Electric unicycle and bicycle dynamics - gyro effects on steering

[yoos]

I don't think "as vertical as possible" is better. It appears racing tires like the mc tire above have roughly the same traction in a quite wide range of leaning angles. I think that the body of the motorcycle, or the pedals of an EUC limits the max lean angle. Thus, you lean the EUC/bike to the max safe angle of the vehicle and any further lean is just by using the riders body. 

[rcgldr]

17 hours ago, Paul A said:

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

This doesn't work for an EUC. With an EUC, the turning radius is a function of EUC lean angle (and tire parameters) and independent of speed (other than contact patch deformation due to lateral load) due to camber effect. If an EUC is leaned less, the turning radius becomes larger, if an EUC is leaned more, the turning radius becomes smaller. For a given EUC lean angle and turning radius, at slower speeds, the rider leans less than the EUC, and at higher speeds, leans more than the EUC, and for some speed range in between, about the same as the EUC. As for the turning radius, visualize the contact patch of an EUC idealized as a truncated cone, with the outer diameter larger than the inner diameter. If you extend this virtual truncated cone to a full cone, the point of the cone would be the center of the circle a leaned EUC will tend to follow. This is called camber effect.

Motorcycles turn because the front tire is turned inwards of the rear tire, called tracking. Ignoring contact patch deformation, for a leaned motorcycle in a constant speed, constant lean turn, if you virtually extend the axis of the front and rear tire, they will cross at some point below the pavement, and the point on the pavement directly above the point where they cross will be the idealized center of the circle that the motorcycle will turn. Due to contact patch deformation (slip angle), the actual turning radius will be somewhat larger, and the point on the pavement above where the virtual axis cross will follow a small circular path, instead of just being a single point.

 

Edited August 30, 2021 by rcgldr

[NSFW]

Thanks for the interesting discussion, everyone.

I tend to analyze everything I do, and understand the physics as much as possible, so learning to ride an EUC was just bizarre. It felt like my body did a reasonably good job figuring it all out, while my brain was mostly just confused the whole time. But the more I rode the better I got, so my brain has been trying to reverse engineer what my body has been doing. I think I get it now, but I'm curious as to whether or not this aligns with how more experienced riders think about this stuff.

So, below is how I've come to think of EUC steering. I started with a King Song S22 - a tall heavy EUC with a large heavy wide tire, so that shapes my perspective a lot:

At very low speeds, it's mostly about brute-force yawing the EUC chassis, with the yaw being powered by hip/torso twist and arm flail. It's awkward and inelegant, but as I get better I'm able to keep the yaw corrections small, which reduces the need to flail... but it doesn't go away.

As speed increases, camber effect gets more useful, and the need for fail-induced yaw tapers away. I use weight shift to force the chassis to lean into the turn, and the camber effect produces the yaw. 

As speed increases further, gyroscopic precession becomes increasingly useful, and with enough speed it becomes the only approach. I use my outside knee to push the EUC to lean inward, but due to precession that push only manifests 90 degrees later, and the ECU yaws instead of leaning. A steady push on the top of the wheel becomes a steady yaw and the ECU takes me around a corner.

 

[rcgldr]

21 hours ago, NSFW said:

I use weight shift to force the chassis to lean into the turn, and the camber effect produces the yaw. 

As speed increases further, gyroscopic precession ...  A steady push on the top of the wheel becomes a steady yaw and the ECU takes me around a corner.

Camber effect is a response to the tilt angle of the EUC, regardless of any weight shift. The yaw from tilt steering is mostly due to camber effect. Gyroscopic precession is a reaction to a torque, and during a constant coordinated turn, there is no torque about the roll (tilt) axis, so there is no precession reaction, just a steady yaw and turn due to camber effect. Precession only occurs during a change in tilt angle, and it's relatively weak, small, and only momentary compared to camber effect.

[NSFW]

Weight shift is how I get the EUC to tilt. Camber effect takes it from there.

In a constant coordinated high speed turn, I'm using my weight to push against the top of the EUC chassis. In skiing lingo, my angulation is higher than it should be, and my CG is a little too much inward. But I don't fall inward because I'm bracing myself with the top of the EUC chassis. That's what provides the roll-axis torque. Precession takes it from there.

Edited July 22, 2022 by NSFW

[rcgldr]

On 7/21/2022 at 10:43 PM, NSFW said:

Weight shift is how I get the EUC to tilt. Camber effect takes it from there.

my CG is a little too much inward. But I don't fall inward because I'm bracing myself with the top of the EUC chassis. That's what provides the roll-axis torque. Precession takes it from there.

EUC are unitrack vehicles, attempting to weight shift inwards will tilt them outwards, but that will cause the EUC to steer outwards from under the rider, leaning the rider inwards, a form of counter-steering. Counter-steering is used to change lean angle, tilt outwards to lean inwards or if already leaned, tilt less to lean more, tilt more to lean less. For EUC, this is somewhat automatic, as the pedal pressure used to lean inwards creates an outwards tilting torque on the EUC, and similarly for any change in lean angle.

If you're bracing yourself with the top of the EUC chassis, which is generating an inwards roll torque on the EUC, then something is causing the EUC to exert an outwards roll torque on you. This could be due to exerting more pressure on the outer pedal and|or a lateral outwards force at the pedals. At moderate to high speeds, the rider needs to lean more than a wheel is tilted for a coordinated turn, which may feel like the CG is too much inwards. Wrong Way made a video about tires and turning. I set the link to 3 view comparison, the wheel on the viewer's left is a typical wheel with a street tire, the middle view is a Z10 (4 inch wide tire) which requires the least amount of tilt to turn, and the right view is a knobby tire, which requires the most amount of tilt to turn, but still less than the rider is leaning and hanging off to the inside. You may want to also watch this video from the beginning where he offers a simple explanation of camber effect and why tire profile and type affect camber effect.

https://www.youtube.com/watch?v=NsXW4OKnmWc&t=314s

Since I ride a V8F, and rarely ride faster than 15 mph (about 18 mph max), I don't know if rider inputs change due to speed. From 8 to 18 mph, I can turn by just tilting my V8F, relying on camber effect. I don't get any sense of a precession response at these speeds. Kuji Rolls compared a street tire versus a knobby tire on a Veteran Sherman, and stated the street tire felt too sensitive above 30 mph. Precession would be about the same in both cases since the tires weigh about the same, but camber effect response will be significantly greater with the street tire. This seems to imply that camber effect is the dominant factor when turning, even at speeds above 30 mph. 

https://www.youtube.com/watch?v=qcRcUIF69LU&t=757s

I also ride a motorcycle (2001 Hayabusa), and there's little resistance to counter-steering inputs at 40 mph or less. The sensation is that the handle bars are being steered without much torque being applied. At 55 mph or faster, I do feel the resistance due to angular momentum of the front wheel, and as speed increases, I have to apply more counter-steering torque on the handle bars to get the bike to change lean angle, and the sensation is the handlebars are barely moving while there is a significant amount of torque being applied. I don't know if EUCs can go fast enough to get a sensation similar to a motorcycle at 55+ mph where there is little tilt movement but a lot of tilt torque.

Edited July 24, 2022 by rcgldr

[NSFW]

On 7/22/2022 at 9:37 AM, rcgldr said:

EUC are unitrack vehicles, attempting to weight shift inwards will tilt them outwards, but that will cause the EUC to steer outwards from under the rider, leaning the rider inwards, a form of counter-steering. Counter-steering is used to change lean angle, tilt outwards to lean inwards or if already leaned, tilt less to lean more, tilt more to lean less. For EUC, this is somewhat automatic, as the pedal pressure used to lean inwards creates an outwards tilting torque on the EUC, and similarly for any change in lean angle.

It seems you were expecting a much longer answer than "weight shift."  But I don't disagree with what you've written.

In snowboarding we use (or, borrowed from skiers) the word "inclination" to describe how far one's body is leaned into the turn, and "angulation" to describe the angle between the snowboard and the hill. Adopting these terms will make this discussion clearer for everyone.

Riders are free to adjust those variables independently. But carefully.

On 7/22/2022 at 9:37 AM, rcgldr said:

If you're bracing yourself with the top of the EUC chassis, which is generating an inwards roll torque on the EUC, then something is causing the EUC to exert an outwards roll torque on you. 

Yes, we agree on that much. But I'm pretty sure that a nontrival part of that "outward roll torque" is the gyroscopic effect of a 14" wheel with a motor on the inside and a 20" x 2.75" tire on the outside.

 

[rcgldr]

On 7/24/2022 at 6:41 PM, NSFW said:

In snowboarding we use (or, borrowed from skiers) the word "inclination" to describe how far one's body is leaned into the turn, and "angulation" to describe the angle between the snowboard and the hill. Adopting these terms will make this discussion clearer for everyone.

I'm pretty sure that a nontrival part of that "outward roll torque" is the gyroscopic effect of a 14" wheel with a motor on the inside and a 20" x 2.75" tire on the outside.

On a snowboard, the riders feet are on the upper surface of the snowboard. On an EUC, the riders feet are on the pedals, about 6 inches above the contact patch. If a rider in a coordinated turn is leaned inwards more than an EUC is tilted inwards, the linear forces involved produce an outwards torque on an EUC, and the rider exerts an inwards torque to counter this (which requires the rider to lean a bit more inwards).

Camber effect is mostly independent of speed. Camber effect is reduced by higher lateral loads that cause the contact patch to flex inwards. The greater the amount of tilt, the smaller the turning radius, again mostly independent of speed, so the rider has to coordinate the amount of lean and tilt to compensate for speed and turning radius. For low speed tight turns, the rider barely leans, but the EUC is tilted a lot. For higher speed turns, the rider leans inwards more than the EUC is tilted, as shown in Wrong Way's video, more "inclination" than "angulation".

I don't know how to quantify the outwards roll torque due to precession, or how significant it is compared to the outwards roll torque due to the riders outwards force near the center of the pedals. I don't understand how a precession response can generate a torque when there's no angular momentum related to precession. I set the link for this video to show an 8 lb gryo spun at several thousand rpm, allowed to precess, and a small stick is used to stop the precession with very little force, since as explained in the video, there is no angular momentum related to precession. He then turns the platform vertical so that the non-spinning gryo drops at about the same speed as it had when precession. The stick was supposed to break, but there was too much play in the hole the stick was stuck into, and the stick just moved a lot.

https://www.youtube.com/watch?v=0L2YAU-jmcE&t=3104s

However, for an aircraft in a turn, the propeller creates a yaw reaction to pitch or a pitch reaction to a yaw. I haven't found out how much this effect is related to precession and how much is related to a differential in relative airspeed over the blades of the prop. For example on a tail dragger, if the pilot pitches the plane down to lift the tail up, the downwards moving blades experience a higher air speed than the upwards moving blades, creating a difference in thrust that would yaw the aircraft in the same direction as a precession effect. Helicopters avoid this effect and stress with the usage of a swash plate and hinged rotors that decouple the rotor from the drive shaft, allowing the rotor to precess independently of the drive shaft and the rest of the helicopter. The rotor doesn't exert any torque, only a force in the direction of it's axis of rotation. The swash plate is setup to advance cyclic inputs by 90 degrees, since the rotor acts as a gyro, where a roll torque induces a pitch response, and vice versa.

Edited July 30, 2022 by rcgldr

[NSFW]

14 hours ago, rcgldr said:

On a snowboard, the riders feet are on the upper surface of the snowboard. On an EUC, the riders feet are on the pedals, about 6 inches above the contact patch.

That seems like a distinction without a difference. In either case, there is a chain of jointed segments between the point of contact and the rider's CG. The chain just has one more link in the case of the ECU. Or maybe not even that - consider the case where a snowboarder has the board tipped up on on edge, at a 45 degree angle. Now there's an addition link between the feet and the point of contact. A shorter link, but it's there.

14 hours ago, rcgldr said:

I don't understand how a precession response can generate a torque when there's no angular momentum related to precession.

[...]

Helicopters avoid this effect and stress with the usage of a swash plate and hinged rotors that decouple the rotor from the drive shaft, allowing the rotor to precess independently of the drive shaft and the rest of the helicopter. The rotor doesn't exert any torque, only a force in the direction of it's axis of rotation. The swash plate is setup to advance cyclic inputs by 90 degrees, since the rotor acts as a gyro, where a roll torque induces a pitch response, and vice versa.

I don't think the video you linked to has significance here. But helicopter rotors provide a great analogy:

When the pilot wants to pitch forward, the swashplate tilts to give the rotor more pitch on the right side and less pitch on the left side (we'll assume the rotor spins clockwise as viewed from above). Naively this would seem to induce a roll to the left - but due to precession the torque manifests 90 degrees later, as forward pitch, for as long as that lift differential is present.

In the case of an EUC, at a speed high enough for precession to be significant, when the rider can lean on the top of the wheel, which creates torque around the roll axis, which manifests 90 degrees later as yaw. And so the wheel yaws while that roll torque is present.

To be clear, I'm not saying camber effect goes away. But precession becomes increasingly useable as speed increases.

[rcgldr]

2 hours ago, NSFW said:

helicopter rotors provide a great analogy:

In the case of an EUC, at a speed high enough for precession to be significant, when the rider can lean on the top of the wheel, which creates torque around the roll axis, which manifests 90 degrees later as yaw. And so the wheel yaws while that roll torque is present.

To be clear, I'm not saying camber effect goes away. But precession becomes increasingly usable as speed increases.

As commented above, helicopter rotors are free to precess independently of the drive shaft and the body of a helicopter. (I forgot to mention other ways this is implemented, such as articulated hubs that are free to angle independently of the drive shaft, normally used on rotors with more than 2 blades). 

Unlike a helicopter, for an EUC, the rotating parts (motor, wheel, tire) are fixed to the rest of the EUC (via the bearings on the axle) and typically weigh a bit less than 1/2 of a EUC, and a rider typically weighs more than double the entire EUC, so the rotating parts only account for about 1/4 or less of the total mass, and any precession has to also affect the non-rotating parts, which reduces the precession effect. In that video I posted a link to, a small stick was able to nearly instantly stop a precessing 8 lb gyro, so there isn't much torque from the rotating parts in the direction of precession. 

Since the rider is exerting an inwards roll torque on the EUC, then the precession from the riders roll torque is in the yaw direction, and it could turn out that the rider ends up causing the rate of precession to match the rate of yaw (even if the rider is unaware of it), in which case none of the outwards roll torque would be due to precession, and only due to outwards lateral force at the center of pedals and inwards lateral force at the contact patch.

 

 

Edited July 25, 2022 by rcgldr

[NSFW]

4 hours ago, rcgldr said:

As commented above, helicopter rotors are free to precess independently of the drive shaft and the body of a helicopter.

What do you imagine provides the forces that cause the fuselage to pitch and roll? It's the rotor, acting on the main shaft.

I have no experience with full-size helicopters but I've got RC models with rotors from ~16 inches to 60 inches, and I assure you that the limited isolation between the rotor blades and the main shaft is just there to reduce vibrations. The lift differential that I describe above, after precession, is what puts roll and pitch torques on the main shaft.

In the video you linked to, the force that caused the spinning wheel to precess just came from gravity pulling the wheel toward the earth. So, the force that the wheel's axle applied to the stick was approximately equal to gravity's downward pull on the wheel.

In other words, if the weight of the axle resting on the stick didn't break the stick, then it would be unreasonable to expect the precession-induced motion of the axle to break the stick. It's the same force, just in a different plane and with a bit longer lever arm.

[rcgldr]

3 hours ago, NSFW said:

What do you imagine provides the forces that cause the fuselage to pitch and roll? It's the rotor, acting on the main shaft.

In the video you linked to, the force that caused the spinning wheel to precess just came from gravity pulling the wheel toward the earth. So, the force that the wheel's axle applied to the stick was approximately equal to gravity's downward pull on the wheel.

In other words, if the weight of the axle resting on the stick didn't break the stick, then it would be unreasonable to expect the precession-induced motion of the axle to break the stick. It's the same force, just in a different plane and with a bit longer lever arm.

On most full scale helicopters, a 2 or 3 axis articulated hub is used to eliminate the rotor exerting a torque via the hub to reduce stress on the hub. The key factor is the flapping hinge, which allows the rotor to rotate about a plane independent of the direction of the drive shaft. When the rotor's axis of rotation is not in line with the drive shaft, the linear lift force from the rotor generates a torque onto the drive shaft and the rest of the helicopter.

https://www.youtube.com/watch?v=MnzVepo7KaE

The stress of torque at the hub isn't an issue for an RC helicopter, so flapping hinges are not normally used, and RC helicopters are a good example of your point about precession from the rotor or any gyro being able to precess the entire model or structure.

For helicopters in general, some argue that it isn't truly precession, since the rotor is not a solid disk, and instead similar to precession, just a delay between maximum blade pitch and maximum blade tilt.

In an early part of the video, a light push on a gimbaled gyro results in almost no movement of the outer frame and precession of the inner frame. However, with a bit more push, the outer frame rotates in response to the push. 

https://www.youtube.com/watch?v=0L2YAU-jmcE&t=110s

As for the video, gravity pulls down on the 8 lb gryo, which due to leverage would translate into about 4 pounds of force where the stick stops the precession. The point of the video was that there was no angular momentum, not that there wasn't any torque. However with a gyro supported at one end, but blocked by a frictionless rod from precessing at the other end, the force at the other end would not fully correspond to the torque induced by gravity, because much of that torque results in the downwards change in angular momentum of the gyro. What left is a small change in the angular momentum of whatever the rod is attached to (eventually the earth).

Back to EUC. Once in a higher speed constant turn, with the riders CG being "inwards", then the rider is exerting an inwards roll torque onto the EUC, and the precession reaction is a yaw in the direction of turn. If the rider exerts just enough inwards roll torque so that the rate of precession related yaw matches the rate of camber effect related yaw, then there is no net torque from camber effect about the yaw axis, and all of the outward rolling torque exerted by the EUC onto the rider would be due to the lateral forces, and not precession. The unknown here is what the riders actual inwards roll torque on the EUC is in a coordinated turn.

Edited July 26, 2022 by rcgldr

[mrelwood]

On 7/21/2022 at 10:23 AM, NSFW said:

At very low speeds, it's mostly about brute-force yawing the EUC chassis, with the yaw being powered by hip/torso twist and arm flail. It's awkward and inelegant, but as I get better I'm able to keep the yaw corrections small, which reduces the need to flail... but it doesn't go away.

The S22 is a large and heavy wheel with a wide tire, which makes the twist steering to require a lot of effort. It also makes it imprecise. It would be useful for you to learn to tilt-steer at slower speeds as well.

Start from the head. Turn your head and let the upper torso follow into the direction of the turn. Then spread your knees by an emphasized amount to allow the wheel to tilt pronouncedly. You'll learn the exact amounts in time, but for now make the knee spread and wheel tilt large enough to feel ridiculous.

The upper body rotation also creates a momentum that helps the turning quite a bit. You can eventually use your hands to aid controlling the rotation more precisely.

[mrelwood]

Here's a video to demonstrate my tilt-steering technique at slow speeds:

 

[rcgldr]

25 minutes ago, mrelwood said:

Here's a video to demonstrate my tilt-steering technique at slow speeds:

There is some yaw steering being used to initiate the turn. I'm not sure why riders can somewhat spin on a wheel using momentum despite friction at the contact patch.The skinny tire (2.125 inch wide) on my V8F limits how tight it can turn with just tilt steering. Wrong Way made a video about tires effect on turning. I set the link to start where he talks about tire width.

 

Edited July 26, 2022 by rcgldr

[mrelwood]

36 minutes ago, rcgldr said:

There is some yaw steering being used to initiate the turn.

There is, but opposite to a solely hip based twist-steering, my hip twists into the turn. With twist-steering the hip turns against the turn during the turn. So my slow twist might even be considered as counter-steering to  initiate the turn. In addition, it prepares my posture for a tight tilt-turn, as can be seen in WrongWay's video as well. I think we actually turn pretty much the same way (at slow speeds at least).

Edited July 26, 2022 by mrelwood

[rcgldr]

28 minutes ago, mrelwood said:

There is, but opposite to a solely hip based twist-steering, my hip twists into the turn. With twist-steering the hip turns against the turn during the turn. So my slow twist might even be considered as counter-steering to  initiate the turn. In addition, it prepares my posture for a tight tilt-turn, as can be seen in WrongWay's video as well. I think we actually turn pretty much the same way (at slow speeds at least).

True, normally arm or upper body twisting is done in the opposite direction, flail left to steer right and vice versa. Tilt steering can be used to prevent the wheel from steering in response to upper body twisting while setting up for a turn, allowing the rider to build up momentum, which is then "released" for the actual turn. 

However for a beginner at slow speeds, attempting to twist into the turn without tilt steering will steer the wheel the wrong way, which creates an issue for balance if a rider hasn't learned to tilt steer yet. I started off using extended arms and arm flailing (flail left to steer right and vice versa), and was able to do laps around a tennis court at 3 to 5 mph on my first attempt. Arm flailing is commonly taught for pedaled unicycles, and I've seen it shown for electric unicycles, but seldom see it taught. It is useful for very slow speeds or if nearly stopped:

 

[NSFW]

20 hours ago, rcgldr said:

On most full scale helicopters, a 2 or 3 axis articulated hub is used to eliminate the rotor exerting a torque via the hub to reduce stress on the hub. The key factor is the flapping hinge, which allows the rotor to rotate about a plane independent of the direction of the drive shaft. When the rotor's axis of rotation is not in line with the drive shaft, the linear lift force from the rotor generates a torque onto the drive shaft and the rest of the helicopter.

The hinge is just there reduce vibration. One of my helis has a rotor head with the same hinges, other use different approaches to vibration damping.

The centripetal force exerted by the blades pulls the hinge very nearly straight. Once spinning the rotor is most assuredly not free to "rotate about a plane independent of the direction of the main shaft." If it was, cyclic pitch would change the orientation of the rotor independent of the fuselage.

 

20 hours ago, rcgldr said:

Back to EUC. Once in a higher speed constant turn, with the riders CG being "inwards", then the rider is exerting an inwards roll torque onto the EUC, and the precession reaction is a yaw in the direction of turn. If the rider exerts just enough inwards roll torque so that the rate of precession related yaw matches the rate of camber effect related yaw, then there is no net torque from camber effect about the yaw axis, and all of the outward rolling torque exerted by the EUC onto the rider would be due to the lateral forces, and not precession. The unknown here is what the riders actual inwards roll torque on the EUC is in a coordinated turn.

That's a whole lot of "if" that we agree on, followed by the unknown that we disagree on.

It feels to me like the inward roll torque exceeds the camber yaw, and induces additional yaw, without which I'd fall to the inside. 

[NSFW]

21 hours ago, mrelwood said:

It would be useful for you to learn to tilt-steer at slower speeds as well.

I'm already doing it. But, as rcgldr noted:

19 hours ago, rcgldr said:

Arm flailing is [...] useful for very slow speeds or if nearly stopped:

 

[mrelwood]

3 hours ago, NSFW said:

I'm already doing it. But, as rcgldr noted:

Sure, when you participate in a contest to spend as much time as possible in a 2m x 2m area, twisting is what you need to do. But it isn't useful in any actual on-road riding situation.

[rcgldr]

13 hours ago, NSFW said:

The centripetal force exerted by the blades pulls the hinge very nearly straight. Once spinning the rotor is most assuredly not free to "rotate about a plane independent of the direction of the main shaft."

Video example of a fully (3d) articulated hub. I set the link to where a full scale helicopter is getting ready to taxi (rotor plane forward) and then take off (rotor plane horizontal). The plane of the rotor changes angle while the wheels remain on the ground and the main shaft is nearly vertical. At the first scene transition, the plane of the rotor is angled much further forwards so the helicopter can taxi. Then at the next transition where lift off begins, the plane of the rotor is nearly horizontal. As the helicopter lifts off, the body pitches up, main shaft pitches back, and the plane of the rotor is adjusted to return it to horizontal. Since the hub allows the plane of the rotor to move independently of the main shaft, the hub only applies a linear tension force in the direction of rotor lift to the top of the main shaft, sort of like a mass suspended by a short rod with a hinged connector (the hub) at the top.

 

Edited July 27, 2022 by rcgldr

[rcgldr]

On 7/26/2022 at 6:53 PM, NSFW said:

It feels to me like the inward roll torque exceeds the camber yaw, and induces additional yaw, without which I'd fall to the inside. 

If during a coordinated turn the rider is leaned inwards more than the EUC is tilted inwards, the linear forces result in an outwards torque on the EUC, and the rider opposes this with an inwards torque (the rider has to lean inwards a bit more).

Camber effect generates a yaw torque on EUC and rider, but in a constant turn, the only torque involved is what needed to yaw the rotating wheel. This yaw torque times the angular momentum of the wheel would cause a outwards roll precession response, but the rider prevents any precession response, which may result in additional outwards roll torque, but I don't know how to quantify what that additional torque would be, other than it would be significantly less than the camber related yaw torque, since torque = rate of change in angular momentum, and most of that would correspond to the wheel be yawed. Since the rider will oppose any outwards roll torque on the EUC with an inwards roll torque to hold the EUC at a fixed tilt angle for a coordinated turn, if there is a precession effect, the rider wouldn't be able to distinguish it from camber effect.

Edited July 30, 2022 by rcgldr

[mrelwood]

If precession were a notable force during turns, it would be so with  knobby tires as well. They even tend to weigh more, yet the force that was suggested doesn't seem to exist. The wheel simply carves with a steeper tilt that can be more easily increased and decreased during turns, as if it were a narrower tire.

Make a test that removes the camber effect: Lift the wheel up and let it speed up to it's maximum speed. Now tilt the wheel to the side as you'd be  carving. How large is the force that starts rotating the wheel to left or right?

Edited July 27, 2022 by mrelwood

[rcgldr]

20 hours ago, mrelwood said:

Make a test that removes the camber effect: Lift the wheel up and let it speed up to it's maximum speed. Now tilt the wheel to the side as you'd be  carving. How large is the force that starts rotating the wheel to left or right?

I don't know how to quantify the force. Precession is a reaction to a torque. Using a helicopter rotor as a similar example, the maximum force on a rotor blade occurs about 90 degrees ahead of the maximum displacement of the rotor blade. Assume a wheel is vertical and rotating forwards, and that a yaw torque to the left is exerted, an unrestricted wheel would precess in a right roll. Using the helicopter rotor analogy, the particles of the wheel experience maximum force at the front and back, and maximum displacement at the top and bottom. However, a second torque about the roll axis prevents any displacement at the top and bottom (similar to a rider holding an EUC at a fixed tilt angle), restricting the wheel to only respond to the combined yaw and roll torques with a change in yaw angle and the associated change in angular momentum (direction changes, but not magnitude).

Edited July 28, 2022 by rcgldr

[mrelwood]

I often have trouble following the terms yaw and roll since they don't have good translations in our language. But based on the images and gifs that Google showed me for "yaw roll pitch", roll is the sideways tilt that the user forces on the wheel, and yaw is the resulting rotation/turn to left and right that the camber effect (or gyroscopic precession) creates.

So, I shot a video on the test I mentioned. First I tilted (roll) the wheel slowly to the left, then on the second run I did the same but rapidly. Each time the V11 was freely decelerating from it's full free spin speed at an empty battery, 66 km/h.

On the first run I wasn't able to feel any force rotating/turning the wheel (yaw) either left or right.

On the second run the force was actually much larger than I anticipated. As I quickly rolled the wheel to the left, the wheel yaw'd very strongly to the left. As if there was a physical link mechanism in place that yaws the wheel when rolled/tilted. And as I let go of the roll and let the wheel return to vertical, the resulting yaw to the right was just as strong.

But as I was holding the wheel in it's tilted roll position and fighting gravity's attempt to return to vertical, there was no precession taking place.

What the test confirms is what @rcgldr was saying from the beginning, that gyroscopic precession only exhibits itself while the roll/tilt of the wheel changes. No matter how hard I'd have to push the wheel to retain a roll angle and fight the camber effect or gravity, precession only takes place as the roll angle changes. And the magnitude of the precession is notable only when the roll/tilt angle changes rapidly.

By my rough estimate, I rarely tilt/roll the wheel during riding as fast as I did in this test. So I'd say that precession rarely participates in creating my turns. 

Edited July 29, 2022 by mrelwood