Vortex Lattice Method

Vortex Lattice Method (aerodynamics/cfd/vortex-lattice-method)

Use when the task is computing wing spanwise loading with the horseshoe vortex lattice method: panel geometry, influence coefficients, circulation solution, and the derived lift and induced drag.

Domain quick reference

• The half wing is divided into spanwise panels; each panel carries a horseshoe vortex whose bound segment sits on the quarter chord and whose trailing legs run downstream.
• The root-side leg of the root panel is dropped, the mirror-image cancellation of the half-wing model.
• The no-penetration condition at the three-quarter chord control points gives a linear system in the panel circulations.
• The spanwise lift distribution follows from the Kutta-Joukowski law per panel; the downwash angles at the bound vortices give the induced drag by the near-field estimate.
• Near-square panels (spanwise width close to the local chord) give the cleanest solutions; the classic collocation converges to the Prandtl lifting-line result for straight wings.

Workflow

1. Build the panel lattice with build_wing (span, root and tip chord, panel count).
2. Assemble the influence coefficient matrix with influence_matrix.
3. Solve for the panel circulations with solve_circulations.
4. Derive per-panel lift, downwash angles, and induced drag with lift_distribution, downwash_angles, and induced_drag_coefficient.
5. Report the lift coefficient, induced drag coefficient, and span efficiency from wing_coefficients.

Pitfalls

• Using panels much narrower than the local chord; the elementary single-row horseshoe collocation develops an alternating checkerboard mode on narrow panels.
• Reporting the root panel downwash as positive; the dropped root leg leaves a small upwash artifact at the root.
• Applying the elementary single-row model to swept planforms; swept wings need a multi-row vortex ring lattice (see the swept-wing-aerodynamics leaf).
• Using the linear model beyond small angles of attack; the method is invalid for |alpha| at or above 45 degrees and never models stall.
• Confusing this method with the analytic lifting-line formula or the parabolic drag polar; those are the lift-curve-slope and drag-polar leaves.

Behavior contract (gate 3)

The horseshoe Biot-Savart, influence matrix, circulation solve, lift distribution, downwash, and induced drag logic is exercised by the gate 3 contract test: scripts/test_vortex_lattice_method.py against scripts/vortex_lattice_method_logic.py (stdlib unittest, offline). Run: python3 scripts/test_vortex_lattice_method.py

Compliance

• NACA Report 824 anchors the section-data context (public domain); summary and physics values only, per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.