Friday, January 11, 2013

Bad Physics, Bad Investment

A typical crank.
Image: Hoangquan hientrang via wikimedia
Investors beware, when something sounds too good to be true, it usually is. Right now an entrepreneur is asking for money to manufacture bicycle parts that he says will give cyclists more power, even though the way he claims it works is contradicted by the laws of physics.

The cranks of a bicycle are what connect the pedals to the front gears. They're lever arms that cyclists exert a force onto the end of, through the pedals, in order to turn the front gears. The front gears pull the chain which then spins the rear wheel, sending the bike speeding along.

Z-Torque cranks. Image from z-torque.com
Just about all the cranks on the market are a straight line from the pedal to turning radius. However a company called Z-Torque claims that their cranks give cyclists more power just by changing the crank arms into a bent shape. The problem is that physics doesn't work like the company claims it does.

The inventor, Glenn Coment, claims that his zig-zag design gives peddlers more leverage resulting in more power, but keeps the pedals at the same distance away from the center of rotation. However even a basic understanding of how levers work would show that this is impossible.

Glenn's nephew Jason is licensing the design to make them out of carbon fiber. In the fundraising video, he gives a brief physics lesson about how his  cranks supposedly work.



“Pedaling your bike is similar to using a wrench to tighten or loosen a bolt. Any mechanic will tell you if you need more torque to loosen a stubborn bolt, just go get a bigger wrench. That’s because by moving your applied force further away from the pivot point, you gain more leverage," Jason Coment said.

So far he's right. Torque is the twisting force a rotating lever or wheel exerts on its axis. Increasing the length of a lever arm, like a wrench, exerts more torque on its bolt. The longer the lever arm, the more torque is produced by the same amount of force pushing on the end of the lever.

A "second class lever" is the same kind
 of lever as a crank.
The same would be true with bicycle cranks, which are fundamentally the same as levers. One could get more torque with longer cranks, but the cyclist would have a greater distance around to pedal. The problem of course is human legs are only so long, and there's no real comfortable way to make the cranks significantly longer without people being unable to reach the pedals.

"That’s why with the patented Z-Torque bicycle crank we have solved that problem for you," Jason Coment claims. "You see we extended the crank arms past the length of a standard crank, giving you more leverage, but we then brought pedal back towards the axle to keep your rotation at the same diameter.”

He incorrectly claims that a cyclist can get more torque by having a crank arm that's "longer" but bends back towards the center, keeping the pedals the same distance away from the axis as a traditional straight crank. Levers don't work like that. It doesn't matter what shape the lever arm is, it only matters how far away the pedal is from the center of rotation.

“Having a wiggly line between one and the other doesn’t do anything about the torque," said David Gordon Wilson, an emeritus professor of engineering at MIT and author of Bicycling Science. “The tortuous form of the crank is just crazy.”

He said one could imagine welding a piece of aluminum straight between the pedal and the axis of rotation on the angled cranks. The leverage of the cranks would be the same whether the crank arm is straight, angled curved, or any other shape. The only thing that matters for leverage is how far the pedals, the source of the exerted force, is from the axis of rotation.

“This Z-crank has no redeeming features whatsoever,” Wilson said.

Coment's design isn't new, designs for curved or angled cranks have been around since the 1930s. He's had prototypes for his Z-Torque cranks since 1995, a patent on them since 1999, and a website selling aluminum versions since at least 2009. Recently he's been trying to expand and make carbon fiber versions. In September of last year, Coment launched a Kick-starter project to raise $50,000 to buy tools and equipment, but missed his goal by more than $47,000. He's now trying again, on a different crowd-funding website, "Rock the Post" with a more modest $7,500 goal.

The website also claims that the cranks give riders "Less perceived effort to pedal." In the medical world, I think they would call that a "placebo."

80 comments:

  1. What would really be great would be a leverage multiplier - such as you get with a block and tackle, or with the lever arm fixed to a large pulley which in turn transmits power via a belt to a smaller pulley. Hey, better yet, to ensure no belt slippage, use cogs and a chain. I can't wait until someone patents that idea and introduces it into bicycle design.

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    1. We have those they are called 'gears'

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    2. And the award for missed joke of the article goes to.. Anonymous!

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    3. Gee ya! Maybe they could even have sets of cogs and mechanisms to move the chain from one set to another for differing ratios! Wow, lets start a kickstarter!

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    4. http://static.themetapicture.com/media/funny-gif-kid-playing-with-water-hose.gif

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  2. That was my first impression, but there is angular momentum as well. If this structure allows significantly lighter crank arm I can see how it will result in less force.

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    Replies
    1. A longer crankarm is going to have more mass, not less.

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    2. You ignored the professor's physics and don't realize how little these cranks weigh and how much "momentum" has zero effect.

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  3. As a mechanical engineer, let's play the devil's advocate for a minute here.

    Look again at the Z-torque pedal. The inventor says it's intended to smooth-out the force at dead spots.

    My review shows that when you step on the Z-torque pedal at top dead center, the crank bends such that the hub advances slightly.

    See the diagram here:

    https://docs.google.com/file/d/0B7JD8P2oq0HoaElrMi1oY0lPaFk/edit

    Thoughts? Likes? Hates?

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    1. I neglected to include a link to another article about these cranks that addresses this issue of dead spots. Quoted from the Bicycle Museum of Bad Ideas

      "'Except for top dead center and bottom dead center, this crank had no dead spots.' [quoted from the Z-Torque website]
      True! Except for top dead center and bottom dead center, no crank has dead spots. And Z-Torque is just a crank."

      http://pardo.net/bike/pic/mobi/d.pmp-cranks/z-torque.html

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    2. No, but you might get a bit more give to the pedal from 3rd order effects like strain and displacement. Maybe that is the desirable feature.

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    3. Engineer here as well. Even if geometrically non-linear effects were not neglectable,which by the look of that crank and considering the average weight of a cyclist they certainly are, you forgot to notice that any geometrically non-linear effect that might be observed in the top dead center wouldn't dissapear. Instead, it would be observed in some degrees off the top dead center. This means that geometrically nonlinear effects don't change anything at all. The only thing that changes is where the equivalent dead center will be.

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    4. I guarantee that on my bike these cranks would be clanking the frame, if not broken to pieces in less than 10 revolutions.

      As a formerly competitive cyclist - I've bent/broken more than my share of cranks (and frames, and forks, and bars, and wheels).

      These cranks will fail at the z-bend, at the bottom of a stroke. They'll either bend - or worse, break.

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    5. Yeah they're gonna snap off. Because they're fucking stupid.

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    6. That's why cycles wear cleated shoes and flex their ankles through TDC and BDC, you can learn to ride one legged with them. Also I bet those Z-cranks would be very hairy in tight high-speed turns since they extend below the foot by quite a bit!

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  4. So my point is that while the inventor may have misidentified and/or overstated the effects or benefits of this design, there is at least one condition where it can be said to affect bicycle performance. Does the effect at bottom-dead-center nullify any benefit? Is the deflection too small to notice? Would the market be willing to add that much metal for this kind of difference? Investors still beware!

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    1. You are incorrect. There is NO such effect. The shape of the arm is utterly irrelevant. And any change in the balance of a crank arm, is exactly offset (and therefor nullified) by the opposing crank arm.

      This is nothing but a perfect example of Howe's Law: "Every man has a scheme that will not work."

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    2. Are these the bicycle equivalent of the mahogany load balancing disks that help to rectify your power output to a more soothing sine wave, and removes harsh over frequencies

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    3. @anon: Assuming a non-rigid crank arm changes the force profile, and the effect will be asymmetric because force application is asymmetric - a stiff non-linear spring will deflect far more on the stronger downstroke than on the upstroke.

      In addition the spring coefficient need not be symmetrical - if the angle can collapse easier than expand (or vice-versa) then the moment arm will be different at an angle of -x than it is at +x.

      Now I doubt the shown design flexes enough to be much of a factor, but it certainly is an interesting idea. What exactly would the effect be if, for example the crank arm were a couple inches shorter at the bottom of the stroke than at the top?

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    4. This has been done to death. There are crankset designs that reduce force at top and bottom and increase it at front and back. I was using Shimano Biopace chainrings back in the 90s that did this.

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    5. Does anybody think an aluminum crank should be designed to flex, or want one that does? What would the service life and failure mode be?

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    6. I'm just gonna point out some common sense here....anytime something gives, its going to absord energy that its not going to return at 100% to the system. Even if we ignore physics, the most this crap would do is steal power from a cyclist.


      this is why I detest mountain bikes for anything but mountain biking.

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  5. You know, I almost want to invest in the guy, because people really are that stupid.

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  6. Why can't we just field test it out if it's at least aesthetic but not more efficient?

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    1. The placebo effect, or even shills, will guarantee that a number of people will claim to notice a difference between the two.

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    2. Exactly. Some might even see some real improvement. I prefer the magic feather. Perhaps a smaller front wheel would let us ride downhill.

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    3. A smaller front wheel means you can simply roll up a small incline with no effort. Make the front wheel small enough and you can roll up quite a steep hill with no energy expended at all.

      Brought to you by the inventor of the Z crank.

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    4. That's why I always set my saddle up higher than the handlebar. I'm always going downhill, even when I'm going uphill.

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  7. He probably already has a bunch made and is just trying to dump them for anything he can get.

    Not sure why he has to make up benefits though. He should just say, "They look cool. Your friends will be amazed."

    Like spinners on cars, stupid but something to look twice at.

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  8. Replies
    1. I used to race with Biopace chainrings, they were good.

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    2. Ah, but you need to keep your chain tighteners in good order. If they are moving sluggishly, it is a recipe for tooth-jumping.

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    3. Love 'em or hate 'em, Biopace rings had real benefits that a rider could use.

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    4. Biopace was great for efficiency, but terrible on the mechanics of the human body in order to "spin" since some of the pros liked spinning. I still have a biopace ring on my mt. bike crank (low gear of course).

      Hence Oval rings we're the compromise.

      In the end, round was the best compromise.

      This Z crank has nothing to do with more leverage or being more efficient in the human anatomy dept. I have a bridge to sell as well...

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  9. Carbon, no less. At least when they shatter, the pieces sticking out of your shins will be a cool shape.

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  10. Oh yeah, not a new idea!

    http://pardo.net/bike/pic/mobi/d.pmp-cranks/index.html

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    Replies
    1. Hot Parody:

      http://web.archive.org/web/20010802141237/http://www.classicrendezvous.com/Rarest_pics3.htm

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  11. Compared to a standard crank, the Z frame appears to facilitate more stored energy and more rotational inertia.

    All that's left is to evaluate the metallurgy and quantify the improvement (double-blind) in terms of acceleration, speed, and expected life-span (e.g. strain-life fatigue)

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    1. Yes, when you have double the amount of material (mass) being propelled, it WILL store more energy.

      That energy is magically created... oh no wait... it's you pedaling. Oh good job. Now you're moving twice as much aluminum for zero gain. But yeah there's stored energy. That you put into it. So much for that.

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    2. "the Z frame appears to facilitate more stored energy and more rotational inertia. " No. Any engineer can take one look at the design and know that NOTHING is gained by this. Draw a strait line from the center of the main sprocket to the center axle of the pedal, and calculate the vector force needed to turn the main sprocket is exactly the same as for this design. NOTHING IS GAINED. If anything a little more force is needed due to the added mass of the extraneous crank design, but that's negligible. This is not difficult math, its pretty basic actually. Interesting that people look at a superficial change to a basic machine and think there's something new, useful, or novel in it.

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    3. Stored energy is BAD in a bicycle crank. You want it to TRANSMIT the energy, not store it.

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    4. "Compared to a standard crank, the Z frame appears to facilitate more stored energy and more rotational inertia. "

      You say that like it's been proven, or is obvious, or something. Evidence please? Facts? No? Thought so.

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    5. "You say that like it's been proven, or is obvious, or something. Evidence please? Facts? No? Thought so."

      I'm neither a physicist nor an engineer, but it seems kind of obvious to me. Tell me if I'm wrong, but it seems to me that any crank system acts as some kind of flywheel that stores a certain amount of energy. You can see this by disconnecting the chain and spinning it. It will spin for a while before it winds down.

      Adding a z-crank would most likely add more mass to this flywheel system, allowing it to store more energy. But it would also require more energy to start pedaling and more energy to stop pedaling. As a cyclist, this doesn't seem beneficial - I don't really want my pedals pushing my feet around any more than they have to. I'm also not interested in adding to the mass I'm carrying around on my bike.

      If this is the source of the benefit, then it could also be realized by simply adding more mass to a traditional straight crank - and without adding the bended parts that are likely to suffer more strain than a straight crank.

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    6. I don't want to live in this world anymore

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    7. I don't want to see this comment anywhere ever again.

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    8. You know what would be awesome? 15kg flywheels on bikes. They'll get you over the hills.

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  12. If this works the way he thinks, why didn't he extend the crank all the way back to center. That way he could get even more torque and not have to move at all!

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    1. Excellent point.

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    2. That is a good mental model. To expand on it. Imagine if the pedal was extended all the way back past the center. Now, step on the pedal. What direction does the chain ring rotate? Counter-clockwise! (aka, the wrong direction.)

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    3. Best reply here.

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  13. Not only are they not better, they are in fact WORSE than normal cranks. The longer z shape will be inherently heavier than a straight crank and the bent shape (especially with the sharp bent corner) will be inherently weaker then a straight crank.

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  14. If only there really _was_ some way to change your leverage when pedaling a bicycle.

    Oh wait: change gears.

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  15. Physics professor here: laughing my ass off. A problem along the lines of "Calculate the mechanical advantage of 'Z-Force' cranks" goes on my next midterm exam...

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  16. It's pretty clear that there's no net mechanical advantage to the 'Z-force' cranks, but it's also pretty clear, at least to me, that there is a difference between a straight crank and a Z crank.

    As someone quoted earlier, "Except for top dead center and bottom dead center, no crank has dead spots."
    (http://pardo.net/bike/pic/mobi/d.pmp-cranks/z-torque.html)

    The difference I'm noticing is that "dead center" on a straight crank aligns with gravity, and "dead center" on a Z-crank doesn't.

    Looking at the reproduced crank pressure graph, the overall energy transfer seems similar, but the pressure on the straight crank is higher at the bottom part of the stroke, whereas the pressure on the Z-crank is higher at the top part of the stroke.

    It's been a long time since I've done much physics or much cycling, so I don't know if what I'm noticing would make a net difference, but it does seem to me that it will make a noticeable difference in the feel of the stroke.

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  17. CallMeBob
    No Top Dead Center? What are we saying again? The crank arm flexes so that when the pedal axle is at maximum height that suddenly there's a lever arm that helps something?
    That "flex" is called "heat" which is "loss of mechanical energy".

    Gosh this is a stupid design. I can only hope z-torque convinces many stupid people to open their wallets for them.

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  18. The 1st of April already.....oh wait....eeh..it isn't

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  19. Simple test: Installing them backwards should have a negative impact.

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  20. Wow, and they claim it is patented. If that doesn't show how badly broken the patent system is...

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    Replies
    1. It could be a 'design' patent, with no functional value.

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    2. This thing has, in fact, been granted an actual US patent, not a design patent. Patent #5,899,119 granted 4 May 1999. http://www.google.com/patents/US5899119

      Best part is that "flexing" of the crank arm is specifically referenced in the patent as the enabling factor.

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  21. Let's see that placebo effect when you are cycling up hill for 10 minutes.

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  22. Too bad for this chucklehead I am a developing a far superior suite of torque-enhancing technologies that will revolutionize cycling. Ha ha! Get it? It's a pun. Anyway, I am also in need of cash for funding additional research and development of my brilliant idea. Since I trust you internet people not to usurp me on the way to the patent office, I will share with you the pith of my genius:

    1. Raise the seat way, way up. 2. Really long cranks. 3. Telescoping stilts which will be fitted to a specialized ProTorqueMaster(TM) ProCycling Shoe.

    And, I must say point three is the real pièce de résistance here. I had the first two figured out pretty early on, but their implementation proved to be somewhat problematic even in experimental settings.

    The ProTorqueMaster(TM) Telescopic ProCycling Stilts will feature an innovative lock-and-release mechanism powered by the force and motion of your very own legs as you pedal. Never before will cycling have been so effortless—and stylish! ProTorqueMaster(TM) Telescopic ProCycling Stilts will be available in XX-Treme Chrome, Traditional Polished Brass, and Premium Oxidized Steampunk Bronze with Actual Rust Accents.

    Send me money. Together we can conquer any supposed "physical limitions" scientists dream up!

    PROTORQUEMASTER. Make torque your b****.

    (Your buddy.)

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  23. not a engineer or physics person...but I noticed a comment earlier that said if you installed them backwards it would cause a negative effect...in my mind it seems to me that it would be a better design than it is now because it would be like a pulley system and lever system combined kinda like pulling on a rope attached to poll that's attached to a wheel creating more force by gravity and transferring from the pedal and lower arm to the upper arm and then to the center or wheel....basically they would be better put on backwards then they might work better...like I said not an expert

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  24. That's a thing of beauty, almost as good as the wind powered bike light I saw once.

    Ground clearance would be interesting on the mountain bikes on his website.

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  25. Why stop with the z shape? Wouldn't a very compact W shape increase the length of the lever even further? We could get two dimensional fractals and probably get a good 250 feet out of it. These are just quick calculations but I'm pretty sure that would mean upwards of 1200mph on a BMX bike. I think we could make millions here.

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  26. I would suspect that they are somewhat mushy feeling due to flex in the arm as the pedal spindle tries to twist the arm.
    Remember the pedal spindle acts as a lever too.
    This mushy feeling is probably the source of the perceived difference over a regular straight/stiff crank arm.
    A thin diameter titanium frame will feel "softer" than an over-sized aluminum one. This is often perceived as being more comfortable and easy to climb with. You are using more energy due to the flex, but the feel of Ti...OH the FEEL!

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  27. I'm sure that Obama will give him your tax dollars. This guy obviously doesn't understand even basic physics, but that hasn't stopped the idiot and chief from giving away your tax dollars before. Why should it stop him from doing it now... Of course after bankruptcy we'll be told by the media that no one could have foreseen this inevitable failure...

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    Replies
    1. -_- Not even on a physics article.......
      Just couldn't resist could you.

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  28. Assuming their data isn't an outright lie, is it possible that the benefits they claim to be seeing in testing actually have no bearing on the "crank" physics of the crank and more to utilizing a slightly differed combination of muscle groups because of the different placement of the pedal at certain points in each stroke?

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    1. No, because (ignoring flexure, added mass and the new and exciting failure mode) this is identical to a straight crank.

      Imagine if you decided to make this stronger without modifying the mechanical properties by joining the connection point for the pedal to the spindle. You then have a normal crank with this extra metal stuck to the side of it. Which you remove, to save weight. Now you have a normal crank.

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  29. Z-Tourque's next product: square wheels for better traction when climbing or descending. More tire on the road means better braking!

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    1. Don't knock the square wheel, it's proven to work... given the right road surface.

      http://www.sciencenews.org/view/generic/id/4877/description/Riding_on_Square_Wheels

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  30. I would love to try out your marvelous IDEA!!! But I am in the Netherlands, so I guess I do not qualify for that. I wish you the best luck. I love people with passion for what they do!! Caroline Kuhn

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  31. "The inventor, Glenn Coment, claims that his zig-zag design gives peddlers more leverage"

    From that alone it is obvious crankery. Only if the pedal, the place where the force is applied, is further from the pivot will you get more leverage. Here's a thought experiment: Take a regular crank and add to it a "z-arm" so it is like a triangle? Do you get more leverage? Take away the original crank arm so you are left with just the z. Do you now get more leverage?

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  32. Guess he should go pedal his bs somewhere else...

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  33. I actually had this same idea several years ago. Then I built a simple prototype out of wood, tested it, and saw that it didn't do squat. Apparently my second thought should have been, "Don't test it, just build it and charge money for it."

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  34. Unfortunitly Jason has it all wrong as to how this crank works. The crank does not give you more leverage. It gives you a high pressure at the chain wheel for a longer period of time. A straight traditional crank during the, "dead spot",(the first 60 degrees of rotation),wastes most of your effort by sending it down the arm to the axle instead of turning the assembly. Remember when you first learned to ride a bike. If you pushed down to soon you picked yourself right up off the bike. Look at the Z-torque in the picture.The long part attached to the axle of the bottom bracket is the real working crank arm. An arm moving out of the"dead spot" when the pedal is at Top dead center. When the small part of the crank arm that runs from the end of this "real" crank arm to the pedal is made at the correct angle and length,it directs your effort away from the axle of the bottom bracket.This allows you to apply all your effort sooner. Increasing your momentum and power. A Z-torque only has a "dead Spot" right at Top Dead Center,(TDC),and Bottom Dead Center,(BDC). Anywhere else you can push down or pull up with all your effort. IT' LIKE TAKING A LONGER SWING WITH A BASEBALL BAT. MORE OF YOUR EFFORT IS EFFICIENTLY TRANSFERRED TO THE BICYCLE. I hope this clears up some of your questions.

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  35. From this perspective, steam locomotives are like huge powerful bicycles with steam-driven "pedals" {main rods]. The potentially crippling dead spot was countered with a 90-degree offset between the R & L main rods. If a Z-shaped eccentric crank would have afforded more power, this would have been the time & place for it with money riding on the discovery. (And toss eccentric crank into delightful stack of puns in this wonderful thread.)

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  36. There's a much more efficient way of getting your bike to go faster/make the effort of biking feel easier.
    It's called "TRAINING." Try two/three hundred miles per week, 50% cruising, 50% 'flat out."

    (And I am a robot, so why do I have to prove it to some idiot who wants me to waste my time deciphering hs idiot word?)

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