# Longitudinal Stability

> Use when you must assess static longitudinal stability of an aircraft: compute the neutral point from the wing aerodynamic center, the tail volume coefficient, the lift slope ratio, and the downwash gradient; derive the static margin at the current center of gravity; and determine whether the aircraft is longitudinally stable for pitch stability. Produces the neutral point location, the static margin, and the stability verdict that gate the longitudinal stability analysis. Trigger: static margin, neutral point, longitudinal stability, pitch stability, center of gravity.

- Skill: `ashfordeou/longitudinal-stability` (Agent Skill, multi-file: 3 files)
- Install (CLI): `npx skillmds@latest add ashfordeou/longitudinal-stability`
- Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/longitudinal-stability/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/longitudinal-stability

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# Static Longitudinal Stability (flight-mechanics/stability-control/longitudinal-stability)

Use when the task is static longitudinal stability analysis: neutral
point, static margin, and the pitch stability verdict at a given
center of gravity.

## Domain quick reference

- The neutral point is the aerodynamic center of the whole aircraft
  (wing plus tail); all positions are fractions of the mean
  aerodynamic chord, dimensionless.
- Neutral point: h_np = h_ac_w + V_h * (a_t / a_w) * (1 - depsilon/
  dalpha), where h_ac_w is the wing aerodynamic center, V_h is the
  tail volume coefficient, a_t/a_w is the lift slope ratio, and
  depsilon/dalpha is the downwash gradient.
- The tail volume coefficient is dimensionless; the lift slope ratio
  and downwash gradient are dimensionless too.
- Static margin = neutral point - center of gravity; positive static
  margin means a stable configuration.
- Longitudinally stable when the static margin meets the minimum
  margin (default 0.05).

## Workflow

1. Collect the wing aerodynamic center, tail volume coefficient,
   lift slope ratio, and downwash gradient.
2. Compute the neutral point with neutral_point.
3. Take the center of gravity position and derive the static margin
   with static_margin.
4. Check the margin with longitudinally_stable.
5. Gate the pitch stability assessment on the verdict.

## Pitfalls

- Reversing the static margin sign: positive margin (neutral point
  aft of the center of gravity) is stable, not unstable.
- Confusing the neutral point with the wing aerodynamic center: the
  neutral point includes the tail contribution, the aerodynamic
  center of the wing alone does not.
- Zero tail volume coefficient: a configuration with no stabilizing
  tail surface cannot produce a meaningful neutral point offset.
- Downwash gradient at or above 1.0: physically invalid for this
  model.

## Behavior contract (gate 3)

The neutral point, static margin, and stability logic is exercised by
the gate 3 contract test: scripts/test_longitudinal_stability.py
against scripts/longitudinal_stability_logic.py (stdlib unittest,
offline). Run:
python3 scripts/test_longitudinal_stability.py

## Compliance

- Standards referenced, not reproduced: FAR-25 and CS-25 require
  positive static longitudinal stability for transport aeroplanes;
  the neutral point and static margin method is common flight
  mechanics methodology, summary-only per standards-map.yaml.
- compliance: STANDARDS-REF, gated: false.