How does a 1-wheeled motorcycle turn?

[DannoXYZ]

I've witnessed 1st-hand with my own eyeballs this guy riding an S-shaped path through chicane at Thunderhill East+West 5-mile combined course with front-wheel IN THE AIR! I believe bike is a Yamaha TZ250, 100-120bhp and 200-lbs weight.

I conducted an experiment to document behavior of single motorcycle wheel using my spare back wheel:

- 17x4" vRossi rear wheel
- 150/60-17 Dunlop Alpha 13-SP rear tyre
- 26 psi tyre pressure

TEST #1 - upright tyre
I stood wheel upright and shoved it down pit lane. It rolled quite a distance with minimal deceleration before finally slowing down enough to fall over. Rough estimate of distance is about 200-ft when I walked down to fetch it.

TEST #2 - leaning tyre
In this test, I stood up wheel about 20-degrees inclined from vertical and shoved it just like before. This time, wheel rolled in decreasing-radius circle (initial one about 20ft radius) in front of me with rapid deceleration and fell over much sooner than straightaway test.Both tests conducted 3x each with similar results. Test #2 confirms what I already knew about cornering, that is it's an energy-consuming action. There is no conservation of energy or momentum, active power is required to be put into system in order for bike to continue around curve at constant speed. Centripetal force required to push bike into curved path comes from scrubbing and distorting tyres and additional power is required to maintain constant speed (more throttle is required compared to same speed in straight line). Ok, let's leave regular 2-wheeled cornering alone for now.

Please discuss what forces and effects come into play when single motorcycle tyre carves curved path... and then reverses curve in other direction. Any applicable equations would be great. Especially if it can predict radius of curve for various lean-angles and speeds of single tyre. Should probably also account for vertical loading of tyre and applied power as these affects size and shape of contact patch.

 

[hutchphd]

Summary: motorcycle carves S-shaped

I've witnessed 1st-hand with my own eyeballs this guy riding an S-shaped path through chicane at Thunderhill East+West 5-mile combined course with front-wheel IN THE AIR! I believe bike is a Yamaha TZ250, 100-120bhp and 200-lbs weight.

View attachment 245414

I conducted an experiment to document behavior of single motorcycle wheel using my spare back wheel:

- 17x4" vRossi rear wheel
- 150/60-17 Dunlop Alpha 13-SP rear tyre
- 26 psi tyre pressure

TEST #1 - upright tyre
I stood wheel upright and shoved it down pit lane. It rolled quite a distance with minimal deceleration before finally slowing down enough to fall over. Rough estimate of distance is about 200-ft when I walked down to fetch it.

TEST #2 - leaning tyre
In this test, I stood up wheel about 20-degrees inclined from vertical and shoved it just like before. This time, wheel rolled in decreasing-radius circle (initial one about 20ft radius) in front of me with rapid deceleration and fell over much sooner than straightaway test.Both tests conducted 3x each with similar results. Test #2 confirms what I already knew about cornering, that is it's an energy-consuming action. There is no conservation of energy or momentum, active power is required to be put into system in order for bike to continue around curve at constant speed. Centripetal force required to push bike into curved path comes from scrubbing and distorting tyres and additional power is required to maintain constant speed (more throttle is required compared to same speed in straight line). Ok, let's leave regular cornering alone for now.

Please discuss what forces and effects come into play when a single motorcycle carves a curved path... and then reverses curve in other direction. Any applicable equations would be great. Especially if it can predict radius of curve for various lean-angles and speeds of a single tyre.

First I believe that you should think about a guy on a unicycle. That is a simpler and largely equivalent system. How does he turn?
(My assumption here is that the residual angular momentum of the front wheel does not matter...)

 

[DannoXYZ]

At first I thought unicycle too. Which steers like a car with an upright wheel pivoting around vertical axis to aim in new direction of travel.

However, in this case, there is no vertical steering of back wheel that I could see, it's aimed down the road at all times. The only dynamic change I could detect is lean angle of rear-wheel.

That's why I did test#2, even when shoved in straight line, leaning tyre wants to carve curved path towards leaning side and then turns even tighter as it slows down. I think there's an equation tying horizontal speed with lean-angle and resultant curvature of turn somehow.

yeah, angular momentum of front wheel doesn't seem to affect anything. Especially since he's able to reverse direction of turning with front wheel still in air.

 

[hutchphd]

At first I thought unicycle too. Which steers like a car with an upright wheel pivoting around vertical axis to aim in new direction of travel.

However, in this case, there is no vertical steering of back wheel that I could see, it's aimed down the road at all times. The only dynamic change I told detect is lean angle of rear-wheel.

That's why I did test#2, even when shoved in straight line, tyre wants to carve curved path towards leaning side and then turns even tighter as it slows down.

I think when in forward motion the unicycle guy steers by leaning ...to one side and slightly back I think. Do you see the physics? Sort of like riding "no hands" on a bicycle,,,

 

[DannoXYZ]

Riding no-hands on bicycle still uses front-tyre for steering though. As it's completely different behavior than doing wheelies and steering.

How does countre-steering cause wheel to turn in opposite direction? I'm pretty sure when wheelieing motorcycle, he leans towards direction he wants to turn. When he lands front-wheel after coming out of S-turn (left-turn), the bike is already leaning towards left, and it continues to turn left after front-tyre contacts.

 

[hutchphd]

Riding no-hands on bicycle still uses front-tyre for steering though. As it's completely different behavior than doing wheelies and steering. How does countre-steering cause wheel to turn in opposite direction? I'm pretty sure when wheelieing a motorcycle, he leans towards direction he wants to turn.

Also on a bicycle the angular momentum of the front wheel makes it turn into the lean when "no hands".
I am thinking that there will be enough angular momentum in the rear wheel to make it rotate the bike to the right (via precession) when he leans. How he reverses this must involve the throttle

 

[DaveC426913]

How he reverses this must involve the throttle

Or he just leans back the other way to right the bike?

 

[hutchphd]

I am not a motorcyclist but how does he do that while leaning in a wheelie? Doesn't sound do-able to me..

 

[DannoXYZ]

Also on a bicycle the angular momentum of the front wheel makes it turn into the lean when "no hands".
I am thinking that there will be enough angular momentum in the rear wheel to make it rotate the bike to the right (via precession) when he leans. How he reverses this must involve the throttle

precession is not at work here because neither on bicycle nor motorcycle does front wheel reverse direction of spin in order to turn the other way. Front wheel in air has no effect on turning direction of bike either.

Precession forces from 1.5-lb bicycle wheel or 5-lb motorcycle wheel spiining at 100 RPMs has negligible impact on 200-lb or 500-lb object moving at 50+mph.

Even when uncoupled from bike and rider, rolling wheel by itself does not turn by itself, showing precession has no effect. Until it slows down enough to tilt (from uneven ground), then the angle of wheel causes it turn rapidly into tightening circle until it falls down. And it falls left and right at even rates.

the key here is the tilt angle. Need to find way to quantify it.

 

[DannoXYZ]

I am not a motorcyclist but how does he do that while leaning in a wheelie? Doesn't sound do-able to me..

Or he just leans back the other way to right the bike?

Yup, I think it's the butt and hips causing changes in lateral tilt. Like riding bicycle no-hands. Tilting bike causes front-tyre to countersteer and causes bike to lean over. Seems this guy is able to teeter-totter left/right to cause tyre to lean.

Throttle only affects longitudinal movement, more or less wheelie angle, but bike and wheels stay in vertical plane.

So I'm trying to model this leaning behavior. I suspect that since a bare tyre carves tight circle when leaned small angles by itself, that adding higher loads from weight and speed lessens this turning effect. Just would like to model more accurately.

 

[A.T.]

Precession is not at work here because neither on bicycle nor motorcycle does front wheel reverse direction of spin in order to turn the other way.

The direction of spin doesn't have to be reversed. The precession steers the wheel to the opposite side to the current lean side. This plays a role (not solely) in self stability with the front wheel on the ground:

Front wheel in air has no effect on turning direction of bike either.

If it is spinning when lifted, it can play a role in balancing and turning like a gyro in single track cars:

 

[DannoXYZ]

Here's related behavior with sidecars. Traditional sidecars that keep tyres vertical requires the motorcycle's front wheel to turn like a car's and generate lots of cornering forces. Result is sidecars must go a lot slower than same motorcycle by itself around curves.

However, uncoupling sidecar from motorcycle so it can lean on its own resolves all that. Single wheel on sidecar generates enough cornering force to cover its own weight, such that this bike+sidecar combo can go around curves at same speed as single bike can at same lean angle.

Experiments have have shown that when detached in middle of turn, sidecar continues going around turn on its own and carves tighter a tighter curve as it slows down and eventually falls inward (like my single tilted wheel experiment).



This cornering force appears to be independent of sprung vs. unsprung mass. Appears to be function of total mass, speed and lean angle.

 

[hmmm27]

Please discuss what forces and effects come into play when single motorcycle tyre carves curved path... and then reverses curve in other direction. Any applicable equations would be great. Especially if it can predict radius of curve for various lean-angles and speeds of single tyre. Should probably also account for vertical loading of tyre and applied power as these affects size and shape of contact patch.

Creative kinaesthetics.

Deke one way and you'll start falling the other way. Turn into the fall to keep balance during the curve, and cut into untilt and continue on a straight line (or go the other way to do an S-curve). Wikipedia's take
(But, I'm not sure anybody's ever learned to ride a bike by figuring out the physics first)

The tire on a bike is turned by the handlebars ; on a unicycle, by the rider's waist - upper torso twists one way, lower body and unicycle the other.

For the sidecar and "test#2", the rotating mass of the tire is a good chunk (or all) of the entire mass, and precession kicks in noticeably which actually changes the tire's direction of travel.

Also, for a round cross-section 'bike tire (as opposed to a square car tire), the more it's tilted, the smaller the radius... a bit too late at night to think properly, but that probably adds to the decreasing spiral, as well.

 

[hutchphd]

The precession steers the wheel to the opposite side to the current lean side.

Great videos with lots of good information.
One correction to commentary: the precession will turn the front wheel towards the direction of the lean. If you lean right the wheel steers right.

 

[A.T.]

One correction to commentary: the precession will turn the front wheel towards the direction of the lean. If you lean right the wheel steers right.

Yes, of course. Fixed it.

 

[waross]

A tilted wheel acts as a cone, hence the curved path.
At a given speed and a given tilt angle, the center of the curve radius is the point where an extension of the axle meets the horizontal plane of the roadway.
As the wheel slows, it loses centrifugal force and leans more to establish equilibrium. Hence the decreasing radius of the curve.

Motor cycles and counter steer.
At very slow speeds, the motor cycle may be steered with a combination of steering effort and body movement.
At higher speeds, counter steer becomes significant. The amount of counter steer effect varies from model to model.
Don't try this at home. I have tried it on at least two bikes, but I cannot and will not vouch for all bikes.
Riding at speed and hands off: I gently pushed the end of the right hand handle bar forward. GENTLY.
This should make the bike curve to the left, right.
Wrong.
This causes the bike to fall to the right.
The front wheel now acts as a truncated cone and the bike curves to the right.
Counter steer. Counter intuitive.
Think cone for curves of one and two wheeled vehicles.
At slow speeds the wheel may be turned to initiate a curve and the body weight shifted to counteract the centrifugal force generated.
At speed shifting body weight (mass?) will initiate a curve. Counter steer may be required to shorten the radius of the curve.
True story.
Riding a bike fast and coming into a corner.
Leaning would not shorten the radius enough to stay on the road and I was about to go cross country.
Not a good thing on a mountain highway.
(You-tube: "Arlo Guthry, The motorcycle Song" The version on the Arlo Album)

There was no cop to break my fall.
At the last moment I remembered counter steer and applied steering force towards the edge of the road.
The curve radius shortened up and I stayed on the road.
CAUTION.
THERE MAY BE SOME BIKE MODELS WERE COUNTER STEER MAY CAUSE THE FRONT WHEEL TO TURN THE WRONG WAY AND LAUNCH YOU OVER THE FRONT.
I DON'T KNOW.
IT DEPENDS

 

[rcgldr]

Unicycles can be steered by twisting (yaw) and|or tilting (roll). Twisting directly steers the tire, while tilting relies on camber (cone) effect to steer the tire. For any uni-track vehicle, counter-steering is used to initiate or adjust lean angle. Steer outwards to lean inwards, and once leaned, steer more to lean less (or straighten up), steer less to lean more.

In the case of a motorcycle doing a wheelie, the rider can twist and|or tilt the bike by moving with respect to the bike, generating internal forces and|or torques via weight shifting, foot and hand forces, depending on the riders center of mass with respect to the contact patch. Standing up allows for more effect. Stunt video:



Unicycles with seats limit the amount of tilt and speeds are relatively slow, so the primary means of steering is to use momentum to twist the tire, such as flailing extended arms left to steer right and vice versa. Advanced riders can use pedal pressure to invoke twisting motion. This is done for balance and direction. At sufficient speed, tilting | camber effect can be enough to turn.

Electric unicycles (EUC) use a similar front | back balancing setup that Segways use, so the rider only has to balance left | right, and at sufficient speed, an EUC becomes stable if riding in a straight line, due to riders momentum causing the EUC to tilt and steer into direction of fall. Electric unicycles without seats can be tilted much more than the early ones that had seats, and speeds are typically faster, so tilting | camber effect is the primary means to steer. I bought an electric unicycle (Inmotion V8F) back in August 2021. I first used arm flailing | twisting | yaw steer at 3 to 5 mph, doing laps around a tennis court. I then moved to a long straight outdoor parking lot, and found my V8F became stable at around 7 mph, and I could relax my arms. Becoming proficient at tilt steering (inner foot down, outer foot up) takes a while, because the camber response to tilting depends mostly on tire parameters (wider tires are more responsive, knobby tires are less responsive, ...), and not speed. Tilting generally steers with a fixed radius regardless of speed (within reason), but the rider has to lean based on lateral acceleration (speed^2 / radius), so what takes a while to learn is how much to tilt the EUC and how much to lean, depending on speed and turning radius.

As for motorcycles with both tires on the ground, there is no camber effect. The camber effect from one tire could only occur if the entire bike twists, requiring the other tire to skid sideways. Camber effect on the front tire could cause it to steer inwards, but trail is the dominant effect: the contact patch is behind the virtually extended pivot axis of the front forks, and when leaned, the upwards force from pavement at the contact patch steers the front tire inwards, usually enough to return the bike back to vertical, and the rider has to oppose this with a bit of counter-steering torque on the handlebars to prevent the self-correction in order to hold a lean angle. Since a rider typically is counter-steering all the time to initiate, control, or adjust lean angle, this isn't an issue.