Prandtl lift distribution for conventional configurations?

[nestofdragons]

That was my understanding as well

I admid that many wing-thinkers might be puzzled by this way of designing a wing. But ... it is like Albion Bowers (retired NASA-chief-engineer) said:
"Assumptions are the unseen walls we use to create ... the box".

Most wing-design-books start with the assumption that elliptical lift distribution is the best way to design a wing. Just a few papers in history took this in question. Albion Bowers took those papers to heart and studied them for more than a decade to reverse engineer the flying wings of the German Horten brothers. And he succeeded to understand the system. All of the classic wingdesignbooks i have at home never talk about this BSLD-system. So ... it is very hard to convince the people inside the box to look sideways and make their design-horizons wider.

It has become the classic story of not seeing outside the box. Some day ... some day ... a new book will be used in the aviation-schools. BSLD is just too good to be forgotten.

 

[pictsidhe]

The planform that was evolving with my spreadsheet looked an awful lot like later Horton ones. I had different shaped control surfaces. That led to a healthy reduction in induced drag away from the design point. The appeal of bsld for me is that it is optimum for BWB, needing a very large root chord. Increasing the root chord past that where Cl matches the lift distribution gives a better match to bsld across the speed range. That drops in well to BWB.

And hey, a flying wing is cool!

 

[proppastie]

"Assumptions are the unseen walls we use to create ... the box".

perhaps what needs to be done or perhaps others have done it....is to design your wing, calculate the distribution, using all the methods discussed and then test the wing to see which distribution calculation is most correct. How one would measure the distribution is probably a whole different discussion.......I see lots of strain gauges or manometers in a wind tunnel, but really do not know how it is done.

I would assume the CFD software makes assumptions as to the distribution which would only validate the the calculation distribution which matches the software's assumptions.

 

[peter hudson]

I guess I am missing something.....I thought Lift Distribution Calculations were attempts to calculate the lift distribution of a wing, not a method to design a wing. ...

No you not missing something...my next step was to analyze the lift distribution and adjust the wing planform and/or twist to get the desired distribution.

Here are my results comparing a 3 tapered segment pair of wings. I used a design lift coefficient of 1.0 (a good enough number for a sailplane).
I matched the shape of the lift distributions (based on VLM) and made sure the local cl at stall was lower for the outboard wing panels (because what's the point if the stall sucks.) I double checked the wing bending moments (the BSLD actually came out a little lower at the root). And, as a way to think about what this means to a pilot, I assumed a 450 pound glider with a messy 2 ft^2 of flat plate drag area and produced some performance plots.

enjoy, and fire away!
-Peter-

 

[WonderousMountain]

Graph below shows some easily generated math relations. One is a circle, that can become elliptical either at one flight point, or if the wing is an ellipse of equal lift coefficient, up to stall. Also, we have a pure delta shape (1.25C). Probably, you will not get exactly a Delta Lift pattern. Next up is my favorite; 1-x^2 inverse Parabola. As you can see, it takes up less area for the same span. 2/3rds Surface of a rectolinear planeform.

Like the Ellipse, it starts out Lateral, or normal to Forward, but terminates at an angle which would intersect the lateral exactly 1/2 Semispan. That comes from the X^2 relation. Following that, we haves squared the same Parabola. As you can tell it is Bell Shape, this can only be acheived at design point. Our special distribution of airfoil & twist, go to less AoA as in a dive - and your tips will go negative, putting any remaining lift towards the center. If you go to higher AoA, the lift distribution will approximate your actual form (inverted Parabola), until it reaches stall.

Now we have another option, other than mirroring form. We can take a Single taper, and design to a BSLD, upside is single taper wings are relatively easy to make, compared to parabolas & ellipses. Also, this gives us a pretty fair center section across the span to customize airfoils. The tips drag less than square ones, and the Root chord is nice & long. If we pick the right Bell, Proverse Yaw can be attained.

Another option, would be to build the ellipse plane form, which is thought to look good, and reflex the tips. When we go to high AoA in an Ellipse, the distribution approaches planeform, which is some better (efficient) than rectolinear wings. Manuevering, climb performance and flap effectiveness, are discussion points.

I should say, the Bell is not acheived as shown.
My Root is faired into the body at a lower lift coefficient than about 1/3rd out. This pushes my bell sides out some from zero body ideal.

 

[pictsidhe]

perhaps what needs to be done or perhaps others have done it....is to design your wing, calculate the distribution, using all the methods discussed and then test the wing to see which distribution calculation is most correct. How one would measure the distribution is probably a whole different discussion.......I see lots of strain gauges or manometers in a wind tunnel, but really do not know how it is done.

I would assume the CFD software makes assumptions as to the distribution which would only validate the the calculation distribution which matches the software's assumptions.

The tricky bit is keeping drag reasonable away from the design point. Regular aircraft with elsd-ish lift distributions don't vary too much. But with bsld, the span efficiency can vary a lot away from the design point if you aren't very picky about the planform.
Yes, you can see what a given planform and twist does, but it is a much, much slower way to optimise a bsld wing than calculating at least one variable to get a desired distribution. I went with twist. I made my spreadsheet after getting fed up with my glacial progress in XFLR5. Once I knew what sort of planform I needed, then I could test in XFLR5 across AOA and not have it tell me that turkeys fly far better.

 

[peter hudson]

The tricky bit is keeping drag reasonable away from the design point. Regular aircraft with elsd-ish lift distributions don't vary too much. But with bsld, the span efficiency can vary a lot away from the design point if you aren't very picky about the planform.

The results I posted above bear that out. Around the design lift coef (about 38 MPH in this example) the BSLD gave better L/D and minimum sink but by 45 MPH the elliptical distribution wins out. For a non-racing sailplane that flies around at min sink or best L/D all the time the BSLD appears to have some benefit.

 

[proppastie]

You certainly understand what you are doing but my confusion here is you have a "wing design" called a "lift distribution" the semantics I believe are poor. Also it appears your CFD software (based on VLM ?) has calculated your lift distribution but I can not read the posted graphs titles...so that is another perhaps miss-assumption. I use the area platform lift distribution as it is easier to calculate and easier to understand. Looking at your wing designs and using the area to calculate the lift distribution one wing will have an approximate triangular lift distribution and the other would have combination rectangular to triangular distribution......I only calculate distributions for stress analysis purposes I leave the aerodynamics/performance to others......Thank you for your work on low speed platforms.

 

[peter hudson]

but I can not read the posted graphs titles....

Let me try posting that graphic as a thumbnail. it's too small for me to read in that earlier post.

Fundamentally, I guessed at a planform that would get me close, then adjusted twist, let openVSP (using the VLM method) calculate the lift distribution. I compared the results to the theoretical Prandtl or elliptical distribution, then reiterated the twist until the calculated lift distribution and the ideal were very close (the top graph's compare the Openvsp result to the desired "ideal" distributions.). The comprimises to those ideals were to allow for a lower local Cl at the outboard parts of the wing (to promote better stall behavior) the third graphs show the local lift distribution at CL max (the airfoil in the analysis [eppler 748] has a CL max of 1.8). Then I looked at the bending moment (2nd graphs) from the final lift distributions for both wings and the performance in a glider.

The important thing to note is that the Prandtl lift distribution on a 50 foot span produced slightly less bending moment than the elliptical distribution on a 40 foot span. That extra span reduced the induced drag at slow speeds compared to the short span elliptical wing.
So if we say bending moment is the main driver of wing weight, and weight is our limitation for an ultralight sailplane. And if we plan to mostly fly around at best L/D or Min sink then I guess I agree with the 1933 Prandtl rather than his more youthfull elliptical math!

-Peter-

 

[peter hudson]

OK one more try at readable graphs...

 

[peter hudson]

But ... it is like Albion Bowers (retired NASA-chief-engineer) said:
"Assumptions are the unseen walls we use to create ... the box".

With this in mind...I began thinking. "what if the real benefit to Prandtl's mathmatically sweet bell shape is really just unloading the tips enough to reduce the bending moment thereby increasing the span. If the shape isn't so important then a straight tapered wing with enough linear twist might accomplish the same result with fewer problems from all the variations in twist and planform. So I ran a 49 foot straight tapered wing with enough twist to create good stall behavior and less bending moment than the 40 foot Elliptical wing. The lift distribution is appalling based on most texts that aim for good "span efficiency" numbers but the results are compelling. In fact it performed better than the 50 foot Prandtl distribution. It may be if I continued to iterate on bending moment they would come in closer but that is a bit of a pain.


So each of the three wings so far have basically the same root chord (spar height), bending moment (therefore wing weight), and wing area. For this application with a draggy self launched ultralight sailplane the tapered twisted wing with the "crappy" distribution beats the elliptical distribution pretty noticably. [L/D of 22.7 vs. 20.5 and min sink of -137 fpm vs. -162 fpm]

Maybe the examples have been out there all along with wings like the Carbon dragon's, Not exactly bell shaped distributions but taking advantage of tapered twisted wings to reduce weight.

-Peter-

 

[pictsidhe]

What you seek is a low induced drag to bending moment ratio. R.T. Jones wrote a naca report you may find insightful. He also determined that bsld was the way to get low bending moment. He did not stop at sin³.
Are you calcukating span efficiency?

 

[peter hudson]

What you seek is a low induced drag to bending moment ratio. R.T. Jones wrote a naca report you may find insightful. He also determined that bsld was the way to get low bending moment. He did not stop at sin³.
Are you calcukating span efficiency?

I'm not really calculating span efficiency since I'm not sure how to relate them for distributions that change with lift coefficients. Also, since I'm letting aspect ratio float, I'd be comparing wing "A"s span efficiency to wing "B"s, but have to compensate some how for wing "B"s different aspect ratio.

I'm just now looking through that R.T. Jones paper. It looks like a closed form optimization of the trade space of keeping bending moment fixed and minimizing induced drag...pretty much what I was slogging through by trial and error with VLM. I'll spend some time with it, thanks for the reference! I'm thinking about tweaking his analytical optimization approach by restricting the distributions to only shapes that can be achieved with a single tapered wing with linear twist. (I'm not sure I'm sharp enough to generate the math for that).

At a glance he confirms that the elliptical lift distribution is not the ideal for a design constrained by weight and operating at high lift coefficients.

-Peter-

 

[pictsidhe]

If optimising for single taper with linear twist, I suspect you find taper wants to be more than is practical. Decide what can be built, then play with twist. Only one variable. With a constant span you can calculate a bending moment to drag ratio and select the winner.
This is probably a better approach than deriving the theoretical optimum shape, then trying to work out how in the world to build it.

 

[peter hudson]

If optimising for single taper with linear twist, I suspect you find taper wants to be more than is practical.

Right that R.T. Jones paper describes his lift distribution as :

Which seems a little bit of a challenge to achieve

And my experience with optimization is that depending on how you set up and constrain the problem you tend to drive to one corner of your trade space, and that corner is defined by the limits you picked based on some practical guess like what's the smallest tip chord I would accept and what's my upper limit for spar cap loads to meet my arbitrary wing weight budget during the design phase. Also the optimum twist may be limited by having local cl margin for the outboard sections rather than minimum induced drag.

The one thing that seems clear is whether it was Prandtl (1933), or Jones (1950), or this trade study, the idea of striving for an elliptical distribution and good span efficiency is NOT what this sort of aircraft should do.

-Peter-

 

[plncraze]

Studying the original Carbon Dragon for wing efficiency would be interesting because Irv Culver did the air foils and planform. Culver was very smart and experienced. The inner airfoils have a sharper leading edge to cause them to stall first and the outer ones have camber. I can't remember if he went for elliptical at all.

 

[nestofdragons]

Guys, i see you all testing BSLD in many tools. Do not forget that Marko made a few tools that are easy to use and give very quickly good info about BSLD wing platforms. Maybe fine toys for the new BSLD-experimenters.
You find them here: Flying Wing Designer - Nest of Dragons



Airfoil tool too

 

[peter hudson]

Studying the original Carbon Dragon for wing efficiency would be interesting because Irv Culver did the air foils and planform. Culver was very smart and experienced. The inner airfoils have a sharper leading edge to cause them to stall first and the outer ones have camber. I can't remember if he went for elliptical at all.

For a fuji to granny smith comparison; here's the carbon dragon wing lift distribution at Cl=1 (no flaps) and the local Cl at near stall. from open VSP using the Carbon Dragon airfoil coordinates. In the plans, there doesn't appear to be any wing twist (other than aerodynamic based on Cl0 of the airfoils) so this model was run without twist.

Things to notice:
It's nowhere near elliptical OR Prandtl distributions, but it does appear to take advantage of more span by reducing bending moment (less lift at the tips than elliptical). The local Cl looks awful for tip stalls if using a single airfoils but (without predicting Cl max for the airfoils) it looks like that was managed through airfoil design. So it's an easier to build, untwisted but tapered wing, and airfoils that ignore things like laminar flow in favor of managing stall behavior and having straight aft sections to make the full span flaps easy to build. Any desire for "cusps" or more camber are in the hands of the pilot with the full span flaperons. So this is definitely an example of a weight limited aircraft ignoring elliptical lift distributions in favor of span.