4 ms·

The math and physics and engineering behind bicycles is so cool. Such a "simple" device, but so many interesting things to dive into. I wrote my thesis on spoke

The math and physics and engineering behind bicycles is so cool. Such a "simple" device, but so many interesting things to dive into. I wrote my thesis on spoke patterns for the wheels [0]. Another cool thing is how the steering of a bicycle works. You don't really turn the way you want to, you actually turn the other way first to initiate so the bike moves from under you, and you then lean the other way to actually turn. This is why, if you're for instance biking close to a curb and want to get away from it, you really can't and it feels like the curb is "sucking" you closer and closer. Since it "feels" wrong to first turn towards it, but without doing that you actually can't get away from it. [0]: https://news.ycombinator.com/item?id=10410813 https://news.ycombinator.com/item?id=10410813

sam_lowry_ 4y ago
While cyclists learn to turn intuitively, motorcyclists have internalized this knowledge. The avoidance maneuver is part of motorcycle license tests in many countries.
thunderrabbit 4y ago
Wow! This explains the trouble I've had trying to ride with the end of my handlebar sliding along a smooth wall near the sidewalk. Thank you!
- matsemann 4y ago
  I found this short video that very nicely describes what I tried to say with words: https://youtu.be/llRkf1fnNDM https://youtu.be/llRkf1fnNDM
- giraffe_lady 4y ago
  Also about half the time when you hear about a cyclist dying because they "lost control of the bike" in traffic this is what happened. Car passes slow and too close to give you room to countersteer and you fall into and then under it.
michaelteter 4y ago
I have taught several kids to ride bikes. My instructions were very simple: ride, and if the bike starts tipping to one side, turn the handlebars that way. With humans, that's about all you need to say. You very quickly feel how the lean changes based on the steering input, so righting yourself becomes obvious. And when you inevitably overdo it and end up leaning the opposite way, you turn the bars that new direction. WOBBLE WOBble wobble straight.
- itronitron 4y ago
  Do the same steering physics apply to riding a bicycle on rollers? That's so much more difficult I wouldn't be surprised if the fundamental steering behavior is changed somehow.
  - sritchie 4y ago
    Iirc what makes rollers so tough is that the contact patch is much shorter on the roller than on the road, so the wheel turns more easily. Your reactions need to be that much quicker. I had a winter of long roller rides (3.5 hours was the longest) and by the time I hit the road again I could ride on the white line with no effort. I think the dynamics are the same, just higher stakes on the rollers!
    - samstave 4y ago
      This is one of the challenges of riding on such a thin (narrow) line (like a plank - or even just the painted line on the side of the road) is so difficult. The thing is that in order keep a srtraight line on a very narrow path, you need much finer motor control of your arms, a good 'feel' for your bike, some good components, and the ability to remember to be able to look farther in front of the bike, but keep your awareness of where you are steering based on your inputs to the bike, but not looking down. If you want to be impressed by one of the best in the world at steering difficult scary /r/sweatypalms courses: https://www.youtube.com/channel/UC9kOkY1nYc0uADWRiRH64Rw https://www.youtube.com/channel/UC9kOkY1nYc0uADWRiRH64Rw Watch the "do a wheeelie" vid on his YT home -- doing a wheelie on a train-rail, and jumping to the other train-rail without losing your wheelie or momentum - but all his vids are mind blowing.
alhirzel 4y ago
The way this is described in a control systems framework is that the dynamics are non-minimum phase. A cool high-level video from Mathworks[1] explains in more mathematical detail. Being an experienced rider but having not looked into bicycle models in detail, I think it would make intuitive sense if the dynamics were only NMP for some operating points, particularly very low roll rates at very low roll angles. Or equivalently, the system behaves differently when it's in a banked turn (moderate roll with low roll rates) because gravity is starting to couple into the steering more. There is an angle where the steering switches modes depending on the geometry of the bike, and I think this is why road bikes "feel" "twitcher". [1]: https://www.youtube.com/watch?v=jGEkmDRsq_M https://www.youtube.com/watch?v=jGEkmDRsq_M Edit - also OP, very cool thesis work!
- kevin_thibedeau 4y ago
  Road bikes are twitchier because they have less trail. Even 25 year old MTBs are twitchy compared to modern equivalents succumbed to the fashion for negative stem lengths and slack head tubes trying to imitate DH bikes.
  - alhirzel 4y ago
    Good point and makes sense - probably the reduced trail dominates most of the feel. I wish I had time to dive into a model to see if there really is any non-minimum-phase behavior. Also, I skimmed the following to help my understanding; others may find it useful too: https://www.cyclingtips.com/2018/11/the-geometry-of-bike-handling-its-all-about-the-steering/ https://www.cyclingtips.com/2018/11/the-geometry-of-bike-han...
mc32 4y ago
There are people who can ride bikes on rails. I would not be able to do that. It seems impossible, but I guess they are able to minimize the amplitude of deviation from straight to such a low value they can correct tiny deviations with shifting their weight and manoeuvering the front wheel.
kqr 4y ago
This is also why it's impossible to balance a bike without at least a tiny amount of speed. (Even a trackstand that looks completely still uses tiny amounts of forward and backward wiggle to allow the bike to move sideways under the rider.) The handlebars aren't really used to steer the bike, the way most people think of steering. What they do is shift the bicycle further away from under the rider, which then, due to the bicycles naturally self-stabilising, steer to upright itself.
xtiansimon 4y ago
Well, that explains why I did an endo riding my bike down the ramp of a Ryder box truck when my tire hit the edge of the ramp—fortunately I was wearing my wool beanie. It was Burning Man, 1998. Seemed like a good idea at the time

sam_lowry_ 4y ago

While cyclists learn to turn intuitively, motorcyclists have internalized this knowledge. The avoidance maneuver is part of motorcycle license tests in many countries.

thunderrabbit 4y ago

Wow! This explains the trouble I've had trying to ride with the end of my handlebar sliding along a smooth wall near the sidewalk. Thank you!

matsemann 4y ago
I found this short video that very nicely describes what I tried to say with words: https://youtu.be/llRkf1fnNDM https://youtu.be/llRkf1fnNDM
giraffe_lady 4y ago
Also about half the time when you hear about a cyclist dying because they "lost control of the bike" in traffic this is what happened. Car passes slow and too close to give you room to countersteer and you fall into and then under it.

michaelteter 4y ago

I have taught several kids to ride bikes. My instructions were very simple: ride, and if the bike starts tipping to one side, turn the handlebars that way. With humans, that's about all you need to say. You very quickly feel how the lean changes based on the steering input, so righting yourself becomes obvious. And when you inevitably overdo it and end up leaning the opposite way, you turn the bars that new direction. WOBBLE WOBble wobble straight.

itronitron 4y ago
Do the same steering physics apply to riding a bicycle on rollers? That's so much more difficult I wouldn't be surprised if the fundamental steering behavior is changed somehow.
- sritchie 4y ago
  Iirc what makes rollers so tough is that the contact patch is much shorter on the roller than on the road, so the wheel turns more easily. Your reactions need to be that much quicker. I had a winter of long roller rides (3.5 hours was the longest) and by the time I hit the road again I could ride on the white line with no effort. I think the dynamics are the same, just higher stakes on the rollers!
  - samstave 4y ago
    This is one of the challenges of riding on such a thin (narrow) line (like a plank - or even just the painted line on the side of the road) is so difficult. The thing is that in order keep a srtraight line on a very narrow path, you need much finer motor control of your arms, a good 'feel' for your bike, some good components, and the ability to remember to be able to look farther in front of the bike, but keep your awareness of where you are steering based on your inputs to the bike, but not looking down. If you want to be impressed by one of the best in the world at steering difficult scary /r/sweatypalms courses: https://www.youtube.com/channel/UC9kOkY1nYc0uADWRiRH64Rw https://www.youtube.com/channel/UC9kOkY1nYc0uADWRiRH64Rw Watch the "do a wheeelie" vid on his YT home -- doing a wheelie on a train-rail, and jumping to the other train-rail without losing your wheelie or momentum - but all his vids are mind blowing.

alhirzel 4y ago

The way this is described in a control systems framework is that the dynamics are non-minimum phase. A cool high-level video from Mathworks[1] explains in more mathematical detail. Being an experienced rider but having not looked into bicycle models in detail, I think it would make intuitive sense if the dynamics were only NMP for some operating points, particularly very low roll rates at very low roll angles. Or equivalently, the system behaves differently when it's in a banked turn (moderate roll with low roll rates) because gravity is starting to couple into the steering more. There is an angle where the steering switches modes depending on the geometry of the bike, and I think this is why road bikes "feel" "twitcher". [1]: https://www.youtube.com/watch?v=jGEkmDRsq_M https://www.youtube.com/watch?v=jGEkmDRsq_M Edit - also OP, very cool thesis work!

kevin_thibedeau 4y ago
Road bikes are twitchier because they have less trail. Even 25 year old MTBs are twitchy compared to modern equivalents succumbed to the fashion for negative stem lengths and slack head tubes trying to imitate DH bikes.
- alhirzel 4y ago
  Good point and makes sense - probably the reduced trail dominates most of the feel. I wish I had time to dive into a model to see if there really is any non-minimum-phase behavior. Also, I skimmed the following to help my understanding; others may find it useful too: https://www.cyclingtips.com/2018/11/the-geometry-of-bike-handling-its-all-about-the-steering/ https://www.cyclingtips.com/2018/11/the-geometry-of-bike-han...

mc32 4y ago

There are people who can ride bikes on rails. I would not be able to do that. It seems impossible, but I guess they are able to minimize the amplitude of deviation from straight to such a low value they can correct tiny deviations with shifting their weight and manoeuvering the front wheel.

kqr 4y ago

This is also why it's impossible to balance a bike without at least a tiny amount of speed. (Even a trackstand that looks completely still uses tiny amounts of forward and backward wiggle to allow the bike to move sideways under the rider.) The handlebars aren't really used to steer the bike, the way most people think of steering. What they do is shift the bicycle further away from under the rider, which then, due to the bicycles naturally self-stabilising, steer to upright itself.

xtiansimon 4y ago

Well, that explains why I did an endo riding my bike down the ramp of a Ryder box truck when my tire hit the edge of the ramp—fortunately I was wearing my wool beanie. It was Burning Man, 1998. Seemed like a good idea at the time