# Coker and Flywheel effect

I am trying to decide whether I need a Coker, or should wait for the
commercial availability of the uni.5 * hub to have an effectively
large, yet physically small wheel. Not having an opportunity to try
any of these options, and also for fun, I have developed the following
reasoning.

When you ride your uni and tend to fall to the front, you step more
heavily on the front pedal to correct the imbalance. “Conventional
thinking” (if such a thing exists here) has it that said action
accelerates the wheel and brings it back under your centre of mass.
(Likewise, if you fall to the rear, you apply more backwards pressure
on the pedals to decelerate the wheel and again bring it back under
you.)

If you ride a 20" or smaller unicycle, the forward acceleration or
deceleration of the wheel is indeed the main effect from varying pedal
pressure. However, when riding a larger wheel such as a Coker, the
acceleration/deceleration is more sluggish, and requires that pedal
pressure be sustained for some time to take enough effect. One could
say that the pedal ‘resists’ the downward force. Hence, if you step on
the front pedal when you tend to fall forward, you also upright
yourself (with the hub as pivot point) as if you were standing on
solid ground. This of course is a very natural and easy process, that
most humans learn around the age of 1 y.o. Both effects (pedal
resistance and wheel acceleratation) combine and work in the same
direction - preventing you to fall. I think that this is the basis for
the common assertion that a Coker is so easy to ride (once going).

The fact that the pedal ‘resists’ any downward force is commonly
ascribed to a ‘flywheel effect’ of the Coker, with its heavy tyre/rim
at large distance from the hub. I would however argue, that the same
sluggishness would to a large extent also be present in the
hypothetical case that the rim and tyre of a Coker had no mass at all.
Namely, if you step on the front pedal, friction with the ground
prevents the wheel from instantaneously accelerating. Lest you fall,
the wheel can only accelerate if the whole mass of uni + rider is
accelerated, which on a large wheel is inherently a sluggish process.
The work going into the linear acceleration of the total mass is
considerably larger than the work going into increasing the rotational
velocity of the wheel only, even in the case of a Coker.

Now consider a 24" wheel with a uni.5 hub, and the same length of
cranks as implicitly assumed above. The work going into the linear
acceleration of the total mass is almost the same as in the Coker
case, since the total mass is not that much different. Similarly, the
required pedal force is roughly the same (as 24" x 1.5 = 36"). The
work going into increasing the rotational velocity of the wheel (up to
the same velocity at the circumference) may be somewhat less than in
the Coker case, if the tyre and rim are lighter. (The fact that they
are closer to the hub doesn’t matter since we speak about equal
circumferential velocity. Regardless, as argued previously, this part
of the required work is a small fraction of the total work required.)
Hence, the resistance of the pedal to downward forces should be very
much comparable between the Coker and the 1.5 x 24" case. So the
so-called ‘flywheel effect’ should be the same as well, leading to a
comparable ease of riding, ‘cruise control’ effect or whatever you
want to call it. With a 1.5 x 29" (in stead of 24") the effect would
even surpass that of a Coker.

over bumps, or aesthetic effects, are left out of the equation. But
hey, so are the advantages of a uni with a switcheable hub.

I welcome any thoughts on above analysis, or on practical experiences
in this respect re the comparison between Coker and uni.5 or
Blueshift.

Klaas Bil

• A uni.5 hub is an internally geared hub in which the wheel rotates
1.5 revolutions for every full revolution of the cranks. It exists in
the prototype stage.

(Disclaimer: I have never ridden a Coker nor a geared uni. Everything
in this post is from experience riding wheels up to 29", and some
basic physics reasoning.)

## Klaas Bil - Newsgroup Addict

Grizzly bear droppings have bells in them and smell like pepper spray. - UniBrier

Much of your reasoning seems more or less correct.

The rotational velocity of two rims of different sizes on unicycles travelling at the same speed may be similar. Put simply, the smaller wheel goes round more!

However, for the flywheel effect, you also factor in the mass, and the distribution of the mass relative to the centre of the hub.

So a 24 with an identical rim section and tyre to a Coker would be lighter, because there would be less of the rim and tyre.

The bit about the pedal resisting the foot, rather than the wheel ‘shifting’ underneath the rider is valid. Intuitively, I think that’s what happens on a standard Coker.

Be that as it may, I know that riding a long way fast on a Coker with 150s is easier in every respect (except tight turns) than riding the same distance as fast on a 29 with 110s. The lighter smaller wheel is noticeably ‘twitchier’. This seems to be because of the lack of mass. In theory, if we all weighted our rims, we would have unicycles with sluggish acceleration and turning, but ‘softer’ balance characteristics.

Hmmmm.

Re: Coker and Flywheel effect

The rides would be comparable, but not the same. As you mentioned, the Coker will roll over things better due to its larger diameter. Along with this, it will also be more stable due to its greater mass. This is what you give up in exchange for the smaller, easier to store wheel. But the ride won’t be quite as easy, or stable.

Wow, that’s a lot for my brain to try to follow. I can pass on a recent comment I heard that might help. Several of the Seattle area riders did a 20+ mile Coker ride recently on an old converted railroad grade. With us was Andy Cotter, who’s probably done as much distance riding on a Coker as anyone. He rode Harper’s Blueshift for the full ride, and generally stayed at the front of the pack, a combination of the “true” 45" wheel size due to the shift ratio, and the fact he was the superior rider in superior shape. Near the end I asked him if the shiftable uni was easier than the Coker for the distance. While I don’t have it verbatim, the essence of his answer was “No, for regular distance riding I’d take the Coker. The shift ratio while technically faster also takes a more mental energy to maintain the balance, and is harder to correct over bumps, obstacles, etc., since it isn’t 1:1.” You might try mailing him and Harper directly for their input, since they’ve both done some significant comparing now.

The practical considerations mentioned above, especially ala Andy Cotter, are the most significant thing to consider. There are others, such as portability, parts availability, tire choice, tire/tube price, and the like, which favor the 29er.

However, with reference to your analysis, Klaas, I have a few comments, mostly vague and intolerably muddy:

1. “Flywheel effect” does not take into account linear aspects of motion at all. Hence, a wheel with no mass has no flywheel effect. f=ma, so for a given torque, as rotational mass decreases, the rotational acceleration increases. So when you stomp on the massless wheel, it’s gone and you are on the ground, unless you are so far ahead of the balance point that it wants to launch you into space.

2. The way fore-aft balance works is the same for all unicycles, massy or not. As the rider falls forward ahead of the balance point, necessitating correction, he must accelerate the wheel underneath him, both linearly and rotationally. When he has accelerated the wheel to velocities that will solve the balance problem in the right amount of time, he then must stop the acceleration, leaving the wheel at the faster velocity until the proper time, then he must decelerate the wheel until he is again at steady state with the overall linear motion of the uni/rider system, at which time he must halt the deceleration in order to stay at that velocity.

3. In light of #2, it should be clear that the skill and efficiency of the rider at controlling that mechanism is the key, not the mass of the wheel. A skilled rider on a massy wheel can spend a lot less energy doing the same thing as a lesser-skilled rider on a less massy wheel.

4. It is true that the rider’s mass enters into the balance mechanism. When he accelerates the wheel underneath him as in (2) above, he is partially accelerating himself as well. However, as the rider’s skill increases, that factor will decrease. Through body motion and better pedalling technique, he will accelerate the least amount of mass the minimum amount to achieve balance. This is not a conclusion as much as it is the definition of a “skilled” rider.

5. One of the tools a skilled rider uses is to have the wheel push him upwards against gravity, thus slowing the wheel slightly. The reverse is true also. However, again, with an efficient rider, the amount of work he does this way is minimized.

6. Based on (4 and 5), we can say that the only significant work the skilled rider to maintain fore-aft balance on a level surface is the work that he does on the wheel, not the work he does on his body. Moreover, we can say that for a rider equally skilled on both the 36 and the geared-up 24, the work just mentioned will be similar, if not exactly the same. This accounts for steady-state.

7. What we are left with are macro-situations where the rider must do work on the entire system, rider and wheel. These situations include: starting, speeding up to a new steady state, slowing down to a new steady state, stopping, climbing a hill, descending a hill, turning, handling bumps of various kinds, hopping, and micropositioning such as one does when mounting.

8. Although for two riders, one on a 24 and one on a 36, going at the same speed, the circumferential velocity is the same, the rotational energy stored in the wheel is not, since the larger wheel has much more mass much farther away from the center. This means the large wheel will want to climb bumps easier, will want to climb up a hill more readily at first, will resist turning more, and will want to resist speeding up on a change to a downhill slope. In addition, starting and stopping will require much more energy input, as will micropositioning. Hopping will require more energy as well, but is irrelevant because it does not involve rotational work, which is our topic. Situations where circular asymmetry of energy input is predominant (i.e., situations where pedal position is a big deal), such as climbing a hill which is long or steep enough that one has to “chicken climb”, will favor the wheel with less mass, because the rider is continually accelerating the wheel rotationally. However, there is a complicating factor of the gearing up, in that when one “stomps” a geared-up wheel, the linear motion one gets is different from a non-geared-up wheel of the same size. But I guess that this is primarily a matter, once again, of rider skill, and not a difference between unicycles. Finally, the larger wheel, merely by geometry, takes less of a rotationally-decelerating hit from bumps up to a certain size, and so would have the advantage over a smaller wheel geared up to the same size. The extreme example of this is a pothole that would stop the smaller wheel, but that the large wheel could straddle. This difference drastically affects the rider’s need to pay attention to bumps.

9. Andy Cotter’s experience might be different if he had spent as much time on a geared-up uni as on a non-geared up uni. Then the (probably large) difference in his skill on each would be gone, and he would be able to see other factors that make the two different.

So in summary, a) for steady-state, the linear acceleration of the rider is negligible for a skilled rider, not the predominating factor; b) a massless wheel will be miles ahead before you hit the ground on your butt, c) the “flywheel effect” is much larger for the larger wheel, and affects the two wheels differently for different aspects of riding, and d) even for a highly skilled and insightful rider like Andy, it would be difficult to form truly meaningful experiential conclusions based on one test ride.

Whew! I hope somebody reads this through!

Interesting thread. I’m busy working out the equations of motion for unicycles at the moment to see if a robot unicycle project might make sense, so a lot of the math is pretty fresh in my head.

One basic rule of thumb for wheels with most of the mass in the rim can be taken from basic physics. If you work out the momentum and energy equations for a rolling hoop with all the mass in the rim you find that it behaves as if it were exactly twice it’s actual mass. Acceleration and deceleration take twice as much force, and when it’s up to speed it stores twice as much kinetic energy. So, to a pretty good aproximation, a uni wheel is going to behave as if it had twice the mass of the rim, tire and tube. (the error due to omitting the spokes and hub is offset by the fact that the mass of the rim, tire and tube aren’t at the same radius as the contact patch.) In other words, if you took the 24" wheel and injected goo into the tube until it weighed the same as the Coker wheel it would have very similar inertial properties.

The second, and more important effect, is that the thrust you can produce with a given power input decreases with speed. To a very good aproximation thrust (or braking) for a constant power input (or output) is inversely proportional to the speed. Likewise, the kinetic energy input to gain (or lose) an increment of speed is much higher when you are going fast than when you are going slow. This is one reason why cars are so quick going from 10 to 20 mph, and so slow going from 110 to 120 mph. So some of the Coker “flywheel effect” might just be the perception that it’s much harder to acclerate and decelerate at Coker speeds. In other words, you have to work twice as hard or twice as long to produce the same speed change at 10 mph as you would goging only 5 mph. This effect is totally independent of wheel size, so it would be the same on a uni.5 as a Coker.

Another factor that might come into play in the “cruise” effect of a Coker is that you are a little higher off the ground. A unicycle can be thought of as an inverted pendulum. Just as regular pendulums swing slower when they get longer, inverted pendulums take longer to fall when they get longer. (Try balancing a 10’ pole on one end. Easy, eh? Now try it with a paper clip…

Cruising at “altitude” (on a Coker or giraffe.5), you have a little more time to think and react than you do on a uni.5, so some of the perception of ease might simply be less mental energy. On the smaller uni the shorter time constant means that you are always a little slower to react, and therefore have to over-compensate more often. This takes more energy.

The rest of the reason why the Coker has a “flywheel effect” is due to the flywheel effect. Coker wheels, because they are heavy and moving with higher rim speeds, have much greater gyroscopic stability than ligher, slower uni wheels.

Actually, I think Klaas Bil was correct - there are two mechanisms at work maintaining front/back balance on a uni.

The most obvious one is the one you mention.

The other mechanism may be most obvious when doing straddling standstills - such as a standstill between two rungs of a ladder. In this “obvious” example, stepping on the front pedal does not accelerate the uni (or rider) at all. Instead, what it does is to tilt the rider backwards (or less forward) moving his center of gravity (CG) backwards relative to the axle. This same effect is also present on all unicycles, but only “obvious” on large/heavy tired unis, like the Coker, where the resistance to rotational velocity changes is relatively high. (Maybe it is also obvious on unis with moderate size/weight tires having very short cranks?)

To stop overly-forward-balance, most(?) people think of increasing pressure on the forward pedal as accelerating the tire to get it to roll back under them. However, as a mental model, thinking of it as tilting themselves backwards to reposition their CG over the axle is just as valid - when thought of this way, the acceleration that happens is “just” a side effect of the rebalancing effort.

.duaner.

Re: Coker and Flywheel effect

“cyberbellum” <cyberbellum.vqeom@timelimit.unicyclist.com> wrote in message
news:cyberbellum.vqeom@timelimit.unicyclist.com
>
> Interesting thread. I’m busy working out the equations of motion for
> unicycles at the moment to see if a robot unicycle project might make
> sense, so a lot of the math is pretty fresh in my head.
>

It does make sense. I saw a unicycle robot on TV a while ago: I am sure
the balance was autocorrecting and I think the direction was radio
controlled. I cannot remember the title of the programme but suspect a
google may well find it as well. I think they may have had the batteries
and other heavy bits below the axle height to increase stability with a low
C of G, and which would make forward/backward balance something of a doddle.

Like me though, I don’t think it could freemount

Naomi

I agree with you both that there are 2 aspects, rider and ridee – see number (4) in my entry. Obviously the rider’s mass allows him to exert force on the pedal, and that mass will be accelerated by his pressure on the pedal, just as the wheel is. The two form a system.

However, Klaas is saying that, because the Coker’s mass is larger than a 20", say, that the linear-rider-acceleration side of things is more dominant during steady-state motion than the rotational-wheel-acceleration side of things.

He says, “Lest you fall, the wheel can only accelerate if the whole mass of uni + rider is accelerated, which on a large wheel is inherently a sluggish process. The work going into the linear acceleration of the total mass is considerably larger than the work going into increasing the rotational velocity of the wheel only, even in the case of a Coker.”

I am disagreeing. Consider a skilled rider who, by definition, is efficient with his use of energy, is endeavoring to maintain a constant speed on a level surface. Linear acceleration of the entire system can only be achieved by rotational means, (e.g., decelerating the wheel so that he falls forward, then accelerating the wheel again so that it pushes forward against his body). It follows that the primary balancing mechanism for all sizes of wheel is rotational. Linear accelerations and decelerations are wastes of energy. On a Coker compared to other sizes, the mechanism takes place on a longer time base, but still has to be the primary mechanism.

The reason that a 20" feels different is because we are not being efficient while riding it, because we don’t have to. So we can accelerate linearly without worrying too much, because it is easy to zoom the wheel underneath us and decelerate linearly to compensate.

However, a skilled freestyle rider, trying to be smooth, will ride in this efficient way. This is like skilled Coker riding, but on a different time base.

So why would a Coker seem easier to cruise with, when (as I purport) we have to pay more attention and can’t use those inefficient mechanisms? Because it forces us into a different mode of behavior. At first, when you climb on a Coker (however you manage it), you try to ride it like a 20", which is wrestling it all over the place. After a while, that disappears, because it is dehabilitatingly inefficient, and your control mechanism centers back into a behavior that minimizes the wrestling.

Take a look at the video of John Stone idling in the Strongest Coker gallery (link below). It’s apparent how little energy he uses, because he isn’t wrestling the wheel all over the place.

Anyhow, that’s how I see it.

When cruising you stay on top by moving the uni under you.
E. g. if you hit a bump that slows the wheel down your body continues its forward motion and you have to reaccelerate the wheel to keep up with your body.

Thus, the effort of keeping your balance depends more on the effort it takes to move the uni than the effort it takes to move you.

So I think the momentum of the wheel is a relatively big factor in the flywheel effect.

Disclaimer: This is purely speculation.

Klaas,

I think maybe if you go ahead and get a Coker & ride it until a “Harper hub” becomes available, then you will enjoy the “Harper hub” more, but still won’t be able to part with your Coker.

You guys think too hard. Just enjoy the ride.

-Mark

Me too!

Guys, guys, I’m trying to eat my lunch here while I’m reading all this stuff.Now I have a headache and think I’ll go throw up.
May I suggest the following…just go ride the thing and have fun…you think too much! Pass the Asprin!

I have to agree with Andy Cotter. Though I definitely have more big wheel and Coker miles in, I have ridden various forms of geared-up unicycles many times. I geared up my giraffe in 1980, I rode a standard 20" geared to 40" in 1982, I rode the Harper hub in three different forms, and have ridden several other geared up unicycles over the years.

The consensus by most of the people who have actually ridden these cycles, rather than theorized in front of their computers, is that geared-up unicycles have their advantages, but one of them is not being easier to ride than a big, heavy wheel.

I don’t know what the difference is, other than what I’ve already mentioned. Part of it may be loss of power or reaction time through the drivetrain. Whatever it is, it’s easier to cruise on the big heavy wheel. I think most of it is the size and weight of the wheel, and this is very easy for me to understand. When I’m going at or above running speed, I want a stable platform. A large, heavy wheel gives me this.

And yes, there is that other force, of you body going the opposite way when you press on a pedal. You can see it in action by riding up to a wall or curb, then pressing on the forward pedal. If you do it right, you can go from leaning with your upper body almost touching the wall, to shooting away from the wall in almost no time, with no rotation of the wheel to get you started.

Re: Coker and Flywheel effect

Wow, a lot of brainpower went into those responses. Thanks all!

Mikefule was right in pointing out that a Coker wheel has more mass
than a small wheel even with the same tyre and rim type. I overlooked
that somehow. But it isn’t core to my reasoning.

U-Turn made me realise that for the wheel to accelerate, the rider
need not accelerate as well (or as much). Good point. Borges pointed
out the same thing.

Duaner exactly understood what I was trying to say - and expressed it
much better. The ‘straddling standstill’ example was excellent.
Another example could be a VERY large wheel, say 100 metres in
diameter. (It might be normal sized and very highly geared up to be
100 m effective, or it might be really that large, and still somehow
pedal-driven in a 1:1 ratio, similar to the large one in
<http://www.xs4all.nl/~klaasbil/monrovia1998.jpg>.) Let’s assume that
(1) left-ride balance would not be an issue on this giga-unicycle, and
(2) there are normal-length cranks on it. Then if you would tend to
fall to the front, you would step on the front pedal. But the heavy
wheel and the puny leverage factor would prevent any significant
acceleration of the wheel. Still you would upright yourself because
the front pedal almost provides solid ground to push against. So,
there is a mechanism to maintain fore-aft balance without accelerating
the wheel back under you.
If you now change 100 m into 36", you have the Coker (resp. the 1.5 x
24") from the original post. Same story, only less extreme.

Duaner also wrote:
>(Maybe it [the other mechanism] is also obvious on unis
>with moderate size/weight tires having very short cranks?)
I doubt that. You imply that with short cranks it is more difficult to
accelerate the wheel back under you. Correct. But the uprighting
torque you can get from stepping on those shorter cranks will be
proportionally smaller too. So I would think that by varying crank
size alone, the two effects keep the same ratio relative to each
other.

Cyberbellum and Naomi mentioned computer-controlled unicycles. Mike
Hinson provides some useful links on those:
<http://mike.hinson.unicyclist.com/>.

I apologise to Cokerhead and terrytoon if I caused them a headache.
Some people like theoretising (SP?) more than others.

## Klaas Bil - Newsgroup Addict

Grizzly bear droppings have bells in them and smell like pepper spray. - UniBrier

Re: Re: Coker and Flywheel effect

Heh. Good point; I hadn’t thought of that. I was just trying to think of other cases where the leverage to mass ratio was low (like a Coker). I missed realizing that shorter cranks would also decrease the ‘tilt back’ leverage; obvious once you mention it.

Re: Re: Coker and Flywheel effect

I think this is not correct, Klaas. Let me try to explain.

First to present your initial assumptions:

A1. falling to the front: this means a) that the rider has an initial linear velocity slightly greater than the wheel, and b) that the rider has a slight initial rotational velocity. It also means, by extension, that the rider/wheel system has a slight forward rotational momentum about the center of mass of the rider/wheel system.

A2. the wheel cannot be accelerated because it is too massy.

A3. the leverage the rider has on the wheel is insignificant.

Now with the goal:

G1: to recover rider/wheel balance so that…
G2: the rider no longer has a forward linear velocity, and
G3: the rider no longer has a forward rotational velocity, and
G4: the rider/wheel system no longer has a forward rotational velocity.

To achieve G1, all of G2, G3, and G4 must be achieved.

Now with the discussions:

D1: To achieve G2, the rider has to exert a force on the ground sufficient to brake himself linearly. The only way he can do this is through the unicycle, by getting the seat to push him backwards as the ground pushes on the unicycle. Pushing on the pedal, whether the uni weighs as much as the moon or not, is not sufficient, because the linear velocity we are talking about is relative to the ground. He has to get the wheel ahead of him and get himself down and slightly behind the seat so that the seat can push him backwards enough to stop him. However, by A2, the rider cannot reposition the wheel to achieve that configuration, so G2 is not achievable.

D2: To achieve G3, the rider has to come up with a torque that will tend to rotate his body backwards, until his forward rotation is cancelled. Normally this would be accomplished by accelerating the wheel so that the rear pedal pushes against the rider’s foot, as well as the seat pushing forwards against his butt. However, by pushing against the forward pedal with Klaas’s massy wheel, the rider could cancel his forward rotational velocity, if he had enough leverage. However, by A3 he does not, so G3 is not achievable.

D3: To achieve G4, the rider has to achieve a torque on the overall rider/wheel system to counter its overall forward rotation. The only way to do this, aside from grabbing a “sky hook”, is to exert a force backwards on the ground using the wheel. However, since by A2 (and A3) he cannot accelerate the wheel, by f=ma he cannot exert a force on the ground. Therefore, he cannot achieve G4.

So I think that your assumptions are so restrictive that they make it impossible for the rider to maintain balance. Increasing the mass and size of the wheel does not change that. The rider HAS to be able to accelerate and decelerate the wheel in order to maintain fore-aft balance.

True. Without a plane, there are no test pilots.

Carrying the thought experiment a bit further:

The earth is free to spin, right? When you walk you put one foot in front of the other and balance for-and-aft. Each push you make on the earth to balance yourself changes the spin of the earth, just like pushing for and aft on the pedals of a uni changes the spin of the uni.

The only real difference between a Coker and the earth is that the Coker is constrained by traction to roll on a surface. Ride a coker in orbit and, aside from the slight difference in mass, the two systems have the same physics. (well, ok, there are other differences. The Earth’s hub is a giant ball of molten metal, and it has oceans that slosh. Details, details…)

We’re all just riding a giant multi-person uni orbiting the sun.

Re: Coker and Flywheel effect

I will put my comments in between, while quoting your full argument.

On Fri, 24 Oct 2003 05:59:17 -0500, U-Turn
<U-Turn.vsvkz@timelimit.unicyclist.com> wrote:

>
>Klaas Bil wrote:
>> ANOTHER EXAMPLE COULD BE A VERY LARGE WHEEL, SAY 100 METRES IN
>> DIAMETER… THEN IF YOU WOULD TEND TO FALL TO THE FRONT, YOU WOULD
>> STEP ON THE FRONT PEDAL. BUT THE HEAVY WHEEL AND THE PUNY LEVERAGE
>> FACTOR WOULD PREVENT ANY SIGNIFICANT ACCELERATION OF THE WHEEL. STILL
>> YOU WOULD UPRIGHT YOURSELF BECAUSE THE FRONT PEDAL ALMOST PROVIDES
>> SOLID GROUND TO PUSH AGAINST. SO, THERE IS A MECHANISM TO MAINTAIN
>> FORE-AFT BALANCE WITHOUT ACCELERATING
>> THE WHEEL BACK UNDER YOU…
>>
>I think this is not correct, Klaas. Let me try to explain.
of indicating its flaws (as I see them) easier.
>
>First to present your initial assumptions:
>
>A1. falling to the front: this means a) that the rider has an initial
>linear velocity slightly greater than the wheel, and b) that the rider
>has a slight initial rotational velocity.
Correct.
>It also means, by extension,
>that the rider/wheel system has a slight forward rotational momentum
>about the center of mass of the rider/wheel system.
Questionable statement. The wheel itself has a forward rotational
momentum because of its rolling forward. That it itself does not
relate to falling to the front. If you ignore the rotational momentum
stored in the wheel then the statement is correct.
>
>A2. the wheel cannot be accelerated because it is too massy.
I was going to say “correct”. But then when I came to your f=ma
argument I had to get back and say “almost correct” because the wheel
can be accelerated ever so slightly. It has a large mass but not an
infinite mass.
>
>A3. the leverage the rider has on the wheel is insignificant.
Partly correct. It is insignificant in terms of accelerating or
decelerating the wheel, but it is sufficient to serve other purposes.
>
>Now with the goal:
>
>G1: to recover rider/wheel balance so that…
>G2: the rider no longer has a forward linear velocity, and
You should add: “with respect to the wheel”. The rider needs not to
stop riding to recover balance.
>G3: the rider no longer has a forward rotational velocity, and
Correct.
>G4: the rider/wheel system no longer has a forward rotational
>velocity.
Questionable as per above remark.
>
>To achieve G1, all of G2, G3, and G4 must be achieved.
Correct with above provisos.
>
>Now with the discussions:
>
>D1: To achieve G2, the rider has to exert a force on_the_ground
>sufficient to brake himself linearly.
Incorrect. Since the rider should decrease his forward linear velocity
with regard to the wheel, it is sufficient if he exerts a force on
the unicycle. In fact, the wheel will exert a counter-force on the
ground but as per A2 and A3 these forces don’t change the wheel’s
linear velocity to any appreciable amount.
> The only way he can do this is
>through the unicycle, by getting the seat to push him backwards as the
>ground pushes on the unicycle. Pushing on the pedal, whether the uni
>weighs as much as the moon or not, is not sufficient, because the linear
>velocity we are talking about is relative to the ground. He has to get
>the wheel ahead of him and get himself down and slightly behind the seat
>so that the seat can push him backwards enough to stop him. However, by
>A2, the rider cannot reposition the wheel to achieve that configuration,
>so G2 is not achievable.
The rider cannot accelerate the wheel, but he can reposition himself
with respect to the wheel. The rider’s mass is not very high.
>
>D2: To achieve G3, the rider has to come up with a torque that will tend
>to rotate his body backwards, until his forward rotation is cancelled.
>Normally this would be accomplished by accelerating the wheel so that
>the rear pedal pushes against the rider’s foot, as well as the seat
>pushing forwards against his butt. However, by pushing against the
>forward pedal with Klaas’s massy wheel, the rider could cancel his
>forward rotational velocity, if he had enough leverage. However, by A3
>he does not, so G3 is not achievable.
Indeed, accelerating the wheel is not possible. But A3 should not
prevent the rider to change his own forward rotational velocity by
applying a torque on the cranks.
>
>D3: To achieve G4, the rider has to achieve a torque on the overall
>rider/wheel system to counter its overall forward rotation. The only
>way to do this, aside from grabbing a “sky hook”, is to exert a force
>backwards on the ground using the wheel. However, since by A2 (and A3)
>he cannot accelerate the wheel, by f=ma he cannot exert a force on the
>ground. Therefore, he cannot achieve G4.
Since the set of assumptions and goals is not fully correct in my
view, this D3 is difficult to comment. As I see it, the rider can
exert a torque on the pedals and use the counter-torque to decrease
his forward rotation and even make it temporarily negative. That
action will increase the forward rotational momentum of the wheel with
a small amount (that we do not bother about).
>
>So I think that your assumptions are so restrictive that they make it
>impossible for the rider to maintain balance. Increasing the mass and
>size of the wheel does not change that. The rider HAS to be able to
>accelerate and decelerate the wheel in order to maintain fore-aft
>balance.
Well, I don’t agree.

The discussion would become easier if we add the assumption that the
wheel doesn’t rotate initially. It would simplify some of above
Assumptions and Goals. I think we have implicitly assumed that we
don’t have to bother about left-right balance anyway.

Let’s attack the issue from a different perspective. Assume:
a1: the wheel initially doesn’t rotate at all;
a2: the wheel is very massy;
a3: left-right balance is maintained without rider interference.
Then it would be as if the wheel is fixed to the ground in a
stationary position. That means that the pedals are also in a fixed
position. Now this is equivalent to the situation where the rider (or
any person) stands with two feet on the ground, one to the front, one
to the rear. Surely he would be able to upright himself if he tended
to fall forward? Or what am I missing?

(It becomes a bit more complicated if the cranks are not horizontal,
but the person would still be able to upright himself.)

Gosh, I don’t believe I wrote this much.

## Klaas Bil - Newsgroup Addict

Grizzly bear droppings have bells in them and smell like pepper spray. - UniBrier

Re: Re: Coker and Flywheel effect

Actually, I think the two of you are in violent agreement.

The missing bit is in your assumption a2 - that the wheel is very massy. Even though it’s mass is huge, it isn’t infinite, so it still accellerates a finite amount when forces are applied.

If I add the initial condition assumption a0 that the rider is falling forward, then the rider/wheel system initially has a net forward momentum. Since the wheel IS extremely massy, the momentum is negligable compared with the inertial of the system. But it is finite.

When the rider stops his fall forward, where does this momentum go? One of the fundamental tenets of physics is that momentum is ALWAYS conserved. Either:

A) The wheel exerts a reversing force on the ground to kill the momentum, or

B) The momentum still exists in the rider/wheel system.

In reality, both occur. Initially the momentum is transfered from the rider into the wheel, causing it accelerate a negligable bit in the direction of the rider’s fall. I could go into details on the exact mechanics of how this happens, but the details are unimportant. Momentum is always conserved.

Assuming the rider wants the wheel to stay in place he will allow the wheel to get slightly ahead of him (or her) to move the system mass behind the contact patch. This create a tiny, negligable BUT STILL FINITE reversing torque on the wheel. Over time the wheel will slow, and if the rider keeps it up long enough, the wheel will reverse direction.

If the rider then moves forward to put the mass of the system in front of the contact patch he can bring the wheel to a stop. If he (or she; or “it” in the case of my robo-uni project) repeats the fore and aft cycle then he/she/it is idling the wheel.

So what does this have to do with Cokers and the flywheel effect? The bottom line is that as the wheel mass increases control is achieved more by rider weight shift and less by wheel acceleration. A small, and therefore low mass wheel, is going to move around under the rider more than a large, high mass wheel, and therefore will feel twitchier and less stable. (But of course this is obvious to anyone who rides.)

Now I’m going to get suited up and see if I can break my current record of 120 feet on my twitchy, beat-up 20" uni…

DANG I have to go away for the weekend… I’ll read these when I get back. Good stuff!