A wing section on springs in an airflow. Push the airspeed or the angle too far and it stops
sitting still — the airflow itself starts feeding energy into the motion. This is the exact
mathematical model from Dr Chawin's PhD thesis.
flow state
attached
pitch θ
–
eff. angle α
–
lift CL
–
moment CM
–
attached flow f
–
Try a scenario
The airflow
How fast the air moves compared with sound. Changes the whole aerodynamic
character — stall angle drops as M rises.
The "reduced airspeed": wind speed measured against how stiff the springs are.
The classic flutter dial — push it up and stability runs out.
The angle the pitch spring tries to hold the wing at. Near the stall angle
(≈15° at M 0.30) the flow starts detaching — the interesting zone.
The structure
How heavy the wing is compared with the air around it. Light wings (low μ)
are pushed around more easily.
Bounce-spring frequency ÷ twist-spring frequency. When the two motions are
tuned close together they can trade energy — a flutter ingredient.
Friction on the twisting motion. Damping eats the energy the airflow feeds in.
Friction on the up-and-down motion.
Advanced geometry (thesis defaults)
Where the springs attach along the chord (−0.5 = quarter-chord).
Centre of mass sits this far behind the springs. Couples bounce into twist.
How spread-out the wing's mass is around the springs.
Model: 2-DOF pitch–plunge aerofoil + full Leishman–Beddoes dynamic stall
(16 coupled equations, NACA 0012 data, simplified effective pitch rate).
Angles beyond ±60° are outside the model's validated range — the badge turns red.
What am I looking at?
A wing section held by two springs: one lets it bounce up and down (plunge), one lets it twist (pitch). Air flows past from the left.
The orange ribbon on top of the wing shows how much of the airflow is still attached. When it retreats, the flow is separating — stall. A swirling vortex appears when the wing sheds one; that vortex briefly adds lift, then dumps it.
The chart tracks twist angle (coral) and bounce (blue). A closed repeating loop is a limit-cycle oscillation — flutter that neither grows nor dies.
Drag the sliders — the simulation reacts live. The presets jump to three characteristic behaviours.
The takeaway
An aircraft wing can extract energy from the very airflow that holds it up. Below a critical airspeed the motion dies out; above it, the wing settles into a self-sustained dance — and repeated stalling makes that dance violent and hard to predict.
This is why flutter testing is a life-or-death part of aircraft certification — and why wind turbine and helicopter blades, which live near stall, need dynamic stall models like this one.