# Chain reactions

At this year’s Royal Society Summer Exhibition, scientists and engineers from Bristol University presented some interesting work on improvements to the drive chains used by Team GB in the Rio Olympics. They reached clear conclusions about the design of the chain and sprockets, taken up by Renold. Current research is exploring the the problem of chain resonance.

Bicycle chains and sprockets and sprockets tend to receive less attention than aerodynamics, for several reasons. As noted in previous blogs, the power required to overcome aerodynamic drag scales with the cube of velocity, whereas frictional effects scale simply in proportion to velocity. Furthermore, a good well-lubricated drive chain typically has an efficiency of around 95% or more, so it is hard to make further improvements. Note that a dirty chain has significantly lower efficiency, so you should certainly keep your bike clean.

The loss of power comes from the friction between links as they bend around the chainring and the rear sprocket. Using a high precision rig, the researchers demonstrated that larger sprockets are more efficient than smaller ones. For example, with a gear ratio of 4:1, it is more efficient to use a 64/16 than a more conventional 52/13.

In fact, one of the experts told me that the efficiency of the drive chain falls off sharply as the sprocket size is reduced from 13 to 12 to 11. This is because the chain has to bend around a much sharper angle for a smaller sprocket. If you think about it, the straight chain has to bend to a certain angle that depends on the number of teeth on the sprocket. Recalling some school maths about the interior angles of polygons, for 16 teeth, the angle is 157.5º, whereas for 11 teeth, the angle is 147.3º. For the larger sprocket, each pair of links overcomes less friction bending through 22.5º and back, compared with a more dramatic 32.7º and back for the smaller one.

Note that this analysis of the rear sprocket applies to single speed track bikes. On a road bike the chain has to pass the two derailleur cogs, which typically have 13 teeth, whatever gear you choose. However, the argument still applies to the chainring  at the front, where the gains of going larger were shown to exceed the additional aerodynamic drag.

The Bristol team also explored the effect of a number of other factors on performance. Using different length links obviously requires customised sprockets and chainrings. This would be a major upheaval for the industry, but it is possible for purpose-built track bikes. Certain molybdenum-based lubricating powders used in the space industry may be better than traditional oils. Other materials could replace traditional steel.

A different kind of power loss can occur when the chain resonates vertically. A specially designed test rig showed that this can occur at frequencies, which could be triggered at certain pedalling cadences. Current research is investigating how the tension of the chain and its design can help mitigate this problem (which is also an issue for motor cycles).

In conclusion, when we see Tony Martin pushing a 58+ chainring, it may not be simply an act of machismo – he is actually be benefitting from efficiency gains.

## Author: science4performance

I am passionate about applying the scientific method to improve performance