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Merge pull request #13 from flexcompute/docs/cleanup-and-polar-types
docs: remove legacy investigation pages, add polar types and differences-from-xfoil
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‎docs-site/docs/internals/differences-from-xfoil.mdx‎

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---
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title: Differences from XFOIL
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sidebar_label: Differences from XFOIL
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sidebar_position: 9
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description: Known behavioural differences between RustFoil and XFOIL
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---
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# Differences from XFOIL
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RustFoil is a faithful, function-by-function port of XFOIL. The goal is
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bit-level reproducibility of XFOIL's behaviour, including its known limitations
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and failure modes.
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## Analysis (OPER)
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The core analysis pipeline — inviscid panel method, boundary layer solver,
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viscous-inviscid coupling, and transition prediction — has no known behavioural
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differences from XFOIL. Validation results:
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| Component | Agreement |
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|-----------|-----------|
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| Paneling (PANGEN) | ~4e-7 RMS position error |
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| Inviscid CL, Cp, γ | 5–6 significant figures |
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| Closure relations (Hk, Hs, Cf, DI) | Formula-identical |
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| Viscous-inviscid coupling | Same Newton system |
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| Transition (e^N) | Same DAMPL correlation |
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| Polar types 1/2/3 | Same Re-scaling formulas |
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See [Inviscid Validation](./inviscid-validation), [Paneling Validation](./paneling-validation),
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and [Formula Comparison](./xfoil-formula-comparison) for detailed evidence.
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## Design Modes
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### QDES (Mixed-Inverse)
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RustFoil's QDES uses **Gaussian basis functions with damped least-squares**
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rather than XFOIL's original `MIXED` Newton solver. The interface is the same
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(prescribe target Cp/velocity on a surface segment), but the internal algorithm
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differs. Results may not match XFOIL exactly for the same target distribution.
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This is an intentional choice for numerical robustness in the browser
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environment.
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### MDES (Full-Inverse)
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The circle-plane conformal mapping is ported from XFOIL, but with known gaps:
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- Chord normalization is approximate — output chord may differ slightly from input
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- CL computation is approximate; full Karman-Tsien integration not yet ported
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- No interactive Fourier coefficient editing
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MDES and QDES are marked **experimental** and have not been exhaustively
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validated against XFOIL reference cases.
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### GDES (Geometry Design)
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Geometry operations (flap deflection, TE gap, LE radius, thickness/camber
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scaling) match XFOIL's approach. Flap deflection uses a high-resolution
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intermediate representation for sub-0.001c precision at the hinge.
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## Reporting Differences
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If you find a case where RustFoil's analysis output differs from XFOIL's for
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the same airfoil and operating conditions, please report it as a bug at
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[github.com/flexcompute/flexfoil/issues](https://github.com/flexcompute/flexfoil/issues).
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Include the airfoil coordinates, operating conditions (Re, Mach, Ncrit, alpha),
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and both outputs.

‎docs-site/docs/internals/paneling-validation.mdx‎

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---
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sidebar_position: 6
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title: Paneling Validation
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description: Comparison of XFOIL and RustFoil curvature-based paneling (PANGEN)
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description: Validation of RustFoil curvature-based paneling against XFOIL's PANGEN
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---
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# Paneling Validation: XFOIL vs RustFoil
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# Paneling Validation
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This document compares the paneling algorithms between XFOIL's `PANGEN` subroutine and RustFoil's `resample_xfoil()` implementation.
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## Algorithm Overview
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Both implementations use **curvature-based panel distribution** with identical parameters:
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RustFoil's `resample_xfoil()` function is a faithful port of XFOIL's `PANGEN` subroutine. Both use **curvature-based panel distribution** with identical parameters:
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| Parameter | Value | Description |
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|-----------|-------|-------------|
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| `RDSTE` | 0.667 | TE panel spacing ratio (RTF = 0.334) |
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| `IPFAC` | 5 | Newton refinement factor |
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### PANGEN Algorithm Steps
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### Algorithm Steps
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1. Compute arc-length parameterization of buffer airfoil
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2. Calculate curvature at each buffer point: κ(s) = |d²r/ds²|
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3. **Find leading edge via Newton iteration** (tangent ⊥ to chord)
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3. Find leading edge via Newton iteration (tangent ⊥ to chord)
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4. Average curvature over 7 points near LE → κ_avg
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5. Set artificial TE curvature: κ_TE = κ_avg × CTERAT
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6. Smooth curvature with tridiagonal diffusion
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## Validation Results
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### Symmetric Airfoils (NACA 0012)
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All tested airfoils match XFOIL's paneling to numerical precision (~4e-7 RMS position error):
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**Perfect match achieved:**
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| Foil | XFOIL LE Index | RustFoil LE Index | RMS Error |
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|------|----------|-------------|-----------|
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| NACA 0012 | 79 | 79 | 4.05e-7 |
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| NACA 2412 | 81 | 81 | 3.97e-7 |
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| NACA 4412 | 82 | 82 | 4.42e-7 |
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| Metric | Value |
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|--------|-------|
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| RMS Position Error | 4.05e-7 |
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| Max Position Error | 5.92e-7 |
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| LE Index Match | ✓ (idx=79) |
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### Point-by-Point Comparison (NACA 0012)
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```
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First 5 points comparison:
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idx xfoil_x xfoil_y rustfoil_x rustfoil_y error
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0 1.00000000 0.00126000 1.00000000 0.00126000 0.00e0
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1 0.99167960 0.00242145 0.99167973 0.00242143 1.36e-7
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2 0.98036920 0.00398137 0.98036941 0.00398134 2.14e-7
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```
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### Cambered Airfoils
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**LE detection mismatch identified:**
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| Foil | XFOIL LE | RustFoil LE | LE Diff | RMS Error |
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|------|----------|-------------|---------|-----------|
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| NACA 0012 | idx 79 | idx 79 | 0 | 4.05e-7 ✓ |
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| NACA 2412 | idx 81 | idx 83 | +2 | 7.29e-3 |
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| NACA 4412 | idx 82 | idx 85 | +3 | 1.13e-2 |
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## Root Cause Analysis
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The discrepancy for cambered airfoils originates in the **leading edge detection** (`lefind` function).
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### XFOIL's LEFIND Algorithm
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From `xgeom.f`:
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```fortran
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C---- Find leading edge location (SBLE) using Newton iteration
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C to find where tangent is perpendicular to chord line
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XCHORD = X(N) - X(1)
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YCHORD = Y(N) - Y(1)
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C---- Newton iteration
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DO 10 I=1, 50
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XPRIME = DEVAL(SBLE,X,XP,S,N)
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YPRIME = DEVAL(SBLE,Y,YP,S,N)
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C------ Dot product of tangent with chord should be zero at LE
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RES = XCHORD*XPRIME + YCHORD*YPRIME
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DSLE = -RES / (XCHORD*X2 + YCHORD*Y2)
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SBLE = SBLE + DSLE
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IF(ABS(DSLE) .LT. 1.0E-6) GO TO 11
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10 CONTINUE
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```
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The key is finding where:
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```text
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t(s_LE) · chord = 0
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```
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where `t` is the tangent vector and `chord` connects TE upper to TE lower.
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### Issue in RustFoil
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RustFoil's `lefind` implementation may have subtle differences in:
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1. Initial guess for Newton iteration
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2. Convergence tolerance
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3. Spline derivative evaluation
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## Fix Applied
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The original RustFoil implementation had **incorrect symmetry enforcement** in the final node positions (lines 484-492 of `spline.rs`). This worked for symmetric airfoils but caused LE drift for cambered airfoils.
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**Fix**: Removed the symmetry enforcement, matching XFOIL's behavior which relies purely on curvature-based distribution without post-processing symmetry.
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## Final Results (All Fixed!)
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| Foil | XFOIL LE | RustFoil LE | RMS Error | Status |
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|------|----------|-------------|-----------|--------|
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| NACA 0012 | idx 79 | idx 79 | 4.05e-7 | ✓ Perfect |
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| NACA 2412 | idx 81 | idx 81 | 3.97e-7 | ✓ Perfect |
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| NACA 4412 | idx 82 | idx 82 | 4.42e-7 | ✓ Perfect |
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**All three airfoils now match XFOIL to numerical precision (~4e-7)!**
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## Root Cause & Fix
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The bug was **forced curvature symmetry** in `resample_xfoil()`:
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```rust
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// THIS WAS THE BUG (lines 241-247)
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for i in 0..n_buffer / 2 {
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let avg = (curv_buffer[i] + curv_buffer[j]) / 2.0;
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curv_buffer[i] = avg; // WRONG for cambered airfoils!
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}
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```
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**Why it mattered:** For cambered airfoils, the curvature is naturally asymmetric:
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- NACA 2412: 26% higher curvature on lower surface near LE
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- NACA 4412: 59% higher curvature on lower surface near LE
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By forcing symmetry, we were averaging out this natural asymmetry, which caused the Newton iteration to place panels incorrectly.
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**XFOIL does NOT force curvature symmetry** - it uses the natural asymmetric curvature for cambered airfoils.
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## Conclusion
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1. **All airfoils now match**: ~4e-7 RMS error (numerical precision)
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2. **Root cause**: Incorrect forced curvature symmetry
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3. **Fix**: Removed two forced symmetry operations in `spline.rs`
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Leading-edge detection, curvature distribution, and final node placement all match XFOIL exactly for both symmetric and cambered airfoils.

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