The Large Pendulum Wave is a kinetic light art installation based on physical laws. There are no tricks (such as additional motors) involved.
The Pendulum Wave is a physical phenomenon based on a number of independent pendulums that are very accurately adjusted concerning swinging period (or frequency). On a steady frame 15 pendulums are mounted. Each pendulum can swing independently from each other. Due to the different length of each pendulum the swinging frequency is different for each pendulum. Once the frequencies are very accurately adjusted according to a mathamatical sequence, the pendulums produce a dance of standing and running waves and quasi chaos.Most common is the small version that has 12 or 15 pendulums of approximately 30cm. The longest pendulum swings exactly 51 times per minute, the second exactly 52 times per minute and so on. There are some popular videos of the small versions available on the internet. The main theory behind the phenomenon can also be found here. A large version, on this scale, however, has never been built, correct me if I’m wrong…
When things are scaled up, as always, nothing seems to be the same anymore and solutions needs to be found. This is where the fun starts… A brief overview of the issues we encountered and the solutions to tackle them, can be found below.
Small vs Large version
The small version with pendulums of approximately 30cm is relatively easy to build (for more info see chapter ‘Links’). With some patience it is a wonderful do-it-yourself installation to make. When scaling up to the size presented here, several challenges appear:
– How to keep the sequence relatively fast
– How to deal with friction in the bearings
– How to calibrate the swinging period of each pendulum
– How to bring to pendulums into position
– How to let go the pendulums at the same time
– How to stop the pendulums after the sequence
– And many minor issues
How to keep the sequence relatively fast
The swinging period of a pendulum is depending of the length and independent of it’s mass. As a pendulum of approximately 30cm has a swinging period of about 1 second. A pendulum of 400cm…has a swinging period of about 4 seconds. This means that the sequence would increase from 1 minute to 4 minutes, which would make it less spectacular. Without adding external forces to the pendulum a simple method to speed up the long pendulum is to put a relatively large mass somewhere in the middle of the pendulum. The long pendulum will behave as a shorter pendulum as the centre of mass is closer to the bearing. This will only work with rigid pendulums made of e.g. steel pipes. After adding masses of 40kg to each pendulum we were able to reduce the total sequence time from 4 minutes to 2 minutes and 43 s. (a good sequence time to maintain the concentration of the spectators).
How to deal with friction in the bearings
If the pendulums have pivoting points with variable friction coefficient, it is not possible to calibrate the swinging periods and consequently the patterns do not appear in the sequence. In the large version the bearings become even more important because of the longer sequence time. For the small version the pendulums are often made of a small mass hanging on two strings. As mentioned above, strings are not possible as we want to speed up the swinging periods using a heavy mass on a rigid pendulum pipes. A bearing ‘queeste’ eventually led to the most desirable solution: air bearings! These special air bearings, see IBS at ‘Funding and Sponsors’, are made of (poreous) graphite that minimizes the air flow. Each pendulum has its own set of 3 bearings, one cylidrical main bearing and two flat bearings to prevent the shaft from horizontal movement. One pendulum weighs about 60kg and it’s floating on a 0.004 mm layer of air!
How to calibrate the swinging period of each pendulum
Each pendulum has it’s own swinging period that needs to be constant within 5 ms over the entire sequence of 3 minutes. If the deviation is more the patterns won’t appear as beautiful as they could be. The first step is to accurately measure the swinging period of each independent pendulum. Close to the bearing at the top of the pendulum a optical switch is mounted that registers each pass of the pendulum. After adding some data analysis a swinging period is sent to the PC. Step two is to calibrate the swinging period. The 40kg mass mentioned above is to speed up the pendulum but is not movable along the length of the pendulum. To calibrate the exact period, there is a movable mass of 5 kg inside the pendulum pipe. By adjusting the height of this small mass the swinging period can be calibrated according to the theoretical table. If necessary, this movement can be automated using a stepper motor and a spindle.
How to bring to pendulums into position
The pendulums must be brought to a postion of about 25° from their vertical position. From that point it’s important to release all 15 pendulums at exactly the same time. With the small version one can use a metal/wooden bar and push or pull the pendulums into position and to let them go, quickly pull down the bar. With the large version this cannot be manually performed. The15 pendulums at 25° weigh 450kg together! The solution was found by a 12m wide motorised see-saw mounted on the main frame.
How to let go the pendulums at the same time
Underneath this see-saw 15 electromagnets can be activated to pick up the pendulums and pull them upwards. Once the see-saw is in position (@25°) the electromagnets are switched off by a relais and all 15 pendulums are released instantaneously.
How to stop the pendulums after the sequence
After one sequence the pendulums can be easily stopped by hand with the small version. With the large version this needs some extra tooling. Once the sequence is finished, a brake mounted on the see-saw are automatically brought into the right angle towards the pendulums. The brake consists of a rubber band that gently decreases the amplitudes of the pendulums towards standstill position. The electromagnets can now grab the pendulums without causing any hard collisions that could damage the air bearings or RGB spots inside the spheres..