Going Flat

8. The Bumpy Bike Path

Going Flat

Riding around on a flat tire is no fun. It feels really bumpy. But a square wheel may be the ultimate flat tire. There's no way it can roll over a flat, smooth road without jolting the rider again and again.

If the road itself has evenly spaced bumps of just the right shape, however, flat-sided tires can be the secret to a smooth ride!

Believe it or not, the bumps on the aliens' road (see "The Bumpy Bike Path") are the perfect shape to produce a smooth ride on a square-wheeled bike. It can't be just any old square-wheeled bike, though. Each side of the square tires must be related mathematically to the bump's height.

The bumps on the aliens' road are the shape of upside-down, or inverted, catenaries. A catenary is the curve formed by a chain or rope hanging loosely between two supports.

A hanging chain, fastened at its two ends, forms a catenary shape.

TRY IT!

Create your own inverted catenary.

You will need:

• piece of string, rope, or chain about 10 inches (25 centimeters) long
• sheet of paper

What to do:

1. Hold one end of the string in your left hand and the other end in your right hand, each hand at about the same height.
2. Let the string hang loosely between your hands. It forms a catenary!
3. Carefully lay it down on a sheet of paper without changing the string's shape.
4. Turn the paper so the string forms an upside-down U.

Now you can picture the cross section of each bump of the alien roadway. A series of such bumps, lined up in a row, would be the perfect surface on which to ride a square-wheeled bike.

How a square wheel rolls over a roadbed consisting of a sequence of inverted  catenaries. Wikipedia

See also "Riding on Square Wheels."

NEXT: Triking Around