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Is there an IGH that gives one the maximum overdrive-ratio that one might get with a 39-53T crankset and a 11-34T freewheel? If not, what is the mechanical roadblock in making one ?

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I don't know the answer, but note that the 53 - 11 combination practically never gets used, so there may be IGH's with the same useful range, but different actual ranges. –  Batman Apr 21 at 15:43
    
@Batman I have retrofitted a paddle-assist hub motor. I use a 48-11 combination all the time. I wish I had a higher overdrive ratio. –  Ayan Mullick Apr 21 at 17:56
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1 Answer 1

If we use the Sheldon Brown Gear Calculator set to metres development (although any other unit will work adequately), we see that the range for a 39-53 x 34-11 system is 2.5 to 10.4 metres developed per crank revolution, yielding an overall range of 416%.

The widest range options from various companies are the Shimano Alfine 11 hub, which has a range of 409% - essentially the same - and the Rolhoff Speedhub 500/14, which has a quoted 526% range.

Compare to a Sturmey-Archer AW three-speed hub, with an overall ratio of 178% based on its stated ratios of 1.33, 1.00 and 0.75.

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But the mentioned crank-sprocket setup will provide a maximum overdrive ratio of 4.8[53/11]. Whereas Shimano-Alfine-11's is 2.11. And I couldn't quite figure out that of Rolhoff-Speedhub-500/14's. But I don't think it'd be close to 4.8 ie. the wheel turning 4.8 times with each revolution of the paddle. –  Ayan Mullick Apr 21 at 8:51
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Yes, but you can adjust the overall balance of an IGH by changing the chainring and sprocket combination. To have the same high gear on the Alfine 11 as on the example derailleur system, you would need a crank:sprocket ratio of 2.27 (for example 45/20, available in the Alfine range, gives 2.25), as the ratio of the crank to sprocket link and then sprocket movement to wheel movement multiply to produce the final drive ratio. –  jbuk Apr 21 at 11:46
    
Yes, but that would be thru a combination of the IGH, chainring and the sprocket, altogether. Isn't there a hub individually capable of a 5:1 overdrive like this gives a 1.5:1 ratio. If not, is there a mechanical roadblock to it? –  Ayan Mullick Apr 21 at 17:42
    
@jbuk - Actually, IGH manufacturers set a limit for the amount of torque their system can take, so you are limited in the choice of sprocket you can fit. Rolhoff is very restrictive about it, Shimano seems to be far more permissive. –  mac Apr 22 at 13:09
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@AyanMullick - I have no idea, but I suspect you are underestimating the complexity of a IGH... Rohloff, which is the closest to "handmade IGH" you can go, has basically only one product (speedhub): it took them a full 2 years to develop, and it has over 120 moving parts sourced from 80some different factories around Germany... –  mac Apr 22 at 22:57
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