3D Vortex Lattice Method for a Swept and Tapered Wing

This repository contains a MATLAB implementation of the 3D Vortex Lattice Method (VLM) for calculating the aerodynamic characteristics of a finite, swept, and tapered wing at a given angle of attack. The code computes lift, induced drag, and spanwise circulation using a panel-based approach with cosine spacing.

✈️ Features

• Handles swept and tapered wing geometries
• Cosine spacing for improved panel resolution
• User-defined control point and bound vortex placement
• Computes:
  • Circulation distribution (Γ)
  • Spanwise lift distribution
  • Total lift and induced drag
  • Lift and drag coefficients (CL, CD)
  • CL correction using Prandtl’s lifting line theory
• Plots:
  • Γ vs. ideal elliptical distribution
  • Spanwise lift distribution

🔧 Parameters

Key adjustable parameters in the script:

• N: Number of spanwise panels (e.g., 50)
• Span, c_r, c_t, Lambda: Geometry (sweep, root/tip chords)
• alpha: Angle of attack (degrees)
• BVP, CPP: Chordwise positions of the bound vortex and control point

📊 Example Output

With:

• Span = 10 m, Taper ratio = 0.5, Sweep = 5°, AoA = 5°, V = 50 m/s, N = 50

The results are:

• CL: 0.8829
• Corrected CL: 0.4382 (Prandtl’s theory)
• CD: 0.04275
• Matrix Condition Number: ~1724 (well-conditioned)

📁 Files

• VLM_Cosine.mlx: Main script (geometry, solver, plots)
• README.md: Project overview

▶️ Usage

1. Clone the repo:

   git clone https://github.com/your-username/vlm-swept-wing.git
   cd vlm-swept-wing

2. Open VLM_Cosine.m in MATLAB and run.
3. Edit the geometry or flow conditions in the script header to customize.

📌 Notes

Inviscid, incompressible, and steady flow assumed
Thin wing theory: camber and thickness effects are not modeled
No viscous drag or compressibility modeled
Results are reliable for moderate angles of attack (≤ 10°)
for any change in parameters, a validation is needed

📚 References

Katz, J., & Plotkin, A. (2001). Low-Speed Aerodynamics
Anderson, J.D. (2011). Fundamentals of Aerodynamics
Bertin, J.J. & Smith, M.L. (1998). Aerodynamics for Engineers

🧑‍💻 Author

Developed by Mohammad Hossein Mosalmani, Aerospace Engineering graduate from Sharif University of Technology. If you use or build upon this code, feel free to mention or credit.

📄 License

This project is licensed under the MIT License — see the LICENSE file for details.