Gear hub madness

Today I came across a good description of how the new SRAM G8 hub works, and I worked through the ratios in a spreadsheet. Its a strange hub and it took me a while to figure out what was going on, even when someone had already attempted to explain it. This got me thinking about another difficult nut to crack, the Alfine 11.

As far as I can determine, no one has done a teardown of an Alfine 11, counted the teeth, or posted any particular information about how its ratios are created.  In the past, I've thought it was quite similar in design to a Nexus 7, but now I've changed my mind.  However before that, lets go on a tour of gear ratios in hubs.

Gear hubs are made up of planetary gear sets: http://en.wikipedia.org/wiki/Epicyclic_gearing

Generic three speed:

The most basic hubs have one gear set, giving three speeds.  In the middle there is direct drive, then one ratio increased and one ratio decreased (the inverse of the increased ratio).

gear	1	2	3
ratio	0,750	1,000	1,333
ratio change		33 %	33 %
name	1/A	-	A
calculated ratio	0,750	1,000	1,333

SRAM P5:

This was extended to make 5 speeds such as the SRAM P5 by placing two gear sets into one module, so that one of two ratios could be used at a time, either up or down.

gear	1	2	3	4	5
ratio	0,633	0,781	1,000	1,281	1,579
ratio change		23 %	28 %	28 %	23 %
name	1/A	1/B	-	B	A
calculated ratio	0,633	0,781	1,000	1,281	1,579

SRAM S7:

This also worked for 7 speeds, such as the SRAM S7.

gear	1	2	3	4	5	6	7
ratio	0,574	0,677	0,809	1,000	1,236	1,476	1,742
ratio change		18 %	19 %	24 %	24 %	19 %	18 %
name	1/A	1/B	1/C	-	C	B	A
calculated ratio	0,574	0,678	0,809	1,000	1,236	1,476	1,742

SRAM i-Motion 9:

It even worked for a 9 speed, the i-Motion 9.  This hub was basically a failure on the market, apparently because it was too heavy, rough running, expensive, and poorly sealed against weather.  However it was apparently well constructed, and it did achieve 9 tight and evenly-spaced ratios while using only one planetary gear at a time, potentially giving high efficiency.  I think its a shame it didn't make it.

gear	1	2	3	4	5	6	7	8	9
ratio	0,542	0,621	0,727	0,853	1,000	1,172	1,375	1,611	1,844
ratio change		15 %	17 %	17 %	17 %	17 %	17 %	17 %	14 %
name	1/A	1/B	1/C	1/D	-	D	C	B	A
calculated ratio	0,542	0,621	0,727	0,853	1,000	1,172	1,375	1,611	1,844

Shimano Nexus 4:

But there are other fun things that might be done.  Consider a Nexus 4, which made four ratios from a set of three planetary gears, by only increasing ratios.  Leaving out the ability to decrease ratios simplified the hub.  This simplification, where each planetary gear is only used to either increase or decrease ratio but not both, is a major theme of all recent hubs.  There i-Motion 9 above might well have needed only 4 planetary gears to get 9 beautiful-looking ratios, but those 4 gears were too complicated.

gear	1	2	3	4
ratio	1,000	1,244	1,500	1,843
ratio change		24 %	21 %	23 %
name	-	A	B	C
calculated ratio	1,000	1,244	1,500	1,843

Shimano Nexus 5:

But all these hubs have fairly large steps between the gears.  Especially the gap between direct drive and the first ratio up or down was problematic.  While i-Motion 9 got this down to 17%, it was apparently unpleasant.  Even the 22% gap on Nexus 8 leads to some gear whine.  So Shimano got busy with dual-stage compounding its planetary gear sets.  Below is the Nexus 5, which used three planetary gears in two sets, and has no direct drive ratio at all, but is very smooth in my experience.

gear	1	2	3	4	5
ratio	0,750	1,001	1,159	1,335	1,545
ratio change		33 %	16 %	15 %	16 %
name	1/A	B/A	C/A	B	C
calculated ratio	0,750	1,001	1,159	1,335	1,545

Shimano Nexus 7:

The Nexus 7 is similar, but with four planetary gears arranged in two sets.  I've used two of these extensively and never been satisfied with either their smoothness or efficiency, but they seem to sell in vast quantities in Denmark.

gear	1	2	3	4	5	6	7
ratio	0,632	0,741	0,843	0,989	1,145	1,335	1,545
ratio change		17 %	14 %	17 %	16 %	17 %	16 %
name	1/A	1/B	C/A	C/B	D/B	C	D
calculated ratio	0,632	0,741	0,844	0,989	1,145	1,335	1,545

Shimano Nexus 8 / Shimano Alfine 8:

But thats not the only way to do multi-stage compounding.  The Nexus/Alfine 8 is a lot like the old Nexus 4 with a new planetary gear enabling the four original ratios to be used twice.  This leaves a direct drive gear in place which is good, but creates an odd situation where the least efficient gear (4) is right next to the most efficient (5), and switching between the "high" and "low" gears can be problematic.  Still, this seems to be a robust design.

gear	1	2	3	4	5	6	7	8
ratio	0,527	0,644	0,748	0,851	1,000	1,223	1,419	1,615
ratio change		22 %	16 %	14 %	18 %	22 %	16 %	14 %
name	1/A	B/A	C/A	D/A	-	B	C	D
calculated ratio	0,527	0,645	0,748	0,851	1,000	1,223	1,419	1,615

Rohloff:

And then there is the monsterous 14 speed Rohloff, that uses 5 planetary gears in three sets.  Gears 3 and 5 actually use triple-stage compounding, which is hard to notice in my experience.  In some ways this combines concepts which are found on both Nexus 7 and Nexus 8, sort of a combination of those designs.

gear	1	2	3	4	5	6	7	8	9	10	11	12	13	14
ratio	0,279	0,316	0,360	0,409	0,464	0,528	0,600	0,682	0,774	0,881	1,000	1,135	1,292	1,467
ratio change		13 %	14 %	14 %	13 %	14 %	14 %	14 %	13 %	14 %	14 %	14 %	14 %	14 %
name	1/B * 1/A	1/C * 1/A	D/B * 1/A	1/A	E/C * 1/A	D/A	E/A	1/B	1/C	D/B	-	E/C	D	E
calculated ratio	0,279	0,317	0,360	0,409	0,464	0,528	0,600	0,682	0,774	0,881	1,000	1,135	1,292	1,467

SRAM G8:

Here is the SRAM G8 in all its confusing glory.  Five planetary gears in two sets, sort of arranged like a backwards Nexus/Alfine 8.  No direct drive, and 6 of the 8 ratios are two-stage compounded.  http://sheldonbrown.com/sram-g8.html

gear	1	2	3	4	5	6	7	8
ratio	0,609	0,710	0,803	0,903	1,054	1,204	1,355	1,581
ratio change		17 %	13 %	12 %	17 %	14 %	13 %	17 %
name	1/B	1/C	E/A	E/B	E/C	D/A	D/B	D/C		1/A	D	E
calculated ratio	0,609	0,710	0,803	0,904	1,054	1,204	1,356	1,580		0,5411	2,2258	1,4839

Shimano Alfine 11:

Then finally we get to the Alfine 11.  I spent some time on this.  There are lots of ways to make a good approximation of the published ratios, but the way I am most satisfied with uses four planetary gears arranged in three sets.  The main difference between this and Nexus/Alfine 8 is that one gear (number 7) is able to combine with gears 8 and 9 to create ratios 10 and 11.  Then all those resulting 5 ratios are re-used in positions 2-6.  This very nicely explains the 29.2% gap between gears 1 and 2... its same ratio as gear 7 has.  This also has no planetary gears which are used to both increase and decrease ratios, which appears to be very much out of style, it explains the alternating 13% and 14% ratio changes, and it explains how the 11 speed is able to match the weight of the 8 speed.  Essentially, the same number and strength of gears needed to be used.

There is no direct drive ratio, which is instead replaced by a triple-compound approximation, I imagine to achieve mechanical simplicity.  The only difference between 2-6 and 7-11 is whether or not the "low range gear" is active.

gear	1	2	3	4	5	6	7	8	9	10	11
ratio	0,527	0,681	0,770	0,878	0,995	1,134	1,292	1,462	1,667	1,888	2,153
ratio change		29,2 %	13,1 %	14,0 %	13,3 %	14,0 %	13,9 %	13,2 %	14,0 %	13,3 %	14,0 %
name	1/A	B/A	C/A	D/A	(B*C)/A	(B*D)/A	B	C	D	B*C	B*D
calculated ratio	0,527	0,681	0,770	0,879	0,995	1,135	1,292	1,462	1,667	1,889	2,154

Further reading, here is the grand daddy of complicated bike gear hubs: http://sheldonbrown.com/elanratios.html