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#1
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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 |
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#2
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Coker and Flywheel effect
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. -- Mikefule - Roland Hope School of Unicycling Freedom's just another word for nothing much to lose. Nothing ain't worth nothing, but it's free. ------------------------------------------------------------------------ Mikefule's Profile: http://www.unicyclist.com/profile/879 View this thread: http://www.unicyclist.com/thread/28435 |
#3
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Coker and Flywheel effect
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 "jfoss" at "unicycling.com" www.unicycling.com "In three months or so, he won't be doing that any more." -- Kris Holm's cousin Derek, 13, on Kris' unicycling now that he's married ------------------------------------------------------------------------ johnfoss's Profile: http://www.unicyclist.com/profile/832 View this thread: http://www.unicyclist.com/thread/28435 |
#4
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Coker and Flywheel effect
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.... ------------------------------------------------------------------------ tomblackwood's Profile: http://www.unicyclist.com/profile/3762 View this thread: http://www.unicyclist.com/thread/28435 |
#5
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Coker and Flywheel effect
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' (http://www.unicyclist.com/gallery/albup39) -- Dave Stockton ------------------------------------------------------------------------ U-Turn's Profile: http://www.unicyclist.com/profile/691 View this thread: http://www.unicyclist.com/thread/28435 |
#6
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Coker and Flywheel effect
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... ------------------------------------------------------------------------ cyberbellum's Profile: http://www.unicyclist.com/profile/4550 View this thread: http://www.unicyclist.com/thread/28435 |
#7
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Coker and Flywheel effect
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 - - ------------------------------------------------------------------------ duaner's Profile: http://www.unicyclist.com/profile/4297 View this thread: http://www.unicyclist.com/thread/28435 |
#8
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Coker and Flywheel effect
"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 |
#9
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Coker and Flywheel effect
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' (http://www.unicyclist.com/gallery/albup39) -- Dave Stockton ------------------------------------------------------------------------ U-Turn's Profile: http://www.unicyclist.com/profile/691 View this thread: http://www.unicyclist.com/thread/28435 |
#10
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Coker and Flywheel effect
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 ------------------------------------------------------------------------ Borges's Profile: http://www.unicyclist.com/profile/925 View this thread: http://www.unicyclist.com/thread/28435 |
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