FarHorizon

Should I opt to convert my recumbent to an internally geared Shimano Nexus 8 hub, what front chainwheel size should I run?

Recumbent = 20" rear wheel
DF bike = 700c or 26" rear wheel

I'd like to have the same gear-inch ranges that are common on DF bikes with the Nexus 8. It seems to me that with a smaller diameter wheel, the wheel would have to spin faster to achieve equivalent speed. That faster rear wheel speed would require a larger front chainwheel to maintain the same cadence for that same speed (assuming the rear cog doesn't change)?

Retro Grouch 

Internal hub gears are usually indicated as percentages. I imagine that you can get them from the manufacturer. Figure the gear inches of the chainring and rear cog that you are using and apply the percentages to that.

John E

Either use a simple ratiometric equation, i.e., your new chainring should have 26/20 or 27/20 times as many teeth as the one on your road bike, or convert everything into the common coin of "gear-inches" = (chainring teeth * wheel diameter in inches / cog teeth) * internal hub gear ratio.

8th (1:1.617)
7th (1:1.419)
6th (1:1.223)
5th (1:1)
4th (1:0.851)
3rd (1:0.748)
2nd (1:0.644)
1st (1:0.527)

To obtain a 100-inch top gear with an 18-tooth cog on the Nexus hub, you need to solve: 100 = 1.617*20*T/18, where T = number of teeth on the chainring = 18*100/(20*1.617) = 55.65, i.e., 55 or 56 teeth. In turn, this will give you a low gear of 0.527*20*55/18 = 32 gear-inches. If you need something lower for climbing with your 'bent, you will either have to settle for a lower top gear or go to double chainrings and a tensioner (non-shifting rear derailleur).

grolby

For a recumbent with a 20" rear wheel, I would instead suggest the new Sturmey-Archer 8-speed hub. The lowest gear is direct drive, with the highest being a 305% overdrive. As such, it's very well-suited for small-wheeled bikes, giving them respectable gear ranges without the need to resort to unusually small sprocket sizes. Unfortunately, it means you get absurdly high gearing with full-size wheels, but such is life. Why not play around with Sheldon's gear calculator? Just bear in mind that you can only use a 23 or 25 tooth cog with the S-A 8-speed,according to the sales blurb on another part of the website.

FarHorizon

Hi John!

I like your ratio idea, but shouldn't I use the ratio of circumfrences rather than the straight ratio of diameters? That would take care of the gear inch stuff automatically. Thanks.

FarHorizon

Too late, grolby - I've already got a Nexus 8! I bought the hub for another project, but it'll have to do for this one. Thanks.

John E

Ratio of circumferences = ratio of diameters, since C = pi * D

Gear-inches are defined using diameters, to provide a direct comparsion to the crank speed / road speed ratio of a penny-farthing or "ordinary" bicycle of a particular wheel diameter. The Europeans not only use meters instead of inches, but they also use circumference instead of diameter, with the result that a 100-inch gear is an 8-meter gear.

In any event, a 52 to 56T chainring / 18T cog combination should be about right for you, depending on personal preference.

John E

I didn't know about that. That certainly is a great tip for folks with small wheels. I am glad good ol' S-A is still in business.