paperlined.org
prominence > juggling_and_balance
document updated 14 years ago, on Sep 29, 2009
The classic inverted pendulum can be used for the study of balance, not just a study of physics.

As long as possible

The longer the pendulum, the lower its frequency, and thus, the easier it is to balance. So you might take up the goal of building as long of a pendulum as possible.

However, extremely long poles become increasingly unweildy (even pikemen's weapons maxed out at 22 feet), and become increasingly vulnerable to catastrophic failure when falling.

The best balancing poles are those that are rigid (making it easier to handle, because a pole that has multiple concurrent wobbles is one that's very hard to predict) and lightweight (making it less likely to suffer damage as a result of a fall, and easier to decellerate by hand once a fall ensues). However, rigidity and weight are in direct opposition to each other — the way to make a pole more rigid is by increasing its cross-section, but increasing the cross-section directly adds to weight.

One solution to this is to use a hollow tube (putting all of its weight on the periphery, and thus contributing maximally to rigidity), but that can only get you so far.

The other solution is to use material that has a high stiffness to weight ratio (eg. wood is worst, plastic is midway, aluminium is great).

As long as possible — Cost

Extremely long balacing poles can be made surprisingly cheaply.

Usually the biggest challenge is 1) finding a joining method that is strong enough, and 2) finding a joining method that can be quickly assembled/disassembled in the field. (20'-30' poles can not moved through doors)

total cost
@max len
maximum practical length pole material joining method
~$3 16 feet 1"×2" wooden board
($0.10/ft !)
overlap boards by ~1 foot, and secure with two bolts-and-washers (one at each end of the overlapped section)
~$5 20 feet? 3/4" electrical conduit
($0.30/ft)
Put a 2' sheath over the joint, which is made of either a 1" plastic pipe or a 1" conduit. This won't be a perfect fit though, so you either have to wrap the 3/4" conduit in tape to fill the gap, or use screws through the outer pipe to wedge the inside pipe. (or both)