# I analyzed 2 nearly identical flying wing in XFLR5, how come the one with the thinner tip chord has a higher cD?

I made two flying wings, one with half the wing tip chord as the root chord and one with the root and tip chord being equal.

I then did VLM2 analysis on both at 7 m/s, and used the same airfoil on both. surprisingly, the wing with the thinner wingtip chord had a higher coefficient of drag (which i believe leads to higher drag). How come?

Everything I know leads to less drag, less induced drag because a thinner chord, thinner airfoil due to proportions, and same parasitic drag because everything else is constant. What causes the one with a thinner wingtip to have a higher CD? Does this make sense, or is it just the inaccuracies of trying to calculate CL and CD?

XFLR5 project file

I designed another plane with the same 30 deg sweep, same airfoil and an aspect ratio of 10 (span .5m, root & tip chord .05 m, no twist). Performance keeps getting worse. Only AOA at 0 makes sense to me but that's out the window.

• Are you certain they've been non-dimensionalized properly? Have you tried comparing CL^2 vs CD between the two configs? – JZYL Dec 17 '19 at 0:02
• I can't find cl^2 so I compared Cl^3/2 vs cd (not sure if this is what you were going for), and it look similar, but again the thinner chord tapers off after 2-3 deg AoA. I ran the analysis through 3d panel and LLT analyses and got very similar results. – ohitstarik Dec 17 '19 at 0:11
• What do you mean you can't find it? You just have to plot CL, multiply by itself and plot against CD on Excel – JZYL Dec 17 '19 at 0:13
• Oh duh. completely forgot you could export data for a second. Yeah gotcha, just did it and updated the main post. Cl^2/cd ratio higher now on the main wing. – ohitstarik Dec 17 '19 at 0:32
• Could you share the XFLR5 project file? – AEhere supports Monica Dec 18 '19 at 15:11

In addition to Chris' answer, I have had a look at your project file and could not readily reproduce your problem. I suspect the issue was in a combination of poor discretization (I increased the resolution of the airfoil and wing somewhat) and incorrect methodology (fixed-speed instead of fixed-lift).

Here are the XFLR5 results for fixed-lift tests (using 0.4 kg) on the following designs:

• Baseline: your original wing ($$AR=5.0, \;S=0.05\;m^2, MAC=1.0$$)

• Tapered: your original tapered variant ($$AR=6.67, \;S=0.038\;m^2, MAC=0.78$$)

• Tapered - equalized AR: the tapered variant with the root chord increased to match the aspect ratio of the Baseline ($$AR=5.0, \;S=0.05\;m^2, MAC=1.08$$)

• Tapered - equalized area: the tapered variant with the span extended to match the area of the Baseline ($$AR=8.8, \;S=0.05\;m^2, MAC=0.78$$)

As expected, efficiency gains are proportional to AR increases. You can have a look at the updated project file here (make sure to click Show all Polars).

• This is it i believe, I used fixed speed instead of fixed lift. I still have a couple semesters until my aero classes. I'm guessing we use fixed lift comparing the two airframes because they have their own optimized flight window right? i.e., the higher AR aircraft would want to fly a little faster to perform better, etc. – ohitstarik Dec 24 '19 at 19:26

First, this isn't quite an apples-to-apples comparison. The aspect ratio of the first wing is higher than the second wing, so you're varying more parameters than just the tip chord.

The way to think about this is that the CD of a wing is going to be strongly dependent on the aspect ratio $$AR$$, the taper ratio $$\lambda_T$$, the chord and twist distribution along the wing, as well as the airfoil distribution. Is the airfoil t/c constant across both wings? That will also have an effect.

It would be clearer to look at a polar of CL plotted against CD; the best point of comparison is to look at the drag generated at the same CL, not the same angle of attack (because the zero-lift angle of attack will change with wing design as well). The second wing is generating less drag, but also less lift at a given angle of attack; the comparison isn't really fair. If you're using a VLM what you're measuring is the CDi of a wing geometry, which is going to be most strongly dependent on CL.

• The aspect ratio is higher, so why is there more drag? Shouldnt a higher aspect ratio lead to less induced drag if the wingspan is the same? You have the same parasitic drag if the wingspan is the same, etc. I'm definitely starating to get it now though with the CL vs CD graph, but the thicker wing still definitely excels there. The only graph where the thinner wing does better is CL/CD vs Alpha, which kind of clicks? The airfoil is the same t/c in both of the aircrafts (i'm assuming this is thickness % at chord of airfoil) – ohitstarik Dec 18 '19 at 22:55
• One more graph is the Moment vs Alpha graph, where the thicker wing is generating MUCH less CM at any given alpha, and the thinner wing is generating negative/stable CM. Could this also lead to the higher cd? – ohitstarik Dec 18 '19 at 23:05
• The right way to compare the two wings is looking at the CD values of the wings at the same CL, not the same alpha. So if that bottom plot is indeed CL vs. CD, you can see that the higher aspect ratio wing has lower drag at the same CL; this is what you would expect. Typically in flight alpha will be adjusted to give the target CL (and hence airspeed); the specific alpha value is not that significant. Pitching moment doesn't have an effect on drag. – Chris Dec 19 '19 at 1:33
• Thats what was confusing me so much. The XFLR5 is the complete opposite of that expectation, the lower AR wing has higher CL at the same CD. I messed up the data on the google sheets CL^2/CD graph that i made (wrong CD values for LowAR wing). It makes sense that this doesnt make sense right? – ohitstarik Dec 19 '19 at 3:54
• Does your method show the breakdown between viscous drag ($C_{D_{p}}$) and induced drag ($C_{D_{i}}$)? From the screenshot it looks like you're running a viscous analysis (coupled to a vortex lattice?). If you're only looking at $C_{D_{i}}$, then higher AR should give lower drag. If you're including $C_{D_{p}}$ there may be more going on. – Chris Dec 19 '19 at 15:44