200 years bicycle – On the democratization of a formerly upper-class vehicle

Almost every person knows a form of transportation, which can been learnt in childhood and used by nearly everyone until old age: cycling. Whether one thinks of the athlete that places himself in the aerodynamically optimal position almost belly down flat on the frame or the elderly lady sitting comfortably upright on the bike seat, both give the impression of an entirely elegant and harmonious movement. Behind this perception lies a noteworthy fact: the efficiency in the conversion of metabolic into mechanical energy for the sake of movement stands at about 25% for the bicycle, a value that is not even close to being reached by any other form of human movement. Such efficiency (on the ground) is also not matched in the entire animal kingdom. The bike is the most efficient means of transport on our planet(after the aerial flight of birds where the glide of the albatross is particularly impressive with regard to energy efficiency, albeit the bird takes advantage of wind energy). For the sake of comparison: the efficiency of the Otto motor can go up to 40%, but this is only possible by means of great temperature differences during its cycle; plus a car is, of course, much heavier: with one hundred calories cyclists have the energy to drive up to almost five kilometers, while a car will only make it 85 meters with that amount of energy.

Such a miraculous means of transportation should have been invented at the latest by the wise Greeks or the technically inspired Roman engineers in antiquity, one would think. Wheels (including spokes for the use in vehicles) the Sumerians used already over 4000 years ago. But no, the two-wheeled vehicle, the “bicycle”, is a comparatively new human invention. Precisely 200 years ago, on June 12, 1817, the Freiherr Karl von Drais of Baden came out with his wooden “running machine”, which he had constructed, and went for a first ride from the Mannheim Castle to the horse post halfway to Schwetzingen(the best road in the area of Baden, Germany). This new useful as well as efficient means of transport – with this running bicycle one can travel more than twice as fast as with the horse coach – was based on an important conceptual innovation, which gave people an entirely new experience: to move forward on two wheels in an unstable balance which needed to be permanently maintained. One would assume that an object like the bicycle with only two points of contact to the ground, which is already an extremely wobbly matter in the static case, should be even more so in motion. But every child knows today: While it takes acrobatic skills to keep a still bicycle in the balance, this can after some practice be achieved quite well by almost anyone in case the bicycle is moving.

Still today the precise physics of cycling is familiar to only very few people. At the beginning of the 19th century though it was completely unknown, which is probably the reason for the rather late invention of the bicycle (more than 50 years after the steam engine). Among other things it is the angular momentum of the rotating wheels and the thus resulting forces that allow for stable equilibrium positions of the bicycle while moving forward, which are physically not achievable in a resting state. If you are cycling in such a dynamic equilibrium position, slight changes in the steering angle or very small weight shifts are sufficient to restore a balance if such is slightly disturbed. Therefore, after to some practice, achieves the necessary balancing equilibrium almost insouciantly, e.g. we intuitively grasp that we can counteract an imminent tipping of the bicycle inone direction during driving by swinging the handlebars in the same direction triggering a short bend, which leads the bicycletobeing raised again to the other side by the centrifugal force. Andwith special dexterity one can achieve stability solely by shifting the body weight appropriately (i.e. that person achieves free-hand riding). The precise equilibrium positions possible are the result of the interaction of various forces and angular momenta the mathematical analysis of which often requires complicated calculations some of which have not even been fully understood in detail yet today. For example, why a bicycle can roll stably even without a driver has remained an open puzzle until just a few years ago (see the article: JP Meijaard et al., Linearization equations for the balance and steer of a bicycle: a benchmark and review, Proceedings of The Royal Society (August 8, 2007)). “Everybody knows how to ride a bike, but nobody knows how we ride bikes”, writes Mont Hubbard, an engineer who studies sports mechanics at the University of California, Davis.

Hence the bicycles originating from the Draisian running machine developed to their present form rather by trial and error than by precise theoretical and mathematical understanding of the underlying physical interrelations. The historical development of cycling iscomparable to how children learn to ride a bicycle today. At the beginning of the 19th century it was still completely uncanny for people to take their feet off the ground when cycling, just as three-year-olds do not do so on their first runner bikes. But already Drais noticed that for riding a curve the driver has to turn the handlebar briefly into the opposite direction. Decades were to go by before his invention was taken up again and further developed. It was only in the 1860s that the bicycle was fitted with a pedal onto the front wheel, which made it necessary to take the feet off the ground when riding. People had needed a while to figure out that this actually works. Balancing while driving on the so-called “Velocipedes” (“fast foot”) was however an art in itself that had to be acquired by training. However, a pedal rigidly attached to the front wheel did not permit any too great velocities. Hence, the front wheels were to get bigger in order to get a better translation (in today’s words: higher gears). This led to the well-known “penny farthing”. However, the era of high wheels did not last very long, because of the danger of plunging from high above the ground, which led to serious accidents. A safe variant of cycling was developed in the 1880s in England, with two wheels of the same size, a diamond-shaped frame and pedals between the wheels at the rider’s foot driving the rear wheel via a chain (which eventually allowed appropriate gearing). Another innovation made riding a bicycle even more comfortable and faster: the air-filled tire. The bike in its present form had been found.

When in the late nineteenth century the bicycle became cheaper and cheaper through mass production, so that workers and clerks were able to afford such a vehicle, it also began to play an important role in social politics. It gave its owners a far greater radius of movement, and thus the possibility to leave the cramped dwellings close to the factory. In various “workers’ bicycle unions”, workers grouped together across the countryand among other things articulated socialist and social-democratic goals. In the 1920s the bicycle finally became a means of mass transportation. When, starting in the 1950s with the economic upturn and rising incomes many people were able to afford a car, the bicycle boom came to an end. The bike received the stigma of a “losers’ vehicle”. In the 1970s and 1980s, however, with the emerging fitness wave it became a popular sports and leisure device. It is only in recent years that the bicycle has been gaining broader acceptance again. In large cities, for example, urbanplanners are using it to remedy increasing car traffic and air pollution.

Meanwhile the advantages of the bicycle have become more and more prominent: its unrivaled energy balance, its environmental friendliness and its role in health provision. These will give it a great role in the world going forward, more than 200 years after its invention. And who knows: Perhaps more engineering surprises are awaiting us. For the physics of the bicycle might still bear the one or the other secret