Optimizing Constant Chord Wings for Speed

[SoarNeck]

Hi all,

If one was forced to use a wing with constant chord and thickness, is there any fault with the logic that says one could decrease the high-speed drag produced by the wing using slight wash-in at the tips? It seems to me that this would be more efficient since the local CL requirements at the tips are so low, and there is so much extra area at the tip of a constant chord wing.

Is there anything else that can be done to improve on such a design?

This would be for a racer, so I don't want to compromise high-speed turn performance.

Thanks,
Adam

[Purdue Aero Man]

In aerodynamic optimization design classes, we did many such optimizations for minimum drag with constant chord wings. On a constant chord wing, an elliptic loading gives the minimum induced drag because it produces uniform downwash in the Trefftz plane (actual cause of min induced drag). The wing tips should actually be turned downwards relative to the fuselage angle of incidence. I'll try to dig up my old matlab scripts to show you.

[SoarNeck]

Please do...I'd appreciate it. I don't quite follow what you're referring to by turning the wingtip downwards...trailing edge up or down?

Trailing edge up would improve the lift distribtuion towards the elliptical ideal, but trailing edge down would make the local CL distribution more equal. I think that the latter would be more efficient at high speeds for constant chord.

[Petri Nygren]

Soarneck,

From purely profile drag(Cdp) minimizing wiewpoint your idea does make sense IF you have a very narrow drag bucket like with ultra-thin profiles. By using wash-in, you could create a wing which has a uniform Cl distribution, aimed at precisely one optimum Cl value for a given (high speed)trim. In constant chord wing that would mean elliptic wash-in from root to tip.

OTOH induced drag(Cdi) would be an absolute nightmare. Although it might not matter too much in fast straight and level flight since Cdi is at it´s minimum when Cl total is at it´s minimum, but in turns the Cdi would rocket off the scale. This is because the wash-in was used to fight the Cl drop in tips due to the tip vortice. Wash-in made not only the Cl distribution but also the lift distribution a straight line since those two are the same with constant chord. What we have now is a enormous increase in tip vorticity strength because our lift distribution was made further away from the elliptic optimum.

Not to mention how the landing would feel like! I would seriously consider installing landing gear on the roof of such a model and landing it inverted.

Despite the problems, I feel this mental excercise is a very useful one. Many molded performance model wing planforms do try to keep an uniform Cl distribution for the main part of the span, except for the extreme wingtip, while aiming for elliptic lift distribution at a wide speed range. This requires zero wash-out/in, a carefully tailored narrowing towards the tips and right amount of sweep.

[Purdue Aero Man]

I think I just found what I want to show you. Just let me get matlab reinstalled so I can run the darn thing.

[Sail 'n Soar]

Hi all,

If one was forced to use a wing with constant chord and thickness, is there any fault with the logic that says one could decrease the high-speed drag produced by the wing using slight wash-in at the tips? It seems to me that this would be more efficient since the local CL requirements at the tips are so low, and there is so much extra area at the tip of a constant chord wing.

Is there anything else that can be done to improve on such a design?

This would be for a racer, so I don't want to compromise high-speed turn performance.

Thanks,
Adam

I've scanned most of this thread and the one question you didn't appear to have addressed is what is driving the requirement for constant cord and thickness. Unless your plane is equipped with flaps, at high speed you have more than enough area for lift and induced drag is relatively small, which drops most of the rationale for messing around with tailoring the lift distribution with washin.

[Purdue Aero Man]

Alright soarneck, ran the old code real fast.

"The objective of this homework was to minimize the drag of a wing with a given set of wing geometry. The wing had a total span of 70 feet, flew at 10,000 feet, a velocity of 200 ft/s, no quarter chord sweep, a root chord of 10 feet, and a tip chord of 5 feet."

Notice that the amount of lift required wasn't stated....the prof built onto this HW later in the semester. Aslo, this isn't a constant chord wing, but the results are similar for the CC wing. For reference, the airfoil was a NACA 63-412, and our design CL was at .4, right in the middle of the airfoils drag bucket at the Re the plane is flying, approx. 7.4E6

In the graphs, Dy is the location along one wing.

I included a constand chort alpha distribution as well. Notice the purely elliptical shape for the CC wing, whereas the tapered wing had an unusual shape. Hope this helps explain it a little better.

[Petri Nygren]

Constant chord does not give elliptic lift distribution -see the graph. I´m adding a modern planform as a comparison. There the lift distribution is closely elliptic and Cl-distribution near-straight line except for the tips.
I bet Soarneck´s CC-case is Q500 racer. There´s little you can do for them.

[Purdue Aero Man]

A constant chord, unswept wing can obtain an elliptic lift distribution with twist. I don't undestand how there can be any argument about that.

[Petri Nygren]

A constant chord, unswept wing can obtain an elliptic lift distribution with twist. I don't undestand how there can be any argument about that.

There isn´t any argument about that. I just wanted to clarify a often-quoted misconception.

[Sail 'n Soar]

A constant chord, unswept wing can obtain an elliptic lift distribution with twist. I don't undestand how there can be any argument about that.

The argument isn't whether or not a constant cord wing can achieve an elliptical lift distribution at one specific angle of attack. The question is at high speed, why bother? As CL gets small, i.e., at high speed, CDi becomes very small with the square of CL.

SoarNeck, I ask again, why are you being forced to use a constant cord wing? There are both aerodynamic and structural reasons why that isn't the best choice.

[Petri Nygren]

The question is at high speed, why bother? As CL gets small, i.e., at high speed, CDi becomes very small with the square of CL.

Soarneck´s question is a good one, it just wasn´t about lift distribution or CDi. The way I understood it, he asked about lowering Cdp, not Cdi, by getting Cl-graph more even from root to tip. In CC-zero-twist wing Cl must be high at root because it is low at tip. Straight Cl distribution line would make profile selection easier and might thus facilitate lower CDp.

[SoarNeck]

Hey guys,

Thanks for all this info over the weekend - I wasn't able to get to it, so I'll need a little while to catch up. 12 hours of painting and barn maintenance this weekend...sheesh.

Anyway, Petri was right...what originally prompted this was a design for a Q500 racer. Very restrictive race class, since it's intended to promote racer skill rather than equipment design. As a result, I'm facinated at the thought of trying to work within that restrictive ruleset. Basic parameters:

-500sq" min
-50-52" wingspan
-must be constant chord over the inner 47,5"
-thickness must be at least 1 3/16" (AMA rules) or 11.25% (Cdn rules) for the same inner span

Pretty limiting...hence my question. Thoughts on whether tip plates would be useful to try to reduce wingtip vortex generation?

Thanks again...
Adam

[Purdue Aero Man]

If Cdp is gonna be the big thing in your instance, no tip plates. Even if Cdi was gonna be the big deal with your plane, the reduction in Cdi, if any, would be too small to warrant the tip devices.

[Sail 'n Soar]

Soarneck´s question is a good one, it just wasn´t about lift distribution or CDi. The way I understood it, he asked about lowering Cdp, not Cdi, by getting Cl-graph more even from root to tip. In CC-zero-twist wing Cl must be high at root because it is low at tip. Straight Cl distribution line would make profile selection easier and might thus facilitate lower CDp.

That still gets back to what is the mean CL while flying at race cruise speeds. Now for a little math. For the sake of argument, assume a 50" span, 10" constant cord. Then the average CL will be ~ 86% of CL, max. If you assume a cruise speed of 100mph, then q = 25.6 psf. If the wing loading is 24 oz/sq ft, or 1.5 psf, then CL,average at cruise will be 1.5/25.6, or .06. At that CL, average, the CL at the root will be .07 and that at the tip will be 0. That translates to the local angle of attack will differ by less than .7 degrees from the root to the tip. CDp isn't going to very much over that small alpha range. But what about during the turns? How much time are you flying around pylons vs. on the straights?

This is a nice academic discussion, but I don't think there is much gold to mine in those hills.

[Lazy]

Question is: where you find more profit ? On obtain elliptical lift distribution or linear Cl ?

[Petri Nygren]

CDp isn't going to very much over that small alpha range.

Very true. But as I begun with, narrow design point allows you to create a profile with much reduced drag at that very regime. However that was the line of thought before it was revealed that this thread is about Q500 racer. They have their min. profile thicknesses limited and turn a lot so we can forget the whole thing.



But what about during the turns? How much time are you flying around pylons vs. on the straights?
That´s another good reason to forget it. Turn performance is crucial for a racer. Basically you spend at least 50% of a lap at various degrees of turning flight.



This is a nice academic discussion, but I don't think there is much gold to mine in those hills.
I fully agree...


Question is: where you find more profit ? On obtain elliptical lift distribution or linear Cl ?
In case of a racer, certainly from elliptic lift distribution! linear Cl may or may not do the profile selection a bit easier. If overdone, it makes things harder...

[SoarNeck]

Thanks for the feedback guys, very appreciated. I didn't predict a big possible savings, but it never hurts to investigate these things.

That said, any thoughts on the ideal Q500 wing/wingtip? There's not much you can do within the inner 47.5", and not much you can do with the tip either really. My thought was to at least thin/transition the tip airfoil.