uni everesting?

General
41

No they wouldn’t - on a steep hill the bicycle’s speed is limited by the work required to lift the mass up the hill vs the cyclist’s sustainable power output. They will be going at speeds quite ordinary for a unicycle on a flat, and their gear inches will be in the unicycle range. That is not by itself enough to demonstrate that a unicycle is more advantageous, but it immediately puts things into much more direct comparison than they would be on flat terrain. And bicycle race results on 20% grade in the ~8 mph range bear that out (this is after all where they’re barely beating the foot runners).

There could be errors in my figures, but the first thing I did when I determined them was check against the actual uphill bike race on Mt. Washington, and they are fairly closely for that - just under a mile of climb in just under an hour. A quick look at videos shows mostly a steady spin, with relatively little out of saddle time.

In terms of what could be done on a unicycle, there seems to be a lack of data, as people don’t seem to be trying these rides on unicycles with the gearing and crank lengths that would theoretically make a spinning ascent similarly possible, or on terrain that would minimize balance disruptions.

The power I spoke of was the maximum sustainable power over time, and the goal would be to use that, since it is what the cyclist is supposedly rated at producing for an hour or more duration.

But that’s a power for efficient spinning, so the goal was to avoid things like standing on the pedals - and yes, that means the force has to be reasonable, hence a low gear or small wheel is required. The assumption from the bike world inherited here is that maximum sustainable output is achieved by spinning lots of repetitions at limited force, rather than a few at high force.

One thing I want to calculate next is the effective “winch radius” of a pedal powered elevator that would lift the rider upwards at the same rate as the vertical component of those in the table. If this where the same as the crank length, you’d need your full weight on the pedal (and for the full cycle, not just the horizontal peak) so standing and pulling on a bar would be required. If it’s below half the crank length, things are more reasonable. Bike cranks of course tend to be a little longer.

And yes, the simplification of looking only at the vertical component of the effort looses validity on the more shallow grades - on the steepest it presents a sort of best-case limit, as things can only get worse when the other losses are included.

42

This is a very interesting discussion, and I’m hoping it doesn’t devolve.

Subtle comments which impugn the intelligence/integrity/motives of the other participants aren’t helpful to this inquiry; they prevent both sides from thinking clearly and therefore become impediments to getting at the truth.

43

Here are the “winch” numbers you’d need to exert 5 W per lifted kilogram lifting yourself on a pedal powered elevator (they also apply for exerting the same power output when riding on a flat, it’s just the “task” is no longer as directly related to the theoretical energy density of the rider).

Cadence vs Winch radius in inches vs % lifted weight pushed on 170’s


30        6.39     96%
40        4.80     72%
50        3.84     57%
60        3.20     48%
70        2.74     41%
80        2.39     36%
90        2.13     32%
100      1.91     29%

The implication here is that turning 170’s at 30 rpm, you’d need to push a pedal with an average of 96% of the lifted weight (body + cycle) throughout the entire cycle, to achieve theoretical sustainable power. That’s standing on the pedal, yanking on the bar, and then some - clearly inefficient even if achievable at all.

But at 70 RPM you’d only need to exert an average of 41% of lifted weight, and at 80 RPM only 36%. Somewhere in there (actually regardless if on a hill or a flat) the force exerted becomes reasonable for seated spinning, at least on a bike.

The really meaningful question is then, if (on a perfectly smooth paved hill, without wind, etc) a unicycle with the same mechanical advantage could also be spun.

A number of people have argued “no” - but the actual attempts seem to generally be made on unicycles which do not have comparable mechanical advantage in the selected crank vs wheel size, so they don’t really answer that question.

44

An interesting question might be why nobody is using the mechanical advantage which is “theoretically optimal” in events where they’re trying to go as fast as possible.

Though let’s do the numbers anyway - 5W/kg equates to a climb rate of 0.5m/s, so on the 20% grade you think is optimal that’s 2.5m/s speed (5.6mph) and on a 29er with ~2.3m rolling diameter that’s a cadence of 65rpm, so only just below what you seem to think is optimal. We’re already not far off what people do use to climb hills.

So let’s do it from the other direction - when I last did a hill climb I did it on a 29er with 150 cranks, so if we assume 80rpm is optimal (which doesn’t seem unreasonable - it’s a comfortable climbing cadence on a bike, and going from the 170s to the 150s you’re only raising the ratio of lifted weight to 41%) then your speed is 3.07m/s (6.9mph) and the required gradient for 5W/kg is ~16%. So there we have a typical uni used for hill climbing on a typical gradient which meets your optimal mechanical advantage - yet it’s still significantly slower than the bikes. Have we put the “they’re not using the right gear ratio” to bed?

FWIW the hill climb I did was about a 10% gradient and that was something I could pedal up at a reasonable cadence without being reduced to half revs or zig zagging. I tried the 127 hole, but it was too much of a struggle - I’d be very surprised if I could have happily climbed a 16% gradient smoothly on that setup. I admit I’m not the most skilled uni rider, though I’m not that bad at climbing and I think the only bike I beat was a woman with her child in a kiddy seat - the people who I kept pace with on bike rides were way faster than me.

Because we come back to the same point, you can do all the calcs you like on this, but you’re still wasting energy balancing and wobbling on a unicycle.

45

I really appreciate your taking time to run through a scenario. However this still strikes me as a bigger wheel and shorter cranks than the unicycle likely to make it’s best possible showing in comparison to a bike with matched gearing, nor are you making a comparison between equivalent setups to begin with.

If we want to argue strictly about the benefits of a unicycle configuration vs. a bike configuration, then I think that the unicycle’s best advantage will be on a hill where the bike has to use gear reduction (gear inches smaller than wheel size), probably down around 24. The unicycle should have a wheel matching those gear inches, and be using cranks as long as the bike’s.

Otherwise, if the bicyclist is spinning comfortably in an endurance mode, and the unicyclist straining, it’s not really a comparison of one wheel vs. two, but rather most prominently a comparison between the power output achievable with two different gear ratios.

In terms of the validity of comparison, there’s no way you get a bike vs. unicycle speed difference out of my tables, because they make no consideration of which is being ridden - the only way you get out a speed difference predicted by those tables is to place the two riders in different places on them with different gear ratios.

Only once you have the two riders on the same gearing and crank setup could argued losses to unicycle-unique challenges be measured, and presumably we’re trying to pick a regime where those are likely to be as minimal as possible.

46

That’s the first thing you’ve said right!

47

Glad we finally reached agreement on the importance of testing only one variable at a time.

When the energy analysis predicts there shouldn’t be a speed difference, then you’re finally in a position to look at what real word factors might produce one.

But as long as the unicyclist and bicyclist are riding with different ratios in different regimes of output even before you start to look at those factors, you really aren’t comparing unicycles vs bicycles, but rather comparing two different gear strategies for hill climbing.

No question that bikes win on low grades. No question that runners win when it gets steep enough. But the interesting question is if there’s somewhere in between where a unicycle might, or if not at what grade it would come closest to matching.

48

I don’t think there’s any paved road in the world that top runners would beat top cyclists at. Runners don’t win until the terrain gets unrideable for bikes.

And the question of whether unicycles can beat bikes (given equivalent riders) is only interesting if you start by ignoring the fact that they can’t.

The question of why unicycles can’t beat bikes is moderately interesting. When you’re done fooling around with meaningless tables, let me know and I’ll chime back in.

49

This idea defies logic.

  • First, there’s no specific threshold of “unrideable” - only “more and more absurdly difficult” - when you are no longer riding straight up the hill but zig-zagging, is that unrideable? When the rider is doing increasing extreme things to keep from falling sideways, is that unrideable?

  • Given that the bicyclists are barely beating the runners up Mt. Washington, where the bikes are still riding fairly normally, it’s pretty obvious that a bit steeper and things will turn out the other way. People run up stairs (design guideline 7/11 or 63% grade) all the time.

Steep hill bike vs. run races do seem like they’d make entertaining videos, kind of surprised I’m not finding any.

50

Well you can’t compare equivalent setups, because a bike has gears and a unicycle doesn’t. As for a smaller wheel and longer cranks, I’m wondering whether you appreciate that those have disadvantages on a unicycle which will likely make the efficiency worse (we did mention wobble) - a 29er with 150s is quite a decent sweet spot.

Except that on climbs we’re discussing, when the unicycles are on the limit of the gear they can turn the bikes will typically be using a higher gear (that was certainly the case on the climb I did - the bike riders were spinning a higher gear with a faster cadence). This is a purely theoretical suggestion which doesn’t happen in the real world. You could if you like force the bike riders to use the same gear you can manage on a uni, but they would still beat you because they’d easily spin faster. A hill where the bike rider is having to gear down is one where the unicyclist will be zigzagging and using half revs, whatever wheel size they’re on.

Except it only does if you ignore the energy losses on a unicycle. Rather than attempting to analyse differences in gearing, or equalise the gearing it would make a lot more sense to step back and look at the bigger picture first. Let’s start from the basic premise that a bike is faster at climbing than a unicycle (trust me on this, every single piece of experimental evidence supports that hypothesis). So now rather than pick on a single difference let’s look at all the differences and see which ones are important.

51

Only if you misunderstand the idea - he did mention “terrain” rather than “gradient” - I can think of all sorts of terrain which isn’t rideable on a bike, no matter how much you zig zag (in a conventional sense - when you’re starting to do trials style hopping then you’re no longer really riding). In fact I’ve done quite a lot of “taking a bike for a walk” on races I’ve done! You even give an example of such terrain at the end of your reply!

It’s not obvious at all - in fact it’s a bit of a fallacy. Just because something is getting closer together doesn’t mean it will ever meet let alone cross. I’ll just throw out a mathematical analogy here - start with 1, add a half, then add a quarter, then add an eighth, then a sixteenth, etc. Already after adding the sixteenth you have barely less than 2 - is it therefore obvious that if you continue that sequence of adding you will eventually have more than 2?

52

What I actually did was propose equalizing everything else to the guidance of a model that ignored them, specifically so that you could compare what those losses actually are in the real world.

If you don’t equalize everything else, you can’t make a meaningful comparison in a race - you have to either be putting equal work into both systems for different results, or accomplishing equal useful work with both at different work applied.

Otherwise you have an experiment with too many independent variables, and learn little.

53

So you get the bike riders to use the same gear ratio and crank length as the unicyclists, and as I’ve explained above they’ll still be faster because they’ll spin that gear faster (given they can already spin a bigger gear faster). It really doesn’t need doing, you can do it by thought experiment. The independent variable you think is important isn’t.

54

That’s dangerously close to saying that the bicyclists are faster “because they’re faster”.

To validate the claim you’re trying to make, you’d have to do something like relocate both to stationary bikes with power meters, task them with the equivalent of pushing the same hill, and verify that under those conditions they score equally.

To validate the conclusion that bikes will always win, you’d also have to demonstrate that the regime tested is the one where unicycles come closest to matching bikes.

55

Okay, running out of M&M’s.

Remind me to never move into a building where I have to use one of those to get to my apartment.

“Equivalent” isn’t really possible if you are comparing a vehicle with two wheels vs. a vehicle with one. But if you want to ignore that difference, which is the key difference, at least have the bicyclists on fixed-gear bikes. Use a bicyclist that’s also a unicyclist, of equal skill to your other unicyclist. Have them each repeat the experiment several times on both vehicles. That should at least get you somewhere. If you used a bike and unicycle with equal effective gearing, and the bicycle always won no matter who was riding, that should get you a little further.

Argued losses to unicycle-unique challenges are the key difference. Arguing that they aren’t may be the breakdown here. Or you could look at it from the point of view of the bicycle having the key advantage of a second wheel, even though it makes the vehicle weigh more.

If, as Tom suggests, they are always won by the cyclists, that would make them less entertaining. It does make me wonder, a little, but for the most part, these sorts of races are based on a given piece of terrain. That terrain is generally never going to be of a fixed grade, which would give your bikes a distinct advantage over unicycles. All this theorizing doesn’t help outside of laboratory-like conditions.

Again, a smaller wheel is only a plus if the course stays close to a very consistent grade. Any deviation from that puts the advantage back on the bicycle (in addition to its second wheel).

That’s why you don’t hear much about people doing big climbs, or long rides in general, on smaller wheels because they’re just not fast. If I ever go to ride up Mt. Diablo again, (based on what’s available today) I will choose 36" again. Maybe 32", but I have next to no experience with that. Here’s why:

The first time I rode up Mt. Diablo it was with a group. On the long grinds of the upper part of the mountain, I was riding my 29" Muni (it was a Muni ride down after), with Mike Scalisi on a Coker. It was the kind of slope where it was basically one step at a time, though not super slow. Riding was limited to how fast you could make each step based on your ability to process oxygen (something like that). The bigger wheel was faster. We switched places and the bigger wheel was still faster. We switched a couple of more times with the same result.

That was interesting. Results would likely have been different on a less-steep slope, but not on a steeper one, until you got to the point where the 36" was too hard to keep pushing. I don’t know how to explain the “rhythm” we used to maintain a pace, but it seemed to be a relatively fixed pace, regardless of which wheel we were on.

I will add that Mike and I seemed to be of relatively equal fitness level, which I suppose “helps” the experiment. A few years after that, I again ended up riding near him in a big group training ride for Ride The Lobster. We passed each other a few times, but were pretty equal in terms of speed. He ended up on the faster team, however, with Tom Holub in “Totally Doable”. :slight_smile:

We don’t seem to know the why, but we seem to accept “the bicycles are faster”. In climate change, we observe that the world has been setting annual heat records. You don’t hear the oil companies denying this (much), but that doesn’t answer the why.

But if it’s true that the bikes are always faster, going back to that comparison of equally geared uni and fixie bike, on various slopes, and it might make a good starting point for experiments. Especially if you are able to swap the riders.

Ignoring the fact that most stationary bikes only have one “wheel”, any such test would be meaningless because it would be bike vs. bike. That would be like ignoring chapter 21 of the Physics book; the one about all the differences between a unicycle and a bike.

No, I haven’t read that one either… :stuck_out_tongue:

56

I do not believe there exists a paved surface on the planet which is faster to run up than ride a bicycle up. I also do not believe there is a paved surface which is faster to unicycle up than to ride a bicycle up. Those beliefs are backed by every existing piece of a large body of empirical evidence.

There are clearly unpaved surfaces which are faster to run up than ride a bicycle up. The unicycle probably loses to the bike regardless of surface.

You think a bike record of 49:24 is “barely beating” a running record of 56:41? Over seven minutes in a 50 minute race? I’m pretty sure if I finished seven minutes ahead of someone on Mount Washington and was already on my second beer when he got to the top that I wouldn’t feel like I barely beat him.

And no, it’s not at all obvious that a steeper road would close a 15% gap between bike and running speeds.

57

When the difference was comparable to the spread between first and sixth places for bikes last year? Yes, I consider it “barely” beating the runners.

That’s not to deny that there’s a statistically significant advantage at that grade, but it’s rather slight - clearly there were a lot of fit runners who made it up faster than a lot of fit bikers.

58

The point of that test would be as a control to verify that the riders who you then compare on unicycles vs bikes with the same gearing, are comparable in personal power output capability - to show that you’re comparing the efficiencies of the machines, not the power output of the riders.

That’s interesting, because if you were on a grade where you could not maintain a cadence above 80 RPM on the larger wheel, this would seem to defy the usual beliefs about best cycling power output. Perhaps there’s something worthy of investigation there.

59

And I’ve beaten a lot of fit bicyclists on Mount Diablo, but my bike time is still ~20% faster than my unicycle time.

As I said at the beginning, this has been tested. We did a whole series of tests with different wheel sizes and crank configurations on the same climb in training for Ride the Lobster. What we found was that the rider was by far the most important factor (I believe the place ordering was the same on every attempt), and that riders were always the fastest on the configuration they were most comfortable with. And that they were ~20% faster on bike.

60

That’s an interesting spin of the topic :slight_smile:
I’m definitely in line with Aracer’s and John’s statements.

What I would like to emphesize in first part of the discussion regarding the rotational weight is that even when climbing, we on unicycle slow down and speed up the wheel several times each revolution to maintain the balance. And even if these are micro slow downs and speed ups for an experienced rider, we loose a lot of energy on that and that is where wheel weight makes the difference.

Secondly, I haven’t experimented much with smaller wheels climbing, so I can only think about selecting an uphill where I can spin quite consistently on my uni (27.5 with 137 cranks currently). And it won’t be a very steep hill. And definitely I expect myself going faster on my CX bike on that hill.

I’m not the exceptional climber, but I have some experience in that both for leisure rides and in races. I have beaten lots of bikers on various hills, but I must assume they were weaker than me and the hill just took away the advantage the bike would give them if we were riding on flat. I still haven’t found a hill where I’m faster on the unicycle and I don’t hope to get one.