Electric unicycle and bicycle dynamics - gyro effects on steering

[rcgldr]

I've seen posts here and at other forums that incorrectly describe how gyroscopic reactions affect steering. 

Electric unicycles can be steered by yawing them into the desired direction, the simplest method is to arm flail left to steer right and vice versa, called yaw steering, as seen in this video, set to start with a rider essentially stopped and yaw steering:

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

Electric unicycles can be leaned by moving the inside foot down and the outside foot up. Depending on tire parameters, diameter, profile, the lean angle determines cornering radius due to camber effect. The center of the tire has a larger radius than the side of the tire, and when leaned, the outside edge of the contact patch has a larger radius than the inside edge, essentially a truncated cone, causing it to follow a circular path. Foot steering can be done at low speed, but as seen in this video, the pedals or riders feet may contact the pavement, causing the rider to walk off the EUC.

https://www.youtube.com/watch?v=83gEm6MzODw

At low speeds, the EUC needs to be leaned more than the rider to maintain balance. At higher speeds, the EUC needs to be leaned less than the rider to maintain balance. At some speed in between, the EUC lean angle is about the same as the riders to maintain balance, a somewhat self stable situation.

Bicycles and motorcycles - these are self stable because of steering geometry, the main factor in most cases is trail: if you extend an imaginary line from the steering axis to the ground, it intercepts the ground in front of the front tire's contact patch. When leaned, gravity pulls down at the front tires axis, and pushes up at the front tires contact patch, causing it to steer inwards, and above some minimal speed, enough to cause the bike to tend to self-correct to a vertical orientation.

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.

For bicycles and motorcycles, this resistance opposes the self-correction related to lean, but if not at high speeds, it acts as a damper, reducing or eliminating over-correction. This resistance does require the rider to use more counter-steering effort to change lean angle as speed increases. At high speed (100+ mph), this resistance dominates, and if a rider relaxes on the handlebars while leaned over, the motorcycle will tend to hold the current lean angle rather than tend to return to vertical, and the lean angle will only change in response to counter-steering.

Edited August 12, 2021 by rcgldr
no need for the math stuff

[Planemo]

2 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.

Good post, but I slightly disagree, precession is definitely present and working on our 'little' wheels. It's why you don't 'steer' an EUC left and right at speed at all, you apply pressure downwards onto one pedal to initiate the steer, then remove pressure once you are on the correct trajectory (if the wheel rides neutral). The precession (acting at 90 degrees) does the steering for you.

What I find really amazing though is how a human can ride an EUC at varying speeds because obviously precession doesn't happen at very low speeds and depending on the wheel (Z10 for example) theres all sorts of other forces to overcome and deal with in addition to the usual, again needing different methods at different speeds.

It's a miracle that any of us can ride euc's tbh, and we don't even think about it when we're doing so! 

 

[Surfling]

...the next time someone ask me how the EUC rides, I gots me the answer...... "you do yaw steerin' and wheelin"....

3 hours ago, rcgldr said:

The center of the tire has a larger radius than the side of the tire

..mmmm.....have you seen the mten3 tire?

[RockyTop]

@rcgldr So how many ways can we steer an EUC? I can turn without leaning the tire,  I can lean the tire without turning. I can do either at any speed. ( 3?  Yaw, tire curve, weight distribution without lean.) FYI I can lean the tire to the left and turn right. The weight overcomes the tire curve friction. 

As a beginner, I remember scraping my pedals when I turned large circles. Now not using yaw, I can turn very small circles without any worry of pedals scape. You just have to hang to the inside. 
 

 

 

[Tawpie]

Dorsiflexion!

 

 

nope, that's how you make it go. but it's a kewl word.

[RockyTop]

2 minutes ago, Tawpie said:

Dorsiflexion!

 

 

nope, that's how you make it go. but it's a kewl word.

I had to look that up. Ha! 
 

🎶 cue the music!!!  ( Kung fu fighting)
Everybody was...  dorsiflexion!! 

        Those EUC’s were fast as. .. LIGHTNING!! 

[Surfling]

6 minutes ago, Tawpie said:

Dorsiflexion!

.....shout-out to the tibialis anterior and co. for some fine acceleration

[Tawpie]

At least for me, when at speed (>20 mph on a 16" wheel), it's usually not enough to simply unweight one leg and turn, I have to use my knee to haul the thing into a tilt. This is the gyroscopic effect as I understand the gyroscopic effect... the angular momentum of the spinning wheel is creating torque at the axle that is trying to keep the wheel vertical. There is a video (of course) of a guy suspending a wheel by one end of its axle.

On my MTen, the wheel diameter (radius) is so small that the generated torque is also small and it tips side to side like a drunken sailor on meth. Turning on it is entirely different than on my 16" wheel, and seems entirely governed by weight distribution between the left and right pedals.

[Tawpie]

6 minutes ago, RockyTop said:

I had to look that up.

note to self... a wise one once said "Never use a big word when a diminutive one will do".

 

 

I generally disregard the wise ones.

[RockyTop]

3 minutes ago, Tawpie said:

On my MTen, the wheel diameter (radius) is so small that the generated torque is also small and it tips side to side like a drunken sailor on meth. Turning on it is entirely different than on my 16" wheel, and seems entirely governed by weight distribution between the left and right pedals.

Absolutely. Yaw and weight distribution. No need to lean. Last time I did all three on a MTen3 I rear ended myself. 

[Surfling]

1 minute ago, RockyTop said:

I rear ended myself. 

  hey now!

[Dgar]

Does this also explain how a larger EUC reacts to a berm on the road? I first learned how to ride on a KS14 and it seems I never felt the berms. Once I went to a V11 with a larger wheel, it was hard to maintain a vertical stance on a berm until I got used to it. I still have to focus when going down the road and switch from one side the other because of how I have to change my stance to account for the EUC trying to lean one way or another.

[RockyTop]

7 minutes ago, Dgar said:

Does this also explain how a larger EUC reacts to a berm on the road? I first learned how to ride on a KS14 and it seems I never felt the berms. Once I went to a V11 with a larger wheel, it was hard to maintain a vertical stance on a berm until I got used to it. I still have to focus when going down the road and switch from one side the other because of how I have to change my stance to account for the EUC trying to lean one way or another.

Yes good example!!! 

I am sure that this is the curvature of the tire trying to turn you. You are riding on the side of the tire without leaning. Yet you somehow resist. As your skills improve you don’t even notice that or the wind or many other things. 
 

While I do remember what you are describing. I don’t feel it anymore. I would never even notice it. You simply distribute your weight without thinking. 

Edited August 12, 2021 by RockyTop

[rcgldr]

Gyroscopic precession: "Precession is the change of angular velocity and angular momentum produced by a torque." 

https://en.wikipedia.org/wiki/Precession#Classical_(Newtonian)

The point here is that precession is a reaction to a torque, not an angle. If the angle is not changing, there is no net torque and there is no precession. When there is a torque on an uniform wheel, the precession reaction is 90 degrees "behind" the torque. This is why the cyclic (pitch and roll) control on helicopters is effectively advanced by 90 degrees, so that a pitching torque from the rotor blades results in a roll reaction, and a rolling torque from the rotor blades results in a pitch reaction.

For electric unicycles, you have two primary axes for precession reaction to a torque, yaw - vertical axis, roll - forwards | backwards axis. A left yaw results in a right lean, and vice versa, but yaw steering is normally done at low speed only, so any precession effect is minimal. A left roll results in a left yaw (steer), right roll results in right steer, but as speed increases, the rate of change in precession angle decreases. Again these reactions only exist during transitions. One a yaw or lean angle is established and not changing, there is no torque. Technically as an EUC turns, there is rotation about the yaw axis, but this rate is slow except for small radius turns.

Gyroscopic effect is a more general term referring to the tendency of a wheel to maintain it's angular momentum. In addition to precession, it also explains why counter-steering effort to lean a motorcycle increases with speed, since the front tire is resisting any change in steering angle.

 

 

Edited August 12, 2021 by rcgldr
correction ... resisting change in steering angle

[rcgldr]

Camber effect - a tire acting as a truncated cone, causing it to steer in the direction of lean relative to the ground. The amount of camber effect depends on the tire characteristics: diameter, profile, pressure, stiffness, ... . In this video, of a (non-electric) unicycle on a cambered road, at 60 psi there isn't much camber effect because the contact patch is smaller, but the same tire at 35 psi has a larger contact patch and significant camber effect, so that the rider has to lean the unicycle outwards and his body inwards to go straight. With another tire, probably using a stiffer compound, which also reduces camber effect, again there isn't much camber effect:

https://www.youtube.com/watch?v=1MPSdfdA1mU

 

[yoos]

11 minutes ago, rcgldr said:

The point here is that precession is a reaction to a torque, not an angle. If the angle is not changing, there is no net torque and there is no precession.

If the wheel is leaning then there is a non-zero net torque produced by gravity and ground reaction, since these two vertical forces are now applied at points which are offset horizontally. This torque leads to a change in angular momentum direction (precession), which results in turning.

[RockyTop]

Ok, but the force is not always there. ( low speeds) The force is NOT necessary to turn. The force can be countered. The force  can help or hinder steering. I can see how it works. It is simply not all powerful. It is not the only factor in turning. I can follow all your rules to turn left and turn right. 

 

Camber effects: whole new can of worms. Scientists are still to this day arguing about how a bicycle works. It is may things not one. A bicycle does not need “the force “ and it does not need camber. But they are nice to have. 
 

 

 

 

[rcgldr]

1 minute ago, yoos said:

If the wheel is leaning then there is a non-zero net torque produced by gravity and ground reaction, since these two vertical forces are now applied at points which are offset horizontally. This torque leads to a change in angular momentum direction (precession), which results in turning.

If the turn is coordinated, the inwards torque from gravity and ground reaction is countered by the outwards torque due to centripetal force from the ground and the outwards (centrifugal) reaction force at the center of mass for a net zero torque about the roll axis. If the turn is not coordinated, then the lean angle would be changing.

[RagingGrandpa]

I'll just leave this here...

[rcgldr]

2 minutes ago, RockyTop said:

Camber effects: whole new can of worms. Scientists are still to this day arguing about how a bicycle works. It is may things not one. A bicycle does not need “the force “ and it does not need camber. But they are nice to have. 

There is virtually no camber effect on a bicycle or motorcycle. If you have two cones connected to a frame with one cone in front of the other, and with their axes parallel, and you roll it, there will be a lot of sliding, but it will roll straight. This is because the front cone's camber effect is resisted by the rear cone's lateral friction, and likewise the rear cones camber effect is resisted by the front cones lateral friction. Unless the cones are sliding laterally (sideways), the contraption rolls straight. Link to a lighthearted article about this:

http://www.terrycolon.com/1features/bike.html

 

[rcgldr]

Camber thrust is a term describing the centripetal force exerted by the pavement on a tire. It normally used when discussing lateral and rotational deformation of a tire's contact patch in response to lateral loads. This is different than camber effect, which is related to a cone or a truncated cone (such as a leaned tire).

 

[yoos]

8 minutes ago, rcgldr said:

the lean angle would be changing.

the lean angle does not change, but the direction of the angular momentum does. That is precession precisely. For simplicity consider just an infinitely thin wheel (without euc body and rider and without camber effect to think of). There is indeed a coordinated solution where the rolling wheel has a constant lean, constant absolute angular velocity and constant turn rate. The angular momentum in this solution exhibits precession and can be explained in gyroscopic terms: due to the torque created by the lean (it's most convenient to calculate torque with respect to the contact point at each moment of time) the angular momentum rotates, always staying in a vertical plane perpendicular to the wheel.

[RockyTop]

Here is how I see it working. 
The unicycle can move forward or backwards not side to side. It maintains balance front to back not side to side. This creates a vertical axis stable front to back and only allows movements side to side. You create yaw on this axis when you distribute your weight. Like a ball in a pan. You can turn regardless of the mentioned forces. 
 

An EUC with a weightless infinitely narrow wheel would still work as long as it maintained proper traction to the ground and balance front to back. 
 

[Planemo]

24 minutes ago, rcgldr said:

Gyroscopic precession: "Precession is the change of angular velocity and angular momentum produced by a torque." 

https://en.wikipedia.org/wiki/Precession#Classical_(Newtonian)

The point here is that precession is a reaction to a torque, not an angle. If the angle is not changing, there is no net torque and there is no precession. When there is a torque on an uniform wheel, the precession reaction is 90 degrees "behind" the torque.

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

24 minutes ago, rcgldr said:

This is why the cyclic (pitch and roll) control on helicopters is effectively advanced by 90 degrees, 

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... 

24 minutes ago, rcgldr said:

For electric unicycles, you have two primary axes for precession reaction to a torque, yaw - vertical axis, roll

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

[rcgldr]

3 minutes ago, yoos said:

the lean angle does not change, but the direction of the angular momentum does. That is precession precisely. For simplicity consider just an infinitely thin wheel (without euc body and rider and without camber effect to think of). There is indeed a coordinated solution where the rolling wheel has a constant lean, constant absolute angular velocity and constant turn rate. The angular momentum in this solution exhibits precession and can be explained in gyroscopic terms: due to the torque created by the lean (it's most convenient to calculate torque with respect to the contact point at each moment of time) the angular momentum rotates, always staying in a vertical plane perpendicular to the wheel.

In a coordinated turn, the direction of angular momentum only changes about the yaw (vertical) axis, there is no change about the roll axis, and other than small radius turns, the rate of yaw is low. Also the precession reaction due to rotation about the yaw axis would be a response in the roll axis, meaning that the lean angle would be changing, but since this is a coordinated turn, the lean angle is not changing. The rider's control inputs (steering, leaning of the EUC, leaning of the rider), keeps the turn coordinated.