Aerospace & Aeronautical Engineering / Wing Torsional Divergence
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LABORATORY 39 · AEROSPACE & AERONAUTICAL ENGINEERING

Aeroelastic Torsional Divergence and Wing Torsional Rigidity

Measure elastic wing twist theta under aerodynamic loading in a wind tunnel and extrapolate the critical divergence dynamic pressure q_div and airspeed V_div. Explore interactive wind tunnel simulation, flight dynamics, and aerospace engineering telemetry.

AERODYNAMICS · PROPULSION · FLIGHT DYNAMICS

Your virtual aerospace engineering laboratory.

TWIST METRIC 1 - ALPHA_0/THETA—
FLIGHT & TEST CELL TELEMETRY

Ready to sample with q = 1.0 kPa.

1.0 kPa
Airfoil chord c: 150 mm

Adjust q, 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

Linear divergence theory assumes 2D strip aerodynamics without 3D wingtip vortex relief. Linear regression of the twist metric against dynamic pressure yields a slope m = 0.3125 kPa^-1 corresponding to q_div = 3.200 kPa with R^2 > 0.999999.

Aeronautical apparatus & wind tunnel sensors.

Aeroelastic Wind Tunnel Test Wing

NACA 0012 rigid aerodynamic foam shell mounted over a flexible internal steel torsion rod (elastic axis at 45% chord).

Variable Speed Aeroelastic Wind Tunnel

Delivers controllable dynamic pressures q from 0.1 to 2.5 kPa with safety catch nets.

Laser Tip Optical Inclinometer System

Reflects laser beam from tip wing mirror onto optical sensor to measure twist angle theta with 0.01 degree accuracy.

Aerodynamic Center Offset Mount

Adjusts aerodynamic center-to-elastic axis offset e from 15 mm to 35 mm.

Dynamic Pressure Pitot-Static Sensor

Continuously records test-section dynamic pressure q in kPa.

Aeroelastic Safety Interlock System

Automatically trips wind tunnel power if wing twist angle exceeds 8.0 degrees to prevent model destruction.

FOLLOW THE METHOD

A reason behind every step.

Measure elastic wing twist theta under aerodynamic loading in a wind tunnel and extrapolate the critical divergence dynamic pressure q_div and airspeed V_div. Standardized parameter settings: 0.3, 0.6, 0.9, 1.2, 1.5, 1.8 kPa.

01

Zero Airspeed Angle Setting

Set the root incidence angle to an initial geometric angle of attack alpha_0 = 2.0 degrees with zero wind.

02

Laser Inclinometer Baseline Alignment

Zero the optical laser mirror receiver, confirming theta = 0 deg relative to root incidence.

03

Low-Speed Dynamic Pressure Initialization

Run the wind tunnel to dynamic pressure q = 0.30 kPa, recording steady-state aeroelastic twist angle theta.

04

Systematic Dynamic Pressure Stepping

Step dynamic pressure through q = 0.60, 0.90, 1.20, 1.50, and 1.80 kPa, recording twist angle theta at each plateau.

05

Twist Amplification Metric Calculation

Compute total incidence (alpha_0 + theta) and calculate the non-dimensional metric (1 - alpha_0 / theta).

06

Divergence Extrapolation Regression

Plot (1 - alpha_0 / theta) versus q, perform linear regression to determine slope 1 / q_div, and calculate divergence dynamic pressure q_div = 1 / m.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into aerodynamic insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Wing Torsional Divergence mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b
\left(1 - \frac{\alpha_0}{\theta}\right) = \frac{1}{q_{\text{div}}} \cdot q \implies \left(1 - \frac{\alpha_0}{\theta}\right) = m \cdot q_{\text{kPa}} + b
#Dynamic Pressure q (kPa)Twist Metric 1 - alpha_0/theta (dimensionless)Wind Tunnel Dynamic Pressure q (kPa)Twist Amplification Metric 1 - alpha_0 / thetaRemove

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CHECK YOUR UNDERSTANDING

Explain what the aerodynamic metrics mean.

What physical condition triggers aeroelastic wing torsional divergence?

Why does an unswept wing tend to twist nose-up under aerodynamic lift?

For a measured regression slope m = 0.3125 kPa^-1, what is the critical divergence dynamic pressure q_div?

What structural technique allowed the forward-swept Grumman X-29 to fly without wing divergence?