The neighborhood kids riding their bicycles up and down the streets on a summer afternoon are not likely to be thinking about science as they feel the warmair against their faces or struggle to pedal up a hill. But in today’s highly competitive sports environment, world-class racing bicyclists have to be part-time scientists, interested in the role mathematics, physics, and engineering play in improving the design of wheels, gears, frames, and other parts of a bicycle.

They also need to understand the aerodynamics of cycling. Comprehension of these variables provides information that can help them shave valuable seconds off their time in a race and gain an edge over other competitors.

Wheels and Tires

Wheels have come a long way since the ancient Mesopotamians invented them around 3500 B.C.E. It was not until the Industrial Revolution that the wheel was made useful for “human-powered machines.” The development of the pneumatic tire helped turn cycling into an immensely popular activity in the late nineteenth century.

The earliest bicycles were “high-wheelers,” or bikes with a huge wheel in front and a small wheel in back. These bikes did not have gears or even chains; pedals were connected directly to the bike’s front wheel. Because the wheel was so large, a cyclist was able to travel as far as 140 inches with a single rotation of the wheel, making this bicycle remarkably fast on level ground.

They were dangerous, though, especially on rough surfaces, because they were hard to pedal uphill, and the rider sat so high over the front wheel. It was not until the 1880s that the so-called safety bicycle was developed. With the rider suspended on a metal frame between two equally sized wheels.

These bicycles were much safer and easier to pedal than the older varieties.

An important part of a bike’s wheel is the spokes. They help reduce the weight of the bike (because the wheel is not solid) and make the wheel more efficient. Spoking can be done in two ways: radial or tangential. Radial spokes run directly from the hub of the wheel to the rim in a straight line. Tangential spokes, in contrast, connect the hub and the rim at a slight angl-eat a tangent to the hub. Whereas the front wheel of a bike can be spoked radially, rear wheels have to be spoked tangentially; otherwise, they can not transmit torque (turning power) out from the hub to the rim efficiently.

Tangentially spoked wheels are also stronger, and thus better able to with-stand the forces created by steering, braking, and bumping up and down on an irregular road surface.

Early tires were made from leather or solid rubber, so cycling was a pretty bumpy affair. Pneumatic, or air-filled, tires provide a more comfortable ride. Road bikes and touring bikes use thin tires that are inflated to 100 or 120 pounds per square inch. This high pressure keeps them from “flattening out” on the road, which can create friction and slow the rider down.

Flattening out is often referred to as “rolling resistance” and describes how much energy is “lost to the road” as the wheel moves forward. Unlike road bikes, mountain bikes use fat tires, which flatten out on smooth surfaces but tend to “float” on top of rough surfaces.

Drives and Gears

Leonardo da Vinci developed the idea of a chain and cog in the fifteenth century, but it was not until the 1880s that the chain drive was commonplace on bikes. On a bicycle with a chain drive the rider is positioned between the two wheels, providing better balance and safety.

A chain drive without gears works well enough on flat surfaces, but headwinds and uphill climbs demand the use of gears. Without gears, one turn of the pedal equals one turn of the wheels. But gears allow the rider to change that ratio such that one revolution of the front wheels creates, say, two revolutions of the back wheel. Competitive bikers know exactly what the ratio is for each gear on their bike and chart the best ratio they need depending on conditions, for example whether they are going uphill or downhill.

Closely related to gearing is cadence, or the rate of pedaling. A competitive cyclist’s goal is to find the most efficient cadence, or the cadence at which his or her body delivers the most energy to the bike. Road racers’ cadences tend to range between 75 and 120 revolutions per minute; mountain bikers, on the other hand, tend to strive for a cadence of about 50 cycles per minute, though the wider range of conditions in mountain biking demands a wider range of cadences.

Frames

In deciding on the best material to use in a frame, bike makers measure three factors. The first is elasticity, or the ability of a material to return to its original shape when bent. The second is yield strength, or the amount of force needed to bend the material to a point where it can not return to its original shape. The third is ultimate strength, or the amount of force needed to break the material.

Recent years have seen a revolution in the types of materials used to construct bicycle frames. Early frames were made of steel tubing. Although steel is strong and has high ultimate strength, it made early bikes quite heavy, often over 80 pounds. Steel frames are still used today, but the tubes have thinner walls and are much lighter. A major advantage of steel is that it is inexpensive.

Cost, however, is not likely to be a major consideration to a competitive racer, who is likely to choose one of three other materials. One is aluminum, which is much lighter than steel but does not have as much yield strength, so the tubing has to be of a relatively large diameter. Another is titanium, which is extremely strong relative to its weight and has high elasticity—but at a cost up to 15 times that of steel. A third is carbon fiber,  whose major advantage is that it does not have to be forged like tubing. It is more like a fabric that can be molded and tailored to provide maximum strength at stress points in the frame. It also does not have to be round. Carbon fiber can be formed into an oval or even teardrop shape, making the bike more aerodynamic. Frames made of either titanium or carbon fiber, because of their high elasticity and high ultimate strength but relatively low yield strength, have to be well designed to be stiff enough to resist pedaling forces.

Aerodynamics

Every cyclist is familiar with wind resistance (aerodynamic drag) which accounts for 70 to 90 percent of the resistance a cyclist feels while pedaling.

Aerodynamic drag consists of two forces: direct friction and air pressure drag. Direct friction is created by the air’s contact with the surface of the rider and the bicycle. Of greater importance, though, is air pressure drag.

As the rider and the bike cut through the air, they create an area of high air pressure in front and an area of lower pressure behind. The two forces combine to literally pull the cyclist backward.

Cyclists calculate drag by factoring in velocity, wind speeds, the rider’s weight, and the grade of the road. The result of their calculation is expressed in “newtons,” defined as the unit of force needed to impart an acceleration of one meter per second to a mass of one kilogram. With this information the cyclist can then calculate the propulsive power needed to maintain velocity, usually expressed in watts. With this information the cyclist can calculate the number of calories per minute he or she has to burn to maintain speed. In a major race such as the Tour de France, cyclists burn up to 10,000 calories per day.

Competitive cyclists minimize drag by:

1. Selecting frame materials and shapes that have a good strength-to-weight ratio while improving aerodynamic efficiency;

2. Using disc wheels, which, while heavier than spoked wheels, reduce the number of drag-producing “air eddies” that spokes create;

3. Using drop bars, which reduce the size of the surface area their bod- ies present to the air;

4. Wearing tight, synthetic “skinsuits,” which reduce direct friction; and

5. Drafting.

Drafting, an important technique in competitive road racing, is riding in the low-pressure area created by the air-pressure drag of a rider in the lead,  which is sometimes just inches away. This low-pressure “eddy” can actually suck the rider forward. The lead cyclist even gains an advantage by having the low-pressure eddy filled by another rider. In a race, cyclists compete for position in packs called “pelotons,” or in diagonal pace lines called “echelons.” By riding in a group cyclists can save up to 40 percent of their energy compared to a rider cycling alone. Because a road’s width can accommodate only so many riders, cyclists especially value the “gutter” position, the final place in the echelon line, where the benefits of drafting are most pronounced.

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Reference

Jones, David E. H. “The Stability of the Bicycle.” Physics Today (April 1970): 34–40.

Perry, David. Bike Cult: The Ultimate Guide to Human Powered Vehicles. New York: Four Walls Eight Windows, 1995.

Whitt, Frank Rowland, and David Gordon Wilson. Bicycling Science. Cambridge, MA: MIT Press, 1982.