Help on lift and drag coeff calculations please....

[fpm]

Hi guys,
I hope you can help me, I've got 3 questions (a bit greedy I know...)

I'm researhing into simple wing designs, and have come up with the following queries, I intend to run
some CFD on some designs, but I want to have a feel for the numbers I should be seeing, rather than just blindly accepting the 'pretty pictures'!

1) When trying to numerically calculate lift coefficients for 3D wings, I've found 2 formulae:
Cl = Cl alpha*(alpha + alpha0)
and Cl = Cl alpha*(AR/AR+2)*(alpha + alpha0)
(alpha=angle of attack, alpha0 = angle of attack at zero lift, AR=aspect Ratio)
(I've calculated '3D' CL alpha from '2d' airfoil graphs using another formula, and the figures look good)

Now as the AR goes to infinity, the 2 agree (effectively an airfoil), but for 'sensible' AR, say around 4, the 2 formulae give very different results. Which is more correct? Is one more correct than the other?


2) Looking at these results:

http://www.aerospaceweb.org/question/airfoils/q0150b.shtml

and these:

http://www.aeronautics.nasa.gov/docs/rpt460/fig7.gif

They show very different behaviours after initial stall. Common sense tells me that a wing will give a lot of downforce when held at 45 deg to the airflow. OK, so its not 'proper' downforce, the wing has stalled and the drag is big, but it makes sense that it'll produce a big force in the y direction. However the second set of graphs don't seem to show this. Is it due to the difference in Re number?

3) When trying to calculate drag numbers, I've found the following:

Cd=CDmin + (Cl)^2/(pi*AR*e)

(Where e = efficiency factor, CDmin = a base level of (skin friction?) drag.

However, using this calc, gives me tiny Cd, say 0.05 for a wing at 10 deg AOA, say about 2.2kg.
But from literature, I've seen numbers from a similar sized wing give around 20kg, Cd about 0.5.
Why are my drag calculations so small? Is there a better formula?


I know there's a lot of questions in there, but if anyone could enlighten me on any of them, I'd be most grateful. As I said, I want to have a feel for the numbers before going to CFD.

Thanks muchly...
FP

 

[rb1957]

1) i think your 1st equation is for 2D airfoils (since it doesn't mention AR)

2) the 2nd grpah looks as though its interested only in practical AoA (ie airfoil performance up to stall) ... i don't see data going to 45deg; but as you say, at that high AoA it probably is behaving like a deflector, and the "lift" can probably be calculated from the momentum equation.

3) i think your number makes more sense that 0.5 ... that's huge. compare your calc with the data on your 2nd pic.

 

[fpm]

Thanks rb.
1) I thought this too, although the 1st equation contains the term 'Cl alpha' as the lift slope of a 3d wing, I thought maybe this was enough to take into account the 3d effects. That being so, the 2nd equation then takes into account AR in 2 places: in he equation itself, and in the 'Cl alpha' term...

2) OK (although I don't understand how you would differentiate the 2, when taking readings?!)

3) I don't know...I was beginning to think maybe the 0.05 is more of a '2D' figure?? But then it includes AR!? I don't have them to hand, but I'll dig up where I saw the bigger numbers mentioned. I think they were in a book on racecer aerodynamics. Do you know anywhere I can findany 3D drag figures, to see if I'm in the right ballpark?

Thanks,
FP

 

[rb1957]

"Cl alpha" is just the slope of the Cl curve

your Cd includes Cl (ie lift effects = induced drag = 3D)

 

[fpm]

As regards the drag figures, I've dug out the 2 books I was thinking of:
Competition car Aerodynamics: Simon McBeath.

He gives an example of a wing, 1.2m wide, giving a lift force of 769N, and 195N of drag. He doesn't give speed or chord, but guessing speed of 45m/sec, and chord of 0.3, that equates to a Cd of 0.44. This is backed up by graphs in the same book ('based on published data points of wing lift-to-drag ratio versus Cd') showing Cl vs Cd, which gives approximately:
Cl:1,Cd:0.1 Cl:2,Cd:0.6 Cl:3,Cd:1.1

These figures are about 10 times more than the Cd's that I've calculated...?!

However, In 'Race Car Aerodynamics': Joseph Katz,
He calculates the induced drag of a wing 0.5m chord, span of 2m, and gets 0.027, using the formula for Cd I gave in my first post.

Any idea where the disconnect might be?

Also, Katz gives the formula for the lift of a finite wing as Cl = Cl alpha(alpha+alpha0). He reasons that the 3D portion of the equation is taken up by the fact that the Cl alpha used, needs to be the lift slope of the finite wing, rather than an infinite airfoil. What do you make of it?

Thanks..
FP

 

[rb1957]

on your 1st point, i suspect that the airfoils are stalled out, hence creating alot of drag. alternatively they might be highly cambered, and so deflecting the airflow more than creating aerodynamic lift.

on your 2nd point, why would you ? ... i mean if you have the 2D lift curve and a means to adjust this for 3D, why would you want to test each 3D wing to generate the 3D lift curve ?

for your posts i suspect that you're building a wing for a car ... i'd use the body of knowledge closest to my application ... airplane aerodynamics may not apply to vehicles ... things like ground effect come into play. the things you want the wing to do are going to quite different and the theory has been developed in response to the need, and may not apply in a different situation.

 

[GregLocock]

L/D for /wings/ on F1 cars are around

Front 8

Rear 3

Figures taken from Peter Wright's book on the 2000 Ferrari

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[fpm]

rb, you're right, this is a racecar application. Problem is, by its very nature, specific data is hard to come by as people are secretive with it!

Yes, if I have the lift slope then I can convert alpha to Cl quite easily, but my query was as to why the 2 formulas (both seemingly for 3D wings) gave such different answers.

On the drag question, I'm not sure if the wings are stalled. Theres another graph in the J.Katz book, from an SAE paper, showing the rearwing of an '87 Indycar. Cd goes from approx 0.5 to 1.25, with a Cl of 1.75 to 3. Interestingly, the Cd plot is linear and has a very similar slope to the Cl line. The Cd doesn't seem to follow the square of the lift. I just can't believe that they would be running the wing in stall over such a very big range of AOA (about 25 deg range). Is there another Cd term that is actually much bigger than the induced (Cl^2) drag, and gives rise to the big coefficents?

 

[rb1957]

we've answered the cl question, no ? if you measure the 3D lift curve slope for your specific wing, then the expressions are essentially the same; the 2nd adjusts the 2D lift curve slope for 3D effects.

a Cl of 3 for a plain airfoil is pretty darn good, and probably has a lot of camber (much more than a conventional wing). you've got the drag equation we all use, though i'm not sure if there is something different with your application (like i mentioned, ground effects). i think you need to look at how other people do things in your field ... very expensive CFD programs, and/or lots of testing ... i don't think you'll get accurate results with two lines of equations.

good luck

 

[fpm]

Thanks rb!

Yes, correct, I was incorrectly using 3d lift slope in the 2nd equation, which was effectively reducing the Cl by the AR twice, giving me smaller numbers. Thanks for pointing that out, bit of brain fade on my part...!

As for the drag I'll have to keep looking, theres something I'm missing. Ground effects don't come into play, since I'm looking at rear wings, I just can't figure out where the 'factor of 10' is coming in.

I'm planning to use CFD to validate my design, but I really would like to have a handle on the approximate expected values first, which is the reason for my persuing a 'hand-calc' for Cd.

Thanks for the input!
FP

 

[sreid]

Remember that the wing "End Fences" have a huge effect on both the lift and the drag of the wings. The end fences act as if the A/R of the wing is increased.

 

[salmon2]

Just throw out what I know about this - maybe not making any sense.

1) I think the 2nd formula should be: Cl = Cl alpha*AR/(AR+2)*(alpha + alpha0) instead of Cl = Cl alpha*(AR/AR+2)*(alpha + alpha0) which will reduce into formula 1 when AR -> infinity.

2) when the AoA is too big, the leading edge vortex will depart from the wing backside, which is called stall - no more lift, not as much drag as well.