# Constraint Analysis > Use when you must run the aircraft constraint analysis matching chart in conceptual design: compute the stall constraint wing loading from the maximum lift coefficient and the stall speed, the takeoff distance constraint thrust to weight curve, the climb gradient constraint from the excess thrust and the lift to drag ratio, the cruise constraint, and the maneuvering constraint from the load factor, then assemble the feasible design region lower bounds that gate the conceptual design trade. Produces the constraint dict, the feasible region boundary, and the required thrust to weight at the design point. Trigger: constraint analysis, matching chart method, feasible region, stall constraint, takeoff distance, climb gradient, cruise constraint, maneuvering constraint, load factor. - Skill: `ashfordeou/constraint-analysis` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/constraint-analysis` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/constraint-analysis/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - License: Apache-2.0 - Author: ashfordeOU (https://skillmd.com/u/ashfordeou) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/ashfordeou/constraint-analysis --- # Aircraft Constraint Analysis (vehicle-design/conceptual/constraint-analysis) Use when the task is aircraft constraint analysis for conceptual design: the matching chart method that computes required thrust to weight and wing loading from the stall, takeoff distance, climb gradient, cruise, and maneuvering constraints, and the feasible design region that bounds the propulsion and wing sizing trade. ## Domain quick reference - Wing loading W/S is in N/m^2, thrust to weight T/W is unitless, air density rho in kg/m^3 (default 1.225 kg/m^3, sea-level ISA), speeds in m/s, takeoff distance in m, flight path angle gamma in rad, load factor n unitless, and g = 9.80665 m/s^2. - Stall constraint (maximum wing loading): W/S = 0.5 * rho * CLmax * VS^2, from lift equal to weight at the stall speed VS. - Takeoff distance constraint (required T/W): T/W = 1.21 * (W/S) / (rho * g * CLmax * s_TO), with s_TO the takeoff distance in m. - Climb gradient constraint (required T/W): T/W = 1/LD + gamma, the level-flight drag term plus the small-angle climb term, gamma in rad; equivalently the excess thrust fraction (T - D)/W equals the climb gradient. - Cruise constraint (required T/W at speed V): T/W = 0.5 * rho * V^2 * CD0 / (W/S) + k * (W/S) / (0.5 * rho * V^2), the zero-lift drag term plus the lift-induced drag term, k = 1/(pi * e * AR). - Maneuvering constraint (required T/W in a level turn at load factor n): T/W = 0.5 * rho * V^2 * CD0 / (W/S) + k * n^2 * (W/S) / (0.5 * rho * V^2); the induced drag term grows with n^2, and at n = 1 the maneuvering curve reduces to the cruise curve. - The matching chart plots required T/W against W/S, one curve per constraint. At a given wing loading the feasible region lower bound is the maximum of the required T/W values over the active constraints; the boundary of the feasible design region is the set of those lower bounds across the wing loading sweep, and every point above the boundary is feasible for the constraint set. - FAR-25 (14 CFR Part 25) and CS-25 set the certification context (stall speed, takeoff field length, and climb gradients for transport-category aeroplanes); the constraint equations are common conceptual sizing practice. ## Workflow 1. Set the design point: stall speed, maximum lift coefficient, air density, takeoff distance, lift-to-drag ratio, climb gradient, cruise speed, zero-lift drag coefficient, induced drag factor k, and the maneuvering load factor. 2. Compute the maximum wing loading allowed by the stall speed with stall_constraint. 3. Compute the required T/W from the takeoff distance with takeoff_constraint. 4. Compute the required T/W from the climb gradient with climb_constraint. 5. Compute the required T/W at the cruise speed with cruise_constraint. 6. Compute the required T/W in the level turn with maneuvering_constraint. 7. Sweep candidate wing loadings, evaluate the constraint curves, and assemble the feasible region lower bounds with feasible_region_lower_bounds; the returned (W/S, T/W) pairs bound the feasible design region and gate the conceptual design trade. ## Pitfalls - Mixing units: wing loading in kg/m^2 instead of N/m^2, or gamma in degrees with the small-angle formula; keep everything SI with gamma in rad. - Forgetting the density default: rho defaults to 1.225 kg/m^3 (sea level); at altitude the lower density tightens the takeoff and climb constraints. - Treating the climb term as 1/LD only: the gamma term is the climb gradient itself; dropping it understates the required T/W. - Using the maneuvering curve at n = 1 for a turn case: the induced drag term scales with the load factor squared; the required T/W in a sustained turn is larger than at level flight. - Averaging the constraint T/W values instead of taking the maximum: the feasible region lower bound is the maximum, not the mean, and it defines the boundary of the feasible design region. - Using the stall constraint as a required T/W curve: it gives a maximum wing loading boundary, not a thrust requirement. - Passing an empty constraints dict to feasible_region_lower_bounds; the module raises ValueError instead of guessing. ## Behavior contract (gate 3) The stall, takeoff distance, climb gradient, cruise, and maneuvering constraints plus the feasible region lower bound logic are exercised by the gate 3 contract test: scripts/test_constraint_analysis.py against scripts/constraint_analysis_logic.py (stdlib unittest, offline). Run: python3 scripts/test_constraint_analysis.py ## Compliance - Standards referenced, not reproduced: FAR-25 is US government work (public domain) and CS-25 is a free EASA download; the constraint equations are common conceptual design methodology, summary-only per standards-map.yaml. - compliance: STANDARDS-REF, gated: false.