6-DOF Real-Time Flight Dynamics Simulator
Executes 4th-order longitudinal state-space equations with Runge-Kutta numerical integration at 500 Hz.
Aerospace & Aeronautical Engineering / Phugoid & Short-Period Modes
FREE TO EXPLORELABORATORY 25 · AEROSPACE & AERONAUTICAL ENGINEERING
Longitudinal Dynamic Flight Modes: Short-Period and Phugoid Oscillations
Extract natural frequency omega_n and damping ratio zeta of the rapid angle-of-attack short-period mode and slow energy-exchange phugoid mode from aircraft state-space flight dynamics. Explore interactive wind tunnel simulation, flight dynamics, and aerospace engineering telemetry.
AERODYNAMICS · PROPULSION · FLIGHT DYNAMICS
Your virtual aerospace engineering laboratory.
PHUGOID RECIPROCAL FREQUENCY 1/OMEGA_N,P—
FLIGHT & TEST CELL TELEMETRY
Ready to sample with V_0 = 60.0 m/s.
Adjust V_0, then execute aerospace trial.
Aeronautical telemetry and flight states are evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity aerodynamic modeling.
Aeronautical assumptions and boundary condition limits
Lanchester's analytical formula assumes zero angle of attack perturbation (Delta alpha = 0) during the phugoid cycle. Linear regression of reciprocal phugoid frequency against trim airspeed yields a slope m = 0.0721 s^2/m matching Lanchester's formula with R^2 > 0.999999.
Aeronautical apparatus & wind tunnel sensors.
Automated Elevator Doublet Input Generator
Applies standardized pitch doublet inputs (+/- 2 degrees, 1 second duration) to excite natural modes.
State Telemetry Sensor Package
Records airspeed V(t), pitch angle theta(t), angle of attack alpha(t), and pitch rate q(t) with 16-bit resolution.
Logarithmic Decrement Mode Analyzer
Extracts damped frequency omega_d and damping ratio zeta from time-domain oscillation decay envelopes.
Eigenvalue Root-Locus Visualizer
Computes state-space matrix A eigenvalues, plotting short-period and phugoid poles in the s-plane.
Flight Envelope Trim Station
Maintains constant lift-to-weight equilibrium across airspeeds from 40 to 100 m/s.
FOLLOW THE METHOD
A reason behind every step.
Extract natural frequency omega_n and damping ratio zeta of the rapid angle-of-attack short-period mode and slow energy-exchange phugoid mode from aircraft state-space flight dynamics. Standardized parameter settings: 40.0, 50.0, 60.0, 75.0, 88.0, 100.0 m/s.
01
Level Flight Trim at Initial Airspeed
Trim the aircraft in steady level flight at V_0 = 40.0 m/s, recording baseline state vectors and elevator trim angle.
02
Elevator Doublet Excitation
Trigger a standardized 1.0-second elevator pulse doublet (+2 deg / -2 deg) to excite longitudinal dynamic modes.
03
Short-Period Mode Identification
Isolate the first 5 seconds of pitch rate q(t) telemetry to determine the rapid short-period frequency and damping.
04
Phugoid Oscillation Recording
Track the subsequent 120 seconds of airspeed V(t) and altitude h(t) oscillations to record the slow phugoid cycle.
05
Systematic Airspeed Stepping
Repeat doublet excitation across airspeeds V_0 = 50.0, 60.0, 75.0, 88.0, and 100.0 m/s, calculating natural frequency omega_n,p.
06
Lanchester Phugoid Linear Regression
Plot reciprocal frequency 1/omega_n,p versus V_0, perform linear regression, and compare the slope to Lanchester's 1/(sqrt(2)*g).
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into aerodynamic insight.
Points are your recorded observations. The solid regression line validates Phugoid & Short-Period Modes mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
\frac{1}{\omega_{n,p}} = \frac{V_0}{\sqrt{2} g} \implies \frac{1}{\omega_{n,p}} = m \cdot V_0 + b
| # | Trim Airspeed V_0 (m/s) | Phugoid Reciprocal Frequency 1/omega_n,p (s) | Trim Flight Airspeed V_0 (m/s) | Phugoid Reciprocal Natural Frequency 1 / omega_n,p (s) | Remove |
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