uni everesting?

[tholub]

@Engineer on a Unicycle

In fact, they do. The research that went into that comment found a lot of indications of 17 lbs plus, with under 15 considered to create tradeoffs, yes, under 14 lbs is possible. It’s also possible to make a carbon unicycle for an ideal hill, removing the strength reserve normally there for all-around riding.

Rotating vs fixed weight only matters in starting and stopping and changing approach; I did specifically mention a steady hill. Actually, for steady progress a high rotating weight is ideal, as the flywheel helps to even out the pedal cycle.

Rotating vs. fixed weight matters for all acceleration and deceleration. It is empirically 100% clear that bikes are faster than unicycles on grades gentle enough to have a flywheel effect in unicycles (which is extremely negligible in any case). On steep grades, unicycles are constantly being accelerated and decelerated with every pedal stroke.

Terry built up a unicycle with a 700 road bike wheel, likely for the larger end of such tires , but it’s an open question if his one weighed more than a bike’s two.

I’ve ridden unicycles like that. They suck, and they greatly increase the amount of force going side to side (squirriliness).

Unclear that this is actually going to matter much; a bike cranking hard wobbles too, though it may not follow as sinuous a path. A wheel (or bike gear) sized to the hill would be one allowing a normal cadence for rider efficiency, rather than an extreme cranking one, so wobbling is likely to be fairly minor. But note that a sinuous path is just a micro zigzag, actual street-wide zig-zag is used as a strategy by some with either wheel count, presumably because they either don’t have a low enough gear, or because ascending straight up with available energy output would imply rolling rate too low to achieve lateral stability via the usual micro-steering; for the purposes of the original question, that would be a poorly chosen hill.

Look, it’s pretty simple. Bikes are faster than unicycles climbing hills. All hills, all bikes, all unicycles. I’ve actually run tests. There is absolutely zero empirical evidence supporting any possibility that unicycles can be faster for a given rider. So you could put your engineer brain to work on describing the observable conditions, or you can keep inventing fatuous ideas and couching them in scientific terms as if that makes them valid.

[Engineer_on_a_Unicyc]

@tholub

Rotating vs. fixed weight matters for all acceleration and deceleration.

None of which occurs on a steady hill.

On steep grades, unicycles are constantly being accelerated and decelerated with every pedal stroke.

Only if mis-chosen in size, ie, gear ratio. And the part that is being accelerated and decelerated doing work to climb is the rotating weight, so the energy input to accelerate it it is returned when the wheel slows by lifting the rider up the hill - in other machines this is called a flywheel.

[tholub]

@Engineer on a Unicycle

None of which occurs on a steady hill.

Of course it does. Here’s an empirical observation: Every unicycle ever observed riding up any hill ever accelerates and decelerates. All you have to do is watch them to reach this conclusion, but I’m sure strain gauges would measure it as well. You can start your research by googling “unicycle hill climb video”. Here’s one of Jamey and Tim Lovasen, two strong climbers, climbing Fargo Street.

uniFargo

Here’s another one from CA MUni Weekend 2014. I’m the one going straight up and coming in second to Jamey.

Fargo Street Challenge - October 18, 2014

Note that every rider on every configuration is dramatically decelerating and accelerating with every pedal revolution, whether going straight up or not.

For that matter, bikes also accelerate and decelerate on each pedal stroke, though less so than unicycles. This difference is probably one of the sources of additional speed on bikes vs. unicycles. You might want to calculate that.

Only if mis-chosen in size, ie, gear ratio. And the part that is being accelerated and decelerated doing work to climb is the rotating weight, so that energy is conserved - in other machines this is called a flywheel.

The null hypothesis should be that bikes are faster than unicycles, because that is what we know from observation. If you’d like to suggest that there’s a perfect unicycle for a perfect hill, and a perfect rider who can spin all the way up it without ever decelerating, that’s fine, but realize that you’re fighting an uphill battle against observable phenomena.

[Engineer_on_a_Unicyc]

Here’s an empirical observation: Every unicycle ever observed riding up any hill ever accelerates and decelerates. All you have to do is watch them to reach this conclusion

This happens to a notable degree only because your gearing is too tall for the hill - you are not pedaling anywhere near the cadence rate of a human’s ideal sustained energy output on cycle cranks. As previously mentioned, it may be that the hill is simply too steep such that trying to spin up it in low gear in a smooth ideal energy output manner would mean traveling below a comfortable stability speed.

But even though you are accelerating and decelerating, the work done is being conserved - as you exit the power phase, the wheel continues lifting you up the hill and slows, as you enter the next power phase it speeds up. But that’s not a mechanism that wastes energy. In this regime losses at higher speed are not notably higher than at lower, so the speed oscillation is for all pratical purposes energy conserving.

[tholub]

@Engineer on a Unicycle

This happens to a notable degree only because your gearing is too tall for the hill - you are not pedaling anywhere near the cadence rate of a human’s ideal sustained energy output on cycle cranks. As previously mentioned, it may be that the hill is simply too steep such that trying to spin up it in a smooth ideal energy output manner would mean traveling below a comfortable stability speed.

You are making an assertion here. Do you have a basis for that assertion? We can observe that on various different wheel size and crank configurations, climbing Fargo Street, or any other steep unicycle climb observable in person or on YouTube, that acceleration and deceleration occurs. You are asserting that this observed phenomenon goes away for some configuration of wheel and hill.

When? How? Why? Do you have a basis for your belief other than your own belief? Can you provide an example?

By the way: On hills less steep than Fargo, the difference between bikes and unicycles is greater than on Fargo.

But even though you are accelerating and decelerating, the work done is being conserved - as you exit the power phase, the wheel continues lifting you up the hill and slows, as you enter the next power phase it speeds up. But that’s not a mechanism that wastes energy. In this regime losses at higher speed are not notably higher than at lower, so the speed oscillation is for all pratical purposes energy conserving.

Now you’re just making shit up. There is no energy conserved in a slowed or stopped wheel. To any extent that the wheel slows, additional force will be required to reaccelerate it.

It is so fundamentally evident that pedaling a unicycle up a hill requires additional force with every pedal stroke that I have to wonder if you have ever ridden a unicycle up a hill.

[Engineer_on_a_Unicyc]

@tholub

We can observe that on various different wheel size and crank configurations, climbing Fargo Street, or any other steep unicycle climb observable in person or on YouTube, that acceleration and deceleration occurs.

Again, because you aren’t using a small enough wheel to achieve sufficiently low gear to smoothly spin at an ideal rate. And again, it may be that such a solution for a hill this steep would be impractical for stability reasons.

Ultimately it doesn’t look like you’re really getting any benefit from having a wheel at all - once “stepping” the wheel like that, you might as well leave the cycle at home and walk.

There is no energy conserved in a slowed or stopped wheel. To any extent that the wheel slows, additional force will be required to reaccelerate it.

Seems like the central message of a physics lecture or two was missed. All sorts of oscillatory systems, some of them rotary, would in fact be perpetual motion machines if there were not losses in the bearings and air. But at the speeds in question here, the nonlinearly incremental loss during the time one is going faster than needed vs. at a steady rate is insignificant. So the unevenness does not mean energy is wasted, rather it is in fact conserved.

It is so fundamentally evident that pedaling a unicycle up a hill requires additional force with every pedal stroke

Only because the hill continues. But the “excess” work you did in overspeeding the wheel is returned to you as it coasts up the hill. Of course you won’t feel the coasting, because the hill is still there, but during the phase where the wheel slows it is returning energy to you by lifting you up the hill and you are doing less work than you would be if it were not. You still get out essentially everything you put in, apart from the extreme actions to correct balance mistakes which should not have been made.

[UniDreamerFR]

Where the hell is my 1 gallon pop corn box?

[tholub]

@Engineer on a Unicycle

Again, because you aren’t using a small enough wheel to achieve sufficiently low gear to smoothly spin at an ideal rate. And again, it may be that such a solution for a hill this steep would be impractical for stability reasons.

Ultimately it doesn’t look like you’re really getting any benefit from having a wheel at all - once “stepping” the wheel like that, you might as well leave the cycle at home and walk.

Seems like the central message of a physics lecture or two was missed. All sorts of oscillatory systems, some of them rotary, would in fact be perpetual motion machines if there were not losses in the bearings and air. But at the speeds in question here, the nonlinearly incremental loss during the time one is going faster than needed vs. at a steady rate is insignificant. So the unevenness does not mean energy is wasted, rather it is in fact conserved.

Only because the hill continues. But the “excess” work you did in overspeeding the wheel is returned to you as it coasts up the hill. Of course you won’t feel the coasting, because the hill is still there, but during the phase where the wheel slows it is returning energy to you by lifting you up the hill and you are doing less work than you would be if it were not. You still get out essentially everything you put in, apart from the extreme actions to correct balance mistakes which should not have been made.

Look. There’s no place for the unicycle to store energy other than the wheel itself; it doesn’t have a flywheel. So if the wheel is moving at a given speed, the amount of kinetic energy it contains is calculable. There’s not some magical “return of energy” that comes back to help you with the next pedal revolution.

Let’s say that climbing a hill you’re averaging about 3 m/s. During the fastest part of the pedal stroke you’re moving 4 m/s, and during the slowest part you’re moving 2 m/s. How do you intend to accelerate from 2 m/s to 4 m/s?

[Engineer_on_a_Unicyc]

@tholub

Look. There’s no place for the unicycle to store energy other than the wheel itself; it doesn’t have a flywheel.

The wheel - the very rotating mass you were complaining about - is a flywheel.

So if the wheel is moving at a given speed, the amount of kinetic energy it contains is calculable. There’s not some magical “return of energy” that comes back to help you with the next pedal revolution.

Indeed it is precisely that calculable energy from the slowing of the wheel that comes back, but not at the next revolution, rather at the next part of the revolution where your energy output drops below what would sustain your current rate of rotation and travel up the hill. This is physics 101.

Let’s say that climbing a hill you’re averaging about 3 m/s. During the fastest part of the pedal stroke you’re moving 4 m/s, and during the slowest part you’re moving 2 m/s. How do you intend to accelerate from 2 m/s to 4 m/s?

You put in more energy sometimes, and you get it back as the wheel rolls you up the hill at others. Basic physics.

If you are talking about pulsing of the travel speed of the mass of the rider - so what, you get up the hill either way. (Ultimately there’s probably an inverted pendulum interaction with the wheel too - human walking is full of all sorts of short term energy storage in the swing of various body parts, but that’s beyond the point here).

To argue that this is an efficiency loss you have to argue that what is slowing you is a wasteful mechanism like muscle braking, and not the useful application of work in lifting you up the hill. The fact that you wouldn’t pule the wheel anything like that on a flat demonstrates that it is the work of rolling up the hill, not muscles or dissipative losses, which is causing the slowing.

Incidentally, I ran some numbers. A good cyclist should be able to output 5 watts per kilogram of body mass for over an hour. That translates to about 1800 vertical meters per hour, or 1.1 vertical miles per hour.

As a reality check on the power numbers, the just-under-a-vertical-mile Mt. Washington road races on a bit less than 20% average grade have slightly sub-hour records at both of their unrelated events for bikes and running, with the bike record only beating the running record by a few minutes - 49 vs 56 minutes for men and 58 vs 68 minutes for women (not 100% sure the endpoints are the same).

Translating to Fargo at an apparent 33% grade, to keep going for an hour plus the rate of travel straight up the face of the hill would be a bit under 4 miles per hour; that’s faster than people appear to do it, but already slow enough stability may indeed start to need specific effort rather than fairly passive micro-steering. In contrast to Mt. Washington, is probably a grade where running beats any kind of cycling.

An actual “everesting” would probably need to be at a power output that can be produced for well more than 10 hours in a 24 hour period, so slower still.

[tholub]

@Engineer on a Unicycle

The wheel - the very rotating mass you were complaining about - is a flywheel.

Indeed it is precisely that calculable energy that comes back, but at at the next revolution, rather at the next part of the revolution where your energy output drops below what would sustain your current rate of travel up the hill. This is physics 101.

The energy doesn’t “come back”. It’s in the wheel because you put it in there. And if you want to get the wheel moving faster again, you have to put more energy into it. Accelerating from 2 m/s to 4 m/s requires exactly the same amount of energy every time.

You put in more energy sometimes, and you get it back as the wheel rolls you up the hill at others. Basic physics.

At the moment that you stop putting additional, new energy into the wheel, you will no longer be riding up the hill.

If you are talking about pulsing of the travel speed of the rider - so what, you get up the hill either way. To argue that this is an efficiency loss you have to argue that what is slowing you is a wasteful mechanism like muscle braking, and not the useful application of work in lifting you up the hill.

First: The discussion of the illusory flywheel effect came up when we were talking about rotating weight. Unicycle wheels have more rotating weight than road bike wheels, therefore this cycle of deceleration and acceleration requires more energy. The amplitude of the difference is also larger on a unicycle than on a bike.

Second: The force vectors on a unicycle with each pedal stroke have a greater component which is not in the direction of travel than the same force vectors on a bicycle.

These are what I would suggest are the two major components of the observed speed differential between unicycles and bikes on hill climbs. [The second one is probably much larger than the first one.]

As a reality check on the power numbers, the just-under-a-vertical-mile Mt. Washington road races on a bit less than 20% average grade have slightly sub-hour records at both of their unrelated events for bikes and running, with the bike record only beating the running record by a few minutes - 49 vs 56 minutes for men and 58 vs 68 minutes for women (not 100% sure the endpoints are the same).

Translating to Fargo at an apparent 33% grade, to keep going for an hour plus the rate of travel straight up the face of the hill would be a bit under 4 miles per hour; that’s slow enough stability may indeed start to be a challenge. An actual “eversting” would probably need to be at a power output that can be produced for well more than 10 hours in a 24 hour period, so slower still. And this is probably a grade where running beats any kind of cycling.

It seems particularly odd from a scientific perspective that you provide empirical evidence that cycling is faster than running, and then use that evidence as the basis for an assertion that running is faster than cycling.

[Engineer_on_a_Unicyc]

@tholub

The energy doesn’t “come back”.

That kind of answer would fail your physics exam.

It’s in the wheel because you put it in there. And if you want to get the wheel moving faster again, you have to put more energy into it. Accelerating from 2 m/s to 4 m/s requires exactly the same amount of energy every time.

And decelerating it returns exactly the same amount of energy, every time.

When you fail to grasp basic physics, you’re left with only personal experiences - those are valid, but they don’t generalize; they are feelings, not explanations.

What’s actually slowing the wheel each cycle is a fractional version of the same principle that allows you to “bowl” a car tire and have it continue some distance up a hill as it slows, converting rotational and kinetic energy of the velocity of the center of mass, to the potential energy of being higher on the hill.

It seems particularly odd from a scientific perspective that you provide empirical evidence that cycling is faster than running, and then use that evidence as the basis for an assertion that running is faster than cycling.

You missed that one was about a sub 20% hill and the other about a 33% hill - part of the whole point was trying to identify the crossover in advantage. There may also be an issue of duration, though I hadn’t commented on that.

[tholub]

@Engineer on a Unicycle

That kind of answer would fail your physics exam.

And decelerating it returns exactly the same amount of energy, every time.

When you fail to grasp basic physics, you’re left with only personal experiences - those are valid, but they don’t generalize.

That’s a pretty rich assertion.

Call me back when you can point to a single real-world example that matches your fantasy version of the way that physics is working here. Maybe once you get beyond Physics 101 you’ll learn that you have to first comprehend the system you’re analyzing before you can start making assertions about it.

[Pinoclean]

Very interesting discussion! Thanks guys. I think Engineer on a unicycle makes some very good points and from my own experience on using physics to build the best wheel possible the numbers don’t lie, it was a much better wheel. So as long as his numbers and theories hold up then I think they probably have something.

My own experience is that unicycles climb easier than bikes but I need to compare against a decent rider. I also had a theory that perhaps it’s the ability to hold onto the handle and pull yourself directly down into the cranks while on a bike you can stand and put weight in the pedals but can pull against something to drive into the pedal. You have the handlebars but where they are located is not as useful for pulling yourself into the pedals.

[aracer]

@Engineer on a Unicycle

In fact, they do. The research that went into that comment found a lot of indications of 17 lbs plus, with under 15 considered to create tradeoffs, yes, under 14 lbs is possible. It’s also possible to make a carbon unicycle for an ideal hill, removing the strength reserve normally there for all-around riding.

You didn’t check my garage for your research - I have a 15lb road bike hanging there, no tradeoffs at all involved, it’s all quite standard stuff and nothing particularly exotic. You won’t get a practical unicycle (suitable for riding at speed uphill) weighing 7lb, let alone 5lb. Though it’s a moot point anyway, because even if you were getting your claimed 10lb advantage, that’s only ~6% of a typical light rider/cycle combo - and this weight saving appears to be the only possible advantage for the unicycle which has been proposed. Yet there are far larger inefficiencies involved in riding a unicycle, some of which you touched on without really considering them properly.

@Engineer on a Unicycle

To argue that this is an efficiency loss you have to argue that what is slowing you is a wasteful mechanism like muscle braking
…
Translating to Fargo at an apparent 33% grade, to keep going for an hour plus the rate of travel straight up the face of the hill would be a bit under 4 miles per hour; that’s faster than people appear to do it, but already slow enough stability may indeed start to need specific effort rather than fairly passive micro-steering.

Because the point seemingly being missed by both of you is that there is a lot of energy expended in balancing on a unicycle - your muscles are doing a lot of work which doesn’t help your progress up the hill at all. You appear to be looking at the problem as if you only have to mechanically roll the wheel up the hill without doing any balancing (though even then the weaving is significant - there’s probably more than 6% inefficiency right there). It’s easy for experienced riders to underestimate the amount of work we do to balance - even when it is seemingly effortless or “passive” there are still a lot of micro adjustments going on, and those certainly aren’t passive as far as your muscles are concerned.

[aracer]

@Pinoclean

My own experience is that unicycles climb easier than bikes

You’re comparing you on a unicycle to you on a bike? I find that extremely hard to believe - as already pointed out, all the evidence suggests that simply doesn’t happen. It may be that you’re going slower up the hill than you realise on your unicycle compared to the bike (it’s worth pointing out that the typical “gear” on a unicycle is way lower than that on a typical bike - the bottom gear on the 15lb bike I own is ~40", yet I can get up some pretty steep hills on that which I’d be walking even with a much lower geared unicycle).

I also had a theory that perhaps it’s the ability to hold onto the handle and pull yourself directly down into the cranks while on a bike you can stand and put weight in the pedals but can pull against something to drive into the pedal. You have the handlebars but where they are located is not as useful for pulling yourself into the pedals.

It’s certainly not that - because when riding a bike (or indeed a unicycle) efficiently uphill you won’t be using your upper body strength at all - that’s wasted energy. The limiting factor given proper gearing isn’t your strength.

[Engineer_on_a_Unicyc]

@aracer

You didn’t check my garage for your research - I have a 15lb road bike hanging there, no tradeoffs at all involved, it’s all quite standard stuff and nothing particularly exotic. You won’t get a practical unicycle (suitable for riding at speed uphill) weighing 7lb,

I specifically mentioned the existence of 14 and 15 lbs bikes. But you haven’t considered taking that lightweight road bike and building a unicycle with the same technology. You’ll be leaving more than half of it in hacksaw trimmings on the ground - about the only thing that would end up weighing more is the saddle and tire, but there’s only one of those. For comparison an off-the-shelf Nimbus E-sport weighs 8.5 lbs, and to my knowledge incorporates no carbon composites at all.

The limiting factor given proper gearing isn’t your strength.

Indeed, it is not, and that’s a critically important point.

Let’s take 5 watts per kilogram of body mass, a reasonable hour+ endurance output number for a fit two-wheeled athlete spinning cycle cranks (since they talk about this kind of data all the time) and look at what this means in terms of hill grade where a cadence can be maintained, when considering only the power expended lifting the body mass up the hill - the weight of the cycle, friction losses, and the small power used in moving horizontally are not considered. Those simplifications probably make the table substantially less accurate at low grades and larger wheels.

“Gear Inches” is a traditional term for the effective size of a geared bicycle wheel; it’s also of course directly equivalent to the size of an actual unicycle wheel, though some unicycles have rolling diameters a little different from their commonly named size.

What should immediately jump out from this is that Fargo at 33% is too steep for a typically fit rider to maintain optimal endurance output near the low end of that cadence range at 80 rpm even on a 16 inch unicycle. And a 16 inch unicycle is probably impractically small to ride in real world conditions without wasting a lot of energy on balance tasks.

Essentially, this means that anyone riding Fargo strait up on a unicycle (or a bike without their rear chainring near twice the size of their front) is not using a proper gear for endurance efficiency - instead, they’re in a strength challenge mode.

However, in riding switchbacks across the hill as often seen, the energy expended in climb per unit time can be lowered, potentially putting the rider back in an endurance rather than strength mode, and increasing the travel speed such that balance can be maintained more by low-cost microsteering rather than by balance-specific exertions.

Looking at the table below, my suspicion is that a hill in the 20% range ridden on a 24 inch wheel is likely where a unicycle shines most - it looks like it can be ridden fast enough to be “rolled” rather than “stepped” and most of the exertion is still going to climb, so weight matters a lot. (Past posts indicate that while the grade is in this range, the poor surface quality of the Mt. Washington Auto Road presents quite a few challenges to unicyclists itself)

[tholub]

@Engineer on a Unicycle

Looking at the table below, my suspicion is that a hill in the 20% range ridden on a 24 inch wheel is likely where a unicycle shines most - it looks like it can be ridden fast enough to be “rolled” rather than “stepped” and most of the exertion is still going to climb, so weight matters a lot. (Past posts indicate that while the grade is in this range, the poor surface quality of the Mt. Washington Auto Road presents quite a few challenges to unicyclists itself)

Speaking as someone who has ridden enormous numbers of 20% grades, on 24" unicycles, 29" unicycles, and bikes: Bikes are faster, and it’s not close. There’s no human being who can ride up a 20% grade on a unicycle and “roll” it. Have you tried it? Do you have video of someone trying it? Do you have any evidence other than your own assertion that it should be ideal?

For most unicyclists, a 20% grade is in the “I can’t ride that” category. For strong climbers, it’s an extremely strenuous and slow climb.

Maybe the problem is that you took Physics 101, but never took the lab where you learn how to test hypotheses. Here’s the way the lab report should start:

Objective: Given that we observe that bicycles are faster than unicycles on hill climbs, despite the lower mass of unicycles, we intend to test for possible explanations. We will test both physiological and mechanical explanations. Physiological explanations could include differences in ability to provide force to the pedals due to requirements for balance. Mechanical explanations could include differences in translation of force input to forward momentum.

Methods: (you can take it from here)

[johnfoss]

Whew!

Now I’m out of popcorn, so I feel obligated to post something.

Uh…

I have no ammo from Physics class, since I never took one. All my physics knowledge comes from real-world experiences, and watching a lot of sports and circus. Some things are obvious enough, while others are subtle and probably invisible to someone not familiar with the activity.

Mr. Engineer, I know you’re riding on some hills because Manhattan and the Bronx are not flat. But you’re a relatively new rider, and if your concentration has been on covering distance, you probably haven’t “studied” uphill riding much yet. What is your engineering background, btw? We get all sorts of interesting people in unicycling, with interesting skills and knowledge.

Tom Holub has a ton of hands-on experience with uphill riding, and I’m pretty sure he’s right about a bicycle being basically the more efficient vehicle for going uphill under any conditions. As you can see he likes to nerd-out on some of these topics and not yield while he still thinks he can explain something.

Unicycles only have one wheel. They do not track in a straight line, even if you try really hard. An efficient climber learns how to minimize this, but doing so involves expending energy with each pedal “step” to keep the wheel pointed straight. I pendulum my non-seat-holding arm as part of that. On a bike you only need to make some tiny steering inputs to keep yourself pointed in the most efficient direction up the hill.

Engineer’s descriptions of riding up the hills seem to involve a constant spin being maintained. Naturally this would be the most efficient way to ride, but your spin starts to break down as the slope gets steeper. As you hit a hill with speed, you can spin into it. but if it gets steep, that spin will slow (unless you have a little wheel), and after that you will be “lugging”, with power pushes alternating between little gaps of power as the pedals pass through vertical. As it gets steeper, it becomes more of a series of big pushes, that might have to include little micro-rests between steps. This is a good way to ride up a steep hill that’s long.

Anyway, all of that is pretty inefficient. Too bad we can’t downshift. 36" wheels are horrible for riding up anything steep. We only put up with them because they’re so much better than smaller wheels when the going is flat or downhill.

I’ve been to Fargo Street once, at the 2014 CA Muni Weekend. I brought my 24" Miyata with 125mm cranks (a “Track” uni), and my 26" Roger Davies carbon Muni with 150mm cranks. I’m not sure which one I ended up using, but I think it was the Muni because it’s really light, and had more leverage. I couldn’t get very far going straight up (and I consider myself a pretty good uphiller), and switched to zig-zagging to avoid a dismount. I did eventually stop, more than once, to “replenish oxygen” before I made it to the top.

We don’t really get to spin “efficiently” up things that are considered steep, unless we’re riding relatively small wheels. If I were to seriously challenge Fargo Street, with conditioning and training, I think I might opt for a very light 700c wheel with “medium” cranks. Medium means I think I’d end up with something not real long, and definitely not very short. For that street.

The guy who has the unicycle record (far as I’m aware) for Mt. Diablo, Greg Drummond I think was his name, used a Coker that was super stripped down and lightened. I think he went crazy with a drill on it, though I haven’t seen the uni myself. Coker (or any other 36") tires are notoriously heavy, but I think he preferred that to a smaller wheel. I have also ridden a 36" up Mt. Diablo. The higher half of the ride is mostly fairly steep, and much of it is accomplished half a revolution at a time. Then there’s that last bit, which is somewhere north of 20% and I could only make it up that a little bit at a time (many stops).

Anyway, the key points I guess I’m making are that unicycles generally don’t get “spun” up long slopes that are steep; it usually ends up being a series of pushes; how hard depending on the grade. Also that, because unicycles don’t go in a straight line, a unicyclist has to use a bunch of additional energy just to try to keep an efficient line.

Also, with my armchair physics knowledge, every time people apply “textbook” physics arguments to unicycles here, they inevitably seem to make assumptions or leave out small details that aren’t actually that small. All the mechanics of riding a unicycle must be hellishly messy in mathematical format.

Anyway, thanks for that fascinating discussion, and feel free to pick my post apart now. I am now armed with a bag of M&M’s!

[Engineer_on_a_Unicyc]

@johnfoss

Engineer’s descriptions of riding up the hills seem to involve a constant spin being maintained. Naturally this would be the most efficient way to ride, but your spin starts to break down as the slope gets steeper.

That’s specifically why I calculated the grades where a fit cyclist (which is to say, not me!) could maintain spinning, based on commonly used numbers for their (not my!) sustainable power output. Reduce them a bit if you like, the point wasn’t to show what is possible, but rather what isn’t - to explain why the medium-wheel steep-hill climbs we see are out of the spinning regime.

Once you’re out of that regime and “stepping” the wheel (and I personally am at far, far lower slopes), you have a nice personal strength challenge, but you’re no longer riding efficiently. Likely you’re better off walking, except for the lacking feeling of accomplishment.

Anyway, the key points I guess I’m making are that unicycles generally don’t get “spun” up long slopes that are steep; it usually ends up being a series of pushes

That may be tradition and/or because the travel speeds and small wheels for a spinning ascent are insufficient for low-cost stability, but from a sustainable energy output perspective, it’s unwise. I think anyone wanting to accomplish the proposed “everesting” would have to find a course and wheel where they could stay in a smooth spinning, seated regime. And yes, it sounds a lot like riding a century up a hill on a 24, which doesn’t sound fun at all.

Also, with my armchair physics knowledge, every time people apply “textbook” physics arguments to unicycles here, they inevitably seem to make assumptions or leave out small details that aren’t actually that small. All the mechanics of riding a unicycle must be hellishly messy in mathematical format.

The primary physics dispute concerned the beneficial side of the big wheel flywheel effect, something already well established in threads here more than 10 years ago, and intuitively observable in bowling bowl in a halfpipe type experiments.

[aracer]

@Engineer on a Unicycle

I specifically mentioned the existence of 14 and 15 lbs bikes. But you haven’t considered taking that lightweight road bike and building a unicycle with the same technology. You’ll be leaving more than half of it in hacksaw trimmings on the ground - about the only thing that would end up weighing more is the saddle and tire

I did, even if I wasn’t explicit enough about it for you. That bike is all standard off the shelf parts, so let’s apply the same principle to the unicycle. In the same way as for many issues on this thread you’re dismissing the important point in passing - there’s a pound and a half extra right there in the saddle and tyre, quite significant when you’re suggesting a 7lb uni for that 8lb saving. It simply doesn’t scale in quite the way you seem to think.

when considering only the power expended lifting the body mass up the hill - the weight of the cycle, friction losses, and the small power used in moving horizontally are not considered. Those simplifications probably make the table substantially less accurate at low grades and larger wheels.

or for unicycles, where the power used for things other than climbing the hill isn’t so insignificant!

increasing the travel speed such that balance can be maintained more by low-cost microsteering rather than by balance-specific exertions.

It’s still not as low cost as you seem to assume.

@johnfoss

What is your engineering background, btw? We get all sorts of interesting people in unicycling, with interesting skills and knowledge.

I know you weren’t asking me, but if we’re throwing around authority, I have an engineering degree. I specialised in electronics and computers, but also studied mechanics and structures, so have what could reasonably be described as degree level knowledge of those. Most importantly though, my training taught me how to correctly apply critical thinking, and not to ignore the important issues for the sake of simplification…

Unicycles only have one wheel. They do not track in a straight line, even if you try really hard. An efficient climber learns how to minimize this, but doing so involves expending energy with each pedal “step” to keep the wheel pointed straight. I pendulum my non-seat-holding arm as part of that. On a bike you only need to make some tiny steering inputs to keep yourself pointed in the most efficient direction up the hill.
…
Also, with my armchair physics knowledge, every time people apply “textbook” physics arguments to unicycles here, they inevitably seem to make assumptions or leave out small details that aren’t actually that small. All the mechanics of riding a unicycle must be hellishly messy in mathematical format.

Right there even without any formal qualifications you get to the heart of the issue.

@Engineer on a Unicycle

That’s specifically why I calculated the grades where a fit cyclist (which is to say, not me!) could maintain spinning, based on commonly used numbers for their (not my!) sustainable power output.

But the issue is that on such a hill where you can maintain a spin on a unicycle (and even with such a spin you’re still using lots of energy on micro balancing however good you are) a bicycle would already be going faster than a typical unicycle on the flat. Because such a gradient is way lower than you seem to assume. In order to maintain a spin, the force put into each pedal stroke has to be low enough that you’re not outputting that max power you mention. On a bicycle you can just mash the pedals around with no control input.