The phrase "just like riding a bike" is used to refer to something that, once learned, you never forget how to do. As it turns out, bikes make that easy on us. If a typical bicycle is moving forward fast enough, it tends to remain upright and steer in a straight line, even if the rider takes his or her hands off the handlebars. In fact, you can set a bicycle rolling without a rider at all, and it tends to remain upright and roll in a straight line.

Attempts to understand this stability have been around almost for as long as bicycles have existed, and most people have accepted explanations focused on gyroscopic forces and the location of the steer axis. But a team of engineers has now built a bicycle that eliminates both of these features, but still manages to stay upright.

The authors of the new paper do an amazing review of how the popular explanations for a bicycle's stability got so, well, popular—their first reference dates back to 1869, and 10 of the 19 are over 100 years old. In one case, they spot a mathematical error (a reversed sign) in a 1910 reference.

Most people have seen a gyroscope in action, so the stability of a rapidly rotating wheel should be fairly intuitive, making this a focus from the start. People have built bicycles with counter-rotating wheels and found that they still remain upright, so that can't be all of the story. Another focus has been on the fact that the area where the front wheel touches the ground is a bit behind the axis of steering, which also seems to add stability to traditional bicycle designs.

To test the relative contributions of these factors, the authors eventually built their own computer model of a bicycle and started playing around with various features. It turned out that they could eliminate both the gyroscopic and the negative trail factors, and the bike would still be stable as long as it was moving faster than 2.3 meters (7.5 feet) per second. They could even move steering to the rear wheel and produce a stable design.

The apparently unreasonable stability of different bicycle designs must have suggested that their model had probably lost touch with reality, so the authors went out and built a bike with a counter-rotating wheel to get rid of gyroscopic effects, as well as a negligible (4mm) trailing between the front wheel and the steering. As their model predicted, it tended to stay upright, and would steer into any falls that their grad students tried to induce.

What their math can't apparently tell them is why so many different bike designs tend to stay upright. "Why does this bicycle steer the proper amounts at the proper times to assure self-stability?" they muse. "We have found no simple physical explanation equivalent to the mathematical statement that all eigenvalues must have negative real parts." In other words, they can see why the math works out the way it does, but can't figure out what physical properties correspond to that.

The best they can surmise is that the stability is related to the ability of the bike to steer into a fall if it starts to lean, and that there are multiple ways of constructing a bike that does this.

Science, 2011. DOI: 10.1126/science.1201959 (About DOIs).