airfoil_comparison.py is a Python wrapper around the XFOIL program that simulates aerodynamic properties of NACA airfoils. It automates the process of generating airfoil data (lift coefficient CL, drag coefficient CD, and moment coefficient CM) over a range of angles of attack using XFOIL's command-line interface.
plots.py is a data visualization and analysis script for the results received from the aforementioned airfoil_comparison.py. It features KDE plots,
- Multi-Airfoil Support: Analyzes multiple NACA airfoils (2412, 0012, 0009) simultaneously
- Angle of Attack Sweep: Automatically sweeps angles from 0° to 14° (customizable range)
- Reynolds Number Variation: Generates multiple simulations with varied Reynolds numbers using normal distribution
- Data Export: Saves results to clean, structured CSV files for further analysis
- Robust Parsing: Handles XFOIL convergence issues and output parsing gracefully
- Offline Operation: Fully offline, runs with local
xfoil.exe - Progress Tracking: Real-time progress indicators with detailed completion status
- Python 3.x with the following packages:
numpy- For statistical Reynolds number generationsubprocess- For XFOIL process managementcsv- For data export
- XFOIL executable in your project folder
# Clone the repository
git clone https://github.com/dhruv114523/airfoil_comparison.git
cd airfoil_comparison
# Install dependencies
pip install -r requirements.txtDownload and place xfoil.exe in your project folder.
python airfoil_comparison.pyThe script generates:
test.csv- Raw simulation data- Console output with progress tracking
Use the included plots.py to generate visualizations:
python plots.py- KDE plot
- Line Plot for lift vs AoA with confidence intervals
- Line Plot for lift vs drag
- Line Plot for lift to drag Ratio vs AoA
- Line Plot for moment vs angle of Attack
Uses simulated data to explain effects of NACA geometry parameters on lift coefficient (Mean_CL). Two models are compared to address residual autocorrelation.
Predictors: Alpha, Alpha², M, P, T, TopXtr, BotXtr
Predictors: Alpha, Alpha², Alpha*M, M, T, TopXtr
Changes from OLS: Removed P (statistically insignificant, p=0.478) and BotXtr (p=0.400); added Alpha*M interaction term.
| Metric | OLS | GLS (Improved) |
|---|---|---|
| R² | 0.735 | 0.784 |
| Adjusted R² | 0.731 | 0.782 |
| RMSE | 0.1915 | 0.2052 |
| MAE | 0.1376 | 0.1553 |
| Durbin-Watson | 0.403 ❌ | 1.771 |
| AIC | -253.4 | -872.3 |
Key Findings:
- GLS dramatically improves autocorrelation (DW: 0.403 → 1.771, near ideal value of 2)
- Better model fit (R²: 0.735 → 0.784) and information criterion (AIC: -253 → -872)
- Higher prediction error (RMSE/MAE increased) suggests GLS trades point accuracy for better statistical properties
- The
Alpha*Minteraction term is marginally insignificant (p=0.174) but retained for theoretical reasons
| Variable | Coefficient | Interpretation | p-value |
|---|---|---|---|
Alpha |
+0.1232 | Base lift increase per degree | <0.001 *** |
Alpha² |
-0.0064 | Stall behavior (nonlinear effect) | <0.001 *** |
M |
+0.0655 | Max camber effect | <0.001 *** |
T |
-0.0251 | Thickness reduces lift (thicker = lower CL) | <0.001 *** |
TopXtr |
-0.3100 | Earlier top transition reduces lift | <0.001 *** |
Alpha*M |
+0.0009 | Camber amplifies AoA effect | 0.174 (ns) |
P |
(removed) | Position insignificant in OLS | 0.478 |
BotXtr |
(removed) | Bottom transition insignificant | 0.400 |
Generated in lm_plots/:
- Residual histogram (
residuals_hist.png) - Shows non-normal distribution - Geometry correlations (
{M,P,T}_vs_cl.png) - Linear relationships with lift - QQ plot - Reveals heavy tails (kurtosis = 9.9 in GLS)
- Residuals vs Fitted - Checks for heteroscedasticity (addressed with HC3 robust SE)
- Breusch-Pagan test: LM = 232.89, p < 0.001 ❌
- Solution: HC3 robust standard errors applied (confidence intervals widened appropriately)
- High condition number (1080) in GLS
- Likely due to
AlphaandAlpha²correlation (expected, theoretically justified) - VIF analysis recommended
- Jarque-Bera test: JB = 1273.06, p < 0.001 ❌
- High kurtosis (9.9) indicates outliers/heavy tails
- Likely caused by post-stall regime (AoA > 12°)
- Post-stall underprediction: Quadratic
Alpha²term insufficient for high AoA (>12°) behavior - Non-normal residuals: Heavy tails suggest piecewise regression or robust methods needed
- Multicollinearity warning: Condition number >1000 (acceptable given polynomial terms)
- GLS RMSE trade-off: Better R² but worse point predictions vs OLS
airfoil_comparison/
├── airfoil_comparison.py # Main simulation script
├── plots.py # Data visualization script
├── legacy/ # Legacy R-based analysis
│ └── airfoil comparison.R # Original R script for basic graphs
├── README.md # This file
├── xfoil.exe # XFOIL executable
├── lm.py # Linear model
├── MODEL_SUMMARY.md # Summary of OLS Linear Model
└── MODEL_SUMMARY_GLS.md # Summary of GLS Linear Model
flowchart LR
A[airfoil_comparison.py] -->|Generates| B[(LM.csv)]
B --> C[lm.py]
C -->|OLS Model| D[MODEL_SUMMARY.md]
C -->|GLS Model| E[MODEL_SUMMARY_GLS.md]
C -->|Diagnostics| F[lm_plots/*.png]
A2[airfoil_comparison.py] -->|Generates| B2[(airfoil_results.csv)]
B2 --> C2[plots.py]
C2 -->|Visualizations| D2[images_new/*.png]
- Airfoils: NACA 2412, 0012, 0009
- Reynolds Numbers: Normal distribution (μ=100,000, σ=2,000), 10 samples per airfoil (for testing)
- Angle Range: 0° to 14° (1° increments)
- Viscous Analysis: Enabled with Ncrit = 9
- Iteration Limit: 100 iterations per point
Airfoil,Reynolds,Alpha,CL,CD,CM,TopXtr,BotXtr
NACA2412,100000,0.0,0.2731,0.01663,-0.0681,0.8966,1.0
...- GUI Interface: User-friendly graphical interface
Note: The legacy version (R-based) is preserved in the
legacy/folder. While part of the same project, the scripts serve different purposes:
- Python Script (
airfoil_comparison.py): Full XFOIL wrapper with simulation capabilities, with a linear model and plotting- R Script (
legacy/airfoil comparison.R): Basic plotting and analysis tools
This project is open source and available under the MIT License.
Dhruv - LinkedIn Profile
Project Link: https://github.com/dhruv114523/airfoil_comparison