The Taipei 101 damper

The 660-tonne ball that swings on purpose.

2 · The question

A 508 m skyscraper sways in the wind, so engineers hung a 660-tonne ball near the top. What does the ball do?

3 · Play first

Start the wind. Free the ball. Tune it until the tower calms down.

Sway

Oil warmth

Ball’s cable: 5.0 m, swings every 4.5 s (tower: 6.8 s)Ball swings too fast: make its cable longer.

Now survive the storms

You’ve tuned the ball once. Can you keep the tower standing through five typhoons, each worse than the last?

Building the city…

Sway hugely exaggerated, and the game’s ball is heavier than the real one (3% of the swaying mass, not 0.6%) so a storm plays out in 40 seconds.

4 · What's happening

1
Wind pushes the tower in time with its own sway, about once every 7 seconds, like pushing a swing.
2
The ball hangs on cables, so it is a pendulum. Give it the same beat as the tower and it swings hard.
3
It swings a quarter-beat behind the tower, so its pull always works against the tower's movement.
4
Pistons squeeze oil through small holes. The sway's energy ends up as heat in the oil.

5 · The maths

A pendulum's swing time depends only on its cable length, not on how heavy it is. So engineers tune the ball by choosing the cable.

T = 2\pi\sqrt{\dfrac{L}{g}}

L = \dfrac{g\,T^2}{4\pi^2} = \dfrac{9.81 \times 6.8^2}{4\pi^2} \approx 11.5\ \text{m}

T = 2π √(5.0 m ÷ 9.81 m/s²)=4.5 s

ball 4.5 s<tower 6.8 s

6 · Under the hood

Inside the real damper (for grown-ups)

The ball

660 tonnes and 5.5 m across, made of 41 steel plates welded together. It hangs from cables anchored on the 92nd floor.

Tuned, not just heavy

Its swing is tuned to the tower's sway, about 6.8 s. In the widget the ball is a little heavier (1% of the swaying tower, not about 0.6%) so it settles within a minute, and the best cable still comes out at the real 11.5 m.

What it buys

In the strongest storm expected every half-year, the design cuts peak acceleration on the top occupied floor from 7.9 to 5.0 milli-g, about 37% less. It is for comfort, not to stop the tower falling.

Its biggest swing

During Typhoon Soudelor in August 2015 the ball swung about 1 m, the largest it has ever moved.

7 · Try it yourself

Pendulum timer

Tie a small weight to a string and count its swings in 10 seconds. Then make the string 4 times longer and count again (you should get about half). Tap each time you test a new length.

Build it

A desk damper kit is on the list: a 3D-printed springy tower with a ball you can lock, free and tune.

Tell me when it's ready

8 · Next machine · Week 1The Lever: How a small weight lifts a heavy crate