# What do you think about when stillstanding?

Re: What do you think about when stillstanding?

On Wed, 29 Oct 2003 07:26:56 -0600, cyberbellum
<cyberbellum.w2bvf@timelimit.unicyclist.com> wrote:

>If the upper pendulum CG is high when throwing the weight to the fall
>side, but low on the return swing, then I think dynamically the system
>can be controlled. You can model this by keeping your arms and head
>high when you flailing in the direction of the fall, but low on the
>recovery stroke.

I’m not sure if I understand what you mean by ‘dynamically’, I have
the impression it somehow implies momentum transfer. But if Andrew or
anyone shows that the ‘correct high, recover low’ method gives an
improvement, it might also be explained by the effect of rowing with
your arms through viscous air having a finite density.

## Klaas Bil - Newsgroup Addict

Grizzly bear droppings have bells in them and smell like pepper spray. - UniBrier

Re: Re: What do you think about when stillstanding?

Yeah, there’s a lot going on. Aerodynamic forces contribute too.

I tried to edit in what I meant by dynamically but got timed out. It means taking advantage of changes over time - changes in speed over time (accelerations), changes in position over time (velocities), changes in accelerations over time (jerks), etc.

So I’ll start over and hopefully get it right this time.

When the inverted contraption is perfectly ballanced and the wheel is perfectly still then it is in an unstable equilibrium. All the forces on the contraption exactly cancel out - which means that it is in equilibrium, but if it tips just a bit then it will keep on tipping - which implies an unstable equilibrium.

There are two external forces acting on the contraption. There is the force of gravity, which can be thought of as a pull straight down through the center of gravity; and there is the contact force that the ground exerts on the T bar that resists the force of gravity. When it is in static equilbrium these two forces exactly cancel out. However, when it tips the center of gravity moves to the side a bit. Now these two forces are displaced so they make what is called a “couple” that applies a torque to the system.

The torque from this couple accelerates the contraption, making it tip a little faster. It’s added a little angular momentum. And as it tips further the two forces get even more misalligned and the couple gets stronger. Which makes it tip a little faster - which means even more angular momentum, until it eventually just whacks the ground.

The only way to get the contraption back into equilibrium is to reverse the couple for long enough to erase this unwanted angular momentum. If the contact patch could move, as it does when hopping, pogo-ing BC wheeling or slack-wire walking - then the easy way to reverse the couple is to put the contact patch to the other side of the CG.

However, with a fixed contact patch the only option is to move the CG to the other side of the contact patch. At first I thought this was impossible, but now I see that it happens while the upper part is undergoing a strong angular acceleration like a quick jerk of the torso down and in the direction of the fall, or a whirling of the arms in a circle.

So the trick seems to be to put in a hard angular acceleration before the thing has had time to tip very far (and therefore pick up an insurmountable angular momentum) so that the CG moves to the other side of the contact patch and reverses the tipping couple. Then WAIT for a while until this reversed couple has canceled out the unwanted angular momentum, then straighten up back into equilibrium.

The ideal still-stander would have a very light unicycle or pogo stick, very long and skinny legs (tall inverted pendulums tip slower than short inverted pendulums), a really wide upper body with a high moment of inertia (resistance to rotational accelerations), a really good sense of balance with VERY quick reflexes, and a wicked strong set of abdominal muscles.

Another thing that would probably help is ducking down on the recovery.

I hope this was a bit clearer. (Somehow I suspect I’ve left out a few key clues. Ah, well, it’s just a post. If it were a paper that I could edit it for a week or two I’m sure I could do a better job.)

Cheers,

Tim

Peter,

While still standing I often ponder whether it is better to have my weight on the seat or off of it
Have you come to a conclusion yet? I’ve also been wondering this.

Tim,

I went out for a little attempt then but had trouble changing my style of stillstanding. I’m not very confident with them as it is…15 seconds is my best. I usually get less than 10 seconds. I was actually having trouble in general with stillstands just then. I don’t feel very coordinated today. I have a feeling that the way I’m stillstanding, I rely quite a bit on the arms giving more torque than the lower parts of my body. I’ve come to this conclusion because it makes sence and also because I did a lot better when holding onto two juggling clubs than when just doing plain stillstands without holding onto anything. Although it’s probably a bit of an over-simplified model (since I’m not really in control of all my movements), I think I am using your ‘correct high, recover low’ technique. I’ve got a video of myself stillstanding with the clubs. I can add it to my gallery if you want to see it.

Andrew

Re: Re: Re: What do you think about when stillstanding?

I’m trying to get to grips with this and I think I at least partly understand it. If the rider would perform said angular acceleration while floating in the air or when the wheel rested on, say, frictionless ice, then the wheel would move in the direction of the fall. This is because of the conservation of angular momentum of the whole rider+uni system. However, there is friction on the ground, and this exerts a reaction force away from the direction of the fall. This reaction force, being the only external force acting upon the system, in turn accelerates the mass of the whole system in a direction away from the fall. Hence, the centre of gravity moves back, away from the direction of the fall.

Were you thinking along similar lines?

Klaas Bil

Re: Re: Re: Re: What do you think about when stillstanding?

Bingo.

In a previous post someone recommended using a long pole like the high-wire artists do. The effect of this pole is to dramatically increase the moment of inertia (resistance to rotation) of your upper body. It’s a good idea.

Yeah, makes sense.

I used to kayak a lot and had a pretty decent no-paddle roll. I found that I could do a one-armed roll with a closed hand if I had a rock in my fist. I think your arm can be accelerated a lot harder than the rest of your torso because the shoulder joint is so free; also the inertial effect increases dramatically for masses that are far from the pivot point (it scales with the square of the distance), so your hand/forearm (and juggling club or rock) are the masses that are doing most of the work.

As for the video, I bet you look a lot like a rodeo cowboy. That style of arm swing is probably the most efficient way to balance.

Re: What do you think about when stillstanding?

Reviving this thread after two weeks.

Today I practiced some more still stands but it didn’t go well due to
wind. Anyway, I came up with another physical effect that I think is
counterproductive in stillstanding… Until now we have considered the
support point with the ground as a pivot point. As if it would not
matter if the frame stood on one pointed stick rather than a round
(toroidal) tyre. But it does matter.

If you loose it to the front and you bend your upper body forward, the
frame will rotate backward. Now, as per the definition of
stillstanding, the wheel is not allowed to rotate with respect to the
frame, which means that the wheel will roll backward over the ground.
That brings the support point to the rear, with respect to the
original support point on the ground. That effect in turn aggravates
any forward falling rather than preventing it.

A similar reasoning applies to left/right balance. However, there the
effect is much smaller since the width of the tyre is much smaller
than the diameter of the wheel, so the displacement of the contact
point is much smaller.

That brings me to the conclusion that maintaining forward/backward
balance should be more difficult than maintaining side-to-side
balance. The fact that I haven’t noticed this in practice may be an
indication that I am (unknowingly) cheating with a little horizontal
idle. Today I tried to prevent that by stepping simultaneously on the
pedal and the crank with the forward foot, but there was still some
flexibility.

Hey, I need a brake for stillstanding!

## Klaas Bil - Newsgroup Addict

“My butt has a crack in it , but I can still ride. - spyder”

According to surveys, If any of us males stillstand for more than 7 seconds, we should probably all be thinking about sex or food, mmmmmm, roast beef sandwiches

Re: Re: What do you think about when stillstanding?

Makes sense. Then again, it’s easier to kip forward and back than it is to kip sideways. It’s worth modeling up and seeing how big the difference is.

Re: Re: What do you think about when stillstanding?

I think stillstanding is a bit like standing on one foot – you distribute your weight throughout the “footprint”, putting more force on your toes to correct a forward lean.

I’m sceptical of the angular momentum argument. The object at the end of the pointed stick can redeploy its mass, but it can’t move its CG without an outside force. Neither pushing nor pulling on the stick seems to do it. Pulling off your pads and throwing them would help, but that would be cheating.

There is always air, but in a vacuum I don’t see how it works.

Re: What do you think about when stillstanding?

klaasbil_remove_the_spamkiller_@xs4all.nl (Klaas Bil) wrote:

>If you loose it to the front and you bend your upper body forward, the
>frame will rotate backward. Now, as per the definition of
>stillstanding, the wheel is not allowed to rotate with respect to the
>frame, which means that the wheel will roll backward over the ground.
>That brings the support point to the rear, with respect to the
>original support point on the ground. That effect in turn aggravates
>any forward falling rather than preventing it.

This effect is proportional to wheel size. So the effect is less on a
smaller wheel.

With quick reactions, the angle the frame moves back and forth is small,
so the slight shifting of the support area is small as well. One’s
reactions will naturally take this into account in the feedback loop of
the balance envelope. In other words, it may not be that much more
difficult.

In fact it may be more difficult to keep the wheel stationary with
respect to the ground than with respect to the frame. That’s because it
is easier to keep the angle between the frame and cranks constant than
to constantly vary that angle in sync with the frame angle changes such
the angle between the cranks and the ground remains constant.

>Hey, I need a brake for stillstanding!

In my opinion, if the cranks move no more than one or two degrees
relative to the frame (barely perceptible to the naked eye) that might
be still count as a still stand rather than a horizontal idle, so long
as the direction of the wheel doesn’t change (twisting).

Sincerely,

Ken Fuchs <kfuchs@winternet.com>

Sorry in advance for wording this so poorly but…

You know how the parts of your body that are higher up when stillstanding have more influence on correcting your balance? Well, would the difference in this influence be greater if the separation distance was the same (the rider is the same height, etc) but the whole body was higher (eg. on a tall giraffe)?

Thanks,
Andrew

All good questions. I’m curious, so I’m going to do the math, probably this weekend.

My initial guess it that it cancels out. If the body is the same then the angular momentum is the same regardless of it’s location. Putting the rider mass higher makes the inverted pendulum taller, which slows everything down, but it also increass the leverage of the contact patch which means the restoring force is smaller.

The angular error of a simple (i.e. frozen rider) inverted pendulum grows at an exponential rate that is proportional to the square root of gravity (9.81 meters per second squared) divided by the length of the pendulum. Doubling time, an easier to grasp concept, is inversely proportional to the exponential error growth rate, so it is proportional to the square root of the length of the pendulum.

For comparison purposes all the other constants cancel out. If you figure that the center of gravity of a standard uni and rider is about 1.3 meters above the ground (square root , and the same rider on a giraffe uni has a CG at 2 meters above the ground, then the doubling time for the giraffe is about 24% slower than for the conventional uni.

On the other hand, the lever arm of the giraffe is 54% longer, so the force needed to cancel the angular momentum of the rider’s sudden kipping motion is going to be 35% smaller ( 1/1.54 = 1.35). So if the rider had perfect reflexes then he’d be better off on a standard unicycle.

But humans don’t have perfect reflexes. The human nervous system needs about a tenth of a second to detect and react to things. The giraffe gives the rider a little more time, which probably makes up for its weaker reaction force, so my SWAG (Scientific Wild-Ass Guess) is that still-standing on a giraffe is about as hard as still-standing on as a standard unicycle.

My non-scientific sense is that it depends on what you are used to. It hurts more to fall from a giraffe, and it takes longer to get back on, so I don’t see that there is a real advantage to going higher unless a) it’s your only ride, b) money is involved, c) an attractive woman is nearby, or d) you just want to.

My 2 cents.

Re: What do you think about when stillstanding?

On Fri, 14 Nov 2003 14:19:25 -0600, Beener
<Beener@NoEmail.Message.Poster.at.Unicyclist.com> wrote:

>According to surveys, If any of us males stillstand for more than 7
>seconds, we should probably all be thinking about sex or food

Now I know why I can’t get past that 7 seconds barrier

## Klaas Bil - Newsgroup Addict

“My butt has a crack in it , but I can still ride. - spyder”

Re: What do you think about when stillstanding?

On Fri, 14 Nov 2003 16:44:47 -0600, cyberbellum
<cyberbellum@NoEmail.Message.Poster.at.Unicyclist.com> wrote:

>It’s worth modeling up and seeing how big the
>difference is.

Keep us posted!

## Klaas Bil - Newsgroup Addict

“My butt has a crack in it , but I can still ride. - spyder”

Re: What do you think about when stillstanding?

On Fri, 14 Nov 2003 18:48:49 -0600, cjd
<cjd@NoEmail.Message.Poster.at.Unicyclist.com> wrote:

>I think stillstanding is a bit like standing on one foot – you
>distribute your weight throughout the “footprint”, putting more force on
>your toes to correct a forward lean.
But, unlike with your foot, you can’t do that with your tyre
independently from changing the angle (lean) of the frame.

>I’m sceptical of the angular momentum argument. The object at the end of
>the pointed stick can redeploy its mass, but it can’t move its CG
>without an outside force.
There /is/ an outside force, i.e. the horizontal (component of the)
reaction force that the ground exerts on the tyre.

## Klaas Bil - Newsgroup Addict

“My butt has a crack in it , but I can still ride. - spyder”

Re: Re: What do you think about when stillstanding?

Well, I did the math tonight. I had dinner at a sushi bar and used the paper cover that the chopsticks came in to write on. The sushi chef was amused. He kept asking me if I needed a bigger piece of paper, then laughing. The waitress got into it too - she was so concerned that I ordered another beer to give her something to do.

Anyhow, it turns out that the effect is the opposite of what you would think. The bigger the radius of roll in the direction of tip, the easier it will be to still stand. Rather than go through the math I’ll describe what is going on with a little thought experiment.

Imagine a vertical pole holding a mass up off the ground. It doesn’t really matter if the pole has mass or not, so for simplicity let’s pretend it doesn’t have any mass. All the mass is concentrated at the top of the pole. Now imagine that the bottom of the pole is sharpened like a pencil. When you let go of the pole it will start to tip over and eventually the mass hits the ground. This simple device is called an inverted pendulum, and the time it takes to fall is proportional to the square root of the length of the pendulum divided by the acceleration of gravity.

Now add a lightweight hemispherical shell to the bottom of the pole, as if it were a rod sticking up from the middle of a defective mixing bowl (no flat on the bottom). Oh, and imagine the bottom of this hemispherical shell is coated with rubber or some other non-skid so that it rolls instead of slips.

If the radius of the bowl is very small, like a bb, then the inverted pendulum will still act like an inverted pendulum. If the size is increased a bit, to about 3 inches in diameter, then the pendulum will behave like a still-standing unicycle falling to the side. If the size is increased even further, to perhaps 24", then it behaves like a still-standing uncycle rocking forward or back.

Now imagine that the bowl is increased in size even further, until the radius of the bowl is exactly the same as the length of the rod. It’s no longer a pendulum, is it? When the bowl rolls the mass stays at exactly the same height, so there isn’t any change in the potential energy.

Now increse the size even further. Remember weebles? They wobble but they don’t fall down? When the bowl is rocked it INCREASES the height of the mass, so when you let go it tries to get the mass back to where it started.

Anyhow, I guess the point is that the larger the contact radius the slower and gentler the fall.

Ok, so on to the results. Assuming a normal rider (about 180 cm and 70 kilos) on a 24X3 wheel, the doubling time for falling over sideways is somewhere around 0.26 seconds and the doubling time for falling over front-to-back is on the order of 0.31 seconds. This extra time, plus the easier bending at the waist front to back, should make it easier to correct front-to-back than side to side.

Then again, there is the “getting the CG to the other side of the contact patch” problem… Hmmm… Ok, I will have to solve the whole problem. Keep you posted,

Tim

Re: What do you think about when stillstanding?

<GILD.w0n7z@timelimit.unicyclist.com>
<andrew_carter.w08f5@timelimit.unicyclist.com>@timelimit.unicyclist.com

cjd <cjd@NoEmail.Message.Poster.at.Unicyclist.com> wrote:

>I’m sceptical of the angular momentum argument. The object at the end of
>the pointed stick can redeploy its mass, but it can’t move its CG
>without an outside force. Neither pushing nor pulling on the stick seems
>to do it. Pulling off your pads and throwing them would help, but that
>would be cheating.

If angular momentum doesn’t allow a unicyclist to still stand, then
angular momentum can’t help keep a wire walker on the wire either. A
wire walker could use a balance pole to make things easier. A
unicyclist could use two balance poles (at right angles) to make the
still stand easier. The balance poles simply add the the available
angular momentum of the wire walker and still standing unicyclist
respectively.

Sincerely,

Ken Fuchs <kfuchs@winternet.com>

Re: Re: What do you think about when stillstanding?

OK, thanks, now I think I get it. I start to fall left, then I rotate my arms counterclockwise (left arm down, right up), so the rest of me rotates clockwise, and the rest of me is connected to the pointed stick, so I try move the point of the stick left, but it doesn’t slip, so I move right. Once I’m safely on the other side of the equilibrium, I can sort out the fact that my arms are still rotating relative to my body. The image I have is of an oreo cookie at the end of a pencil, with half of the cookie connected to the eraser and the other half free to rotate.

I still think there’s some shifting of weight within the contact area of the tire. Is it noticably easier to stillstand on a square tire, like a gazz vs a halo/duro?

Re: Re: What do you think about when stillstanding?

I always thought they moved the wire, but now that I understand the angular momentum thing I can see that even works with a tight wire.

Would be interesting to try the balance cross.