Coefficient of Lift?

[indoorff]

Hey all,

I am using the Culver formula to calculate the wing twist for a flying wing design (see the attached formula). This formula requires you to know the lift coefficient for the chosen airfoil. Can this value be extracted from the attached Cl plot? If not, how does one find this value?

Thanks for your help,
Chris

[kcaldwel]

Chris,

You are looking for the design lift coefficient, which is a function of what the airplane is supposed to do. For a fast power plane, that might be as low as Cl = 0.1; for a slope glider it might be 0.3; for a thermalling glider it might be 0.5. It is really a function of what speed you want the plane to fly at, and the wing area, and a bit of planform effects.

Typically you would then choose an airfoil that has it's best performance at your design Cl, set incidence angles or the appropriate twist distribution for a flying wing, for that trim speed. Of course you would want to check the airfoil performance at other important points, such as min sink for a glider, or landing speed for a power plane.

I assume this is for a glider, probably a sloper? You need to decide what speed you want the glider to perform best at, best L/D, high speed, etc., and choose the airfoil and twist distribution to optimize at that Cl.

I'm getting some Hiload 60 foam shortly, so I'll take another shoot at your wing core...

You might want to run Profili over a smaller alpha range, so the Cd/Cl curve gets spread out more and is more useful.

Kevin

[nmasters]

It's been a long time since I read up on the Culver twist but as I recall the design CL is up to the designer. choose your design CL from the Y axis of your chart then go across until you intersect the data curve you're interested in, then go down to read the angle of attack. I believe that would be alpha-zero in the formula. I've drawn two examples on your polar. One is for CDmin which would be for fast low power cruising. The other is a WAG at the best L/D. I just have the basic version of Profili so I don't know exactly what you have on screen but mine shows the cursor position at the lower left hand corner of the screen so all I have to do to get precise numbers is point at the data curve with the mouse. Try it, it's a great time saver

--Norm

[indoorff]

Thanks guys.
This is for a 2m thermal sailplane I am considering, so want to design for min sink.

The info I have on the Culver twist formula says the following about the twist angles:

"IMPORTANT: with this procedure, the incidence at the root (alpha_0) and at each station (alpha_x) is referred to the airfoil incidence line of zero lift, NOT to the airfoil chord"

From this plot, I would take this value to be ~-1.5 degrees? (see attached plot with reduced angle of attack range). So when designing the twist for the wing, the angles should be set in relation to the zero lift angle of the selected airfoil.

For a sailplane designed for flying long distances, you want to be flying at your best lift to drag ratio? This peak occurs at 6.5deg angle of a attack, as seen from the graph, which corresponds to Cl of 0.85 on the other graph. Am I understanding this correctly? And for longest duration (min sink) this is basically just before it stalls, or in the case of this example airfoil, Cl=1.1 at about 11deg.

Chris

[kcaldwel]

Chris,

You've got the idea, but unfortunately it isn't that simple.

First, on the zero lift angle, you have it mostly right. Note that at low Re, the zero lift angle changes, so if you have a tapered wing, you might need to take some of that into account. If the airfoil changes along the span (very common to optimize the airfoil for the local Re), then the zero lit angle would be more important to keep track of.

The Profili airfoil data is all for an infinite span, 2D flow, with no fuselage drag or other real airplane appendages. For a real wing, the aspect ratio, planform, and drag of the pod and fins will effect what speed and therefore angle of attack, where best L/D will occur. And it isn't a clear case for designing even a thermal sailplane for best L/D, since it also will have to fly fast between thermals, and slow while turning in thermals.

XFLR5 is a good program (free!) for looking at real wings. It will even show stability margins, and you can model, fuselages and tails. It is a bit trickier to use than Profili, but there was a good article in RCSD that will get you going. Or maybe Lift/Roll spreadsheet is enough?

Welcome to the world of design compromises!

Kevin

[HerkS]

indoorff -- a fine point here.

Minimum sink is defined by the formula Cl raised to the 1.5 power divided by Cd. When that ratio is a maximum, this is the theoretical point of minimum sink. For most airfoils, this is somewhat lower Cl than - as you put it -- "just before it stalls." This formula holds for a complete wing too - though as kcaldwel has indicated, the theoretical Cl and Cd of a complete wing is quite a bit more complicated than for just an isolated airfoil.

[indoorff]

Thanks HerkS

Wow, that XFLR5 is an impressive piece of software, I had no idea it existed until now! The price is certainly right :-)

Chris

[BMatthews]

Indoor, you should check out the Panknin twist spreadsheet.

I WAS going to say you could download it from www.b2streamlines.com but the site appears to be either down or abandoned. But there's enough of us that downloaded the xls spreadsheet file that you could get it. Using the spreadsheet it's pretty easy to figure out what the CG and twist should be for any given speed range.

For best L/D you obviously want a fairly low twist angle and semi rearward CG. A lot has been written on using variable CG's with flying wings and it may be something to look into if you're serious. If you're not that crazy yet like the rest of us I'd suggest you pick a twist that supports some semi serious wind penetration with the elevon at the zero angle and just input some extra up trim for slow thermal circling. Otherwise the twist will fight you during moderate to quick cruising. And around here with our winds you want to be able to move. Not speed run moving but pretty quick cruising with low energy and altitude loss.

[CloudyIFR]

I made a spreadsheet that used The Panknin formulas and has been added to my website, it's called "Flying Wing Calc". It's only good for a single tapered wing as that's how the good doctor wrote the formula.

Curtis
www.TailwindGliders.com

[indoorff]

Thanks guys, yes wind penetration here on the coast would definately be a good thing!
I have built gliders using the Panknin twist formula, I was just curious to try the Culver approach this time. I have my own spreadsheet too that calculates both types, as well as other data.

Cheers,
Chris