Researchers from the US, Holland and England took more than three years to arrive at a mathematical formula for riding a bike – revealing the complex forces at work that cyclists seem to master instinctively.

Put in as plain a terms as possible, the phenomenally complex equation can be explained as: inertia forces + gyroscopic forces + the effects of gravity and centrifugal forces = the leaning of the body and the torque applied to the handlebars of a bike.

In other words, if you do not pedal fast enough to keep moving while keeping the bike straight, you fall over.

Halfords say they have made use of the research in their drive to teach people to learn to ride as part of National Bike Week.

Dr Arend Schwab of Delft University of Technology in the Netherlands, one of the study's key researchers, developed the equation and explained how it solves a question that is as old as bicycles themselves:

“People more than a hundred years ago were trying to figure out why a two-wheeled bicycle, given forward momentum, like a push, would seem to balance by itself.”

He also outlined its potential to improve bike design in the future:

"Using our equation, we can simulate the motion of a bike and predict whether it will remain stable or not under certain conditions – including if it goes over a bump, or is hit by a gust of wind."

"This equation is aimed at enabling a bike designer to change certain features and to see the overall finished effect on the bike," Schwab explained, "without having to actually manufacture it first."

"For instance, if you are designing a folding bike with smaller wheels, or one with a shorter wheel base, this equation allows you to interpret how design changes will affect the stability and behaviour of the bike.’

However, riding stability doesn’t only come from bike geometry plus human input. The Gyrowheel – a gyroscope within a wheel that its manufacturers claim is self-righting, is now commercially available. This technology also appears in the new, electrically powered Honda U3-X – a micro-wheeled device that has the rather disappointing statistics of 4mph and a battery life of up to an hour, but claims to allow movement in any direction using only the body’s sense of balance.

For a more in depth look at Delft University of Technology's bicycle dynamics study, visit http://audiophile.tam.cornell.edu/ als93/Bicycle/index.htm