This would be easier with pictures, but I haven't figured out how to do
that easily in a regular post so here goes:
Imagine two vertically elongated masses with one stacked on top of the
other and joined together with a powered hinge. The lower mass
represents your legs, hips and the unicycle. The upper mass represents
your torso, head and arms. The hinge and power source are your waist
and abdominal/back muscles.
Since you can roll on a thin rail you can control your fore and aft
balance with normal pedaling. This frees your abdominal/back muscles
from the need to balance a still stand in that direction so there is
more "power" for still-standing in the lateral direction.
So, imagine that you are looking down the rail. Mentally "float" the
two mass system an inch over the rail. ("Matrix" physics rules are in
effect - gravity is suspended.) Imagine the system is perfectly still
and aligned perfectly straight and vertical. What happens if the hinge
"motors" are actuated to bend the top to the right? Conservation of
momentum (Newton's first law) says that the center of mass stays put,
since there are no externally applied forces (the "tire" isn't touching
the rail). Further, there is no reason for the system to rotate as a
whole since there are no externally applied torques either. So the top
and bottom of the system move to the right, and the waist moves to the
left. The center of mass of the upper mass stays on the vertical line
but moves down, and the center of mass of the lower mass stays on the
line and moves up. The overall center of mass stays put.
Now, mentally straighten the masses out again and turn gravity on. The
mass system drops onto the rail and balances. If everthing is PERFECTLY
alligned it will just stay there, however this perfection is only
possible in cartoons and computer simulations. In the real world it
will never happen. Eventually it will begin to rotate around the
contact point on the rail and fall. Why?
With gravity turned on the mass system pushes down on the rail, and the
rail in turn pushes up on the mass system. When the system is perfectly
vertical these two pushes are exactly in alignment and cancel out. When
the mass system tips, even a tiny amount, the two pushes become slightly
offset. This creates something called a "couple" in physics that
creates a pure twisting force or "torque". Since these forces are
externally applied Newton's second law comes into effect - the masses
accelerate. As the masses tip they also start to accelerate sideways
because the rail "up" push is no longer exactly vertical.
Now imagine that the masses are still aligned straight with each other
but have tipped a tiny bit to the right. What happens if the "motor" in
the waist is actuated to rotate the top mass strongly to the right?
In the zero gravity thought experiment the top part rotated to the right
and the lower part rotated to the left. But in the gravity-on case the
"tire" is in contact with the "rail" so the bottop part isn't free to
rotate anymore. In the free-air this floating tire tread would have
moved to the right too, but since it is in contact it can't, so the
whole system is pulled to the left.
Now, mentally stop time: What happens if you bend the system at the
waist and then straighten it in the same instant? The answer is
nothing. It will go back to exactly how it was. So managing time must
be part of the solution for still standing. Ok, start time again:
When the tire patch causes the system to move to the left it causes the
center of mass to move to the LEFT of the rail. Now the tipping couple
is reversed and the masses start to fall to the left. After a suitable
period of time imagine the motor is actuated again to straighten the
system. This causes the center of mass to move to the right, but since
the masses spent some time falling to the left it doesn't go back to
where it started from. If the timing and movements are done perfectly
the center of mass will wind up right over the rail and the system is
back in balance.
So what about the arm windmilling? Well, it's the same thing but with
three masses (and a new powered hinge at the shoulder.) When you start
your arm rotation you cause the tire to pull your center of gravity one
way, and when you stop the rotation it pulls you the other way. Get the
timing right and you stay over the rail.
This form of balance isn't limited to unicycleing. Watch any good
soccer player in slow motion and you will see the arm-swings and waist
bends helping him (or her) maneuver. Or just go down to the bar and
watch the really drunk folks - since their balance and timing systems
are impared you can see in an exagerated sense the waist bends and arm
swings that we all do to just stand and walk on our feet.
Hope it helps. For the video I'd have an illustrator make some
animations. Long leather coats optional for the "Matrix" physics
section.
Tim
--
cyberbellum - Level 1.0 rider!
Optimists think the glass is half full. Pesimists think the glass is
half empty. Engineers think the glass is too big.
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