ashfordeOU Airfoil Shape Optimization (aerodynamics/airfoil/airfoil-optimization)
Use when the task is airfoil shape optimization: design variables and parameterization, aerodynamic objectives, geometric constraints, trade studies, and sensitivity analysis.
Domain quick reference
- Design variables: the NACA 4-digit family gives the low-dimensional set (camber m, camber position p, thickness t, per NACA Report 824); the PARSEC 11-parameter family (open literature) controls the shape directly: leading-edge radius, upper and lower crest position, ordinate, and curvature, and trailing-edge ordinates and angles.
- Objective: lift-to-drag ratio cl / cd at the design condition, maximum lift coefficient clmax requirement margin, or low-drag bucket width (the cl range over which cd stays within a tolerance of the minimum cd, typical of laminar 6-series sections).
- Geometric constraints: minimum thickness for structural depth, camber bounds for hinge-line and pitch behavior, trailing-edge thickness floor. Checked with constraint_violations.
- Trade study: sweep one design variable over a grid, evaluate the objective at every point, rank the candidates. The grid best is a candidate, not a converged optimum.
- Sensitivity: central finite-difference gradient df / dx_i; the relative sensitivity (df / dx_i) * (x_i / f) ranks which design variable moves the objective most.
- Multi-objective: with two competing objectives (for example thickness versus lift-to-drag), keep only the non-dominated designs with a Pareto filter.
- PARSEC convention used here: upper surface y_u(x) = sum a_i * x^(i - 1/2) for i = 1..6, lower surface y_l(x) = sum b_i * x^(i - 1/2), with a_1 = sqrt(2 * r_le), b_1 = -sqrt(2 * r_le), crest conditions y(x_top) = y_top, y'(x_top) = 0, y''(x_top) = y_xx_top (and the lower analogues), and trailing-edge conditions y(1) = y_te_u, y'(1) = tan(alpha_te) (and y(1) = y_te_l, y'(1) = tan(beta_te)). Angles are radians. The series slope and curvature are singular at x = 0.
Workflow
- Choose the parameterization: NACA 4-digit variables (m, p, t) for a low-dimensional study, or the 11 PARSEC parameters for shape level control. Generate section ordinates with parsec_surface for PARSEC; for NACA ordinates use the airfoil-geometry leaf.
- Define the objective: lift_drag_ratio at the design point, clmax_margin against the requirement, or drag_bucket_width from a polar table.
- Define the geometric constraints (thickness floor, camber bounds) and check them with constraint_violations.
- Sweep the design variable with trade_sweep and pick the candidate with best_trade_point; inspect the neighbors of the best point.
- Rank the design variables with central_difference_gradient and relative_sensitivity to find which ones move the objective most.
- With two competing objectives, filter the non-dominated designs with pareto_front.
- Pass the selected section to the xfoil-analysis leaf for polar evaluation and iterate.
Pitfalls
- Treating the objective (lift-to-drag at the design condition) as a constraint (clmax requirement); L/D peaks at the design point while clmax is a limit that must clear the requirement with margin.
- Driving thickness down to gain L/D while ignoring the structural depth floor; always pair the L/D objective with the thickness constraint.
- Reading drag bucket width from a single polar point; the bucket is a cl range and needs the full polar.
- Reporting the grid best of a coarse trade sweep as the optimum; check the neighboring grid points or refine the sweep.
- Using the linear clmax trend model as a physics prediction; it is a local trend that needs a slope calibrated from the user's own polar data.
- Mixing PARSEC convention variants; trailing-edge ordinate and angle definitions differ across the literature, this leaf uses the documented convention above.
- Evaluating slope or curvature at x = 0; the PARSEC series is singular at the leading edge and raises ValueError there.
Behavior contract (gate 3)
The optimization logic is exercised by the gate 3 contract test: scripts/test_airfoil_optimization.py against scripts/airfoil_optimization_logic.py (stdlib unittest, offline). Run: python3 scripts/test_airfoil_optimization.py
Compliance
- NACA Report 824 is US government work (public domain); the PARSEC parameterization is common engineering knowledge from the open literature. Formulas and summary values only, per standards-map.yaml.
- compliance: STANDARDS-REF, gated: false.