Entfaltung: Unterschied zwischen den Versionen

== Gain Ratio - Die [[Sheldon Brown]] Methode zur Berechnung der effektiven Entfaltung ==

Cyclists often find it useful to have a numeric representation of the gearing provided by their bicycles. This allows them to make meaningful choices in customizing their gearing, and can be useful in comparing the performance of one bicycle with another.

There are several systems for doing this, none of them entirely satisfactory. I would like to propose a new, more accurate and more universal system.

Cyclists who are only associated with one narrow ghetto of the cycling world frequently make do by just naming the chainwheel and rear sprocket they are using. This is a bit cumbersome, using two numbers where only one is really needed, and can also be confusing. For example, a 39/14 is the same as a 53/19, but this is not obvious. Since there are only 4 chainwheel sizes in common use on road racing bikes (39,42,52 & 53) this is still usable for the cyclist who only deals with this type of machine.

This system is also pretty much useless when planetary gears are involved.

:The simplest system in common use is the "gear inch" system. This dates back to before the invention of the chain-drive bicycle. It originally was the diameter of the drive wheel of a high-wheel bicycle. When chain-drive "safety" bikes came in, the same system was used, multiplying the drive wheel diameter by the sprocket ratio. It is very easy to calculate: the diameter of the drive wheel, times the size of the front sprocket divided by the size of the rear sprocket. This gives a convenient two- or three-digit number. The examples listed above are all around 74-75 inches. The lowest gear on most mountain bikes is around 22-26 inches. The highest gear on road racing bikes is usually around 108-110 inches. Unfortunately, the handwriting is on the wall for all inch-based measurement systems.

:In countries that use metric measurements, the usual system is "development" in meters. This is the distance that the bicycle moves with each revolution of the pedals. This system is a bit more cumbersome than the gear inch system, for two reasons. First, it is a little more difficult to calculate: wheel diameter in meters x front sprocket / rear sprocket x pi. Having to multiply by a constant (an irrational one, no less!) needlessly complicates things. Also, the resulting value is a less convenient number to work with, a single digit plus two decimals. For example a road bike's 52/13 would be exressed: 8.64. A mountain bike's 24/28 would be: 1.78.  

All of these systems share a common inadequacy: none of them takes crank length into account! The fact is that a mountain bike with a 46/16 has the same gear as a road bike with a 53/19 only if they have the same length cranks. If the mountain bike has 175's and the road bike 170's, the gear on the mountain bike is really about 3% lower!

I would like to propose a new system, which does take crank length into account. This system is independent of units, being expressed as a pure ratio.