THE LOAD CHANGES THE SHAPE. THE SHAPE CHANGES THE LOAD.
Inspect coupled bending and twist, then switch to a typical-section flutter experiment with an unsteady aerodynamic wake.
Drag to orbit · right-drag to pan · scroll to zoom. Bending is magnified ×5; twist is true angle. Flutter uses a typical section, not a full-wing solution. A is amber; B is turquoise.
The wing view solves a cantilever. The flutter view is a two-dimensional typical section; the displayed wing is a visual reference, not a full-wing flutter solution.
Whole-run summary · live values appear above
CAUSE → RESPONSE → COMPARISON
B · solid turquoise A · dashed amber
Time plots share the playback cursor. Design sweeps and phase plots retain their own axes. A stopped run holds its final resolved state.
| Whole-run quantity | A · saved | B · live | B − A | Unit |
|---|
A snapshot includes parameter values and event times. Export retains both configurations and their calculated traces.
THE PHYSICS BEHIND THE RESPONSE
Follow each balance, then connect it to the response above. Open Symbols & units for the notation. A dot denotes a time derivative unless a non-dimensional time is stated.
In static bending mode, the cantilever deflection follows the spanwise lift load. The prescribed time ramp connects static equilibria.
Lift ahead of the elastic axis increases nose-up twist, which changes lift again. The static solver rejects unbounded divergence.
The separate typical-section model combines structural inertia and stiffness with aerodynamic added mass and unsteady wake states.
The two-exponential Wagner approximation represents delayed circulation. Its convective time is different from the reduced velocity used by the control.
Equations describe this bounded teaching model. Assumptions and source references are retained below. Internal calculations use SI units; controls and plots show their own labelled units.
Static half-span 6 m, chord 1.8 m, 36 midpoint load stations, linear Euler–Bernoulli bending/torsion and attached lift. Stress uses E = 70 GPa and outer-fibre distance 0.12 m as explicit teaching assumptions. Dynamic section: mass ratio 20, radius-of-gyration squared 0.24, frequency ratio 0.4, semi-chord 0.5 m, pitch frequency 30 rad/s. h is positive downward; twist is nose-up. Small-disturbance incompressible added-mass + two-state Wagner model. Stops beyond 0.2 semi-chord plunge or 10° twist. No damage, limit cycle, transonic or full-wing flutter prediction.
BYU · Wagner unsteady aerodynamics ↗BYU · Typical-section stability benchmark ↗Numerical checks test the stated equations. They do not establish aircraft certification or experimental accuracy. Schematic flow markers indicate direction; their speed is illustrative. No manufacturer geometry or performance data is reproduced. Version: coupled-labs-v1.1.