Sprocket Size Optimisation for Derailleur Racing Bicycles

Abstract

The traditional design goal for sprocket size on racing bicycles is for it to be minimised for a given gear ratio. However, optimum sprocket size is actually a trade-off; larger sprockets have the advantage of producing lower transmission losses whilst small sprockets have the advantages of lower mass, inertia and frontal area. This paper analyses this trade-off to determine if there are advantages in increasing sprocket sizes for a given gear ratio.

The study is particularly relevant now since there are more available options for sprocket sizes, not just for the drive gears but also for the derailleur pulley gears.

A currently available, compact 11-speed rear cassette is used as a benchmark case, with two alternatives proposed: (i) pulley wheels 45% larger and (ii) all sprockets and chainring averaging 41% larger and pulley wheels 45% larger.? Models for chain articulation efficiency and overall power required for constant velocity cycling are presented and used to show the effect of increased sprocket size on overall performance.

The paper shows that larger sprocket sizes can reduce losses by up to 2.95 watts, representing around 0.5% overall power reduction, for several different cycling applications when compared with the benchmark case. This improvement is particularly pronounced for heavier, more powerful riders when riding minimal gradient courses at maximum effort. For some riders and racing scenarios, increased gear size can result in an increase in the power required of up to 0.35 watts, representing +0.1% increase in power required.

For elite cyclists and triathletes searching for marginal reductions in power losses, using larger sprocket sizes sometimes has clear benefits but it depends on rider physiology and race type. Choosing larger gears also has the advantage of increased smoothness of pedal action by reducing polygonal action in the top span of the chain. Further, reduced wear will lead to better longevity in components and longer optimal performance of the transmission.