Sailplane Speeds - Give me a Good Estimate

[Seadog]

Gentlemen,

(tried this in Scale Sailplane forum with no luck. Any ideas here?)

I am trying to apply aerodynamics theory to my scale sailplanes, in particular to determine the way different airfoils behave at the root and tip of a wing. Mostly this is to help me calculate the amount of washout required to make a wing behave; in particular, strongly tapered wings as are found on some of the vintage and 60's and 70's sailplanes. Obviously, Reynold's Number plays an important role, but as it is directly proportional to the speed of the wing, I need to know how fast our planes fly to get a realistic idea of Rn. So, my question is: how fast do our various scale sailplanes fly? A vintage floater, for instance, or an ASK-18 type at 1/4 or 1/3 scale, or a baby 2.7m DG-600, or a 1/3 Duo Discus, etc., etc.? I guess I am most interested in thermalling (and slower) speeds, as when we step it up a bit the Rn climbs into a zone that I can deal with....but what of my 1/4 scale, slow-flying scale bird with a 4" wingtip? What's the speed, and therefore what's the Rn?

Any definitive answers? Or any really educated guesses?

Thanks....bring on the boffins!

Dave Smith

[Andy W]

It will depend a great deal on the weight. Just as with full scale, model sailplanes will fly faster if heavier loaded. The L/D remains the same, just the airspeed can vary significantly.
The max. L/D for my full scale glider occurs at 51 kts, min. sink at 41 kts (full-span camber can be set). Vne is 135kts. You can fly pretty much anywhere in that range! :)
..a

[Sail 'n Soar]

Actually, I look more at the minimum speed and that is a function of wing loading and airfoil, with minimal dependence on AR. The following chart gives flight speeds for a CL average of 1, with wing loading varying from 8 to 20 oz/sq ft. I've given speeds in fps. Change the wing angle of attack by about 7 degrees and the CL will drop to about .25. At that CL these speeds will be doubled.

[Seadog]

OK, I understand that speed certainly depends on wing loading, and not on aspect ratio; no problem. It also depends on the airfoil, because I have to generate enough lift with a given airfoil at each speed to equal the plane's weight. I can generate more lift by increasing the angle of attack, and flying slower.

Different airfoils stall at different angles of attack at the same Rn, and the same airfoil will stall at different angles of attack at different Rn. Also, the lower the speed and/or the smaller the chord, the lower the Rn (density being equal).

Let me rephrase my original question.

If I know the airfoils at root and tip (I do), and I know the tip chord (I do) and I know the speed (I don't), then I can calculate the Rn, check out the polar for the airfoil at that Rn, and know what alpha it will stall at. I can do the same for the root airfoil, which will be flying at a 2 1/2 times the Rn as it is 2 1/2 times the chord. Now I can figure out how many degrees of washout to add to the wingtip to make sure that it doesn't stall before the root. The only thing I'm missing is the speed, and I am looking for empirical evidence of the speeds that our sailplanes fly at. That is why I listed the types of craft that I did....they all fly at different wing loadings. I am most interested in the ASK-18 type as opposed to the higher loaded more modern ships, but if someone has taken measurements of their modern glass 'Whatzit' at thermalling speed, at least that would be a start.

Thanks

Dave Smith

[Ollie]

http://aero.stanford.edu/WingCal.html

[Seadog]

Ollie, I appreciate a man of few words, but the link doesn't work and I can't find what you are referring to at the higher level page.

Dave Smith

[raptor22]

This link works,

http://aero.stanford.edu/WingCalc.html

However, I don't see its use in this particular situation. Maybe Ollie can clarify.

--Alex

[Sail 'n Soar]

Dave,

Please recheck my previous post. I believe it covers all you asked for. The curve was based on a CL, average of 1.0 and gave V as a function of wing loading. Choose a different CL and all you do is divide the V values I graphed by the square root of the new CL. That's where I gave the one example of decreasing the angle of attack by 7 degrees from what would be required to achieve CL = 1 for your airfoil of choice. That would give a CL = ~ .25 at that angle of attack, whatever the CL = 1 angle is for whatever foil you choose. 1 divided by .5, i.e., sqrt(.25) results in doubling the V's illustrated in my graph. If your favorite foil stalls at .9, then raise those V's by 1/.95. The approximation I did include is assuming a little less than .1 change in CL for a 1 degree change in angle of attack. The slope of that line does depend on AR. But, of course, the higher the AR, the closer better my assumption becomes. The slope of the CL vs alpha also varies somewhat with the airfoil thickness. But when you are considering the relative impact of Reynolds number and model flight speed, those are all second order/ lost in the wash, affects.

In terms of washout, that is more a function of aspect ratio and taper ratio, and not Re. Designed properly you want the max CL to be near the center. No matter what you try, the CL will go to zero as you approach the tip - a consequence of the shed vortex at the tip - ignoring winglets, of course. The following site provides all the design tools you need for a simple taper wing. http://aero.stanford.edu/WingCalc.html Put in your particular geometry, increase the angle of attack to max CL at the particular station, and add washout until the wing stalls where you want it to.

OK, I understand that speed certainly depends on wing loading, and not on aspect ratio; no problem. It also depends on the airfoil, because I have to generate enough lift with a given airfoil at each speed to equal the plane's weight. I can generate more lift by increasing the angle of attack, and flying slower.

Different airfoils stall at different angles of attack at the same Rn, and the same airfoil will stall at different angles of attack at different Rn. Also, the lower the speed and/or the smaller the chord, the lower the Rn (density being equal).

Let me rephrase my original question.

If I know the airfoils at root and tip (I do), and I know the tip chord (I do) and I know the speed (I don't), then I can calculate the Rn, check out the polar for the airfoil at that Rn, and know what alpha it will stall at. I can do the same for the root airfoil, which will be flying at a 2 1/2 times the Rn as it is 2 1/2 times the chord. Now I can figure out how many degrees of washout to add to the wingtip to make sure that it doesn't stall before the root. The only thing I'm missing is the speed, and I am looking for empirical evidence of the speeds that our sailplanes fly at. That is why I listed the types of craft that I did....they all fly at different wing loadings. I am most interested in the ASK-18 type as opposed to the higher loaded more modern ships, but if someone has taken measurements of their modern glass 'Whatzit' at thermalling speed, at least that would be a start.

Thanks

Dave Smith

[Sail 'n Soar]

Another approach to your answer. Mark Drela, in his 2 meter models and low drag airfoils, indicates a CL ~.5 at max L/D. Use something like XFoil and you will see that Mark's relatively low camber foils have drag polars that compare well with whatever model scale foil you may choose. Go to a higher aspect ratio or draggier scale fuselage and that will push CL at max L/D a little higher, but almost definitely not over CL =- 1. Also, wing CL at min sink (vs section CL at min sink) will also be on the order of CL =1 or lower. Take the curve I posted and consider the V's to be reasonably close to min flying speeds for your model planes - more than likely a closer number than measurement accuracy, and a probable max speed for max performance based on best L/D by dividing the V's given by ~.7, i.e., the square root of .5.

With the three posts, have I missed something?

[HELModels]

seadog,
My answer doesnt come from myself, but from a reference written for modelers who may not have the math background but have reasonable amount of common sense. Here it is:

What is your average chord?
What is your wingloading?

Assuming your CL at best glide is 0.8(0.8 is realistic since most airfoils produce minimum drag in that region/above or below that CL, drag goes way up) and Pulling data from an already compiled curve:

If your average chord is 8 inches and your wing loading is about 11.5 oz/ft sq., this data point yields 28 ft/sec. This curve is based on a RN of 120,000 and at the other end, i.e., lower wing loading, larger chord, it yields a wing loading of 6 oz./ft. sq., average chord 10.5 inches for a ft/sec of 21 ft/sec.

The purpose of the curve these 2 data points came from is to optimize wing chord for the wing loading and airspeed you plan to fly. So, I hope you plan to fly somewhere in the range of these 2 data points, At Best Glide.

Looking that curve you can just about draw a straight line through those points and be in the "Ball Park" for wing loading above those 2 points. If you do, err on the side of a large average chord. That will keep your RN up and drag down. If you draw a line through the 2 points, I suspect lower wing loading than 6 oz., the slope goes way up, but who actually builds a 6 - 16 ft span model with a wing loading of less than 6 oz./ft. sq.?

Since 3 points make a line, a third point at higher wing loading is 7 inch chord, 16 oz./ft. sq. loading for 32 ft./sec., RN 120,000.

Oh yeah, I turned the page and you better keep your wing span at or above 6-8 feet for this data to be realistic.

Sail n' Soar is a number cruncher and might be able to corroborate my answer, but I doubt anyone will.

Good Luck and if you would like a copy of the reference manual I used, PM me, anyone, copies are for sale.

[Sail 'n Soar]

Number Cruncher to the rescue :)

This graph gives V in fps as a function of wing loadings between 6 and 24 oz/sq ft for average CL's between 0.2 and 1.0. Go to the aero.stanford.edu site provided earlier to translate CL, avg to CL at a specific wing station and for a given aspect ratio.

Once you've calculated V as a function of CL, avg and wing loading, use the following formula to calculate Re.

Re = 532.5*V*c

Where V is in fps and c is in inches.

Note, I derived my formula from standard atmosphere sea level density and viscosity values from a '60s era text. It's conceivable the standard at mosphere has changed slightly. Also, you will get a who-cares Re change if you use a differrent pressure altitude and temperature. All can be calculated, but it's not worth the effort in almost all cases impacting our model designs.

[Seadog]

Gentlemen,
Thank you all for your well thought out and in-depth replies. I think I am starting to get it. Of course applying the theory ends up giving me a Re that ends up pretty close to what I figured it would be (!) but at least it gives me some confirmation that I am in the ball park. Given a reasonable number I can do the rest and apply the theory to figure out the washout I need for a bit of safety.

Thanks again.....I am going back to digest further!

Dave

[nuevo]

how a radar gun?

fly level at the speed you want at fairly low altitude to reduce the angular error. Thus you can directly measure the air speed assuming no wind, and from that directly calculate Rn.