# Wing Planform Sizing > Use when you must size the wing planform geometry at the design point: compute the wing area from the takeoff gross weight and the chosen wing loading, convert the aspect ratio into the span, set the taper ratio and derive the root chord, tip chord, and mean aerodynamic chord with its spanwise station, and select the sweep angle from the cruise Mach so the section normal Mach stays at or below the section critical Mach. Produces the planform dimensions that feed weight estimation, fuel tank volume, control surface sizing, and the aerodynamic analysis leaves. Trigger: wing planform, wing area, aspect ratio, taper ratio, mean aerodynamic chord, sweep angle, cruise Mach. - Skill: `ashfordeou/wing-planform-sizing` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/wing-planform-sizing` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/wing-planform-sizing/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/wing-planform-sizing --- # Wing Planform Sizing (vehicle-design/sizing/wing-planform-sizing) Use when the task is sizing the geometric wing planform for a given design point: the reference wing area from the wing loading and the takeoff gross weight, the span from the aspect ratio, the root and tip chord and the mean aerodynamic chord from the taper ratio, and the sweep angle selected from the cruise Mach. The output is the set of planform dimensions, not the aerodynamic or structural evaluation of those dimensions. ## Domain quick reference - Units: forces in N, areas in m^2, wing loading in N/m^2, spans and chords in m, Mach numbers unitless, sweep angles in degrees, g = 9.80665 m/s^2. - Wing area from wing loading and takeoff gross weight: S = W / (W/S). Anchor: W = 480000 N and W/S = 6000 N/m^2 give S = 480000 / 6000 = 80.0 m^2. - Wing loading from the area: W/S = W / S. Anchor: 480000 N over 80.0 m^2 gives 6000.0 N/m^2 (round trip check). - Span from the aspect ratio: b = sqrt(AR * S). Anchor: S = 80.0 m^2 and AR = 9 give b = sqrt(720) = 26.8328 m. - Aspect ratio from span and area: AR = b^2 / S. Anchor: the 26.8328 m span over 80.0 m^2 gives AR = 9.0 (round trip check). - Taper ratio: lambda = c_tip / c_root, conventional planforms keep 0 < lambda <= 1. Anchor: c_root = 5.0 m and c_tip = 1.5 m give lambda = 0.3. - Root chord from area, span, and taper: c_root = 2 * S / (b * (1 + lambda)). Anchor: S = 80.0 m^2, b = 26.8328 m, lambda = 0.3 give c_root = 160 / (26.8328 * 1.3) = 4.5868 m. - Tip chord: c_tip = lambda * c_root. Anchor: 0.3 * 4.5868 = 1.3760 m. - Mean aerodynamic chord (MAC): MAC = (4 * S / (3 * b)) * (1 + lambda + lambda^2) / (1 + lambda)^2. Anchor: 80.0 m^2, 26.8328 m, lambda = 0.3 give MAC = 3.2696 m, about 0.713 of the root chord. - MAC spanwise station from the root: y_mac = (b / 6) * (1 + 2 * lambda) / (1 + lambda). Anchor: 26.8328 m and lambda = 0.3 give y_mac = 5.5042 m outboard of the root. - Sweep angle from cruise Mach: the section sees the Mach component normal to the quarter-chord line, M_n = M_cruise * cos(Lambda). Keeping M_n at or below the section critical Mach number selects the minimum sweep Lambda = arccos(M_crit_section / M_cruise) when M_cruise > M_crit_section, and 0 degrees otherwise. Anchor: M_cruise = 0.8 and M_crit_section = 0.7 give Lambda = arccos(0.875) = 28.96 degrees, and the check M_n = 0.8 * cos(28.96 deg) = 0.7 returns the section critical Mach. - FAR-25 (14 CFR Part 25) and CS-25 set the certification context (reference geometry and flight envelope for transport-category aeroplanes); the planform relations are common conceptual sizing practice. ## Workflow 1. Set the design point: takeoff gross weight W, chosen wing loading W/S, aspect ratio AR, taper ratio lambda, cruise Mach, and section critical Mach. 2. Compute the reference wing area with wing_area_from_wing_loading. 3. Compute the span with span_from_aspect_ratio. 4. Set the taper ratio and compute the root chord with root_chord_from_taper, then the tip chord with tip_chord_from_taper. 5. Compute the mean aerodynamic chord with mean_aerodynamic_chord and its spanwise station with mac_spanwise_station. 6. Select the sweep angle with sweep_angle_from_cruise_mach and check the result with mach_normal_component. 7. Summarize the planform with planform_geometry, then hand the reference area, span, and MAC to the sibling leaves: weight estimation (wing mass), fuel tank sizing (tank volume fit), control surface sizing (aileron span), and tail sizing (tail arm and volume coefficients). ## Pitfalls - Confusing this leaf with ws-tw-trade: ws-tw-trade selects the wing loading W/S and the thrust to weight T/W from the matching chart; wing-planform-sizing takes the chosen W/S as given and converts it into the geometric planform. The W/S trade comes first, the planform geometry second. - Confusing the direction of the data flow with weight estimation: weight-estimation predicts component masses from the geometry; wing-planform-sizing consumes the takeoff gross weight and produces the geometry. Use the weight budget to size the area, do not re-estimate the weight here. - Confusing this leaf with the aerodynamics airfoil leaves: airfoil-geometry works on the two-dimensional section (camber, thickness, coordinates); swept-wing-aerodynamics evaluates the aero effects of a given sweep (effective Mach, critical Mach increase); lift-curve-slope applies the aspect ratio and sweep corrections to the lift slope. This leaf selects the planform numbers, the aero leaves evaluate their consequences. - Mixing units: wing loading must be in N/m^2, not kg/m^2; a loading given in kg/m^2 must be multiplied by g = 9.80665 before dividing the weight. - Forgetting that the MAC changes with taper at fixed area and span: a more tapered planform (lower lambda) has a longer MAC, and the rectangular planform (lambda = 1) has MAC equal to the average chord S / b. - Treating the sweep relation as exact for all planforms: the arccos relation gives the minimum sweep from simple sweep theory; in practice round the sweep up for margin, and a supercritical section (supercritical-airfoil leaf) raises the section critical Mach and reduces the sweep needed. - Applying the sweep formula when the section critical Mach already meets or exceeds the cruise Mach: the module returns 0 degrees (no sweep needed), which is the correct design answer, not an error. - Passing a reverse taper (tip chord larger than root chord): the module raises ValueError because conventional planforms taper toward the tip; check the chord order before calling. ## Behavior contract (gate 3) The wing area from wing loading and takeoff gross weight, aspect ratio and span, taper ratio with root and tip chord, mean aerodynamic chord with its spanwise station, sweep angle from cruise Mach, and the planform summary are exercised by the gate 3 contract test: scripts/test_wing_planform_sizing.py against scripts/wing_planform_sizing_logic.py (stdlib unittest, offline). Run: python3 scripts/test_wing_planform_sizing.py ## Compliance - Standards referenced, not reproduced: FAR-25 is US government work (public domain) and CS-25 is a free EASA download; the planform relations are common conceptual sizing methodology, summary-only per standards-map.yaml. - compliance: STANDARDS-REF, gated: false.