Turning by leaning the wheel, why does it work?

[Mono]

Why does leaning/tilting the wheel lead to a turn? Tilting the EUC changes the circumferences of the left- and right-most contact points of the tire. The inner circumference (to which the wheel is tilted) moves towards the sidewall of the tire and becomes shorter, hence the wheel tends to turn towards this side when rolling forward (or backward). 

The natural path, i.e. the path of least resistance and without permanent steering effort (putting aside balancing), of a tilted wheel is a curve. 

Using a simplifying cone model^1, the radius of the curve depends on tilt angle and wheel radius as^2

    curve_radius = wheel_radius * sqrt(1 + tan^2(90˚ - tilt_angle)),

e.g. about
     tilt angle | curve radius / wheel radius (radius with 14" wheel) 
             0˚ | inf  (inf)
             6˚ | 10   (177cm)
            10˚ |  6   (106cm)
            15˚ |  4    (71cm)
            20˚ |  3    (54cm)
            30˚ |  2    (37cm)
            45˚ |  1.4  (26cm)
...modulo mistakes in my calculations  These numbers are not way off my practical experience. 

The force to steer away from the natural path depends on tire deformation, hence on weight and on tire pressure, and would disappear if the tire were non-deformable.

^1 think of a cone with the same axis as the wheel axis, its side touches the ground (i.e. it can roll on its side), its tip is where the prolongation of the wheel axis cuts the ground. Rolling this cone gives a natural path for a given tilt, it becomes a cylinder if the wheel is not tilted at all. I am sure @esaj could draw a small picture in a minute  
^2 I am not sure how accurately the model reflects the actual difference in circumference in the tire

[Jean eRide.ie Community]

Thanks Niko

I thought about this, but not as much as you did, when someone (WayneZengAU) reviewing the IPS Lhotz said that it turned with much less efforts than other wheels, I realised on some IPS Lhotz photos that the shape of the wheel is more in V than other wheels, like the generic I have, which has a wheel with a shape more in U, so your explanation would explain that review perfectly  

So if you want to turn more with less effort, get a wheel with a V shape haha, but I suppose this will make a bit harder to keep a straight line when going very slow...

VS

[dmethvin]

I've notice this effect as well on the Firewheel, which has more of the U-shaped wheel. When I have the wheel inflated hard it's definitely harder to turn.

[playdad]

So the easy way (for non genius like me!) to compare how easily different wheels would turn would be to first run them on a dusty track/road, then turn them off and manually roll them over a clean flat surface. You can then compare tyre thread width... the thinnest one turns most easily!

I'm going to guess the thicker thread width (more resistance on surface) which are harder to turn would also offer the better stability for learning to ride a EUC though!

[Frode]

I think there might be several effects that work together to turn the wheel:

- The shape of the tire is probably important - the "cone" effect as described by you @Niko. This U-shape is at least very important on motorcycles.

- The "gyro effect" (probably not that important, but it contributes in the right direction). Leaning a rotating wheel to the left will set up a force that tries to turn the wheel to the left. Try this with a bicycle wheel (or search for a youtube video)

- Leaning yourself to the left will move the center of mass to the left of the wheel. Since the wheel is the only contact with the ground, this will set up a torque around the center of mass which in turn will rotate you and the wheel around the center of mass. Think of it like trying to move an object (suspended in the air) forward by only pushing it on the rightmost edge. It will rotate left instead of move forward.

 

[Keith]

OK guys, so how does the Onewheel turn https://onewheel.com? It has a wide and above all flat golf buggy type tyre.

I thought that the riders weight compressed the wheel on one side thus making its diameter smaller on that side and it turns, However I read an article on the effect of indicated road speed if a car's tyres are under inflated and it says the tyre surface acts more like a tank track I.e. If the circumference of the tyre surface is (say) 40 inches, then in one revolution it will always go 40 inches regardless of how flattened the bit in contact with the road is. That makes sense to me, but suggests as @Frode describes above, the U or V shape tyre is most certainly not the only effect in play.

[Mono]

My considerations were concerned with the natural path of the tire, or in other words, why turning feels so much easier and smoother when tilting the wheel. No question that it is possible to not following the natural path of the tire, as it is also possible to turn the wheel on the spot. With a skateboard-like position, it is also easier to apply the necessary force to steer in any direction.

Looking more closely at the Onewheel though, I would think that the tire is not entirely flat.^1 I am also not entirely convinced that tire shape is the only factor determining the natural path, but I wouldn't be surprised if it turned out to be the only relevant factor.

 

^1

see at 2:40, top of tire

[Frode]

4 hours ago, Keith said:

If the circumference of the tyre surface is (say) 40 inches, then in one revolution it will always go 40 inches regardless of how flattened the bit in contact with the road is.

The U-shape of a motorcycle tire make it having a smaller circumference on the edges than in the middle. This is an intentionally designed as well as an important feature of motorcycle tires.

[Gimlet]

Even a solid metal disc with square edges will turn if it is set rolling at an angle!

Surely it's trying to follow the arc of the diameter of the wheel when it is at an angle. This would explain why a smaller diameter 10" wheel is so much more manoeuvrable and turns so much quicker than a 14", 16" or 18" wheel.

 

[Mono]

On 9/10/2016 at 9:12 PM, Gimlet said:

Even a solid metal disc with square edges will turn if it is set rolling at an angle!

Good point. 

Quote

Surely it's trying to follow the arc of the diameter of the wheel when it is at an angle.

But why? And doesn't the size of the diameter depend on the angle? This dependency would be expected from the gyro effect, if I am not mistaken.