Cl/Cd of a plane vs Cl/Cd of an airfoil

[Mihai]

I have a dumb question. I'm modeling a flying wing in XFLR5 and in the Xfoil 2D analysis I get beautiful Cl/Cd of 50-60 or so. However, once I model the wing I only get a Cl/Cd of 15-20 although the lift distribution is almost (within 2%) perfectly elliptical and there are no other things on the wing (like fuselage or winglets). Any idea why? I thought that I may lose a bit here and there because the wing is swept a bit (20 degrees) and the taper ratio is not perfect (0.5 or 2) and I have a bit of twist (2 degrees), but I expected about 2-3% loss, not 70%.

Thanks,
Mihai

[BMatthews]

2D analysis doesn't take into accout spanwise flow and wing tip vortices.

Also our models won't ever see L/D ratios that full sized stuff can achieve. That old Reynolds number or scaling effect limits what we can achieve.

I think you'll find that only the best and biggest of our typical model sailplanes can even reach the high 30's for L/D.

[Mihai]

2D analysis doesn't take into accout spanwise flow and wing tip vortices.


Right, that's why I thought that the 3D will be a bit smaller than the 2D. But only a bit - the span flow at 20 degrees of sweep should result in about 3% loss. Then the tip vortices - they account for something, maybe 10% or so, as my AR is not that bad (8). I'm saying that based on the "stream" analysis of XFLR5 that showed almost not vortices for my wing not sure why, maybe because I was far from stalled, so they can't be that much of a problem.

[edit]
To give you an idea of the loss order, if I add two beefy (30cm !!!) winglets the Cl/Cd only changes by less than 10%, so tip vortices should not account
for that much.


Also our models won't ever see L/D ratios that full sized stuff can achieve. That old Reynolds number or scaling effect limits what we can achieve.


Oh, but this is captured equally both in the 2D and in the 3D models - in fact the 3D model uses the numbers from the 2D model at the same Re, so this should not matter in explaining the difference.


I think you'll find that only the best and biggest of our typical model sailplanes can even reach the high 30's for L/D.

Really? Then I don't feel that bad anymore - I had the impression that the top DLGs do better than this, but I admit that it's mighty hard to judge by eye the value of the best Cl/Cd, so you may be right.

But still - why such a big difference between 2D and 3D?
The difference - if real - would be sufficient to invalidate completely all 2D analysis and there are so many great planes (practically all Dr. Drella's as far as I know) designed from 2D analysis.

M.

[MarkusN]

Then the tip vortices - they account for something, maybe 10% or so, as my AR is not that bad (8). I'm saying that based on the "stream" analysis of XFLR5 that showed almost not vortices for my wing not sure why, maybe because I was far from stalled, so they can't be that much of a problem.
It's called induced drag, and the order of magnitude is estimated easily.

Cdi = Cl^2/(Pi x AR) (for elliptical distribution). At high Cl induced drag easily doubles the drag of a wing.

[nmasters]

Mihai--

The cd in the 2D polars only shows profile drag because there's no induced drag if there are no tips. Since drag due to lift and the drag that is not due to lift have opposite slopes when plotted over velocity, as in the attached graph, the best lift to drag ratio is where the lines cross. That's why a real wing can never have an L/D better than half of the airfoil 2D cl/cd. There are also the problems that you can only have an elliptical lift distribution at one speed [unles your planform is elliptical] and RC pilotage is never as precise as in-plane pilotage so you have a situation where you just can't stay in the low drag bucket very much of the time. There was a long thread (http://www.rcgroups.com/forums/showthread.php?t=824797&highlight=25%2F1) about why model gliders don't get very high L/D some time ago in the thermal forum that might be interesting to you, or not

--Norm

[MarkusN]

Since drag due to lift and the drag that is not due to lift have opposite slopes when plotted over velocity, as in the attached graph, the best lift to drag ratio is where the lines cross.
Minor nitpick: That's almost exactly the case in your example, but that hasn't to be so. Minimum total drag is where the slopes of the two curves are equal (with reversed signs).

[Mihai]

I see it now - it was the vortices. Although they don't "look" like much on the stream display, they can affect the minimum Cd a lot, and thus get the ratio way off. Thanks for the reassurance - I thought I was doing something fundamentally wrong with the wing and that the performance will suck big time.

Thanks,
Mihai

[nauga]

Minor nitpick: That's almost exactly the case in your example, but that hasn't to be so. Minimum total drag is where the slopes of the two curves are equal (with reversed signs).While we're picking nits, for the conventional analytical definitions of induced (=K/V^2) and parasitic (=M*V^2) drag, the slopes are equal at the crossover point - they are one and the same. ;)

Nauga,
considering the first two syllables.

[Mihai]

Today I modeled the effect of flaps (30 degrees) down and the Cl/Cd of the plane goes down - way down (to 2-3 if I recall exactly) - this would be interesting to see life - it should slow down (and come down) real nice.

M.