap span=.125
0.43=gap/span constant for gap/span=.250
Reckon these will give me a reasonable drag estimate?

 

[radomir]

Red Baron I wish you all the best,

Snoopy

 

[Rovie]

I can help you with formulas to calculate lift curve slope and induced drag of your configuration.
I would recommend taking a physics approach to calculating each surfaces induced flow field to get a better idea of what each wing is contributing.
You will see large amounts of induced drag even at an AR of 8.

 

[Chickenhawk]

Hello rovie..any help with suggested formulas would be appreciated. davidl@brazosnet.com