Previously, I have tried to find “theoretically” the tooth counts of the Nexus-7 internal gear hub. Some nice numbers were obtained, but there were some suspects (you may think yourself what **can** be wrong with the numbers given in the link). Soon after, I disassembled the real hub and counted the teeth of all rings. Here are **the real numbers**. This is how the hub works:

- The hub has two
**gear systems**, each with own planet carrier. Call “first” the one which is closer to the sprocket. - The
**axle**is immobile. - Each gear system has:
- Two suns. Either can be immobilized by attaching to the axle with the pawls, activated by the shifter.
- Two gears on the planet carrier, each meshing with own sun. The
**smaller**gear on the planet carrier meshes with the ring. - One ring gear. The ring gear meshes with the
**smaller gear**of the planets.

- In lower gears 1 and 2, power input from the sprocket applies to the
**ring**of the first gear system. This carrier lowers down the transmission ratio. Depending on which sun is locked to the axle by a pawl, two step-down ratios are obtained. The second gear system is not involved. - In higher gears 6 and 7, the first carrier is not involved. Power input from the sprocket applies to the
**planet carrier**of the second gear system. Depending on which sun is locked to the axle by a pawl, two step-up ratios are obtained. The first gear system is not involved. - In middle gears 3, 4 and 5, both gear systems are involved, so that the first lowers the ration, the second raises it.

The table explains which exactly rings are engaged, and gives teeth numbers:

Gear | Power transmission |
Sun | Planet meshed with the sun |
Planet meshed with the ring |
Ring | Exact ratio |
Documented ratio |

1 | Ring1->Planets1 | 42 | 14 | 14 | 72 | 12/19 | 0.632 |

2 | Ring1->Planets1 | 36 | 20 | 20/27 | 0.741 | ||

3 | Gears 1 and 6 together | 0.843 | |||||

4 | Gears 2 and 6 together | 0.989 | |||||

5 | Gears 2 and 7 together | 1.145 | |||||

6 | Planets2->Ring2 | 30 | 19 | 14 | 66 | 279/209 | 1.335 |

7 | Planets2->Ring2 | 36 | 14 | 17/11 | 1.545 |

Note that in the step-up ring (Ring2), 30+19+14=63, while the ring has 66 teeth. I do not understand how so big difference (3 teeth) makes a working combination.

I don’t understand, if for example the physical visible sprocket is 32t and the front chainring is 22t then isn’t this the first gear, gear ratio 1.45? Or is the real gear first gear lower than that because the internal gear hub lowers it extra?

The hub lowers the transmission ratio in gears 1, 2 and 3, as the table shows. (Being pedantic, one should say that it lowers the ratio also in gear 4; but 0.989 is in practice so close to 1 that one can think that gear 4 is 1:1.)

Thank you for answering my above question but i still don’t understand because my actual question is what sprocket size on a 3-speed (Sram/Sachs-Torpedo) internal gear hub (with a 22T front chainring) is equivalent to a 44T sprocket on a 4-speed shimano Nexus internal hub (with a 22T front chainring), is it a 44t or instead a smaller sprocket? The reason i am confused is because the table for drive gear ratio for the 3-speed hub shows that the first step starts at 0.75 (does this mean that the first gear is not 1:1?; then what is it?) and the for the 4 speed hub it is 1:1 (http://www.sheldonbrown.com/nexus4.html), so what is the difference for the first gear etc?

> what sprocket size on a 3-speed (Sram/Sachs-Torpedo) internal gear hub (with a 22T front chainring) is equivalent to a 44T sprocket on a 4-speed shimano Nexus internal hub (with a 22T front chainring)

You’ll obviously not get equivalent transmission ratio in every gear (in the end, there are 3 and 4 of them in the different hubs!). Here is how you can calculate the sprocket size which would give you equivalent first gear. The first gear in Nexus-4 is 1. In Sram-3, it is 0.75; so to yield the same transmission ratio, the sprocket for Sram-3 must be 0.75 times smaller. 44:0.75 ~ 59.

> the table for drive gear ratio for the 3-speed hub shows that the first step starts at 0.75 (does this mean that the first gear is not 1:1?; then what is it?)

It is, as your table correctly states, 0.75. (In 3-speed internal hubs, typically the second gear is 1:1.)