corrado33

My other thread on many (many!) speed bikes got me thinking...

With any technology available today, what is the theoretical maximum number of speeds with which one could build a bike?

And the things have to work together, so you can't say "well I'd put a 14 speed rohloff with a 12 speed cassette" because those things can't work together, for a variety of reasons. Obviously such a bike would have quite a few shifters up on the handlebars (or on the downtube perhaps?), but that's to be expected. Yes, you're probably going to run into chainline problems and rubbing derailleurs, but that's still USEABLE. I will allow things to be slightly modified. I THINK you could modify one of those 2 speed bottom brackets to accept 2 chainrings, instead of just one...

Bonus points if you make the bike... useable. So DT shifters + only one set of each type of handlebar shifter. Technically you could use thumb shifters + friction shifters + grip shifters all at once...

I think I know some ways to make the bike have astronomical numbers of gears, but I'll hold my submission until later.

Just a little thought experiment for those of you willing to play.

Ronno6

Sram has the Dual Drive, which is a 3 speed internal gear hub that has a freehub capable of accepting a 10 speed cassette.
Couple all that with a triple chainwheel setup and you arrive at 90 possible combinations, though I am sure there would be several functional duplicates.
There may be other setups capable of more.....

CliffordK

The SRAM Dual drive is currently rated at 3x10.

I have read about some successful quads for the front.

So:
4 Front
3 Hub
10 Rear Cassette

And one gets 4 x 3 x 10 = 120 gear combinations.

One could probably do a bit more with an idler system.

prathmann

You could easily combine the above with the Schlumpf 2-speed bottom bracket to get 240 distinct gear combinations. Or the Pinion gear which gives 6 ratios in the bottom bracket for 720 total gear ratios. But simpler is the Nuvinci N360 planetary gear hub that is continuously variable - so an essentially unlimited number of gears.

AIRC, Bicycling! magazine put together a bike with a ridiculous number of gears sometime in the early/mid '70s. They modified a 5-speed Sturmey Archer hub to accept a 5-cog freewheel (common at the time) and combined that with either 4 or 5 chainrings in front for either 100 or 125 gear combinations.

DiabloScott

Could you put this on a flip-flop hub so you can ride single speed when you get tired of all those choices?

CliffordK

AlexCyclistRoch

What about a CVT for a bike-that would have an infinite number of gear choices.....

Darth Lefty 

With conventional front-rear derailleur groupsets, Campagnolo Athena took it up to 3x11, which is matched by the top three levels of Shimano MTB setups. Bet you could install that on the Dual Drive hub. That would get you to 99

LesterOfPuppets

Mountain tamer has a quint, so that would take us up to 150.

Mountain Tamer Quad Plus

Awwww, looks like it says they're all gone

HillRider

That's what the NuVinci hub is.

Dan Burkhart 

I know it's nowhere near the theoretical limit, but the most ratio combinations I have ever had on a bike of my own was 105.
The bike is a Quetzal recumbent, original drive train had a triple chain ring, driving a 5 speed mid drive cluster which in turn drove a 7 speed cassette on the wheel.
I have since converted the bike to a Rohloff hub and single chain ring. It has a 5 speed mid drive, but no derailleur, so shifting is by means of the greasy fingers method, however any gear other than the primary drive gear would exceed the maximum input ratio, so even though it still has 70 theoretical speeds, I only ever use, or need 14.

Ronsonic 

Sheldon!

fietsbob

Late 50s a friend's dad (with a shop,that Made artificial Limbs)put a 2nd 3 speed hub Up high on the apex of
seat stay seat tube s

Used a 2nd 3 speed ....1 cog attached to the hub shell with a 2nd chain .

so you could fit 2 NuVinci hubs and double the 2 360 Infinite ratio Hubs... for Double Infinity.

next step ... infinite improbability drive..

dabac

While somewhat entertaining, I'm wondering if there firm opinion on how many gears one can actually benefit from for a given speed range.
Would 5% increments make sense?
2%?
Or would 10% suffice?

Wilfred Laurier

Rohloff 14 sp (respaced w/cassette carrier in place of cog) + Schlumpf 2 sp (w/chainring replaced with spider for triple rings) + 12 sp cassette + 3 chainrings = 1008 gears.

Some assembly required.

fietsbob

Rohloff mid drives have been done, hubshell drives a cog mounted on the left end..

Pinion mid drives have even more gears , it can drive a R'off


then, a need will be for a 3rd wheel.. super lows and, just 2, you will fall over.

bud16415

My 3x9 has half step plus granny and I have 15 distinct different gears ranging from 18-100 GI at roughly 5 GI steps. It is all I would ever need. I might add overlap and repeated gears isn’t a bad idea between granny and center rings I overlap 2 there.

Infinity is the answer to your question unless you add in efficiency. Then the answer for me is 15.

Bike Gremlin

On the faster part of the gear ratio range, smaller steps are better.
On the slower side - larger steps are usually more practical.

In the middle - depends on one's taste. Some love it tight, some don't mind larger gaps.

NYMXer

Why is it that when I clean and examine my bike, I am happy with the gearing but then..... I go out on a ride and wish I had another gear to select from?
Gears are likes bikes, it's N+1 all the time!

Darth Lefty 

There's an often-repeated rule of thumb that +-10% is about what feels good. But you can challenge that... and even if you accept it, is it 10% higher/lower gears or is it 10% higher/lower power, which is not the same thing?

MTB cassettes, where it's more important to have wide range than optimize power output, have about 1.15 ratio shifts (or +15% if you like).

Math fun: since an N-speed cassette has N-1 shifts, the average size of the shift ratio is the N-1th root of the ratio of the gear range. For example, for a typical 9x11-34 MTB cassette, the 8th root of 34/11 is 1.1515

dabac

So is there some piece of maths where I input my speed range and get an answer to what my ideal number of gears would be?
Can't miss a chance to live up to the saying: "logic is a way of going wrong with confidence" 😉

I was toying with the idea of mating a quad crank to a 3-speed IGH, to get 12 unique gears 5-6 % apart.

TGT1

There was one kid in the neighborhood that cobbled together a 3 speed hub with a 10 speed (5 cog rear) that I knew of back last mid century (1960's)

Another had a lawnmower engine powered rig.

I was more interested in chemistry and blowin' things up.

LesterOfPuppets

Well, you'd need more factors than just speed range and percentage increase/decrease.

Speed range
Cadence range
Wheel size
Smallest acceptable chainring tooth count
Largest acceptable chainring tooth count
Preferred cog tooth count (or smallest/largest acceptable cog tooth count)

Retro Grouch 

There is no theoretical limit.

There is definitely a practical limit. You can only go so slow before you fall over and, on the fast side, you can only pedal until your power output matches your air resistance. The question is "What's the optimum number of gears to fill in that gap?" My answer keeps creeping upward.