Electric unicycle and bicycle dynamics - gyro effects on steering

[yoos]

@rcgldr there is probably some misunderstanding due to different terminology. I am saying there is a non-zero torque vector M. This vector points along the direction of movement (of the center of the mass). Then there is a vector of angular momentum L. If the wheel was rolling straight it would point along the wheel axis. Since the wheel slowly turns, there is also a small vertical component. If the lean angle does not change then M⊥L. Hence, by virtue of ∂_tL=M we have |L|=const and its direction changes at a constant rate -- that is precisely precession.

[rcgldr]

34 minutes ago, Planemo said:

I'm not sure who your post was aimed at, but the above is also what I said.

I've built many RC helicopters over the years, the first one did indeed have me scratching my head as to why the cyclic inputs had to be setup 90 degrees out of phase... 

Yes, and further makes my comment that humans are amazing to be able to ride an EUC from zero up to 45+mph. We haven't even looked at the results of the precession caused by the motor torque inputs which our brains also subconsciously deal with 

My post was not aimed at you. It was meant to further clarify my original post. Yeah, helicopter cyclic need to be advanced 90 degrees (some swash plate setups take care of much of this). I'm an old guy (69 years), having ridden motorcycles since the mid 1960's, learned about counter-steering in 1968 (you literally steer the tires outwards to lean inwards, and since most bikes tend to self correct back to vertical some counter-steering torque is needed to maintain and|or adjust lean angle).

I'm a beginner to EUC, and for me, it helped to have a basic understanding of how an EUC is able to turn. I use two methods, yaw | arm fail steer, (flail left to steer right and vice versa) for low speed (less than 5 mph), and for normal speed (5 mph or more) foot steer, move inside foot down, outside foot up to lean the EUC, relying on camber effect, so that a leaned EUC is steering me, instead of me steering the EUC. Not having any idea of how much camber effect a V8F would have, I did subtle lean changes to see how it would respond, weaving left and right, eventually progressing into mild carving. I'm still having to make some mid turn corrections with foot steering, not quite coordinating my body lean angle with with my steering | EUC lean angle, but I'm able to steer it where I want it to go, and making progress on this.

Motor torque is in the direction of travel, so it should not contribute to precession. From what I've read, part of the hub of an EUC wheel is the motor's rotor. On a side note, to allow motorcycles to change lean angle quicker, some have the engine rotating backwards to counter the angular momentum in the wheels to make them more "flickable"

Edited August 12, 2021 by rcgldr
motor torque

[rcgldr]

2 hours ago, yoos said:

@rcgldr there is probably some misunderstanding due to different terminology. I am saying there is a non-zero torque vector M. This vector points along the direction of movement (of the center of the mass). Then there is a vector of angular momentum L. If the wheel was rolling straight it would point along the wheel axis. Since the wheel slowly turns, there is also a small vertical component. If the lean angle does not change then M⊥L. Hence, by virtue of ∂_tL=M we have |L|=const and its direction changes at a constant rate -- that is precisely precession.

I'm guessing that your point is that precession in response to yaw (vertical) rotation would counter a small non-zero torque about the roll axis so that the lean angle is not changing, but the rate of yaw is slow for other than very small radius turns. This would translate into a small non-zero torque about the roll axis that is being countered by a small roll precession reaction to a slow rate of yaw. That small amount of torque about the roll axis would translate into a small amount of precession about the yaw (vertical | steering) axis, depending on the slow rate of yaw and the angular momentum of the wheel, which is being resisted by the combined angular inertia of rider and EUC. Nearly all of the steering (yaw rotation) response will be due to camber effect, with only a small fraction being related to that small precession effect. I don't know the math for EUC, but it is possible that small amount of precession is slower than the steering response to camber effect, in which case, the precession is actually opposing the steering reaction of camber effect. This is the case for motorcycle steering at higher speeds, the rate of precession is slower than the lean induced steering reaction related to trail, impeding the reaction, along with angular momentum of the front wheel, which also impedes the lean induced steering reaction.

Edited August 12, 2021 by rcgldr
updated response

[RockyTop]

Think of a hockey skater with only one skate........ 

Think of a drive shaft. Your ankle is a universal joint. Your body is a heavy shaft when you lean to the right and turn your body like a drive shaft you have leverage to turn. Your body is not above and parallel to the pivot point making it easier for the wheel to turn than your body to pivot around to the front. 

Edited August 12, 2021 by RockyTop

[rcgldr]

3 hours ago, RockyTop said:

Think of a hockey skater with only one skate........ 

Think of a drive shaft. Your ankle is a universal joint. Your body is a heavy shaft when you lean to the right and turn your body like a drive shaft you have leverage to turn. Your body is not above and parallel to the pivot point making it easier for the wheel to turn than your body to pivot around to the front. 

Ice skates can turn when leaned because the blade has a convex curve. The larger the profile (the nearly straight center section of the blade), the less the response to leaning. Speed skates have even larger profiles with further reduced lean to steer response. 

I'm missing something with the drive shaft analogy. If initially going straight, and you twist your body inwards, doesn't that initially twist the EUC outwards, such as seen in this video where riders demonstrate yaw steering (flail arms left to steer right and vice versa) to others present to show how to ride slow in a slow speed contest?

https://www.youtube.com/watch?v=ro3o8U9uZeU&t=57s

Also related to my missing something with the drive shaft analogy, the girl in this video is using foot steer to lean the EUC to steer (camber effect) and other than leaning, is almost motionless (no body twisting). At this speed (15 to 20mph), the girl has to lean more than the EUC for a coordinated turn:

https://www.youtube.com/watch?v=-hWMwK3Cfs0

Getting back to my original post, what role does gyroscopic effect play when steering | turning?

Edited August 13, 2021 by rcgldr
video of girl turning on EUC without any body twisting

[Surfling]

....so, is there something of practical use in this discussion or the OP just getting kicks on technicality?

  yet another day has passed without me using algebra once......go figure.

Edited August 13, 2021 by Surfling

[RockyTop]

3 hours ago, rcgldr said:

Ice skates can turn when leaned because the blade has a convex curve.

Unlike Ice skates Hockey skates are almost straight, Very little curve. At any rate they do not have a spinning tire to tilt to make them turn when they lean. 

 

3 hours ago, rcgldr said:

I'm missing something with the drive shaft analogy. If initially going straight, and you twist your body inwards, doesn't that initially twist the EUC outwards, such as seen in this video where riders demonstrate yaw steering (flail arms left to steer right and vice versa) to others present to show how to ride slow in a slow speed contest?

That is beginner low speed stuff that makes you scrape your pedals and swing your arms.  Leaning the wheel is a beginner thing. The wheel should stay mostly upright. If you move your weight into the turn at an angle , and you can because you are about to turn and catch yourself, you gain momentum and inertia leverage keeping yourself from turning and forcing the wheel to turn instead.

(leaning to the side with wheel upright)Your weight becomes like the handle on a ratchet floating in a vacuum, (The socket pivot is the yaw turning pivot not a spinning tire. If you turn the socket at the pivot, Is the handle more likely to move around the pivot point or will the socket turn instead. Both will happen, sure, but the socket will turn much more. - The wheel turns and catches your weight. you let it force you back upright, turn has been completed. you are going straight again.

I found angular momentum but not in the wheel spinning. It is in my body not turning, and forcing the wheel to turn.

As I said in the beginning there are several ways to get the wheel to turn. A spinning wheel is not the main or best way to do it. 

Edited August 13, 2021 by RockyTop

[RockyTop]

1 hour ago, Surfling said:

....so, is there something of practical use in this discussion or the OP just getting kicks on technicality?

  yet another day has passed without me using algebra once......go figure.

Engineers and Physics   I miss the days when I had to translate, muse and answer the question. Why can't we just...............   

Edited August 13, 2021 by RockyTop

[rcgldr]

4 hours ago, Surfling said:

....so, is there something of practical use in this discussion or the OP just getting kicks on technicality?

For me it was practical to know that leaning an EUC causes it to steer me (camber effect), as opposed to me using arm flailing to steer the EUC (yaw steer), neither of which require gyroscopic effects to function. I don't know about the other methods used to steer an EUC mentioned in the posts in this thread. My direct experience with gyroscopic effect is limited to motorcycles, where at 100+ mph, a bike will not straighten up on it's own, requiring significant counter-steering effort to increase or decrease lean angle.

[mrelwood]

5 hours ago, Surfling said:

....so, is there something of practical use in this discussion or the OP just getting kicks on technicality?

These are the physical forces and reactions that every single one of us faces when riding an EUC. For one, understanding them is crucial for effectively teaching beginners to ride. Without them, teaching would be just saying “lean forward and figure it out”.

 Without understanding them, we tend to form our own thought analogies (“put more weight on one foot”, “turn your shoulders”, “rachet in a vacuum” , etc), which do not have the same response in other people. Teaching with them doesn’t work well. But when we understand the actual forces in play, we can explain what exactly has to happen for the rider to turn. In practical terms and examples of course.

5 hours ago, Surfling said:

  yet another day has passed without me using algebra once......go figure.

… knowingly.

 The difference between a physicists and a regular Joes is not that only the physicist uses physics in his everyday life. It’s that the physicist understands how the science is present all around him, all the time.

The EUC is a great example. I lost count about a year ago in how many times I’ve tried to explain why an EUC can’t accelerate faster than the rider’s lean requires, how more torque doesn’t equal more effortless acceleration, how a powerful wheel doesn’t make you lose control, how and why a tilt-back works, and so on. These do not require advanced physics by any stretch of imagination, and they are mostly basic stuff for the ones who know a bit of physics.

 And understanding some physics is what’s required to correct wrong assumptions and to explain how things really are.

So, yet another day has passed with me using a lot of physics and math: I walked to the toilet.

3 hours ago, RockyTop said:

That is beginner low speed stuff that makes you scrape your pedals and swing your arms.  Leaning the wheel is a beginner thing. The wheel should stay mostly upright.

I don’t think such generalizations work here. At low enough speeds on some situations, tilt-turning can be the most effective way of turning. At certain spots, flailing, or twist-turning as I like to call it, actually can make the most sense.

High speed street riders could ride for years without learning to utilize these techniques, as they may not have the need to do so. But ride next to or behind a slowly walking pedestrian, or challenge your skills on rough off-road cliffs, or switch to a very different tire width (or to a knobby) and suddenly you need a much wider palette of turning and balancing techniques.

 Thank you so much @rcgldr for this thread! I loved to see someone here explain the physics behind turning on an EUC! Please keep at it. 

[EMA]

yaw turning is so usefull at low speed and doing off road in general, it's almost mandatory when you have a tire with low cornering radius .

[yoos]

@rcgldr Thanks for your patience, I guess we come from different backgrounds and terminology: you have extensive knowledge on motorcycles and other vehicles and the roll, yaw, pitch axes seem to be standard terminology for all kinds of vehicles (had to google it) and pilot training (I guess). I have modest bicycle and EUC experience backed with purely academic knowledge in physics. I guess that things called precession or attributed to it are different in those two contexts  

Anyway, we are in agreement in general: at slow speeds you turn by rotating the wheel about the yaw axis (by twisting your upper body/arms in the opposite direction) while at high speed you lean into the turn (with the lean being often initiated by counter-steering about the yaw axis). At medium speeds you have some sort of hybrid steering.

If you wish to test how much of the high-speed turn is achieved by the camber effect, and how much is due to precession alone, you can try to lean your body without leaning the wheel (i.e. keep the wheel vertical while moving you own weight into the turn). In this case, with a vertical wheel, camber effect should be absent and the turn would be due to precession alone (again, terminology could differ here). Wide-tyre wheels, especially the Z10 seem to encourage such turning style. It also offers the advantage of better pedal clearance: lower chance of scraping or clipping low obstacles.

[rcgldr]

24 minutes ago, yoos said:

@rcgldr If you wish to test how much of the high-speed turn is achieved by the camber effect, and how much is due to precession alone, you can try to lean your body without leaning the wheel (i.e. keep the wheel vertical while moving you own weight into the turn). In this case, with a vertical wheel, camber effect should be absent and the turn would be due to precession alone (again, terminology could differ here). Wide-tyre wheels, especially the Z10 seem to encourage such turning style. It also offers the advantage of better pedal clearance: lower chance of scraping or clipping low obstacles.

The combination of being an beginner and not understanding how precession from a wheel with maybe 1/8th of the mass of rider + EUC  can generate enough torque to initiate a turn, I'd rather watch a video of this method than try it myself. What I can conceive of is once a yaw rotation of rider + EUC is established (angular momentum about the yaw axis), regardless of what method is used to initiate it, then it would not take much torque to maintain the yaw rotation.  There is the issue of maintaining balance through the turn, which will require something like counter-steering, somehow steering the wheel inwards to decrease lean and outwards to increase lean.

Even with EUC leaning | camber effect steering, as speed increases, the lean angle of the EUC decreases, so pedal clearance should only be an issue at relatively low speeds. In this video, Chooch is leaning the Kingsong 16x significantly to turn at close to 30 mph, and at these speeds, he leans his body and|or hangs off to the side much more than he leans the EUC.

https://www.youtube.com/watch?v=0GdkBSaoAII&t=180s

Other than leaning, the girl in this video is almost motionless (making it easier to understand camber effect), going about 15 to 20 mph, enough that she is also leaning more than she leans the EUC.

https://www.youtube.com/watch?v=-hWMwK3Cfs0

 

Edited August 13, 2021 by rcgldr
cleanup

[yoos]

1 hour ago, rcgldr said:

as speed increases, the lean angle of the EUC decreases, so pedal clearance should only be an issue at relatively low speeds

I think this is not that simple: I would think that only the relative EUC lean decreases while the total lean (rider+EUC) increases. If you try to do the same turn (same turn radius R) at different speeds v, your lean into the turn must increase with v. This should be obvious from bicycle and motorcycle experience. It's a simple geometrical exercise: your centripetal acceleration is v²/R and gravity exerts a downwards force mg on you center of gravity. The sum of those force vectors must point from your center of gravity (c.o.g.) towards your contact point (c.p.) with the ground (otherwise there will be a non-zero torque acting on you, and your lean will change in time). So, your lean in a steady turn (with "lean" defined as the incline of the line between c.o.g. and c.p.) would be arctan(v² / gR). I guess that a high speed lean is best performed by leaning your body more than your wheel as you notice chooch doing on the 16X. This is for clearance/clipping reasons as well as, perhaps, possible loss of grip when the wheel lean is too severe. Note also that chooch is primarily an off-road rider. During off-road pedal clearance and clipping issues is of ultimate importance. On asphalt you can get away with some badass pedal scraping, while on an uneven surface you will soon clip something and receive a strong and dangerous twisting impact.

[RockyTop]

 

3 hours ago, mrelwood said:

I don’t think such generalizations work here. At low enough speeds on some situations, tilt-turning can be the most effective way of turning. At certain spots, flailing, or twist-turning as I like to call it, actually can make the most sense.

 Sure enough, I just use it when I absolutely have to, rough off road stuff or emergency.

@rcgldr Good chat,  I am not disagreeing with the original statement. I am just saying that there are so many ways to turn. Even putting your hand or body out to the left catches air and turns you to the left, 

[mrelwood]

 

3 hours ago, yoos said:

at slow speeds you turn by rotating the wheel about the yaw axis (by twisting your upper body/arms in the opposite direction)

In the previous weekly EUC meet we discussed about EUC contests other than racing, and I ended up comparing the MCM5 V2 to my V11 in an extremely slow speed riding (using as much time as possible to travel a few metres, not allowed to go backwards).

 Some riders guide towards twist-turning, as you mentioned. And with smaller or narrower wheels it does work the best for the competition in question.

But wide tires, such as the 18x3” (actually 80/90-14 motorcycle tire at the moment) on my V11 have so much grip against twisting, that turning that way is both imprecise as well as quickly exhausting. On the V11, tilt-turning yielded better results.

Since I only ride the V11 (and another 18x3” wheel before that) twist-turning has not received much of a place in my toolbox. And I believe that the reason why tilt-turning works well on wide tired wheels, is that the center of the ground contact point moves much further to the side when tilting. This achieves instant balance correction when falling sideways. And also:

 

3 hours ago, yoos said:

In this case, with a vertical wheel, camber effect should be absent and the turn would be due to precession alone (again, terminology could differ here). Wide-tyre wheels, especially the Z10 seem to encourage such turning style.

I believe the range of sideways movement of the contact centerline is the reason that the Z10 encourages a different style of turning.

[Planemo]

5 minutes ago, mrelwood said:

But wide tires, such as the 18x3” (actually 80/90-14 motorcycle tire at the moment) on my V11 have so much grip against twisting, that turning that way is both imprecise as well as quickly exhausting. On the V11, tilt-turning yielded better results.

Yeah good luck to anyone trying to twist turn a Sherman on rough asphalt 

It's not easy to try and stay balanced whilst simultaneously trying to rip off circa 4 blocks of rubber

[Planemo]

12 hours ago, Surfling said:

....so, is there something of practical use in this discussion or the OP just getting kicks on technicality?

Personally I find the subject interesting because I like physics, but as you suggest, I am far from convinced that any rider needs to know anything about how the physics in our EUC's works.

If I am honest I think it would hinder a lot of people. The last thing you need when learning to ride a wheel is overthink it. My daughter is a prime example. She doesn't like physics, has no interest in the subject whatsoever and went glassy eyed as soon as I mentioned how turning works. Very quickly I just told her to do what feels right and left her to it. She learnt at the same speed as I did, and I have been interested in physics all my life.

[rcgldr]

On 8/13/2021 at 3:30 AM, yoos said:

I think this is not that simple: I would think that only the relative EUC lean decreases while the total lean (rider+EUC) increases. If you try to do the same turn (same turn radius R) at different speeds v, your lean into the turn must increase with v. This should be obvious from bicycle and motorcycle experience. It's a simple geometrical exercise: your centripetal acceleration is v²/R and gravity exerts a downwards force mg on you center of gravity. The sum of those force vectors must point from your center of gravity (c.o.g.) towards your contact point (c.p.) with the ground (otherwise there will be a non-zero torque acting on you, and your lean will change in time). So, your lean in a steady turn (with "lean" defined as the incline of the line between c.o.g. and c.p.) would be arctan(v² / gR). I guess that a high speed lean is best performed by leaning your body more than your wheel as you notice chooch doing on the 16X. This is for clearance/clipping reasons as well as, perhaps, possible loss of grip when the wheel lean is too severe. Note also that chooch is primarily an off-road rider. During off-road pedal clearance and clipping issues is of ultimate importance. On asphalt you can get away with some badass pedal scraping, while on an uneven surface you will soon clip something and receive a strong and dangerous twisting impact.

In the 2 videos I posted links to, the riders lean more than they lean the EUC.  For smaller radius turns, the riders slow down before making those turns, rather than performing high g turns. So I should have clarified: for a higher speed and larger radius turn with similar centripetal acceleration, the rider leans more than the EUC, due to the larger radius turn requiring less EUC leaning (assuming camber effect).  In videos of riders tilt steering (what I was calling foot steering) at lower speeds, the EUC is leaned more than the rider. Somewhere in between lower and higher speeds, the rider and EUC lean about the same for a coordinated turn, a somewhat stable and self-correcting response.

I agree with your reply that if turning radius is constant, the EUC lean angle due to camber effect would also be constant (possibly a bit more if the contact patch deforms due to lateral load), but doubling the speed means the centripetal acceleration is quadrupled, probably beyond the comfort zone of most riders. Instead, what I have seen is riders adjust speed for cornering radius for somewhat constant centripetal acceleration: speed = sqrt(centripetal acceleration · radius), except for tight (small radius) turns, where they tend to use reduced centripetal acceleration as well. 

Edited August 14, 2021 by rcgldr
improve response

[supercurio]

23 hours ago, rcgldr said:

Gyroscopic reactions - precession is how a spinning wheel responds to a torque (not lean angle), so it is only present when lean angle is changing, not during a steady lean. Angular momentum of a spinning wheel causes it to resist any change in steering angle, but this resistance is not a significant issue for electric unicycles.

Fantastic read!

However I must disagree on that statement, especially since I'm currently adjusting to a new tire on my Veteran Sherman, the CST C6004.
It's a fairly heavy 2.75-14 (aka 20") tire which offers a surprising amount of actual gyro effect, meaning the higher the speed the more effort it takes to change its rotation axis, noticeable especially on the leaning angle.
I say "actual" gyro effect because tires keeping the wheel upright for various reasons are said to have "gyro" although they're not.

The gyro effect is so significant compared to the previous, lower diameter and lighter tire that some amount of re-learning is required in order to change direction successfully at higher speeds (50+ kph). Due to its rigidity and profile however it is surprisingly manoeuvrable and nimble at low speeds, despite the 35kg of the wheel.

As you describe, some force is needed to steer and then the wheel/tire holds lean angle and consequently, the direction if speed remains constant. Then it becomes easy to increase the turning radius by slowing down, which is an appreciable behaviour.
The most amount of effort is needed if you want to change steering from a left to a right turn, and requires a certain amount of anticipation.

So I'm certain that gyroscopic effect can be very significant on an EUC, provided that the tire diameter of the tire is large enough, its weight heavy enough and above a certain speed.

However, with the right amount of gyro effect, I have to say that it's a very pleasant effect, contributing notably to steering and directional stability.

[supercurio]

18 hours ago, rcgldr said:

I'm a beginner to EUC, and for me, it helped to have a basic understanding of how an EUC is able to turn. I use two methods, yaw | arm fail steer, (flail left to steer right and vice versa) for low speed (less than 5 mph), and for normal speed (5 mph or more) foot steer, move inside foot down, outside foot up to lean the EUC, relying on camber effect, so that a leaned EUC is steering me, instead of me steering the EUC. Not having any idea of how much camber effect a V8F would have, I did subtle lean changes to see how it would respond, weaving left and right, eventually progressing into mild carving. I'm still having to make some mid turn corrections with foot steering, not quite coordinating my body lean angle with with my steering | EUC lean angle, but I'm able to steer it where I want it to go, and making progress on this.

Welcome to you as new EUC rider, by the way!

I hope that you will have the opportunity to try different wheels, but also different tires on the same wheels.
While I'm sure you will have the opportunity to learn, with your analytical approach most of the ways to steer and turn with your V8F, you'll probably experience over time that which single or combination of strategies to change direction is extremely varied.

Then all the basic principles are influenced by the wheel characteristics, weight distribution, its tire, the tire pressure, of course speed by large amounts, terrain and surfaces as well.

Compared to bicycle or motorcycle, there might be so many different ways to get the turn desired that it contributes to the incredible sense of freedom when riding.

[mrelwood]

5 hours ago, supercurio said:

Fantastic read!

However I must disagree on that statement, especially since I'm currently adjusting to a new tire on my Veteran Sherman, the CST C6004.
It's a fairly heavy 2.75-14 (aka 20") tire which offers a surprising amount of actual gyro effect

 

5 hours ago, supercurio said:

The gyro effect is so significant compared to the previous, lower diameter and lighter tire

 

5 hours ago, supercurio said:

So I'm certain that gyroscopic effect can be very significant on an EUC, provided that the tire diameter of the tire is large enough, its weight heavy enough and above a certain speed.

Your example is actually the main reason why I personally don’t believe gyroscopic forces to be very significant in EUC turning.

My heaviest 18x3 tire is the CST C-186, which is identical to the Sherman factory default off-road tire Kenda K262. The lightest 18x3 tire I’ve used on my wheels is the common ChaoYang H-5102.

 The only reason why I only use the C-186 as a winter tire, is because it doesn’t have enough tendency to stay upright. Turning is laborious, because I have to tilt the wheel so far for it to turn, and actively lift it up after a turn, even at high speeds.

 Consequently the lightest tire I had, the H-5102, exhibited a strong “gyro effect”, and wanted to stay upright more than my other tires, significantly resisting tilting at speed.

 Then there is the amount of mass. Common 18x3 sized tires weigh between about 1.2 kg and 2.2 kg. As they are attached to a 10-14kg motor (with about two thirds of it rotating, heaviest being the rim with it’s magnets), the difference in gyroscopic forces between tires cannot be very large. Yet the behavior that’s called the “gyroscopic effect” varies hugely, and often inversely related to the rotating mass.

 

 Why then does the C-186 fall to the turn being hard to keep upright? To the best of my deduction abilities (and based on about a dozen tested tires), a tire consisting only of soft tall knobs like the C-186 exhibits the least amount of what I understood to be called as the “camber effect” (or was it “camber force”?) where the smaller radius of the edge of the tire makes it turn like a rolling cone. The knobs simply give in, rotate and compress too easily for the tire to be able to provide a strong turning force.

 The closest I’ve had to a street style tire is exactly the H-5102, which has barely any tread patterns that could compress, turn and give in. Hence it should provide the strongest “camber force/effect”.

[rcgldr]

6 hours ago, mrelwood said:

“camber force/effect”.

Camber effect - refers to the similarity of a leaned round profile tire to a truncated cone (aka conic section), the inner radius being smaller than the outer radius, causing the tire to follow a circular path. This is one of the ways one wheeled vehicles with round profile tires can turn (tilt steering).

Camber thrust - refers to the lateral friction force at the contact patch that forces the outer part of the contact patch to follow essentially a straight line while in contact with the pavement. Rather than a cause and effect relationship, it is a coexisting relationship, the greater the lateral force, the greater the deformation of the contact patch. This deformation can have both lateral and rotational (contact patch twists outwards) components. The result is the actual path the tire follows is somewhat outwards of the direction the tire is pointed, and how far outwards the actual path is versus the direction it is pointed is called slip angle, although there doesn't have to be any actual slippage.

https://en.wikipedia.org/wiki/Camber_thrust

 

Edited August 14, 2021 by rcgldr
cleanup

[yoos]

Here is a nice short video of a high speed turn with extreme leaning into the turn.

[Paul A]

Would it be better for traction to keep the wheel as vertical as possible? 

Rather than leaning the wheel and having contact creeping closer to the tyre's sidewall?

Like Valentino Rossi hanging off the seat and keeping the bike as vertical as possible:

 

And Wrong Way: