BC Wheels Physics????????

Unicycles and Equipment
1

For my physics class, I had to pick a topic and give a presentation on the physics of it. Obviously, I had chose unicycling. Over the past 4-5 months, I have been slowly garnering all the info on unicycling physics out there.

Now I’ve come to a road block. My sources (and my riding experience) indicate that unicycles are made possible b/c the rider has direct control over the wheel, so they can compensate if they are leaning out too far etc … Therefore, coasting is one of the hardest skills possible on a unicycle.

Now, onto the problem. BC wheels coast. According to the above, then how is it possible to ride one? At first, I thought precession was the answer (a rotating circular body, wheel, will stay upright), but that only deals with side to side balance, not forwards and backwards balance. Then I thought it was because your center of mass is lower than when you coast on a regular unicycle. But center of mass does not affect your balance by much.

Anybody have any thoughts? Thanks.

2

Re: BC Wheels Physics???

“DasDingus” <DasDingus.m9qib@timelimit.unicyclist.com> wrote in message
news:DasDingus.m9qib@timelimit.unicyclist.com…
>
> Now I’ve come to a road block. My sources (and my riding experience)
> indicate that unicycles are made possible b/c the rider has direct
> control over the wheel, so they can compensate if they are leaning out
> too far etc … Therefore, coasting is one of the hardest skills
> possible on a unicycle.
>
> Now, onto the problem. BC wheels coast. According to the above, then how
> is it possible to ride one? At first, I thought precession was the
> answer (a rotating circular body, wheel, will stay upright), but that
> only deals with side to side balance, not forwards and backwards
> balance. Then I thought it was because your center of mass is lower than
> when you coast on a regular unicycle. But center of mass does not affect
> your balance by much.
>
>
> Anybody have any thoughts? Thanks.

I believe coasting is harder than BC because you have don’t have Direct
control over the wheel. You have Indirect control through the frame
only and you are way above the axle rather than on or below the axle with a
BC.

David Winston

3

I don’t have an answer for you, but you may be able to come up with something by looking at videos of people BC’ing. I’ve got one at http://www.unicyclist.com/gallery/andrew that may help. If you come up with anything, please let us know because now that you mention it, I’m also very curious about it.

Thanks,
Andrew

4

In terms of physics isn’t just a case of miving your centre of gravity around?

If you start to fall forwards then move your COG behind the wheel to counter the effect, if you fall back then move your COG forwards.

I’m not sure about your statement:

"But center of mass does not affect your balance by much. "

The position of your centre of mass IS balance.

5

Interesting…

Of course, I’ve never ridden a BC wheel, so anything I write will be even more nonsense than usual, but…

Newton’s 3rd (?) Law of Motion = for every action there is an equal and opposite REaction. So, if you try to move your Centre of Mass (UK older readers (like me) = Centre of Gravity) you need to push against something. Imagine you are balanced on a perfect point; you throw your arm to the right, and the rest of you will move slightly to the left, and the CoM remains in the same place.

Now, side to side balance on a unicycle or BC Wheel is controlled by moving the centre of support (the tyre contact patch) from side to side. This is why we wiggle when we ride. So, you’re falling to the left; you’re still moving forwards, though; you turn the wheel to the left; this tends to work against your forward motion, and your forward momentum swings you back upright. Or you can use a turn left to throw your weight to the right of the wheel, to induce a right turn (countersteering).

What if you’re falling off the back of a unicycle? You slow the wheel down. Your momentum carries you forward, until you are once again above the centre of support. I guess you can slow down a BC wheel by either friction with the wheel or tyre, or by deliberately steering sharply - perhaps zig zagging a bit.

What if you’re falling forwards? On a unicycle, you speed up the wheel, until the centre of support is back under you. As far as I’m aware, there is no mechanism for speeding up a BC wheel, once it’s rolling (other than going down a hill) so I guess that falling off the front of a BC wheel on the flat is pretty much inevitable, once the fall starts.

So:
Side to side balance, move the wheel to counteract.
Falling off the back, slow the wheel down.
Falling off the front, speed the wheel up if possible.
Falling off the front of a BC wheel? Look for a soft place to land?

This leaves out a control method: rotary movement of the arms.

Your arms are surprisingly heavy. More so if you wear wrist weights.

If you move your arms in circles with horizontal axes, then the top of the circle is further from the ground than the bottom of the circle. If I’ve got this right, this means that the extra leverage when the hands are at the highest point of the circle (for want of a better word) ‘magnifies’ the reactive effect. So, e.g., if you rotate your arms as if you were swimming backstroke, this will tend to tip you forwards.

I’m not quite sure of the maths on this, but I do know (from a science museum trip) that if you sit on a swivel chair and hold a rotating wheel by the axle, you can make the chair swivel one way or the other by which way up you hold the wheel. I’ve done it myself, but can’t explain the physics any more clearly. so, I guess that you could influence the balance of the BC wheel ‘to some extent’ by rotating the mass in your arms.

Any better ideas?

6

Reality check:

B.C. wheels work. Yes, they ride a “fine line” of control availability, and yes, they’re easier than coasting on a regular unicycle for the reasons David Winston put forth.

Almost all the basic physics that I read about here is too elementary to cover unicycling situations. The body is fluid. We don’t bend like simple hinged objects, we bend in all sorts of multiple directions and combinations.

Breaking down what makes a B.C. wheel work for a physics class might be hellishly complicated. Obviously the complication is coming from the movements of the human body rather than the extremely simple vehicle. I never took a physics class though, so don’t listen to me on that. All my physics knowledge is “seat of the cycling shorts.”

Somehow, as in coasting on a regular unicycle, with a B.C. wheel you have a small amount of “wiggle room” within your balance envelope. I guess it would equate to cheating, if you were only allowing for basic movements of the rider rather than all the complex movements we can actually do.

When you start to lean too far forward, you must basically bend at the waist. This moves your upper body down, and forward. It also moves your feet forward. In doing this movement, you try to get the wheel back into the place it needs to be in relation to your body’s overall center of mass.

Maybe the reason it works is that your body’s center of mass is constantly adjustable. Whatever it is, every circus performer knows about it. The hard part is probably to express it in equations.

7

I think the basic fore-aft mechanism is fairly simple to describe. I’m not a BC rider, but I think I’ve got it theoretically.

Basically, by bending the body at the waist, one is exercising a small amount of force on the ground, partly because of the slight angle, partly to accelerate or decelerate the wheel. The former has two components, one vertical, the other horizontal in line with the wheel. Manipulating the horizontal component, together with the horizontal component of acceleration of the wheel, allows one to maintain one’s balance within a very narrow tolerance.

The rotational aspect of the torque is not in the fore-aft plane and is not relevant to the question of fore-aft balance.

I’m not sure that I’ve done any better in explaining my understanding, though!

8

I think that the balance for the BC is generated but large motions of the body. When i learned how to BC, a few weeks ago, i found that you have to move your knee back (straight) and arm out forward for falling one way, and bend your knees, and throw your arms out back, for the other way. I’m just not 100% sure which way is fixed by which. So, i also think you can slow your self down, by “hand gliding” on the tire, and speed yourself up, with “rapid hand-scuffing” on the tire, but it isn’t as useful, and it’s much harder, than just trying a few times.

by the way, For anyone else who can ride a BC, have you ever hopped on one, or pedal grabbed? I did this the other day, and it was awesome fun! i think the next step is grinding, and foot-drags are awesome too!

good luck on your project, d’ont know how much this will help, but, it c’ant hurt… or can it?

-Ryan

9

Re: BC Wheels Physics???

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John Foss wrote:

>Almost all the basic physics that I read about here is too elementary to
>cover unicycling situations. The body is fluid. We don’t bend like
>simple hinged objects, we bend in all sorts of multiple directions and
>combinations.

Yes, the body is fluid, but there is no need to model the human body
completely to understand the basic physics of unicycling:

To balance on a unicycle, one’s center of gravity must on average be
directly above the wheel’s point of contact with the ground without ever
going outside the balance envelope (that is beyond the point of
recovering one’s balance). To do this, one actually controls the
position and direction of the wheel which indirectly affects the motion
of one’s center of gravity. To simply further, think of the unicycle as
a broom stick balanced on a finger so the stick is the unicycle frame
and rider and the wheel is the controlling finger. The primary
difference is the finger can move just as easily sideways as forward and
back to maintain balance. However, the unicycle wheel must be moving
forward or backward and be steered toward the direction of any sideways
lean (One can’t otherwise easily regain sideways balance on a unicycle.)
We ignore the possibility of hopping sideways, since a beginning rider
probably wouldn’t have this as realistic option for sideways balance.

>Breaking down what makes a B.C. wheel work for a physics class might be
>hellishly complicated. Obviously the complication is coming from the
>movements of the human body rather than the extremely simple vehicle. I
>never took a physics class though, so don’t listen to me on that. All my
>physics knowledge is “seat of the cycling shorts.”

Balance on a BC wheel is fundamentally different that on a unicycle in
one respect. One no longer has direct control over the speed and
acceleration of the wheel. One still has direct control over the
direction of the wheel which allows indirect control over sideways
balance in exactly the manner it is done on a standard unicycle. Now,
one has to determine and model the primary way that the BC wheel’s
speed is controlled. (If we allow hand wheel walk, we have direct
control of the BC wheel’s speed and acceleration.) However, the BC
wheel is primarily coasted upon with no direct control over the wheel’s
speed, so let us model that instead.

>When you start to lean too far forward, you must basically bend at the
>waist. This moves your upper body down, and forward. It also moves your
>feet forward. In doing this movement, you try to get the wheel back into
>the place it needs to be in relation to your body’s overall center of
>mass.

John explains how to regain balance from leaning too far forward quite
well.

To model forward - backward balance on a BC wheel, the essential action
is bending at the waist. It may be useful to understand the physics of
this action in just a little more detail:

When leaning too far forward, one needs to either move the wheel forward
and/or move the center of gravity backward. Both are effectively done
by quickly bending forward at the waist. The action - reaction involved
causes the center of gravity to move backward and wheel to move
forward. In practice, one does want to do this a bit more then
necessary, so a slight backward lean is established that requires
bending at the waist backward to regain a normal slight forward bend at
the waist (normal riding posture on a BC wheel).

When leaning too far backward, one needs to either move the wheel backward
and/or move the center of gravity forward. Both are effectively done
by quickly bending backward at the waist. Arching of the back backward
can be added due to the waist not being able to be bent backward
much. The action - reaction involved causes the center of gravity to
move forward and wheel to move backward. In practice, one does want to
do this a bit more then necessary, so a slight forward lean is
established that requires bending at the waist forward to regain a
normal slight forward bend at the waist (again normal riding posture on
a BC wheel).

Normal riding posture on a BC wheel is a slight forward bend at the
waist simply because the waist can’t be bent backward as much as it can
be bent forward. This slight forward bend at the waist allows both
leans forward and backward to be relatively recoverable with quick
reflexes.

>Maybe the reason it works is that your body’s center of mass is
>constantly adjustable. Whatever it is, every circus performer knows
>about it. The hard part is probably to express it in equations.

Yes, both the center of gravity and the wheel’s forward - backward
position can be adjusted by bending one’s waist as described above.

Of course, only the primary actions of the body that effect control have
been considered here. Other actions, such as arm circles do have
significant balance effects, but probably far less than the one’s
described above. A far more effective use of the arms is as an
extension of the upper torso:

When the upper torso is bend forward the arms should move forward to add
to the action - reaction (if necessary).

When the upper torso is bend backward the arms should move backward to
add to the action - reaction (if necessary).

In my opinion, other movements can affect forward - backward balance on
a BC wheel, but such movements are wasted energy if they do not mimic
the basic bending movement of the waist to effect maximum action -
reaction with a minimum of angular waist bending. The waist can
only bend forward - backward so much before the physical limits are
reached, so balancing with smaller such movements close to the “idea” BC
wheel riding posture is best (and that would include the arm movements
that magnify the effect of waist bending).

Of course, an experienced BC wheel rider doesn’t need his arms to
maintain his balance and can use them them to juggle balls or clubs
etc. In fact an experienced BC wheel rider can adjust his waist so
slightly for balance purposes that it will largely go unnoticed. Also,
due to such fine balance, he can ride with his upper torso straight up
(not bent forward at all).

Enough said on this subject, I hope.

Sincerely,

Ken Fuchs <kfuchs@winternet.com>

10

If it was my project I would use a modified version of a second or third degree inverted pendulum. It doesn’t exactly model a person on a BC wheel but I think it’s the well known problem that comes closest.

11

Wow I didn’t expect to get this much amount of feedback. Thanks for the contribution.

I meant that the postion of your cm is a factor in balance, but it is only a minor one.

Not to mock, but i’m assuming you’ve never tried a BC wheel. That was one of the first things I tried and I ate pavement.

Thanks again for the info.

12

Ten Minute Rule …

I believe that is due to the force of precession, which keeps the rolling BC wheel stay upright.

I didnt have a BC wheel when i chose unicycling for my project. O well I’ll try my best. O well if my class doesnt like my presentation, I won’t let them try to ride my unicycle then.

:smiley: HAHAHAHAHAHA!