Non-zero induced drag (CDi) at CL≈0 — possible degenerate wing root XSec

[Koaib Kaleem]

Hi all,

I'm running a VLM sweep in VSPAERO on a low-AR fighter-type wing (TotalAR ≈ 2.35, TotalArea ≈ 78.3 m², TotalSpan ≈ 13.6 m) and I'm seeing induced drag (CDi) that does not go to zero as CL → 0, which shouldn't be physically possible for a symmetric configuration at zero sideslip.

Symptom:
- Across a Mach 0.2–0.6 / SL–35,000 ft sweep, CDi at CL ≈ 0 (alpha ≈ -2° to 0°) sits around 0.027–0.035 — nearly as large as CDi at CL ≈ 0.5.
- Plotting CDi vs CL² shows a large non-zero y-intercept instead of a line through the origin.

What I've ruled out so far:
- Wake iterations: reran the same case at 8 vs 15 wake iterations — CDi at CL≈0 is identical to 4 decimal places between the two runs, so this isn't a wake-convergence issue.
- Reference values: TotalArea/TotalSpan read live off the wing (WingGeom parm group) cross-checks exactly against summing planform area/span from only the outer two XSecs — so Sref/Bref aren't corrupted.
- Mesh density: already ran a mesh convergence study; refining panel count doesn't change this.

What I've found:
Dumping the wing's XSec parameters, XSec 0 (root-most section, right at the fuselage attach) has:
- Root_Chord = 1.0, Tip_Chord = 9.88 (taper = 9.88, i.e. tip chord ~10x root chord)
- Span = 1.0, but ProjectedSpan = 0.0
- Input Sweep = 0.0, but the resulting Sec_Sweep (actual local sweep) = 83.6°

So this section has essentially zero planform footprint but a large local sweep and a rapidly flaring chord — it visually reads as a small transition/root section, but numerically it's a near-degenerate, nearly-vertical panel wedged between the fuselage and the start of the real wing (XSec 1: Root_Chord 9.88 → Tip_Chord 2.80, Sweep 42°, ProjectedSpan 5.9 m).

Question:
Has anyone seen a wing root XSec with ProjectedSpan ≈ 0 and a near-90° effective local sweep cause the VLM solver to produce a residual, roughly CL-independent CDi contribution like this? Is this a known failure mode for degenerate/near-zero-span root sections in VSPAERO's Trefftz-plane induced drag calc, similar to the near-zero-chord panel issue mentioned in past threads here? Or is there a recommended way to define a root fillet/transition section that avoids this?

[Rob McDonald]

Your case doesn't run for me, but I might be using a development version or something else different.

However, you case is not symmetric.  There is no reason to expect zero CDi at zero CL.

Run a sweep of alpha.  Use that to interpolate and estimate the alpha for zero CL (it doesn't have to be perfect).  Then, run a single case at just that alpha.

Look at the lift distribution plot for that single case.  You'll see that there are regions of positive lift and other regions of negative lift.  They sum to zero, but they all cause induced drag.

Also, your spanwise resolution on the lifting surfaces is insufficient.

Rob

[Koaib Kaleem]

right,

i am quite confused why its unsymmetric, i have observed that distribution is unsymmteric too but i cannot reach any conclusion
Can u tell me why

thanks

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[Rob McDonald]

Your geometry is not symmetric about the Z=0 plane.  You have a fuselage, V-vertical tails, a horizontal tail out of plane with the wing, etc.  I haven't looked at your airfoils, twist, and incidence, but those may be noon-zero too.

However, just your fuselage and vertical tail are enough to make it not symmetric.

Imagine copying your entire geometry, flipping it Z = -Z -- is it the _identical_ geometry?  If not, then it isn't symmetric.

Rob

[Koaib Kaleem]

i had tried to ensure symmetry wherevr possible, like the skinnig etc but may check it out again

thankyou

[Rob McDonald]

The problem is not Left - Right symmetry.

The cause of non-zero induced drag at zero lift is the fact that you do not have zero lift everywhere when the total lift is zero.  This is caused by some sort of asymmetry in pitch.

There is nothing symmetric about your geometry.  This is not a small modeling error.  This is a fundamental lack of understanding in what matters for the aerodynamics of a problem.



Think about an airfoil:

Symmetric:

Not-Symmetric:

One of these will have zero lift at zero alpha -- the other will not.

Now, imagine you have a wing with a + cambered airfoil at the root and a - cambered airfoil at the tip:

At zero alpha, the root will lift up and the tip will have lift down.  At some alpha, the total lift will be zero.  The below lift distribution is taken at very near the zero total lift condition (CL ~= .001), but notice the lift distribution:



It is zero nowhere (except a crossing point at mid span), but the integral sums to zero -- the positive lift at the root is cancelled by the negative lift at the tips.

However, both the + and - lift both cause + induced drag.  So, the induced drag of this wing is non-zero -- even at zero lift.

The only way to have zero induced drag is to have zero lift _everywhere_.  To do that, you need a perfectly symmetrical geometry -- which your airplane is not.

Rob

[Koaib Kaleem]

right right

thanks alot for taking out time to explain.