10 to 12 miles (15 to 20 km) per hour (the drag force increases in proportion to the square of the speed, thus the power required to overcome it increases in proportion to the cube of the speed). Human factors can also be significant. Rohloff argues that overall efficiency can be improved in some cases by using a slightly less efficient gear ratio when this leads to greater human efficiency (in converting food to pedal power) because a more effective pedalling speed is being used. Overview An encyclopedic overview can be found in Chapter 9 of "Bicycling Science" which covers both theory and experimental results. Some details extracted from these and other experiments are provided in the next subsection, with references to the original reports. Factors which have been shown to affect the drive-train efficiency include the type of transmission system (chain, shaft, belt), the type of gearing system (fixed, derailleur, hub, infinitely variable), the size of the sprockets used, the magnitude of the input power, the pedalling speed, and how rusty the chain is. For a particular gearing system, different gear ratios generally have different efficiencies. Some experiments have used an electric motor to drive the shaft to which the pedals are attached, while others have used averages of a number of actual cyclists. It is not clear how the steady power delivered by a motor compares with the cyclic power provided by pedals. Rohloff argues that the constant motor power should match the peak pedal power rather than the average (which is half the peak). There is little independent information available relating to the efficiency of belt drives and infinitely variable gear systems; even the manufacturers/suppliers appear reluctant to provide any numbers. Details Derailleur type mechanisms of a typical mid-range product (of the sort used by serious amateurs) achieve between 88% and 99% mechanical efficiency at 100 W. In derailleur mechanisms the highest efficiency is achieved by the larger sprockets. Efficiency generally decreases with smaller sprocket and chainring sizes. Derailleur efficiency is also compromised with cross-chaining, or running large-ring to large-sprocket or small-ring to small-sprocket. This cross-chaining also results in increased wear because of the lateral deflection of the chain. Chester Kyle and Frank Berto reported in "Human Power" 52 (Summer 2001) that testing on three derailleur systems (from 4 to 27 gears) and eight gear hub transmissions (from 3 to 14 gears), performed with 80 W, 150