9 ms·

Fresh work on the mathematics of bicycles in motion

165 points by maximz 10y ago

dang 10y ago
We changed this title to something less baity than the original (et tu, Nature?). If someone suggests a better (more accurate and neutral) title, we can change it again.
- nitrogen 10y ago
  Pretty soon all of human language will consist of phrases like, "You won't believe what happens when this one weird news aggregator changes a submission title!" Is there some way we can try to reverse this trend outside of HN?
sdkjfwiluf 10y ago
what was the conclusion ? it's not gyroscopic effects because they still balance with counter-rotating wheels, it's not trail because they can still balance with negative trail. Is it some of each of these effects, if so how much ? What else is involved ?
- jessaustin 10y ago
  According to TFA (and to this avid cyclist it makes sense) it is the combination of the two effects you mention and weight distribution. Novel bikes can be constructed that tweak one of these inputs into an unsuitable range and yet still balance, but I really doubt you could mess up all three and still have a bicycle.
- sliverstorm 10y ago
  I think negative trail works pretty much the same way as positive trail; I think the question is, does a bike with zero trail work. I'm guessing it can be done, but experience with various motorcycles (which have a wide range of rake) suggest trail is desirable for other reasons too.
- IshKebab 10y ago
  Well I haven't read the article (sorry), but on a bike with a rider you balance by active feedback. If you steer the way you are falling to right yourself.
mmf 10y ago
How complex can it be? If you have a bare minimum background in basic physics and control theory, and a bicycle in your hands, the qualitative reasons for balance and stability will jump at you in under 10 minutes...
- Meegul 10y ago
  Alright then, what are the reasons for bicycles being balanced? If it's not anything related to gyroscopic effects, then what is it?
  - mmf 10y ago
    Ok, I guess I could have provided more info. Do this if you own a bicycle: hold it by the saddle perfectly straight, front of the bike forward. Make it lean on the left (no forward movement). Look at the handle, it steers left. When you're moving this means that when you lean left there will be a torque, due to your circular path you'll be following, that will try to make the bike lean right. Bend left -> torque to the right, bend right -> torque to the left. Here you have the basic ingredient for stability: the one torqueless angle is the bike going straight perfectly vertical wrt the ground, while any perturbation leads to a torque in the opposite direction. I felt it was basic stuff maybe it's not?
- jackmott 10y ago
  ok, go on.
- dang 10y ago
  Please don't post unsubstantive dismissals of others' work to HN. If you know more than the rest of us, it would be good to post an informative comment that teaches the reader something. If you don't want to do that, it's fine to post nothing.
  - mmf 10y ago
    If you feel that something is trivial and potentially wasting other people's time by means of wasting pixels, I think it's fine to speak up. (Explaining why something is trivial may not be that effective, in general). I was clearly wrong in that many people disagreed and found this to be an interesting and nontrivial subject.
sevenless 10y ago
It might help if they program humanoid robots to ride bikes. The problem seems to be hard to analyze because there's a person on the bike, and the way the person moves with the bike is hard to track.
- dskhatri 10y ago
  See Murata's Robots: http://www.murata.com/en-us/about/mboymgirl http://www.murata.com/en-us/about/mboymgirl
  - sevenless 10y ago
    That's cool, but the robot there needs a large gyro stabilizer disc to keep balance. Not exactly the way we do it.
- speps 10y ago
  Like this? http://www.cc.gatech.edu/~jtan34/project/learningBicycleStunts.html http://www.cc.gatech.edu/~jtan34/project/learningBicycleStun...
- etib 10y ago
  I believe thats already been done http://global.yamaha-motor.com/showroom/event/2015tokyomotorshow/sp/exhibitionmodels/mgp/ http://global.yamaha-motor.com/showroom/event/2015tokyomotor...
no_flags 10y ago
Avid cyclist, but I have no idea what this is talking about: "...the phenomenon of 'countersteering', whereby the rider can steer to the left only by first briefly torquing the handlebars to the right, allowing the bike to fall into a leftward lean." Am I just doing this subconsciously?
- artimaeis 10y ago
  I've never noticed this on bicycles, but I also haven't ridden anything but a stationary in 5+ years now! But this is very noticeable in motorcycles. Most riders don't really think about the torque they're applying to the handlebars, but when you lean into a turn you're definitely applying that torque to the handlebars. You're kind of putting the side of the wheel to the ground in the process, and the only way to put the side you want to turn to towards the ground is to torque the handlebars in the opposite direction.
  - sliverstorm 10y ago
    I don't know why it's so much more important in motorcycles- even riders who have ridden bikes for many years like myself benefit from pointed instruction in "press right to go right". Perhaps because the rake is so much greater, it's not a natural, immediate carryover from bicycles. Or perhaps because the motorcycle is much heavier, handlebar input becomes all the more important, relative to a bicycle you can steer with your body.
    - CydeWeys 10y ago
      It's that the motorcycle is much heavier. You need to countersteer first to get the wheels out from under the center of mass of the motorcycle, in order to initiate the lean in the opposite direction. A bicycle is much lighter so you muscle it around more solely by moving your body, which significantly outmasses the bike.
    - draven 10y ago
      > even riders who have ridden bikes for many years like myself benefit from pointed instruction in "press right to go right". I was taught that 2 hours into my training when I prepared for the exam to get my license. I remember my instructor telling me to ride in straight lines and try to gently push the handlebar to the left or right and "see what happens." Then he would make me try the slalom part of the exam. I sometimes let go of the handlebar (when decelerating and when there's no traffic around me) and it takes a lot more effort to make minor adjustments to the trajectory by shifting my weight only.
abakker 10y ago
OK - this is probably my ignorance talking, but why is it surprising that bike are balanced? The pedals are basically shoulder width and staggered, which is a very natural position for people to balance in as bipedal creatures? in addition, while the bike is moving, won't the inertia tend to keep things moving in the same direction? This is all coupled by the fact that the rider is actively piloting and adjusting the bike to keep it under control at all times. The bike seems like it would balance to me because the control mechanisms are designed to keep things balanced easily.
- jackmott 10y ago
  bikes are balanced without a person on them
- deleted 10y ago
  [deleted]
- nathanielc 10y ago
  Bike are balanced and symmetric side-to-side. Top to bottom they are not, obviously. The center of mass is above the ground , so a bike that is not moving will fall over to lower its center of mass. But this doesn't happen if the bike is moving. Push a bike without a rider and it will travel for a few feet without falling over, and take longer to fall over if just left standing still.
  - Someone 10y ago
    The surprising thing is that it is way more than "a few feet". Apologies for repeating myself, but watch https://www.youtube.com/watch?v=oZAc5t2lkvo https://www.youtube.com/watch?v=oZAc5t2lkvo (And that is not on smooth terrain) And nitpick: typical bicycles aren't symmetric left-right. The chain and gears make them heavier at the right. Most mass is close to the center line, though, so its moment is negligible, especially when ridden by a human.
- malz 10y ago
  It's surprising to the extent that: balancing on a non-moving bicycle is hard. Riding a unicycle is hard. Riding a bike is easy.
maaaats 10y ago
> ...an ambitious effort that would investigate everything from the strength of wheels... My master touched this. Used AI to find spoke patterns. http://master.matsemann.com http://master.matsemann.com > There were untested geometries out there that could transform bike design. Better hardware and simulations makes it easier to test thousands of these, possibly with the help of AI. I wonder if any drastically new designs will be found in the feature, or if time will show the current design is the best.
- fiftyacorn 10y ago
  Thats an interesting pattern - but the issue is how would you true a wheel like that?
icc97 10y ago
If nothing else I find it quite fascinating how some bikes are easier to ride without holding the handle bars than others. I can balance much better on my 1998 Specialized Stumpjumper mountain bike (comfortable for minutes without hands) than I can on my 1998 Cannondale R900 racing bike (max 5 seconds without hand). But for my colleague - he finds it much easier to balance his racing bike. As the article suggest - the hope is that this will provide better guidelines for building bikes that are more stable. The balance on my mountain bike definitely saved me from two near crashes of a knock to my rear wheel by a u-turning car and being hit on the handle bars by a wing mirror.
- willis77 10y ago
  Some bikes that are hard to ride no-handed have "notched"/"indexed" headsets that are to blame. Small indentations in the headset prevent minor corrections from actually turning the wheel, making it hard to let go of the bars. http://www.sheldonbrown.com/headsets.html#troubleshooting http://www.sheldonbrown.com/headsets.html#troubleshooting (see section on "Indexed Steering")
  - etcet 10y ago
    Thank you so much. My bike has been exhibiting this behavior but I just assumed the headset was designed to 'clip' into place. Looks like I need to see the mechanic.
- davidw 10y ago
  Peter Sagan showing how well some people can ride with no hands: https://streamable.com/2u94 https://streamable.com/2u94 (From today's stage of the Tour de France)
  - theOnliest 10y ago
    And Ilnur Zakarin (also from today's stage) showing how others aren't as good! Starting at about 2:00 in: http://www.dailymotion.com/video/x4l18sa_flamme-rouge-etape-17-berne-finhaut-emosson-tour-de-france-2016_sport http://www.dailymotion.com/video/x4l18sa_flamme-rouge-etape-...
bcook 10y ago
Regarding countersteering & bicycles (and motorcycles), I better understood the phenomenon by picturing a bar shoved horizontally through a basketball. You can steer by either turning the basketball (horizontal plane) or leaning the basketball (vertical plane). In the case of a motorcycle at speed, the bike's effective turning radius is affected more by the lean than by how much the handle-bars are turned. The handle-bars are more about controlling the amount lean.

165 points by maximz 10y ago

dang 10y ago

We changed this title to something less baity than the original (et tu, Nature?). If someone suggests a better (more accurate and neutral) title, we can change it again.

nitrogen 10y ago
Pretty soon all of human language will consist of phrases like, "You won't believe what happens when this one weird news aggregator changes a submission title!" Is there some way we can try to reverse this trend outside of HN?

sdkjfwiluf 10y ago

what was the conclusion ? it's not gyroscopic effects because they still balance with counter-rotating wheels, it's not trail because they can still balance with negative trail. Is it some of each of these effects, if so how much ? What else is involved ?

jessaustin 10y ago
According to TFA (and to this avid cyclist it makes sense) it is the combination of the two effects you mention and weight distribution. Novel bikes can be constructed that tweak one of these inputs into an unsuitable range and yet still balance, but I really doubt you could mess up all three and still have a bicycle.
sliverstorm 10y ago
I think negative trail works pretty much the same way as positive trail; I think the question is, does a bike with zero trail work. I'm guessing it can be done, but experience with various motorcycles (which have a wide range of rake) suggest trail is desirable for other reasons too.
IshKebab 10y ago
Well I haven't read the article (sorry), but on a bike with a rider you balance by active feedback. If you steer the way you are falling to right yourself.

mmf 10y ago

How complex can it be? If you have a bare minimum background in basic physics and control theory, and a bicycle in your hands, the qualitative reasons for balance and stability will jump at you in under 10 minutes...

Meegul 10y ago
Alright then, what are the reasons for bicycles being balanced? If it's not anything related to gyroscopic effects, then what is it?
- mmf 10y ago
  Ok, I guess I could have provided more info. Do this if you own a bicycle: hold it by the saddle perfectly straight, front of the bike forward. Make it lean on the left (no forward movement). Look at the handle, it steers left. When you're moving this means that when you lean left there will be a torque, due to your circular path you'll be following, that will try to make the bike lean right. Bend left -> torque to the right, bend right -> torque to the left. Here you have the basic ingredient for stability: the one torqueless angle is the bike going straight perfectly vertical wrt the ground, while any perturbation leads to a torque in the opposite direction. I felt it was basic stuff maybe it's not?
jackmott 10y ago
ok, go on.
dang 10y ago
Please don't post unsubstantive dismissals of others' work to HN. If you know more than the rest of us, it would be good to post an informative comment that teaches the reader something. If you don't want to do that, it's fine to post nothing.
- mmf 10y ago
  If you feel that something is trivial and potentially wasting other people's time by means of wasting pixels, I think it's fine to speak up. (Explaining why something is trivial may not be that effective, in general). I was clearly wrong in that many people disagreed and found this to be an interesting and nontrivial subject.

sevenless 10y ago

It might help if they program humanoid robots to ride bikes. The problem seems to be hard to analyze because there's a person on the bike, and the way the person moves with the bike is hard to track.

dskhatri 10y ago
See Murata's Robots: http://www.murata.com/en-us/about/mboymgirl http://www.murata.com/en-us/about/mboymgirl
- sevenless 10y ago
  That's cool, but the robot there needs a large gyro stabilizer disc to keep balance. Not exactly the way we do it.
speps 10y ago
Like this? http://www.cc.gatech.edu/~jtan34/project/learningBicycleStunts.html http://www.cc.gatech.edu/~jtan34/project/learningBicycleStun...
etib 10y ago
I believe thats already been done http://global.yamaha-motor.com/showroom/event/2015tokyomotorshow/sp/exhibitionmodels/mgp/ http://global.yamaha-motor.com/showroom/event/2015tokyomotor...

no_flags 10y ago

Avid cyclist, but I have no idea what this is talking about: "...the phenomenon of 'countersteering', whereby the rider can steer to the left only by first briefly torquing the handlebars to the right, allowing the bike to fall into a leftward lean." Am I just doing this subconsciously?

artimaeis 10y ago
I've never noticed this on bicycles, but I also haven't ridden anything but a stationary in 5+ years now! But this is very noticeable in motorcycles. Most riders don't really think about the torque they're applying to the handlebars, but when you lean into a turn you're definitely applying that torque to the handlebars. You're kind of putting the side of the wheel to the ground in the process, and the only way to put the side you want to turn to towards the ground is to torque the handlebars in the opposite direction.
- sliverstorm 10y ago
  I don't know why it's so much more important in motorcycles- even riders who have ridden bikes for many years like myself benefit from pointed instruction in "press right to go right". Perhaps because the rake is so much greater, it's not a natural, immediate carryover from bicycles. Or perhaps because the motorcycle is much heavier, handlebar input becomes all the more important, relative to a bicycle you can steer with your body.
  - CydeWeys 10y ago
    It's that the motorcycle is much heavier. You need to countersteer first to get the wheels out from under the center of mass of the motorcycle, in order to initiate the lean in the opposite direction. A bicycle is much lighter so you muscle it around more solely by moving your body, which significantly outmasses the bike.
  - draven 10y ago
    > even riders who have ridden bikes for many years like myself benefit from pointed instruction in "press right to go right". I was taught that 2 hours into my training when I prepared for the exam to get my license. I remember my instructor telling me to ride in straight lines and try to gently push the handlebar to the left or right and "see what happens." Then he would make me try the slalom part of the exam. I sometimes let go of the handlebar (when decelerating and when there's no traffic around me) and it takes a lot more effort to make minor adjustments to the trajectory by shifting my weight only.

abakker 10y ago

OK - this is probably my ignorance talking, but why is it surprising that bike are balanced? The pedals are basically shoulder width and staggered, which is a very natural position for people to balance in as bipedal creatures? in addition, while the bike is moving, won't the inertia tend to keep things moving in the same direction? This is all coupled by the fact that the rider is actively piloting and adjusting the bike to keep it under control at all times. The bike seems like it would balance to me because the control mechanisms are designed to keep things balanced easily.

jackmott 10y ago
bikes are balanced without a person on them
deleted 10y ago
[deleted]
nathanielc 10y ago
Bike are balanced and symmetric side-to-side. Top to bottom they are not, obviously. The center of mass is above the ground , so a bike that is not moving will fall over to lower its center of mass. But this doesn't happen if the bike is moving. Push a bike without a rider and it will travel for a few feet without falling over, and take longer to fall over if just left standing still.
- Someone 10y ago
  The surprising thing is that it is way more than "a few feet". Apologies for repeating myself, but watch https://www.youtube.com/watch?v=oZAc5t2lkvo https://www.youtube.com/watch?v=oZAc5t2lkvo (And that is not on smooth terrain) And nitpick: typical bicycles aren't symmetric left-right. The chain and gears make them heavier at the right. Most mass is close to the center line, though, so its moment is negligible, especially when ridden by a human.
malz 10y ago
It's surprising to the extent that: balancing on a non-moving bicycle is hard. Riding a unicycle is hard. Riding a bike is easy.

maaaats 10y ago

> ...an ambitious effort that would investigate everything from the strength of wheels... My master touched this. Used AI to find spoke patterns. http://master.matsemann.com http://master.matsemann.com > There were untested geometries out there that could transform bike design. Better hardware and simulations makes it easier to test thousands of these, possibly with the help of AI. I wonder if any drastically new designs will be found in the feature, or if time will show the current design is the best.

fiftyacorn 10y ago
Thats an interesting pattern - but the issue is how would you true a wheel like that?

icc97 10y ago

If nothing else I find it quite fascinating how some bikes are easier to ride without holding the handle bars than others. I can balance much better on my 1998 Specialized Stumpjumper mountain bike (comfortable for minutes without hands) than I can on my 1998 Cannondale R900 racing bike (max 5 seconds without hand). But for my colleague - he finds it much easier to balance his racing bike. As the article suggest - the hope is that this will provide better guidelines for building bikes that are more stable. The balance on my mountain bike definitely saved me from two near crashes of a knock to my rear wheel by a u-turning car and being hit on the handle bars by a wing mirror.

willis77 10y ago
Some bikes that are hard to ride no-handed have "notched"/"indexed" headsets that are to blame. Small indentations in the headset prevent minor corrections from actually turning the wheel, making it hard to let go of the bars. http://www.sheldonbrown.com/headsets.html#troubleshooting http://www.sheldonbrown.com/headsets.html#troubleshooting (see section on "Indexed Steering")
- etcet 10y ago
  Thank you so much. My bike has been exhibiting this behavior but I just assumed the headset was designed to 'clip' into place. Looks like I need to see the mechanic.
davidw 10y ago
Peter Sagan showing how well some people can ride with no hands: https://streamable.com/2u94 https://streamable.com/2u94 (From today's stage of the Tour de France)
- theOnliest 10y ago
  And Ilnur Zakarin (also from today's stage) showing how others aren't as good! Starting at about 2:00 in: http://www.dailymotion.com/video/x4l18sa_flamme-rouge-etape-17-berne-finhaut-emosson-tour-de-france-2016_sport http://www.dailymotion.com/video/x4l18sa_flamme-rouge-etape-...

bcook 10y ago

Regarding countersteering & bicycles (and motorcycles), I better understood the phenomenon by picturing a bar shoved horizontally through a basketball. You can steer by either turning the basketball (horizontal plane) or leaning the basketball (vertical plane). In the case of a motorcycle at speed, the bike's effective turning radius is affected more by the lean than by how much the handle-bars are turned. The handle-bars are more about controlling the amount lean.