## Balancing a Bicycle

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Goemon
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### Balancing a Bicycle

Why is it so much easier to balance a moving bicycle than a stationary one?

Seems like the angular momentum of wheels turning only a few rpm couldn't contribute significantly, considering their mass relative to the rider. But it sure is a lot easier to stay upright on a bike moving even a few kph compared to one that's stationary...
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mattdude
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### Re: Balancing a Bicycle

the answer to this question is essentially the same as the answer to why a gyroscope stays up when you hold one end up.

a change in angular momentum requires a torque. angular momentum is a vector. this means, that a change in angle of the angular momentum _also_ requires a torque. the reason it is easy to stay up on a bicycle going very slowly is a combination of this, as well as our ability to make minute automatic corrections for balance. when you first started riding a bike, you needed your parent to push you to get you going. this was because you didn't have the balance necessary to keep you up at the lower velocities, but instead relied on the larger angular momentum requiring a larger torque to change. it's all about conservation of angular momentum, really. think of the experiment when you stand on a turn table holding a bicycle wheel that is spinning. when you invert the bicycle wheel, it requires some force (or more accurately a torque) because the change in angular momentum causes you to spin on the turn table in order to conserve angular momentum. hope that helped

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### Re: Balancing a Bicycle

I was asking myself this question just last week when I was stuck in traffic and a guy on a bicycle past me.

It is just as the poster above said; Gyroscopic motion gives the bicycle, and any rolling object, a resistance to falling over, that and the rider's ability to make adjustments. The fact that torque varies with the cosine of the angle the wheel is making with the ground also helps in making it relatively easy to balance a bike.
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Charlie!
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### Re: Balancing a Bicycle

Not only does the angular momentum of the wheels help keep you upright, but if you DO start to fall sideways, gyroscope-ness turns them in such a way that centrifugal/centripetal force pushes you upright again.
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mattdude
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### Re: Balancing a Bicycle

Aradae wrote:I was asking myself this question just last week when I was stuck in traffic and a guy on a bicycle past me.

It is just as the poster above said; Gyroscopic motion gives the bicycle, and any rolling object, a resistance to falling over, that and the rider's ability to make adjustments. The fact that torque varies with the cosine of the angle the wheel is making with the ground also helps in making it relatively easy to balance a bike.

sine to the normal, cosine to the horizontal assuming the vertical vector of the bike, inversely true assuming the axle of the wheel. :p that being said, torque is rxF, and cross product is the product of the magnitudes times the sine of the angle between them.... F is gravity going down, r in this case is the vertical vector of the bike...

evilbeanfiend
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### Re: Balancing a Bicycle

theory is all well and fine but if you don't back it up with experiment you are doomed to reach incorrect conclusions

http://www.losethetrainingwheels.org/de ... ev=2&ID=34
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Charlie!
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### Re: Balancing a Bicycle

Erm, wouldn't there still be decent gyroscopitude since the axis of rotation is the line formed by the points where the tires contact the ground, not the point between the two counter-rotating tires?
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evilbeanfiend
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### Re: Balancing a Bicycle

well that would mean the wheels are trying to twist the bike frame to some degree, but every bike i have had has had a rigid (at least in that direction) frame.
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jaap
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### Re: Balancing a Bicycle

I think the gyroscopic nature of the wheels isn't that important.
The most important thing is the self-correcting nature of the steering. The front fork is such that when the bike leans to one side, the front wheel turns into that direction, making the bike turn, and the sideways acceleration a turn brings makes sure you don't fall over.

If you were to make a bike with the front bent the opposite way, it would be near impossible to ride.

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### Re: Balancing a Bicycle

jaap wrote:I think the gyroscopic nature of the wheels isn't that important.
The most important thing is the self-correcting nature of the steering. The front fork is such that when the bike leans to one side, the front wheel turns into that direction, making the bike turn, and the sideways acceleration a turn brings makes sure you don't fall over.

If you were to make a bike with the front bent the opposite way, it would be near impossible to ride.

Isn't the front wheel turning in the direction of the tilt the consequence of the gyroscopic precession?
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Goemon
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### Re: Balancing a Bicycle

evilbeanfiend wrote:theory is all well and fine but if you don't back it up with experiment you are doomed to reach incorrect conclusions

http://www.losethetrainingwheels.org/de ... ev=2&ID=34

Now that's what I call a most excellent experiment! Proof that gyroscopic forces don't contribute significantly to keeping the bike upright.

So in case nobody guessed where I came up with this question: So if you're riding a bike on a treadmill...
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### Re: Balancing a Bicycle

The thing is, the way they made it, the extra wheels aren't allowed to freely precess. The braces keep them from turning thus any gyroscopic effects the extra wheels would have on the entire bike is cancelled by the force the braces provide.

The reason why it's so difficult to ride a rear steering bike is also because of precession. In both cases the "free" wheel will tend to turn towards the tilt. When the wheel that is allowed to precess is in the front this means that the entire bike will tend to turn towards the tilt allowing centrifugal foces to correct the tilt. When in the back the precession is still the same but instead the bike tends to turn away from the tilt and the centrifugal forces from this accelaration tend to increase it.
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Goemon
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### Re: Balancing a Bicycle

Aradae wrote:The thing is, the way they made it, the extra wheels aren't allowed to freely precess. The braces keep them from turning thus any gyroscopic effects the extra wheels would have on the entire bike is cancelled by the force the braces provide.

I think the point is that the precession generated by the extra wheels cancels out the precession generated by the original wheels - thus the resulting bike experiences zero net gyroscopic / precession forces.

And according to the testers, it handles like any other bike, demonstrating that precession is not responsible for keeping a bike upright.

Or is that what you said?
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### Re: Balancing a Bicycle

Goemon wrote:
Aradae wrote:The thing is, the way they made it, the extra wheels aren't allowed to freely precess. The braces keep them from turning thus any gyroscopic effects the extra wheels would have on the entire bike is cancelled by the force the braces provide.

I think the point is that the precession generated by the extra wheels cancels out the precession generated by the original wheels - thus the resulting bike experiences zero net gyroscopic / precession forces.

And according to the testers, it handles like any other bike, demonstrating that precession is not responsible for keeping a bike upright.

Or is that what you said?

It's not that their cancelled out by the precession of the corresponding wheel. Their cancelled out from the frame holding the wheel in place making the only wheel that is free to precess the forward wheel that is on the ground.

Maybe if someone can make a rig where an oppositely spinning wheel is free to precess.
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### Re: Balancing a Bicycle

The precession force is not canceled out by the frame. It's transmitted through the frame, just like any force.

Here's another paper on the subject: http://socrates.berkeley.edu/%7Efajans/Teaching/MoreBikeFiles/JonesBikeBW.pdf.

evilbeanfiend
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### Re: Balancing a Bicycle

yes that was the point about the frame being rigid, it will transmit the force very efficiently.
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meat.paste
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### Re: Balancing a Bicycle

First I learn that the dominant reason why a plane flies because it is pointed upwards and not because of lift on the wings. Now, I learn that precession is not the reason a moving bike stays upright. I still don't understand why the bike is stable, though.
Huh? What?

jmorgan3
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### Re: Balancing a Bicycle

meat.paste wrote:First I learn that the dominant reason why a plane flies because it is pointed upwards and not because of lift on the wings.

What, now?
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Spudgun
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### Re: Balancing a Bicycle

jaap wrote:The front fork is such that when the bike leans to one side, the front wheel turns into that direction, making the bike turn, and the sideways acceleration a turn brings makes sure you don't fall over.

Interestingly, if you go fast enough on a bike (by riding a motorcycle, say) turning the forks slightly to the left will results in the bike leaning and turning to the right, and vice versa. It's known as 'counter steering'.

Macbi
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### Re: Balancing a Bicycle

jmorgan3 wrote:
meat.paste wrote:First I learn that the dominant reason why a plane flies because it is pointed upwards and not because of lift on the wings.

What, now?

Stunt planes can fly upside-down.
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Cynical Idealist
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### Re: Balancing a Bicycle

meat.paste wrote:First I learn that the dominant reason why a plane flies because it is pointed upwards and not because of lift on the wings.

lolWUT?
A plane flies because of the lift produced by the wings. Its engines don't have enough power to actually lift the plane. For proof of this, get in a Cessna and try to fly straight up (that would effectively remove the lift produced by the wings from the equation). We'll be waiting. With medics and firetrucks.

What IS true, however, is that most of the lift produced by the wings is a function of the angle of attack relative to the air. Many airfoil designs produce no lift at a 0 angle of attack, although those tend to only be used in aircraft that are expected to spend some time upside down. Most non-aerobatic, non-combat aircraft have asymmetric airfoils that produce some lift at a 0 degree angle of attack, although that usually isn't enough to support the plane. Therefore a plane (or at least its wings) has to be pointed slightly above horizontal to maintain level flight.
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jmorgan3
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### Re: Balancing a Bicycle

Macbi wrote:
jmorgan3 wrote:
meat.paste wrote:First I learn that the dominant reason why a plane flies because it is pointed upwards and not because of lift on the wings.

What, now?

Stunt planes can fly upside-down.

Because their airfoils are symmetric and, in level upside-down flight, still have positive angle of attack, producing lift to counter the force of gravity. The plane does have to point upwards to achieve that angle of attack, but lift is still produced almost entirely by the wings.
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Mr. Beck
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### Re: Balancing a Bicycle

Yeah, if the wings did nothing to provide lift, then you could saw the wings of a 747 and it'd be ready for liftoff.

oxoiron
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### Re: Balancing a Bicycle

Except for the unfortunate fact that the engines are mounted on the wings.
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Mr. Beck
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### Re: Balancing a Bicycle

Fine, take the wings of an F-15.

...actually, not always.

Zamfir
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### Re: Balancing a Bicycle

Actually, F15's have thrust-to-weight ratio slightly higher than 1, so they could, in principle, take-off when standing on their tail. After sawing off the wings, the weight would be even lower

The question "What causes an aircraft to fly" is much trickier than it seems. Yes, it's the wings, and yes it's the angle of attack. But it is hard to find a non-trivial explanation of lift.

eck
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### Re: Balancing a Bicycle

Like jaap said, if you turn left your forward inertia will try to flip you and the bike over to the right but if you lean left before you turn the gravity will try to flip you over to the left. Gravity pulling left + Centrifugal force pulling right = 0 = balance.
And yes, you are actually using this principle when you are riding straight forward too, it's just that the amount of lean/turn required is very small so you won't think about it.

More reading about the fork-dropout and how it automaticly makes the bike go straight: http://www.gsportbmx.com/tech/steering_geometry.php

For those who still think that gyroscopic forces are in effect, explain how a kickbike with 4cm plastic wheels can stay balanced

But one question still remains: Can you ride a bike on a threadmill?

cspirou
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### Re: Balancing a Bicycle

I don't believe gyroscopic effects contribute to balance unless you are moving quite fast. If gyroscopic effects truly explained balance then what about razor scooters? The wheels are much too small to contribute any sort of gyroscopic effect.

If you are not moving and you lean to the side you fall. But if you are moving and lean to the side you turn instead of falling. To prove this once and for all I think someone has to make an "ice bike" where there's blades instead of wheels. After a convincing run you'll see the effect in action.

edit:ninja'd

meat.paste
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### Re: Balancing a Bicycle

Zamfir wrote:Actually, F15's have thrust-to-weight ratio slightly higher than 1, so they could, in principle, take-off when standing on their tail. After sawing off the wings, the weight would be even lower

The question "What causes an aircraft to fly" is much trickier than it seems. Yes, it's the wings, and yes it's the angle of attack. But it is hard to find a non-trivial explanation of lift.

My real point is that the typical rationale for why a plane flies is that the air movement over the wing creates lift. The major assumption in that theory is that the air cleanly separates at the front edge of the wing and cleanly rejoins at the trailing edge. In commercial jets at least, this assumption is not particularly good. Instead, the attack angle allows for the build up of a high pressure region under the wings, which provides lift. As you cogently state, it is a complicated phenomenon.

I am still interested in knowing why a moving bicycle is more stable than a stationary one if it is not due to gyroscopic stabilization. Could it be related to a human's active balance system? In other words, we (assuming we are all humans) have evolved a dynamic balancing system that allows us to walk upright. Maybe this system is activated when riding a bicycle.

I could easily be wrong, though.
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### Re: Balancing a Bicycle

meat.paste wrote:I am still interested in knowing why a moving bicycle is more stable than a stationary one if it is not due to gyroscopic stabilization.

jaap wrote:I think the gyroscopic nature of the wheels isn't that important.
The most important thing is the self-correcting nature of the steering. The front fork is such that when the bike leans to one side, the front wheel turns into that direction, making the bike turn, and the sideways acceleration a turn brings makes sure you don't fall over.

If you were to make a bike with the front bent the opposite way, it would be near impossible to ride.

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Cynical Idealist wrote:What IS true, however, is that most of the lift produced by the wings is a function of the angle of attack relative to the air.
I think that's what he meant to say. You can design wings which produce enough lift at 0º angle of attack, but design is a compromise. Lift = drag.
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### Re: Balancing a Bicycle

Cynical Idealist wrote:What IS true, however, is that most of the lift produced by the wings is a function of the angle of attack relative to the air.
I think that's what he meant to say. You can design wings which produce enough lift at 0º angle of attack, but design is a compromise. Lift = drag.

Oh, I figured that's what he meant to say. I just felt like being pedantic, and the idea of someone trying to fly a cessna pointed straight up was amusing. Also, I think that the wings on most aircraft--that is, those that are NOT designed for inversion--use an asymmetric airfoil that can produce lift at a 0º angle of attack.

meat.paste wrote:My real point is that the typical rationale for why a plane flies is that the air movement over the wing creates lift. The major assumption in that theory is that the air cleanly separates at the front edge of the wing and cleanly rejoins at the trailing edge. In commercial jets at least, this assumption is not particularly good.

The equal transit time assumption is known to be false (that doesn't stop people from using it, though). That doesn't mean that it isn't the air movement around the wings that creates lift, it just means that most people's idea of how that works is wrong. The main source of lift is the bending of the flow of air produced by the foil.

edit: to attribute a quote
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Charlie!
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### Re: Balancing a Bicycle

Here is, for instance, a picture where people used colored smoke to show the air currents around an airplane's wing: http://upload.wikimedia.org/wikipedia/c ... _edit2.jpg

Awesome, eh? The huge ol' air currents around the wings are the reason something as light as air can support a metal tube.
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### Re: Balancing a Bicycle

Charlie! wrote:Here is, for instance, a picture where people used colored smoke to show the air currents around an airplane's wing: http://upload.wikimedia.org/wikipedia/c ... _edit2.jpg

That's actually the wingtip vortex, which reduces lift (and is the reason why there is a waiting period after a big plane takes off before the runway can be used again). This page offers a better illustration (requires java).
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Charlie!
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### Re: Balancing a Bicycle

Cynical Idealist wrote:
Charlie! wrote:Here is, for instance, a picture where people used colored smoke to show the air currents around an airplane's wing: http://upload.wikimedia.org/wikipedia/c ... _edit2.jpg

That's actually the wingtip vortex, which reduces lift (and is the reason why there is a waiting period after a big plane takes off before the runway can be used again). This page offers a better illustration (requires java).

Oops
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### Re: Balancing a Bicycle

Charlie! wrote:Oops

Heh. It is an impressive image, it just isn't really helpful to understanding lift.

Also, those vortexes scare me. You see how big the vortex from that little single-prop plane is? Now imagine the vortex produced by an "aluminum overcast". Now, imagine flying a little plane, like a Cessna 172, through that kind of vortex. The worst part is that if there are parallel runways, you can hit a vortex from a widebody on the next runway over (they sink and spread out, and are stable for several minutes) without even realizing that you're in danger.
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### Re: Balancing a Bicycle

Cynical Idealist wrote:
Charlie! wrote:Oops

Heh. It is an impressive image, it just isn't really helpful to understanding lift.

Also, those vortexes scare me. You see how big the vortex from that little single-prop plane is? Now imagine the vortex produced by an "aluminum overcast". Now, imagine flying a little plane, like a Cessna 172, through that kind of vortex. The worst part is that if there are parallel runways, you can hit a vortex from a widebody on the next runway over (they sink and spread out, and are stable for several minutes) without even realizing that you're in danger.
And that is why most airports have rules regarding takeoff timings. A few commercial jets have actually gone down due to this.

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### Re: Balancing a Bicycle

The gyroscopic effect of the rotating wheels is a red herring.

If I sit on a stationary bike and I start to overbalance to the right, I cannot correct that overbalance.
If I sit on a moving bike and I start to overbalance to the right, I can steer right and the bike will move to the right. The bike is now underneath me again and I am balanced. It's the same if you are balancing a broom upside down on your finger. When the top of the broom moves in a direction and starts to topple, you move your finger in the same direction underneath it. That way your finger (the bike) stays underneath the center of gravity.

T.

Goemon
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### Re: Balancing a Bicycle

eck wrote:More reading about the fork-dropout and how it automaticly makes the bike go straight: http://www.gsportbmx.com/tech/steering_geometry.php

I interpret "stability" as used here to mean that if the wheel is perturbed to the left (like running over a pebble), the trail and offset tend to push the wheel back to the right. Just means the wheel wants to keep facing straight forward, which (I think) would NOT help with balance. In fact, it might oppose keeping the bike balanced. If you're falling over to the left and try to steer left to compensate, these forces will fight you by trying to push the wheel back toward the right.

dic_penderyn wrote:If I sit on a moving bike and I start to overbalance to the right, I can steer right and the bike will move to the right. The bike is now underneath me again and I am balanced. It's the same if you are balancing a broom upside down on your finger. When the top of the broom moves in a direction and starts to topple, you move your finger in the same direction underneath it. That way your finger (the bike) stays underneath the center of gravity.

I like this explanation. If you're moving forward very slowly, the correction you get from turning the wheel acts slowly too - it takes much longer for the bike to move back under the CG.

Which <sigh> means you shouldn't have any trouble riding on a treadmill
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Starside
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### Re: Balancing a Bicycle

Here is yet more evidence that rotation is not the main ingedient. The ski-bike. No gyroscopic wheels at all.

http://www.ski-bike.org/gallery.html

Although come to think of it the physics of a ski bike may be a little different. Look at the front ski. It is not pointing into the turn. However the geometry of a ski is probably designed to turn into turns. Hell I bet skiing and bicycling mechanics are very similar.

eck
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### Re: Balancing a Bicycle

Goemon wrote:
eck wrote:More reading about the fork-dropout and how it automaticly makes the bike go straight: http://www.gsportbmx.com/tech/steering_geometry.php

I interpret "stability" as used here to mean that if the wheel is perturbed to the left (like running over a pebble), the trail and offset tend to push the wheel back to the right. Just means the wheel wants to keep facing straight forward, which (I think) would NOT help with balance. In fact, it might oppose keeping the bike balanced. If you're falling over to the left and try to steer left to compensate, these forces will fight you by trying to push the wheel back toward the right.

You also have to take into account that when you lean the bike one side of the fork will be closer to the ground than the other thus giving the bike a new lowest-point and making the fork rotate in the direction you are leaning. Otherwhise you wouldn't be able to ride without your hands on the handlebar. It's hard to visualize, i even went looking on my own bike just to see exactly how it works but can't realy see at which fork-angle the bike will find it's lowest point.
It feels like if you lean the bike to the left the absolutly lowest point will come if you turn 90 degrees right which is completly wrong direction. But there is a huge "bump" to get to this point so i guess the rotation is more likely to slide left where there is a continous "fall".

Starside wrote:Although come to think of it the physics of a ski bike may be a little different. Look at the front ski. It is not pointing into the turn. However the geometry of a ski is probably designed to turn into turns. Hell I bet skiing and bicycling mechanics are very similar.

I don't think he even needs the front ski at all. It's the same with bikes, you can ride on only the back wheel and still have realy good steering by just leaning the bike. I know from own experience :]

This made me come up with a new question
Can you turn(or even ride at all) a bike that has locked front fork without lifting the front wheel?