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Old 2017-05-24, 04:48 AM   #16
Engineer on a Unicycle
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Originally Posted by tholub View Post
There is no hill grade at which a unicycle is more efficient than a bike.
When the hill grade is ideal for the unicycle's lever ratio and steady enough and the rider skilled enough that changes in effort for balance are insignificant, then for a fit rider with no extra pounds of their own, the fact that it weighs 8-10 lbs less that have to be hauled up the hill is an efficiency advantage.

It may be true that a bicycle configuration with its handlebar lets the rider exert more torque and hence do more work; but that's effectiveness of the combination, not efficiency of the cycle.

A carefully sized unicyle drive plus a small stability wheel (or even two to create a trike) and frame to support that and handlebar could likely be the ideal "reduced to only what helps" constant hill configuration.

And clearly there's a grade where all of these loose out to walking.
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Old 2017-05-24, 09:20 AM   #17
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Ok, there are obvious things :
Unicycle:
Pro: light
Cons:fixed ratio

Bike:
Pro:a huge amount of gears
Cons:heavy

Since you can put a handlebar on a unicycle they both also have the advantage of a lever.
But there is something that unicycles have got (especially with a handlebar) that bikes haven't : on a unicycle you can use your body+unicycle weight to make it easier to pedal by pushing the balance point further.
On flat it's obvious, when you are very close to the UPD limit you get more speed and cranks torque becomes much lower, it's obvious on a 36er, but on uphill you can still take profit of gravity to help you a bit.
you don't have this option with a bike.

Now, I'm not sure you can take much profit of this phenomenon on very steep hills.
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Old 2017-05-24, 11:26 AM   #18
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I was thinking about unicycle everesting for quite a time, but that is definitely too far from my abilities. I was thinking more about Rysy'ing (Rysy being highest point of Poland at 2499 https://en.wikipedia.org/wiki/Rysy) or Mount Blanc'ing (4,808 m) first.
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Old 2017-05-24, 02:20 PM   #19
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Originally Posted by Engineer on a Unicycle View Post
When the hill grade is ideal for the unicycle's lever ratio and steady enough and the rider skilled enough that changes in effort for balance are insignificant, then for a fit rider with no extra pounds of their own, the fact that it weighs 8-10 lbs less that have to be hauled up the hill is an efficiency advantage.
Unicycles don't weigh 8-10lbs less than decent road bikes. In particular, their rotating weight is higher than the kind of road bike you'd do hill climbing on, because you'd use 700x18-23 rims and tires, which suck for unicycling.

And any advantage of reduced weight is overwhelmed by the vector forces. The pedal force on a bike translates very directly into forward motion. On a uni, not only do you have to counterbalance backwards, but the wheel wobbles also, so more of your force is going to the left and right. This is especially pronounced on steep hills.

A reasonably-skilled rider will always be faster on a reasonably-configured bike than on a unicycle, regardless of grade.
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Old 2017-05-24, 02:39 PM   #20
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Unicycles don't weigh 8-10lbs less than decent road bikes.
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.

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In particular, their rotating weight
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.

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because you'd use 700x18-23 rims and tires
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.

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And any advantage of reduced weight is overwhelmed by the vector forces. The pedal force on a bike translates very directly into forward motion. On a uni, not only do you have to counterbalance backwards
Erroneous idea - you do not, unless you've made a mistake that needs correction.

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but the wheel wobbles also, so more of your force is going to the left and right. This is especially pronounced on steep hills.
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.
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Old 2017-05-24, 03:06 PM   #21
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Originally Posted by Engineer on a Unicycle View Post
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.

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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).

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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.
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Old 2017-05-24, 03:19 PM   #22
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Originally Posted by tholub View Post
Rotating vs. fixed weight matters for all acceleration and deceleration.
None of which occurs on a steady hill.

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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.
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Old 2017-05-24, 03:43 PM   #23
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Originally Posted by Engineer on a Unicycle View Post
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.
https://www.youtube.com/watch?v=91Nw6kxUI68

Here's another one from CA MUni Weekend 2014. I'm the one going straight up and coming in second to Jamey.
https://www.youtube.com/watch?v=5jZZPFQGDSA

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.

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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.
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Old 2017-05-24, 03:52 PM   #24
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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.
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Old 2017-05-24, 04:03 PM   #25
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Originally Posted by Engineer on a Unicycle View Post
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.

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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.
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Old 2017-05-24, 04:10 PM   #26
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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.

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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.

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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.
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Old 2017-05-24, 04:19 PM   #27
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Old 2017-05-24, 04:48 PM   #28
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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?
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Old 2017-05-24, 05:10 PM   #29
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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.

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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.

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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.
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Old 2017-05-24, 05:33 PM   #30
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Originally Posted by Engineer on a Unicycle View Post
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.

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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.

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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.]

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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.

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