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.

I realise that additional Coker advantages, such as better rolling
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.


--
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Klaas Bil wrote:
*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.*
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.


--
johnfoss - Now riding to work

John Foss, the Uni-Cyclone
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"In three months or so, he won't be doing that any more." -- Kris Holm's
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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.


--
tomblackwood - Registered Nurtz

The epitome of Just-Too-Muchery....

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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.

I welcome any thoughts on above analysis


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!


--
U-Turn - Small fish, big pond

Weep in the dojo... laugh in the battlefield.

'Strongest Coker Wheel in the World'
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-- Dave Stockton
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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 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 isn'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 given 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 (and associated
over-compensation or thrashing). The rest is due to the increased
gyroscopic stability of the high-mass Coker wheel.


--
cyberbellum - Level 0.5 rider

If I knew what I was doing I wouldn't be in research...
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U-Turn wrote:
*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.*

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.


--
duaner - -
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"cyberbellum" wrote in message
...

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

duaner wrote:
*
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. ...
when thought of this way, the acceleration that happens is "just" a
side effect of the rebalancing effort.
*
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.


--
U-Turn - Small fish, big pond

Weep in the dojo... laugh in the battlefield.

'Strongest Coker Wheel in the World'
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-- Dave Stockton
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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.


--
Borges - High impact cerabellum workout
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