Best lift/drag ratio

[BarrelRoll]

What's the best cruise L/D ratio realistically achievable for a plane with approx. 50-60" wingspan? One additional condition is the wing loading has to be more than 15 oz/sqft (for stable flight in windy conditions)

Namely, I would be happy with L/D around 20 :rolleyes:

[Neil Stainton]

I would estimate most 50" to 60" span models would have L/D of no more than 12. Either exceptional design and attention to detail, or a larger model, will be required to get anywhere near 20.

Neil.

[BarrelRoll]

I would estimate most 50" to 60" span models would have L/D of no more than 12. Either exceptional design and attention to detail, or a larger model, will be required to get anywhere near 20.

Neil.

Thanks, Neil.
Is that because of the Reynolds number effects?
What would be an educated guess of a minimum size of the plane to get 20+ then?

[Neil Stainton]

> Is that because of the Reynolds number effects?

Yes.

> What would be an educated guess of a minimum size of the plane to get 20+ then?

75" for a superb design, maybe. The Allegro Lite plans indicate that it can achieve 24.5 when ballasted, which seems a bit high for a 2m model, but it is designed by a Prof Drela. Check out the Charles River RC site.

Neil.

[kcaldwel]

DLG are somewhere around a best L/D of 20:1 at 60". Mark Drela's DLG airfoils work very well in that realm, and at the higher wing loading you are talking about the Re won't be that low anyway.

You will need a clean fuselage, fuse/wing intersection, and tails though, but 20 should be achievable.

Kevin

[raptor22]

It also depends on what this is for.

If you go with an extremely cambered section, you may be able to achieve a l/d well over 20, but the performance range would be too narrow for most applications.

--Alex

[vintage1]

It also depends on what this is for.

If you go with an extremely cambered section, you may be able to achieve a l/d well over 20, but the performance range would be too narrow for most applications.

--Alex

Is that true though? I always thought extreme undercamber was a high lift to SPEED ratio, but not necessarily a high lift to DRAG ratio..i.e you might get a very good sink rate, but glide angle would be steep..

[MarkusN]

Is that true though? I always thought extreme undercamber was a high lift to SPEED ratio, but not necessarily a high lift to DRAG ratio..i.e you might get a very good sink rate, but glide angle would be steep..
Yeah, but with a small plane parasitic drag is a somewhat fixed , relatively high figure. You need a fuselage and a tail, and linkages can be optimized only to a degree. So a high lift wing has advantages also on the glideslope.

[kcaldwel]

Best L/D occurs at the speed where parasitic drag = induced drag. You can lower induced drag by increasing aspect ratio normally, but at 60" (1.5 m) spans, low Re effects limit how small it is advantageous to make the chord of the wing.

A low drag airfoil is important. At 15 oz/ft^2, you likely can use some of the higher Re sailplane airfoils. If you can keep the parasitic drag (section drag, airframe drag) low, best L/D will occur at a fairly low Cl (lift coefficient), maybe 0.3? and you won't have to use a highly cambered section. They typically have a higher form drag due to the high camber, and would not be a good choice for this case.

An aspect ratio of 14 or so will likely be in the ball park for the optimum. With a 60" span (max. span within your constraints will make it easier to get the 20/1 L/D), this gives a mean chord of 4.2". This gives a wing area of 257 sq. in., and all up weight of 26.8 oz.

You'll have to tell us whether the overall area and weight numbers make sense for your application. If so, it is then pretty easy to pick a taper ratio, calculate the rough speed stall and best L/D speeds assuming a clean airframe like an F5B model, and pick good airfoils for those Re. The details like tail movements, tail volumes, etc., can then be filled in.

Kevin

[Tom Harper]

Barrel,

The polars for a NACA6409 give a L/D of 22:1 for a CL of .5. That's for profile drag only. Add induced drag + fuselage + stab + rudder and you may hit 12:1(like Neil says above). That's on a calm, low turbulence day.

Big is good because allowable wing loading increases with linear dimension.

The only way to beat the L/D ratio is to go to a laminar section. If you have the building skill to reproduce a laminar section over the span of the model and a simple flight computer to hold it in the drag bucket, you cn probably hit 20:1 or better.

I'd go for a model of 14 sq ft (big enough for accurate construction) with an AR of 5 or 6 to one (ease of construction) and a wing loading that will hold it in the drag bucket.

Tom

[kcaldwel]

At what aspect ratio and Re are you calculating the performance of the 6409? Even at an Re of 200,000 the section L/D is about 40/1 (ref. Soartech 8, Pg. 260, for a built up wing model).

The NACA airfoils are 60 years old, and never designed for low Re applications. Why would you use them?

There are thousands of 60" span DLG models flying, some with built up wings, many with hot wired foam and composites, with L/Ds of about 20 at far lower Re than this model would operate at.

Modern low Re laminar sections do not have low drag buckets, and there is no problem with holding the model at any particular angle of attack to get the performance.

A wing area of 14 sq. ft.???? Wow, at a span of 60", the aspect ratio would be 2!

Here are some modern airfoils with easily usable and buildable performance (there are thousands of RC gliders using them every day). The section L/Ds are over 50:1 at Cl 0.5 and Re's of 100,000 and over.

At an aspect ratio of 10, a Cl = 0.5, at an Re of 100,000, the wing L/D using the AG 16 or AG 18 airfoils referenced below would be about 28:1. There are no drag buckets, and your Re is actually likely to be higher than 100,000 at best L/D.

http://www.charlesriverrc.org/articles/drela-airfoilshop/polars_re100k.pd

With an AR of 10, a span of 60", your wing area would be 360 sq. in., a mean chord of 6", all up weight of 37.5 oz. An L/D of 20 would be easily achievable with a good, modern, airfoil and clean airframe design. A built up wing would be fine, although composites would be nice.
Kevin

[Tom Harper]

Kevin,

The 6409 data is from a L.M.A.L report. Re 3,060,000, corrected for wall effects so no AR. Not recommending it - just a popular free flight section.

40:1 with a 6409 - methinks they are inhaling Lipo fumes. On my chart the 40 is the cp position.

I did not use the 60" span restriction. Just proposed that a large model with a modest AR would be easy to construct and could meet the 20:1 goal.

Thanks for the link. I will check out the AG sections.

Tom

[raptor22]

I think the 20:1 is more than achievable.

Here are the xfoil results for the 6409, a Wortmann FX foil and the MH32.

Both the wortmann and naca foils are heavily cambered sections, showing their advantage over thinner foils like the 32....with a L/D of around 90.

--Alex

[kcaldwel]

Kevin,

40:1 with a 6409 - methinks they are inhaling Lipo fumes. On my chart the 40 is the cp position.

Tom

The 40:1 is for infinite aspect ratio, and isn't particularly high for an airfoil at Re = 200,000. At the 3 million you quote, and infinite aspect ratio (the way most wind tunnel tests are done, no tip losses), the 6409 should have a section L/D of about 83.

I don't know what your reference is, but all the old NACA reports show much higher section L/D than that, as well as all the modern tunnel testing data I have. That must be for a low aspect ratio wing or something, maybe AR about 5?

K.

[kcaldwel]

Here are the xfoil results for the 6409, a Wortmann FX foil and the MH32.

Both the wortmann and naca foils are heavily cambered sections, showing their advantage over thinner foils like the 32....with a L/D of around 90.

--Alex

Alex,

Your attachment didn't work, and he'd be better off with the newer airfoils at an Re = 200,000 or so where a 60" model would be near best L/D. (Mark Drela's, Selig's, or comparable ones).

A great site with over 1,500 airfoils, airfoil comparison tools, polars, etc.:

http://www.ae.uiuc.edu/m-selig/

Kevin

[Tom Harper]

Kevin,

There is a disconnect somewhere.

The Selig plots show increasing L/D ratios right up to the stall point. The old NACA plots show a peak at Cl = .5 then a decreasing L/D for higher alpha.

I understand that Selig, Donovan et al are the annointed ones. However I don't think the NACA plots were made by dummies. What accounts for the difference? If it is the infinite span thing then who cares - it's unattainable.

I do remember a Free Flight heresy of a group that trimmed far enough aft for the model to hang into the wind on the edge of a stall. They claimed that was optimum. Perhaps they were right.

So are you saying that modern sailplanes have the wing set at +20 degrees relative to the horizontal stab? Thats where the Selig plots say to put it.

Tom

[kcaldwel]

Most airfoil plots (including at least the 1940 and 50's NACA ones, and all the modern ones) show Cl (coefficient of lift) and Cd (coefficient of drag) vs Alpha (angle of attack). You have to divide the Cl by the Cd at a given Alpha to get the L/D of the airfoil. The L/D will change over the Alpha range, and have a maximum. I think you are misunderstanding the plots.

Testing is done without tip losses so that the airfoils can easily be compared. It is easy to calculate the approximate Cl and Cd vs. alpha at any aspect ratio using 80 year old theoretical equations. Great free programs like XFLR5 will even do very sophisticated planform and model analysis from the airfoil data.

Not to start yet another decalage war, but the wing angle to the stab does not have much to do with performance, and the plots definitely don't tell you anything about that.

Minimum sink speed will always occur very close to stall speed. A free flight model trying for maximum time from a given launch height, that you can't steer into better air at higher glide speeds, should be trimmed for near stall.

They should also use highly cambered sections, since minimum sink and maximum climb rates are the important parameters, and speed range and best L/D does not matter. For an R/C model with a wing loading we were given as 15 oz/ft^2, you will need an airfoil that has the best L/D at a lower Cl, and I would presume that speed range is also important since he mentioned penetration on windy days.

Kevin

[Tom Harper]

AHA!

I suspect that the Selig plots are computer drawn using the miracles of modern technology. They do assume infinite span and are useful for analysis and comparison of sections.

In my field this is similar to small signal transistor specs, where Beta is tested for 10 microseconds at IC=10A and Vcc=20v. This is useful for characterization of the device, but these are not design parameters.

I also suspect that Joe Balsa Butcher will get results closer to the NACA plots than to those of computer idealizations. Or, do you really think the glider guys are getting L/Ds of 50:1 out of 6409 sections.

Tom

[kcaldwel]

I also suspect that Joe Balsa Butcher will get results closer to the NACA plots than to those of computer idealizations. Or, do you really think the glider guys are getting L/Ds of 50:1 out of 6409 sections.

Tom

Tom,

You'd need a huge aspect ratio, and a very big (larger than a full size sailplane) airplane, to get an L/D of 50 with a 6409 airfoil. And then the speed range would be very narrow. It has nothing to do with computer results. The NACA hand plotted stuff from the 40's show exactly the same results. The modern wind tunnel testing of NACA airfoils agree very well with the old data, and people have extended the testing down to the lower Re (small size, low speed) for models.

Modern full-size sailplanes achieve real L/D's of over 60:1, with fuselages, tails, control surfaces, etc.

I'm not sure I want to try typing that much aero theory, but be assured the performance of the Selig and Drela airfoils does work in real life. It isn't spec-manship, or computer wizardry.

Have you seen a modern sailplane, RC or full size, fly?

Kevin

[raptor22]

Here's another go at the polar attachment.

No arguments here that, for a sailplane, he would be better off going with a modern section than with a big, fat, heavily cambered one. There is a reason why F3B wings get thinner as the servos get thinner.

But, we don't even know if he is building a sailplane; all he asked about was getting the highest L/D.

--Alex

[Tom Harper]

Kevin,

I have watched modern sailplanes and followed the success of model gliders. But, that is not the issue,

We are talking about the ratio of Cl to profile drag. That is what is plotted on the polars.

What does AR have to do with it?

Tom

[kcaldwel]

Here's another go at the polar attachment.

No arguments here that, for a sailplane, he would be better off going with a modern section than with a big, fat, heavily cambered one. There is a reason why F3B wings get thinner as the servos get thinner.

But, we don't even know if he is building a sailplane; all he asked about was getting the highest L/D.

--Alex

Doesn't matter whether he is building a sailplane or powered, if he wants high L/D it is going to end up looking like a sailplane. The same aero laws apply whether it has a motor or not. Variable camber (flaps) would be nice to lower landing speeds and maximize the climb rate on a powered airplane maybe.

Highly cambered sections will not optimize max L/D for a complete airplane within his constraints: "50-60" wingspan? One additional condition is the wing loading has to be more than 15 oz/sqft (for stable flight in windy conditions)".

Those high lift sections are really only suited to minimize sink rate, maximize powered climb rate, slow speed flight, and/or or heavy lift type applications. Even for those, there are better sections.

It would be nice if he told us a few more things about what kind of airplane he wants, and why he wants high L/D in particular.

Kevin

[kcaldwel]

Kevin,

We are talking about the ratio of Cl to profile drag. That is what is plotted on the polars.

What does AR have to do with it?

Tom

Aspect ratio is the determining factor in the induced drag (drag due to the creation of lift) for a non-infinite, real, wing. Neglecting other planform and low Re effects here for the moment.

Cd = cd + (Cl^2/pi*A)

for an elliptical lift distribution.

where:
cd = drag coefficient of an infinite aspect ratio wing
Cl = lift coefficient
A = aspect ratio

The induced drag of a real wing with two tips is highly dependent on the aspect ratio. This is why efficient aircraft of any type, gliders or powered, will have high aspect ratios.

Low Re effects degrade the performance of airfoils though, so even at full size sailplane sizes there is a minimum chord length that will be optimum for slow speed and turning flight. For models the low Re effects are even more critical, and must always be considered for wing planform and airfoil selection.

So, for maximum L/D, or just flight efficiency, you want to make the aspect ratio as high as possible. But Re, roll rate, structural, and other considerations (does the servo fit in the wing?) will limit the optimum AR.

Kevin

[Tom Harper]

Caldwel,

Actually it's:

Cd = cd + cdi

The L/D we are talking about is Cl/cd without the cdi term, so AR is not a factor.

How do you get a 6409 with a L/D of 50?

I believe the difference is that the computer model allows the airflow to remain attached over the entire chord. That makes sense for analysis. However, it doesn't happen in the real world of 6409s.

Tom

[kcaldwel]

Tom,

This is getting way off topic, and we have some fundamental aero issues. I suggest you get a copy of "The Theory of Wing Sections" by Abbott and Doenhoff, first published in 1949, and/or "Theory of Flight" by von Mises from the same era, and pursue these questions off-line.

The L/D numbers are for actual wind tunnel data, and I assure you the modern Computational Fluid Dynamic methods used to generate modern airfoils model all the separations very accurately. And most of the Selig and Drela airfoils have also been wind tunnel tested, and their performance verified. It has nothing to do with flaws in the computer modeling.

Kevin

[MarkusN]

There is a disconnect somewhere.

The Selig plots show increasing L/D ratios right up to the stall point. The old NACA plots show a peak at Cl = .5 then a decreasing L/D for higher alpha.
I assume the NACA data are for AR=5 rectangular test wings. That was a standard used for some time (IIRC F.W. Schmitz also used it in his tests). With the large influence of induced drag that would give the characteristics you describe.

[BarrelRoll]

Wow. Thanks for your inputs, everybody :)

I'll try and elaborate a bit more about the plane we are after.

The challenge is to build a remote sensing micro-UAV carrying a digital camera.
All it has to do is to orbit above some designated area for as long as it possible.

The idea currently is to have her airborne for many hours (up to 24), so the only sensible energy source is solar cells. Therefore the engine is electric, which implies the need for high L/D :)
The relatively high wingloading is required since the camera is high-res and not gyrostabilized, actually it's supposed to be attached rigidly looking straight down (in the plane frame of reference).

The limitation on the wingspan can be stretched a little bit, but no more than 70" (I think).

[Tom Harper]

Kevin,

Thanks - I have well worn copies of both "The Theory of Wing Sections" by Abbott and Doenhoff, and "Theory of Flight" by von Mises.

I am not challenging the wisdom of modern fluid dynamics, just trying to understand the polars.

Interesting exchange.

Tom

[Tom Harper]

Barrel,

Then you have a compromise problem. How much AR can you sacrifice to gain wing area and Re.

I recommend "Low Power Laminar Aircraft Design" by Alex Strojnik. He has a web site and I believe the book is still available.

Strojnik presents the best practical discussion of L/D and of total design examples that I have found.

Tom

[nmasters]

That’s an awfully big "Micro" UAV

--Norm

[BarrelRoll]

That’s an awfully big "Micro" UAV

--Norm

Yeah, it is not exactly "micro" now :)

Actually it depends on classification, some of them say UAVs under 2 kg are "micro", others have 1 kg limit for the micro class, while "mini" goes up to 100 kg (and in some classifications even higher).

[mlbco]

Barrelroll,

It sounds like you are optimizing for duration which does not require maximum L/D, but minimum power factor (CL**1.5)/CD. As others have already mentioned, you will want a different airfoil section for minimum power and this will also impact your overall design when compared to a maximum L/D design. At minimum power induced effects dominate compared to parasite drag. Your design can tolerate more "garbage" hanging out in the flow if you have a good airfoil and the proper aspect ratio. I suggest you study the difference between max duration and max range before proceeding further.

Steve

[BarrelRoll]

Barrelroll,

It sounds like you are optimizing for duration which does not require maximum L/D, but minimum power factor (CL**1.5)/CD. As others have already mentioned, you will want a different airfoil section for minimum power and this will also impact your overall design when compared to a maximum L/D design. At minimum power induced effects dominate compared to parasite drag. Your design can tolerate more "garbage" hanging out in the flow if you have a good airfoil and the proper aspect ratio. I suggest you study the difference between max duration and max range before proceeding further.

Steve

I think you are right, I need maximum duration in the first place.
For some reason both solar powered "big" aircraft I know have extremely high AR and L/D (Helios and SoLong), that's probably the reason I got confused.

At the same time, in our case the cruise speed should be equal to or more than 35mph (55 km/h), otherwise it is going to take too much time to cover the "observation area." The power required equals P = m*g*v/K, where K = L/D. As the speed v is limited from below (which I forgot to mention initially) the only way to minimize the power P is to increase cruise K.

Also the L/D is important if the sun suddenly gets unavailable (clouds, overcast,rain) - to glide back home safely (which could be as far as 10-20 miles, there are LiPo batteries too though)

[mlbco]

Barrelroll,

Another approach to designing this plane is to first write a simulation of the mission in Matlab that can "fly" a virtual design and measure its performance. A key part of this design method is knowing what the design variables, constraints, and performance specification are. For example, you may be asked to design a fixed-size aircraft for maximum duration. In this case duration is the performance measure and size is a constraint. The variables may include wing area, installed power, battery mass, airfoil type, etc.. Make sure you know the difference between design variables, constraints, and performance (sometimes referred to as objective function).

The simulation need not include aircraft dynamics, just the trimmed performance equations for cruise, climb, etc.. You can include functions that predict solar cell performance, lighting angles, prop efficiency, battery storage, airfoil polar data, etc.. You can use a numercial optimizer to solve for the design variables that maximize performance and meet the constraints of the mission. If you have polar data for several airfoils at appropriate Re, you can re-run the optimizatin to find which airfoil is best. This approach may sound complicated at first, but if you can just write the mission simulation you'll find that it isn't so hard.

Steve

Steve

[BarrelRoll]

Steve, that's what I had in mind. Actually I began from the other (apparently wrong) end - developing a simulation of the aircraft dynamics in Simulink.

Are there Matlab libraries for mission performance simulations? I can try to write them myself (and then use the Optimization Toolbox, etc for analysis), just do not want to reinvent the wheel :D

[Sail 'n Soar]

Best L/D occurs at the speed where parasitic drag = induced drag. Kevin

This relationship is only true for ideal airfoils where parasitic drag is constant, i.e., independent of Reynolds Number. Unfortunately, that is not the case except in undergraduate aero exercises.

You need to calculate the Cl vs Cd for variable Re determined by q*CL = constant (a function of wing loading, area, AR and planform) in order to determine the best L/D. Fortunately, one of the XFoil options determines this Cl vs Cd relationship (for this analysis option the reference Re at Cl=1)