Lateral-Directional Flight Dynamics Simulator
Solves full 6-DOF linearized and non-linear lateral equations of motion at 500 Hz.
Aerospace & Aeronautical Engineering / Dutch Roll & Spiral Modes
FREE TO EXPLORELABORATORY 26 · AEROSPACE & AERONAUTICAL ENGINEERING
Lateral-Directional Dynamic Modes: Dutch Roll, Spiral, and Roll Subsidence
Characterize the coupled yaw-roll Dutch roll oscillation, roll subsidence damping time constant tau_roll, and spiral mode divergence/stability. Explore interactive wind tunnel simulation, flight dynamics, and aerospace engineering telemetry.
AERODYNAMICS · PROPULSION · FLIGHT DYNAMICS
Your virtual aerospace engineering laboratory.
ROLL TIME CONSTANT TAU_ROLL—
FLIGHT & TEST CELL TELEMETRY
Ready to sample with x_inertia = 0.15 s.
Adjust x_inertia, 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
Pure roll subsidence 1-DOF approximation assumes zero yaw rate (r = 0) and zero sideslip (beta = 0). Linear regression of the roll subsidence time constant against the inertia parameter yields a slope k = 4.5000 with R^2 > 0.999999.
Aeronautical apparatus & wind tunnel sensors.
Automated Control Surface Pulse Rig
Applies isolated aileron steps (for roll subsidence) and rudder doublets (for Dutch roll).
High-Precision Gyroscopic Sensor Package
Logs roll rate p(t), yaw rate r(t), bank angle phi(t), and sideslip angle beta(t).
Modal Logarithmic Extraction Engine
Separates the roll subsidence decay curve and extracts Dutch roll frequency and damping ratio.
Variable Roll Inertia Emulator
Adjusts simulated roll inertia I_xx to systematically vary the inertia parameter.
Root-Locus Complex Pole Visualizer
Maps lateral-directional s-plane poles across flight speed and inertia configurations.
FOLLOW THE METHOD
A reason behind every step.
Characterize the coupled yaw-roll Dutch roll oscillation, roll subsidence damping time constant tau_roll, and spiral mode divergence/stability. Standardized parameter settings: 0.08, 0.12, 0.18, 0.24, 0.3, 0.35 s.
01
Lateral Equilibrium Trim
Trim the aircraft in wings-level steady level flight at V_0 = 60 m/s with zero sideslip (beta = 0, phi = 0).
02
Roll Inertia Setting
Set simulated roll inertia parameter I_xx / (q S b^2) to 0.08 s, ensuring neutral aileron trim.
03
Aileron Step Excitation
Apply a clean 5-degree aileron step command, recording the rapid exponential rise of roll rate p(t) to steady-state.
04
Roll Subsidence Time Constant Extraction
Determine the time constant tau_roll required for roll rate to reach 63.2% of its steady-state asymptotic value.
05
Systematic Inertia Stepping
Step the inertia parameter through 0.12, 0.18, 0.24, 0.30, and 0.35 s, extracting tau_roll at each setting.
06
Dutch Roll & Spiral Verification
Apply a rudder doublet to record the Dutch roll period and verify spiral mode stability over 60 seconds.
07
Roll Damping Linear Regression
Plot tau_roll versus the roll inertia parameter, perform linear regression to determine slope k, and compute roll damping derivative C_lp.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into aerodynamic insight.
Points are your recorded observations. The solid regression line validates Dutch Roll & Spiral Modes mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
\tau_{\text{roll}} = k \cdot \left(\frac{I_{xx}}{q S b^2}\right) \implies \tau_{\text{roll}} = m \cdot x + b
| # | Roll Inertia Parameter (s) | Roll Time Constant tau_roll (s) | Roll Inertia Parameter I_xx / (q S b^2) (s) | Roll Subsidence Time Constant tau_roll (s) | Remove |
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