as the title says it is a purely theoretical question.
Imagine that you have a gearing system on your unicycle with a fantastic number of gears (like on a bicycle) - let’s say 9 or 13 gear ratios …
what could be the minimum and maximum gear ratio a “normal” unicyclist can withstand?
what could be the spacing between those gear ratios (uniform or not?)
I feel intuitively that the comparison with bicycle gear ratios do not stand…
Physically, I don’t think there’s a significant difference between how bikes and unicycles use gearing. With bike-length cranks, we should be able to push the same kinds of gears that fixie riders do. There’s no particular reason why you shouldn’t be able to run a 80"-90" gear in a flat time trial, for example. Similarly, you should be able to gear down a significant amount. We can ride a 12" unicycle, why couldn’t we ride a 12" gear?
The thing that’s different is that it’s scary to go that fast on a unicycle, and our geared unicycles have slop and sketchy shifting systems.
High gears on unicycles become increasingly hard to control, so it’s not quite the same as on a bike where you’re just providing power to drive the thing along. But probably with practice a good rider could make use of a pretty high gear. Personally I find it very hard to ride a Schlumpf 29er on 150s, which is only about half of a bike on a 90" gear even allowing for the shorter cranks. But people who ride gunis regularly are happy with Schlumpf 36ers on 125s, so perhaps it’s not such a problem with practice.
What’s the highest gear anybody’s been known to ride on a unicycle I wonder? That thing Jogi built with external epicyclic gearing (steampunk work of art!) was about 2.5:1 on a 28/29" wheel wasn’t it? So something like 72" - and somebody raced that at Unicon XIV so it was certainly doable.
Rob
starting with a Rholf as a base line (we are dreaming right?) 14 gears, 13.6% gear steps with 11 as fixed gear.
36" wheel with those gearing ratios would have a bottom end of 10 gear inches and top of 53. not even as high as a Schlumph and lots of people would like a higher gear.
Flip the input and output and make 4th gear the fixed gear and things get much better
36" wheel would then have a low of 24.5 and high of 129 gear inches. not sure if anyone would be able to handle 129 gear inches.
a 24" wheel would have a low of 16 and high of 86. Sounds good to me.
Also because of the wheels’ inertia, stability increases on a b*ke, but for us instability increases at high speeds do to the slop in the hub and the wobbling from the cranks.
Eventually I bet all the slop will be taken out of the hub, so that wouldn’t be contributing to instability, but I can’t see how one would counteract the wobbling from the cranks/pedals aside from holding onto something like the handle or bars.
Bikes have cranks and pedals, too.
Low gears would work great (to a point of ridiculousness, I think). High gears would be much more limited. Everyone remember their first few times riding a geared unicycle? A geared 36" in high gear? Hard to handle, and hard to master. Raise the ratio and it gets progressively harder to master, to the point where it might be no fun at all.
I once rode a short giraffe with a 3:1 ratio, on what I think was a 20" wheel. I could ride it, but the idea of using it to go real fast just seemed stupid at the time. Especially as it was a giraffe, with a small wheel below the crank axle. On a heavy 36" wheel it would be more stable, and probably easier, but I’m having a hard time trying to picture 3:1 on a 36", knowing what 1.55:1 feels like. I think it would reach a point where the stress level on the rider, both physically and mentally, would really suck. But we have yet to find out how high that would be…
I think a Schlumpf is significantly harder to master than a unicycle with more conventional gearing would be, because the frame acting as a lever arm changes the behavior of the unicycle.
If we solve the engineering problem of creating a gearing system with easy shifting and without changing the characteristics of the drive system itself, I think higher gears will be manageable.
[B]I have never rode a Schlumpf, but I am curious as to what behavior your are talking about. Isn’t the frame always a lever? The frame holds the weight (me) above the pivot point (axle).
So is a Schlumpf in the 1:1 gear ratio much harder to ride than a conventional unicycle? I understand there will be a little bit of slop in the drive train, and a bit more weight. Anything else?[/B]
Yes, it is a lever. But you don’t notice when riding. And it’s nothing that affects the stability of the frame. In early days of geared unicycles there was much discussion about that torque effect. People suspecting it would bend the frame, or make the unicycle unridable as the frame would be forced forth or back resulting in immediate dismounts. But nothing of that happened.
You feel the additional weight, especially when riding uphill or downhill.
Then there is some axle tolerance. That is something you notice, but it does not interfere with riding. It kind of feels like a loose crank. But you get used to it quite soon. The only thing you need to be careful about is when the crank actually comes loose. That is harder to notice compared to a non-geared hub.
A Schlumpf in 1:1 gear is more or less like a normal unicycle; somewhat heavier and with a bit of slop, but not anything you’d have a problem with.
A Schlumpf in high gear is significantly different than a normal unicycle. A 24" Schlumpf is much harder to ride than a 36" ungeared Coker, despite the gear ratio being similar. That’s partly because when you’re in high gear, the frame is constantly pushed forward by the lever action of the hub; learning to counteract that action is a skill that takes many hours of riding to perfect, and for me it still causes difficulty in situations like riding down steep hills under braking.
Really? I personally can’t notice that effect on a geared 29" or smaller. On a geared 36" I think I can feel it when I pay attention. But it is nothing I need to care about when riding.
I don’t notice it when I’m riding normally, but I definitely notice it when I’m starting up from a start, when I’m riding technical off-road, or when I jump, among other things.
Then you need the DACKOROMAN DRIVES SYSTEM
sorry, couldn’t resist
Yes, but they don’t contribute to instability because of the second wheel, lower pedal rpm, ability to coast, lower center of gravity, and other aspects of the frame’s geometry.
Never did things like technical off-road riding or jumping in high gear. Maybe I should try …
Live Wire High Gears
Live Wire Unicycles one made a unicycle witha 4:1 ratio! It was raced on a track.
I think that learning to master higher gear ratios is easier that learning how to ride.
The first time I tried a KH with a Shlump gear it only took me about 7 tries to actually start riding it some distance. Within ten minutes I was riding it cross country. The higher gears are different but once you get used to them they become second nature.
Unicorn
The action of pedaling a bike definitely contributes to instability, though less dramatically than it does for unicycles. See Socrates and Berkeley Scholars Web Hosting Services Have Been Retired | Web Platform Services
Bikes have steps ranging from 33% on a three speed to ~15-20% on multigeared mountain bikes. A Rohloff Speed Hub has fourteen 13.6% steps (speeds):
http://www.rohloff.de/en/products/speedhub/
Because a uni does not have the stability of a bike (two wheels, bars), controlling the additional “torque” that is required to push the pedals in high gear on a uni leads to descreased stability. That instability is amplified by having a smaller wheel. The only way to increase stability in high gear is to spin faster, which reduces torque. This reminds me of a HP vs Torque, discussion in automobiles, each use having an advantage/disadvantage for different applications.
For muni, since we are often riding slow, climbing, and working over obstacles, the application and control of torque is going to be a key issue, whereas on a road/touring uni, HP is more applicable, at least on the flats.
Shifting a Schlumpf is not hard, but it is akward, and if you miss your shift it can be a pita. If we had multiple gears, more than three, I’d think that this would necessitate a remote shifter.
Someone, I can’t remember who, asked me a very important question when I was considering a Schlumpf:
“Do you really want to go faster on the trails you ride?”
My answer then was “yes”.
Now that I own a guni, My answer now is “no”.
I can go plenty fast on trails with a 29er 
Anyone want to buy my 26Guni?
Do you know of some mechanical reference other than the frame with which to do this? I’m not trying to argue with you, I’m just not seeing another way to do it. If there is a way then the geared ultimate wheel would be realizable.