High Aspect Ratio Airfoil Selection

[seaotter12398]

hi all,

i'm attempting my first scratch built large scale airplane, a 1/6 scale u-2.

that works out to a 230 inch winspan and a 30 inch chord (at the root).

the data for the u-2 shows that lockheed used an NACA 64A409 foil for the root and an NACA 64A406 foil for the tips.

first question: the difference between the root and tip foils is to provide aerodynamic twist, i.e., washout?

second question: in reading about the 6 series airfoils, it seems that they have a fairly narrow performance band, which i would think would be bad for r/c applications. if this is true, can ya'll share some of your remarkable expertise and make some suggestions on more appropriate airfoils?

thanks in advance

da otter

[Sparky Paul]

The U-2 is optimized to fly about .6 Mach.
Your model will never get there.
Look for something in the Selig group that will operate at the Reynolds Number your model will fly at. Choose the tip profile to have aerodynamic washout of a couple of degrees relative to the root airfoil.
It might be worth noting the -R model, with its much longer wing, was made by adding span at the center, keeping the same wing tip, just moving it further out than the -C model. This added a LOT of wing area compared to the usual practice of stretching the tip to the new span.
I'd bet the wing structure was kept the same, in terms of twist and profile.

[Sail 'n Soar]

Remember, big taper demands big washout for docile stall characteristics.

[seaotter12398]

thanks paul and s'n's

paul, i'm shooting for something in the 75-100 mph range.

nice to know i was right about the airfoils. i was thinking about using an airfoil used on r/c soaring airplanes. i can probably dig up the twist from one of those models.

i don't think i've ever seen twist numbers for the u-2, though i've read some stories about how finicky the wings could be on these aircraft in operational use.

i'd like to stay with the u-2a variant. the tr-1 just doesn't have the graceful lines that kelly johnson gave the original, ya know?
and i'm not looking at a very high wing loading for this design.

[Sparky Paul]

Your wingspan and scale said -R model.
The -C model was an 80 foot airplane, or 160 inches, @ 1/6th scale.
100 mph is pretty close to Vne at sea level for the full scale. :)
It's a climber, not a level flight speeder.
The only models I've seen of the thing typically fly much faster than scale.
What power are you planning?

[BMatthews]

I tend to agree with Paul that you may need to re-asses the scale speed.

As for the full sized ones being touchy in use that's true. But it had everything to do with operating at altitude and nothing to do with the aircraft's shape or wing twist. It came about because the operational cieling was set not by the abilty to climb higher but by the fact that the air density effects caused the stall speed to rise while at the same time the speed of sound was dropped. The U-2 was only able to climb until the rising stall and lowering sonic speeds boxed it into a narrow range of usable speeds. From the books I read about it this occured at various altitudes based on temperaturs and other factors. But they generally climbed until the lower to upper allowable speeds were in the 5 to 10 mph range. At that point it required a very good autopilot on the pitch control to maintain the flying speed within this extremely narrow range.

Again, I doubt you'll need to worry about this with your model... :D

Good luck with your model. It's a design that deserves to be modelled more often. But I'd do your homework agian on the scale speeds for takeoff, climb and cruise to better show it off properly. This isn't a high flypast speed sort of design IMHO.

PS: Oh yeah, the airfoils. You're on the right track with sailplane options. But given the fact you're using power and want to go for higher speeds than most gliders spend much time at I'd shoot for one of the lower camber options of 1 to 1.5% camber. Also since the Reynolds numbers hit our size models harder than the larger ones I'd plan on using some washout in the wings even if the real one did not have any. This could be in conjuction with a different tip airfoil or not. But if you use a different tip airfoil then you can get away with less twist. And since the best option for airfoil shape washout effect is to add camber I'd shoot for a .8 to 1% camber airfoil at the root and a 1.5 to 1.7% camber at the tip. Set the wing twist such that the root and tip reach their respective zero lift angles of attack at the same time. This will ensure that the tips won't stall before the root.

[seaotter12398]

you've both given me lots to think about! thanks!!

paul:
as for the scaling, i'm still working out the details from all the available drawings i've been able to amass. i have plans to run out to the sac air museum near omaha. they have a u-2 out there (it may be a tr-1 but i don't think so). i'm hoping i can make special arrangements to photo the thing to death. i did notice that dimensions vary wildly among the various sources, so i'm hoping the trip to omaha will give me better data.

i've seen the u-2s fly many times out of moffet field in california. they seem to roll about 200 feet then take a 45 degree nose up attitude. they really do climb like the proverbial homesick angel.

i'm looking into using either a 25 lb or 35 lb class turbojet. that should give me more than enough power to make the thing fly (from the old adage about f-4 phantoms).

bruce:
i heard a story once (might have been ben rich) about trying to get a u-2 to fly level. one wing just wanted to flutter and drop a bit, making the pilot a bit nutso. they finally found that adding a strip or two of duct tape to the leading edge corrected the problem.

great info on airfoils. i was looking at gliders that use something called dynamic lift? it apparently has something to do with crossing thermal zones to generate lift. these sailplanes apparently are in the 200 mph class, so their wings should be more than sufficient for what i want to accomplish.

i'm almost positive that i'm going to have to use different airfoils from tip to root. even as large as this structure will end up, maintaining torsional stiffness to maintain a given washout is going to be problematic. i'm planning on experimenting with a true monocoque structure using thin cross-section composites.

ya'll can be sure i'll be asking more questions. this is turning out to be more fun than i've had with engineering in quite a while.

otter

[Ollie]

A real wing has three design points of view:
1. Airfoil
2. Planform
3. Structure

See airfoils for low speed to take off and landing. Know about stall ( high angle of attack and high lift coefficient). Know about reynolds number and polar curves. See:
http://www.nasg.com/afdb/list-airfoil-e.phtml
http://www.ae.uiuc.edu/m-selig/uiuc_lsat.html
http://www.mh-aerotools.de/airfoils/index.htm

Planform about the lift distribution along the span such as twist, taper and aspect ratio. See:
http://aero.stanford.edu/WingCalc.html

Structure space in the wing (thickness and chord) depends on structure strength and stiffness. Consider bending and torque loads. Consider how many high G's (especially for dynamic soaring).

[Sparky Paul]

Ott, The TR-1 designation was an interim thing. The -R model was built in the late '60s... then a new bunch in the '80s.. these were designated TR-1.. but then relapsed to U2R, and now all are the U2S, with a more gruntier motor and late 20th century instrumentation.. in lieu of the mid-20th century steam gages they had. :)
The Squadron-Signal "Lockheed U-2 in Action", #86 is a reliable source for 3-views and data.
I remember when I first worked at Palmdale, noticing there were two sizes of U2s flying around. The differences between the -C and the -R are obvious.

[BMatthews]

The rate of climb at sea level was high for sure. I gather that as it approached it's operational altitude this reduced to more of an uphill glide... :D

The dynamic soaring guys are using the energy that comes from moving though zones of varying velocities and get their speed from the apparent sudden speeding up of the sudden velocity change. In effect they "dive" into the wind shear and aborb some of the energy of the local apparent wind's velocity gain. They only get enough to gain a small bit each time through but do it often enough and you end up with 200 mph models zipping around.

If you watch sea gulls or other soaring birds you can see them do the same thing with free air gusts. They fly across the wind and when a gust catches them they turn into it and jump up 20 feet or more before turning off and crabbing across the wind again. We can also do that with our models if we have the skill and the right sort of model. I spend 20 nerve wracking, armpit drenched minutes one day in stormy conditions doing just this with a glider of mine. Never got up higher than the launch height and often I was down to within 10 feet before I shot up to 40 again. VERY exciting.

For your model you may want to just go with blue or pink foam cores with vacuum bagged on fiberglass, kevlar or carbon skins. At least one layer should be set with the weave at a 45 degree angle. That layer will provide you with all the torsional stiffness you will need.

There's no need for a one off like this to look at thin shell hollow true monocoque structures that require a highly complex external mold..... unless you're just looking for a challenge that is.... :D

Study up on what the latest FAI thermal duration and slope racer guys are using for wing layup schedules. For a model of your size you'll likely want to go a trifle thicker with more layers but then you'll have the wing area to support it as well. But since your airfoils will also be a lot thicker the references Ollie makes about structure come to bear so you don't need to go much thicker in the skin layups either. Just having the skins further apart thanks to the wider chords and thus thicker airfoil shape will ensure that the skins are pleanty strong enough. Remember that even an 8% airfoil chosen for it's speed will still be 2.4 inches thick at the root thanks to that 30 inch chord. And the strength of an I beam structure goes up by the square or cube(I can't remember which at the moment) of the distance between the top and bottom caps that actually withstand the loads.

[Sail 'n Soar]

A few more thoughts about airfoil choice. First, with a scale fuselage powered model your wing loading is going to be sufficiently higher than any flat land soarer that I would stick with a proven moderate camber sailplane airfoil and avoid totally going to a 1 to 1.5% camber foil. Per naming convention the 64A409 had a design CL of .4, which should be a good high speed cruise point for your model. Some of these sailplane foils approach being flat bottemed, which would make accurate assembly less of a hassle - a "thinned" Clark Y would be an excellent choice and wouldn't give up much performance either.

The earleir comments on U-2 low altitude slight dynamics were also right on per my observations. The U-2 appears to fly at about the same indicated speed (vs true airspeed) almost all the time. In order to have sufficient thrust to fly at normal operating altitudes, the engines have enormous excess thrust at sea level. I don't know about their climb rate, but their climg angle is amazing. From the rear you would swear the were going verticle, though obviously not the case.

[seaotter12398]

heyas s'n's!

so yer saying the original u-2 airfoil would be acceptable? that almost makes sense with what everyone else has said. if i remember some study i did some years ago, ultra-high flight results in extremely low reynolds numbers....but they tell me memory is the second thing to go.

in regards to your comment about the u-2 flight profile using a constant ias, something tickled my "say what" button so i emailed a u-2 driver to ask him. his response was:

"As for speed, we flew a constant MACH, which resulted in a decreasing
indicated airspeed as we climbed above FL600. On the way up we held 160
KIAS, and as we transitioned to .715M we'd engage the autopilot and
constantly adjust for max egt. (That entailed a continuous reduction in
thrust as the aircraft climbed due to fuel burnoff, above FL700)

So, holding a constant MACH, our airspeed would bleed off from around 160 to
the high 90's by the end of the flight. Of course, that was with the old
J-75 engine. Now they're flying with the B-2 turbofan, GE F-118-101 engine
that supposedly gets 10K higher, so the throat characteristics (coffin
corner) probably resemble the old A model again. "

for what ever its worth! :)

[BMatthews]

I believe that the series of airfoils with those style numbers were intended to support laminar flow over much of the chord length. But at model reynolds numbers maintaining that level of laminar flow is often very hard or impossible. Far better to rely on the ample choices that have been tested in wind tunnel work at "our" reynolds numbers.

Or at the very least get Profili2 and pay the small price to unlock the Xfoil module and run the scale airfoil through some predictive testing at the speeds and chord lengths that you're expecting. At least that way you're starting with some indication of whether or not the scale airfoils are adaptable to all this.

[Sail 'n Soar]

so yer saying the original u-2 airfoil would be acceptable? that almost makes sense with what everyone else has said. if i remember some study i did some years ago, ultra-high flight results in extremely low reynolds numbers....but they tell me memory is the second thing to go.

Close. I wouldn't go with the U-2 airfoil. Rather, I was suggesting going with a model sailplane foil (or even a scaled version of the Clark Y) with an equivalent design CL, which roughly translates to a similar camber. The 64A409's is something greater than 2%. My sggestion would be something like the Eppler 205 or later low RE foils designed for moderate lift.

The 6-series laminar foils were, as discussed by others above, designed to have a significant fraction of their surfaces with a laminar boundary layer flow, with roughly equal extent laminar on both the upper and lower surfaces (~40% for the 64xxx's.) These airfoils had a sharper LE radius and their max thichness further aft than most other full scale foils of the period. In addition to the laminar boundary layer advantages this gave, it also resulted in a higher critical mach number. This has obvious advantages for an aircraft who's high altitude cruise point was dictated by the convergence of max mach and min stall speeds. But this also resulted in very narrow laminar buckets for the thinner 6-series foils - no problem for an air vehicle which would fly almost entirely within a very narrow IAS / angle of incidence range.

Some of the other comments, above, have dealt with the low Reynolds numbers associated with high altitude / thin air flying. This is a problem for the engine compressor elements, but not for the airframe itself. If you run the math, to first order at a constant CL (or indicated air speed) the Reynolds number is a function of the square root of the aircraft gross weight devided by the square root of the aspect ratio. The U-2 will have roughly the same RE poking along at sea level that it will have "zipping" along at max mach / min stall at its cruise altitude.