Flight Mechanics & Aircraft Structures — Installation

What You're Setting Up

Overview's restoring-moment calculation (τ = r × F) is closed-form and hand-calculable. This section sets up a Python environment for stability-moment and static-margin calculations, plus OpenVSP — NASA's free, open-source parametric aircraft design tool, whose VSPAERO analysis module computes real stability derivatives for an actual 3D aircraft geometry, going well beyond this guide's simplified scalar-torque examples.

Install Python

bash

python3 --version
pip install numpy

Verify Your Setup — Recompute Overview's Restoring Moment

This reproduces Overview's worked example (F = 400 N extra tail force, r = 6 m moment arm) in Python.

python

def restoring_moment(r, F):
    return r * F

tau = restoring_moment(r=6, F=400)
print(f"Restoring moment = {tau} N·m")

Expected output: Restoring moment = 2400 N·m

Matches Overview's hand-computed 2,400 N·m exactly.

A Second Check — Static Margin

A genuinely new calculation: static margin is the standard way real aircraft stability is quantified — the distance between the CG and the neutral point, expressed as a fraction (or percentage) of the mean aerodynamic chord (MAC).

python

def static_margin(x_neutral_point, x_cg, chord):
    """
    x_neutral_point, x_cg: positions as a fraction of chord (0 = leading edge, 1 = trailing edge)
    chord: mean aerodynamic chord length (m)
    Returns: static margin as a fraction of chord, and as a physical distance
    """
    sm_fraction = x_neutral_point - x_cg
    sm_distance = sm_fraction * chord
    return sm_fraction, sm_distance

sm_frac, sm_dist = static_margin(x_neutral_point=0.35, x_cg=0.25, chord=2.0)
print(f"Static margin = {sm_frac*100:.1f}% MAC ({sm_dist:.2f} m)")

Expected output: Static margin = 10.0% MAC (0.20 m)

A POSITIVE static margin (neutral point AFT of CG, as here) confirms
the aircraft is longitudinally stable, consistent with Overview's
requirement that CG sit ahead of the neutral point. A typical
conventional aircraft is designed with a static margin in roughly
the 5-15% MAC range `(needs verification — recheck against current
source: exact typical/target static margin ranges vary significantly
by aircraft category and design philosophy — treat this as an
order-of-magnitude sanity check, not a fixed design target)` — a
NEGATIVE result here would mean the CG is behind the neutral point,
indicating instability, matching Overview's explanation of what
happens when CG crosses that boundary.

Install OpenVSP for Real Aircraft Stability Analysis

OpenVSP is NASA's open-source parametric aircraft geometry tool; its VSPAERO module runs vortex-lattice/panel-method aerodynamic analysis and outputs real stability derivatives for an actual 3D aircraft model, rather than the simplified scalar-force examples used throughout this guide.

bash

# Download the current build for your OS from the official releases:
# https://github.com/nasa/OpenVSP/releases
# (Windows, macOS, and Linux builds are provided)

(needs verification — recheck against current source: OpenVSP release/build details change; confirm current download and build instructions directly at github.com/nasa/OpenVSP before relying on a specific version or install path.)

Verify Everything Works

bash

# 1. Confirm the restoring-moment check prints exactly 2400 N·m

# 2. Confirm the static-margin check prints 10.0% MAC (0.20 m)

# 3. Open OpenVSP, load one of its built-in example aircraft models,
#    run a VSPAERO stability analysis, and confirm it produces a
#    stability-derivatives output file — this is the concrete proof
#    that "static margin and stability derivatives" are real,
#    computable outputs for an actual aircraft geometry, not just a
#    formula on paper

Common Setup Issues

Static margin comes out negative when a stable design was expected

Double-check whether the neutral point and CG fractions are being subtracted in the right order — static margin is neutral-point-fraction MINUS CG-fraction (x_np - x_cg), not the reverse; swapping the order flips the sign and can make a genuinely stable configuration appear unstable in the calculation, even though the underlying design is fine.

OpenVSP's VSPAERO analysis fails to converge or produces unrealistic stability derivatives

Confirm the aircraft geometry model doesn't have obvious modeling errors first (disconnected surfaces, degenerate geometry) — VSPAERO's panel-method solver is sensitive to clean input geometry, and a convergence failure is more often a geometry problem than a genuine physical instability in the design being modeled.

What's Set Up

•Python 3 + NumPy — for restoring-moment and static-margin calculations throughout this guide

•OpenVSP (with VSPAERO) — for real 3D aircraft geometry and stability-derivative analysis beyond this guide's simplified scalar examples

Next Steps

Go to the Fundamentals section to continue building on the static-stability framework established here.