Gear Ratios (Shimano DuraAce 7900 11-28)

Working out Gear ratios
Here is Sheldon Brown’s excellent new gear ratio system, which takes crank
length into account. This system is independent of units, being
expressed as a pure ratio. This ratio would be calculated as follows: divide the wheel
radius by the crank length; this will yield a single radius ratio
applicable to all of the gears of a given bike. A road bike with 170 mm cranks: (The usual generic diameter value for road wheels is 680 mm, so the radius would be 340 mm.)
340 mm / 170 mm = 2.0. (The radius ratio)
Applying the ratio to a gears is done as follows: 2.0 X 53 / 19 = 5.58
This number is a pure ratio, the units cancel out. Call
this a “gain ratio”.  What it means is that for every inch, or kilometer, or furlong
the pedal travels in its orbit around the bottom bracket, the bicycle
will travel 5.58 inches, or kilometers, or furlongs.
The “%” figure indicates the change between individual sprockets and between chainwheels.
The following link provides an online calculator
50 47.1 % 34
11 8.9 6.1
9.1 %
12 8.2 5.6
8.3 %
13 7.6 5.1
7.7 %
14 7.0 4.8
7.1 %
15 6.5 4.5
13.3 %
17 5.8 3.9
11.8 %
19 5.2 3.5
10.5 %
21 4.7 3.2
14.3 %
24 4.1 2.8
16.7 %
28 3.5 2.4

Using the Ratios
Using the above table and playing with the information on a sheet of paper it becomes apparent how ridiculously inefficient and complex even “compact” (50T/34T) double chainwheel system is. It’s amazing that engineers cannot design something better and that we currently pay a small fortune for this rubbish. The problems here are that the 4th gear is duplicated and several ratios are incredibly close so that they are almost duplications too. Only the bottom 5 gears on the small chaniwheel and the top five gears on the big chainwheel are linear. The 10 gears in between flit around between chainwheels and sprockets in a way that would be impossible to achieve in practice – rendering linear gear changing out of the question. Eliminating the impossible flitting around with consideration of the duplication (or almost) of ratios – and avoiding inefficient stretching of the chain diagonally – the best solution appears to be to use sprockets 1(28T) to 7(14T) with the 34T chainwheel and then drop to 4(19T) to 10(11T) for the 50T chainwheel. This gives a linear progression throughout.

The 4th gear on 34T is the same as the 1st gear on 50T so that’s why the big chainwheel felt good for climbing yesterday as this is a good ratio for climbing. 2nd gear on the 50T is between the 5th and 6th gears on the 34T. This gear is interesting because the gap between 5th and 6th is too great when climbing but this ratio with the 50T is different enough that it’s worth looking for. Outside of this exception it’s best to stick to the simple rule at the start of this paragraph. It gets even more complex if we try to “number” the gears from 1 to 20 because the 4th gear is duplicated and so is also the 5th gear. It seems better to refer to gears as 1 to 10 relating to the sprockets and then note the corresponding chainwheel.

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