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Run npx skillmds@latest add ashfordeou/cg-envelope in your terminal (requires Node.js), paste this page's agent-chat prompt into Claude, Cursor, or any MCP-connected agent, or download the SKILL.md file and copy it into your agent's skills directory.

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Is Cg Envelope free to use?

Yes. Installing skills from SkillMD is free. This skill is licensed under Apache-2.

Who published Cg Envelope?

ashfordeOU (@ashfordeou) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Cg Envelope by ashfordeou — Agent Skill

Name: Cg Envelope
Author: ashfordeOU

Cg Envelope

Use when you must analyze the center-of-gravity envelope of a vehicle: derive the cg station from component weights and arms, check the operating cg against the forward and aft limits, test an operating point against the envelope polygon in the cg versus weight plane, compute the static margin from the neutral point normalized by the mean aerodynamic chord, and track the cg excursion as the fuel burns between loading states. Produces the cg station, the limit verdict, the polygon membership with the violated limit, the static margin verdict, and the fuel-burn cg shift that gate the loading analysis. Trigger: cg envelope, static margin, neutral point, forward limit, aft limit, envelope polygon, cg excursion, fuel burn.

ashfordeOU 0822af3 3 files · 20.0 KB Updated Sep 17, 2026

File contents

CG Envelope (vehicle-design/mass-properties/cg-envelope)

Use when the task is center-of-gravity envelope analysis for a vehicle: cg station from component weights and arms, forward and aft limit checks, envelope polygon membership, static margin against the neutral point, and the cg excursion as the fuel burns.

Domain quick reference

Center of gravity: x_cg = sum(w_i * x_i) / sum(w_i) over the components; the same rule applies to the z stations for the vertical cg.
Forward and aft limits: the operating cg must satisfy forward_limit <= x_cg <= aft_limit; a cg ahead of the forward limit is a forward violation, behind the aft limit an aft violation.
Envelope polygon: the allowed operating points (x_cg, weight) form a convex polygon; an operating point outside the polygon violates the forward or the aft limit at its weight.
Static margin: SM = (x_neutral_point - x_cg) / MAC, with MAC the mean aerodynamic chord; a margin at or above the minimum (typically 0.05) passes.
CG excursion: as fuel burns the total weight drops and the cg shifts; the excursion is the cg difference between the two fuel states, positive when the cg moves aft.
FAR-25 (14 CFR Part 25) and CS-25 set the certification context for transport-category loading; the envelope and margin math is common mass-properties practice.

Workflow

Collect component weights and stations: x arms for the longitudinal cg, z stations when the vertical cg matters.
Compute the cg with cg_position or cg_position_2d.
Check the operating cg against the forward and aft limits with cg_limits_verdict.
Test an operating point against the envelope polygon with point_in_envelope; read the violated limit from the verdict.
Compute the static margin from the neutral point with static_margin_verdict; confirm the margin against the minimum.
Track the loading states with cg_excursion to see how the cg moves as the fuel burns.
Confirm the deterministic checks with the contract test scripts/test_cg_envelope.py.

Pitfalls

Mismatched weights and arms lists producing a wrong cg.
Zero total weight dividing by zero.
Reversed forward and aft limits making every verdict fail.
A non-convex or degenerate envelope polygon; the module raises ValueError because the boundary logic assumes a convex polygon.
A zero or negative MAC in the static margin.
Mixing stations: x arms for the longitudinal cg, z stations for the vertical cg.
Reading the excursion sign backwards: shift = cg_after - cg_before, positive is aft.

Behavior contract (gate 3)

The cg, limit, polygon, margin, and excursion logic is exercised by the gate 3 contract test: scripts/test_cg_envelope.py against scripts/cg_envelope_logic.py (stdlib unittest, offline). Run: python3 scripts/test_cg_envelope.py

Compliance

Standards referenced, not reproduced: FAR-25 is US government work (public domain) and CS-25 is a free EASA download; the cg envelope and static margin relations are common mass-properties methodology, summary-only per standards-map.yaml.
compliance: STANDARDS-REF, gated: false.

---name: cg-envelopedescription: Use when you must analyze the center-of-gravity envelope of a vehicle: derive the cg station from component weights and arms, check the operating cg against the forward and aft limits, test an operating point against the envelope polygon in the cg versus weight plane, compute the static margin from the neutral point normalized by the mean aerodynamic chord, and track the cg excursion as the fuel burns between loading states. Produces the cg station, the limit verdict, the polygon membership with the violated limit, the static margin verdict, and the fuel-burn cg shift that gate the loading analysis. Trigger: cg envelope, static margin, neutral point, forward limit, aft limit, envelope polygon, cg excursion, fuel burn.license: Apache-2.0---# CG Envelope (vehicle-design/mass-properties/cg-envelope)Use when the task is center-of-gravity envelope analysis for avehicle: cg station from component weights and arms, forward andaft limit checks, envelope polygon membership, static marginagainst the neutral point, and the cg excursion as the fuel burns.## Domain quick reference- Center of gravity: x_cg = sum(w_i * x_i) / sum(w_i) over the components; the same rule applies to the z stations for the vertical cg.- Forward and aft limits: the operating cg must satisfy forward_limit <= x_cg <= aft_limit; a cg ahead of the forward limit is a forward violation, behind the aft limit an aft violation.- Envelope polygon: the allowed operating points (x_cg, weight) form a convex polygon; an operating point outside the polygon violates the forward or the aft limit at its weight.- Static margin: SM = (x_neutral_point - x_cg) / MAC, with MAC the mean aerodynamic chord; a margin at or above the minimum (typically 0.05) passes.- CG excursion: as fuel burns the total weight drops and the cg shifts; the excursion is the cg difference between the two fuel states, positive when the cg moves aft.- FAR-25 (14 CFR Part 25) and CS-25 set the certification context for transport-category loading; the envelope and margin math is common mass-properties practice.## Workflow1. Collect component weights and stations: x arms for the longitudinal cg, z stations when the vertical cg matters.2. Compute the cg with cg_position or cg_position_2d.3. Check the operating cg against the forward and aft limits with cg_limits_verdict.4. Test an operating point against the envelope polygon with point_in_envelope; read the violated limit from the verdict.5. Compute the static margin from the neutral point with static_margin_verdict; confirm the margin against the minimum.6. Track the loading states with cg_excursion to see how the cg moves as the fuel burns.7. Confirm the deterministic checks with the contract test scripts/test_cg_envelope.py.## Pitfalls- Mismatched weights and arms lists producing a wrong cg.- Zero total weight dividing by zero.- Reversed forward and aft limits making every verdict fail.- A non-convex or degenerate envelope polygon; the module raises ValueError because the boundary logic assumes a convex polygon.- A zero or negative MAC in the static margin.- Mixing stations: x arms for the longitudinal cg, z stations for the vertical cg.- Reading the excursion sign backwards: shift = cg_after - cg_before, positive is aft.## Behavior contract (gate 3)The cg, limit, polygon, margin, and excursion logic is exercised bythe gate 3 contract test: scripts/test_cg_envelope.py againstscripts/cg_envelope_logic.py (stdlib unittest, offline). Run:python3 scripts/test_cg_envelope.py## Compliance- Standards referenced, not reproduced: FAR-25 is US government work (public domain) and CS-25 is a free EASA download; the cg envelope and static margin relations are common mass-properties methodology, summary-only per standards-map.yaml.- compliance: STANDARDS-REF, gated: false.

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