Why the Tacoma Narrows bridge tore itself apart

The textbook story: the wind hit the bridge's natural note and shook it apart, like a singer shattering a glass. It needed no note. Once it twisted, it made its own wind force, and each twist made the next bigger.

What happened

The first Tacoma Narrows Bridge opened in 1940 with a deck stiffened by a solid steel plate eight feet deep, and bounced in wind from day one. On the morning of 7 November the wind on the bridge measured about 42 miles per hour — 19 metres per second. Shortly after ten the bouncing turned into a twist, the roadway's edges rising and falling in opposite directions once every five seconds. About an hour later, at 11:02, a 600-foot section tore loose and fell into Puget Sound.

Why the glass analogy fails

In resonance, something outside pushes at a steady rhythm, and the pushes build up only when that rhythm matches the object's own. Stop pushing and it stops.

The wind that day had no beat. The swirls it shed off the deck edge came about one per second, nothing like the bridge's one twist per five seconds. And the twist appeared not at a frequency but at a wind speed, then grew. Billah and Scanlan, two bridge aerodynamicists, wrote in 1991 saying what engineers had long known: this was not resonance. It was self-excitation.

How a deck feeds itself

Think of the deck as a plank on a torsion spring. Twist it and let go: it swings back, overshoots, swings again. Each cycle loses a little energy to friction in the steel and stirring the air, so the swing dies out. That loss is damping.

Now add wind. Tilted one way, the air pushes on the plank; tilted the other, the push reverses. The wind adds a twisting force that depends on the plank's angle and turning speed — aeroelastic: the structure's shape sets the air force on it.

That force's sign is everything. On a bluff-edged plate the air does not follow the surface; it separates into vortices above and below the deck that take time to form — not the still deck's one-per-second swirls, but ones the twisting deck makes, timed to its own motion. The delay puts part of the force in step with the plank's turning speed, pushing the way it already moves: energy going in, once per cycle, whatever the wind's rhythm.

So the wind's effect on the damping changes sign with wind speed, while the bridge's own losses stay fixed. At low speed the wind adds damping; disturbances die away. At a critical speed it just cancels the structure's losses: a twist neither grows nor fades. Above it the net damping is negative, and the oscillation grows from nothing — a gust, a slipped cable band — with no frequency matching anything. The bridge sets the rhythm; the wind pays.

For that deck's twist, Farquharson's model tests put the critical speed near 18 mph; the 42 mph on the Narrows that morning was more than twice it. Green and Unruh later reproduced the same negative-damping behaviour with a model of the vortices a bluff deck sheds. Modern suspension decks are shaped in wind tunnels to push the critical speed above any wind the site will see: open trusses, central slots, streamlined edges that keep the air attached.

In short

Resonance is being pushed at your own rhythm by something outside. Flutter is pushing yourself. The deck's twist changed the wind force on it, and above a critical wind speed each cycle fed energy in, not out. Nothing matched a note: the damping went negative, and negative damping amplifies whatever it is given until something breaks.