Deriving a unicycle crank length formula?

By imperfect, I simply meant incomplete. It wasn't meant as an insult.
Sometimes I use fairly sterile language like that and it can be
misinterpreted. Sorry.

I certainly agree that long cranks really come into their own on steep
descents. That is their biggest single advantage.


--
Mikefule

So, do you ride with a club?

No, but I carry a heavy spanner.
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Mikefule Wrote:
Slightly behind. To ride a unicycle, you allow it to start to fall
forwards, then you accelerate the wheel so that the uni never actually
falls. When you slow down, you allow the wheel to overtake you,
slightly.

The better the rider, the more control, the smoother the ride, the more
vertical the relationship between the hub and the contact patch.
However, if the contact patch were exactly beneath the hub, you could
never accelerate - including from a standstill.


This is a mixture of truth and fiction. You are correct that the
contact patch is slightly behind the center of mass *when you are
accelerating*. On the other hand, when you are *decelerating* the
contact patch is in front of you. It has to be or else you fall
forwards. And, guess what? If you are maintaining a constant speed the
contact patch is exactly beneath the center of mass.

In reality you are never maintaining a perfectly constant speed. You
constantly waver between accelerating and decelerating, and otherwise
wobble, but it averages out to beneath you, with expert riders keeping
the contact patch consistently closer to under the center of mass.


--
Bruce Dawson
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I think you'll find that at constant speed on a perfectly smooth level
surface, the centre of mass is still very slightly forward of the
contact patch.

For a simple demonstration, balance a broom on your finger and walk
with it.

However, I agree that the better the rider, and the smoother the
surface, etc., the more constant the position of the centre of mass
relative to the contact point. A good rider is not constantly
accelerating and decelerating, but exactly matches his speed to
counteract the downwards deceleration of the centre of mass. It's a
bit like an object in orbit, constantly falling but never landing.


--
Mikefule

So, do you ride with a club?

No, but I carry a heavy spanner.
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On Thu, 6 Oct 2005 01:17:43 -0500, Mikefule wrote:

I think you'll find that at constant speed on a perfectly smooth level
surface, the centre of mass is still very slightly forward of the
contact patch.

I think you're right, but you don't state the reason.

For a simple demonstration, balance a broom on your finger and walk
with it.

Balancing a broom on your finger and then walk with it is relatively
easy indeed. Nevertheless, it's not a simple demonstration. How can
you "simply" demonstrate an effect that is "very slight"?

The reason for the contact patch being forward (both in unicycling and
in the broom case) is air resistance. This effect is probably too
small to discern casually by the naked eye. If you think you see it,
then either your observation is distorted because you focus on the
combination of tasks, or you are still accellerating overall.

Klaas Bil - Newsgroup Addict
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Klaas Bil, I think I was wrong. I think you are right in that, in the
absence of air resistance, it would be possible to ride at a steady
speed without leaning forwards.

If you could breathe. ;0)


--
Mikefule

So, do you ride with a club?

No, but I carry a heavy spanner.
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In message
essage.Poster.at.Unicyc
list.com, Mikefule
writes

Klaas Bil, I think I was wrong. I think you are right in that, in the
absence of air resistance, it would be possible to ride at a steady
speed without leaning forwards.

Only in the absence of rolling resistance and friction in the bearings.
In that case, one could take ones feet off the pedals and continue in
uniform, rectilinear motion until acted on by a force....

Martin/

--
Martin E Phillips nb Boden, Splatt Bridge
http://www.g4cio.demon.co.uk martin/at/g4cio/dot/demon/dot/co/dot/uk
Homebrewing, black pudding, boats, morris dancing, ham radio and more!
The Gloucester-Sharpness canal page http://www.glos-sharpness.org.uk

I think that's probably right. Yes, Klaas was incomplete in his
answer.

If a force is tending to slow down the unicycle, and the unicyclist
wants to maintain a steady speed, he will exert a force on the pedals
to turn the wheel. Newton's law of equal and opposite reaction will
then make the centre of mass move in the opposite direction. Therefore
there needs to be a tilt forwards to allow the effect of gravity to
counterbalance this tendency for the entire unicycle frame and rider to
rotate in the opposite direction to the wheel.

So, although I hadn't got all the details right in my head,I think my
original intuition was right after all.


--
Mikefule

So, do you ride with a club?

No, but I carry a heavy spanner.
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On Fri, 7 Oct 2005 18:55:18 +0100, Martin Phillips wrote:

Only in the absence of rolling resistance and friction in the bearings.

I do agree that my analysis was incomplete. Let's go through some
other effects that push you off-vertical and that you have to
compensate for in order not to fall..

Like Mikefule hints at, friction in the bearings would actually cause
the centre of mass to be BEHIND the contact patch, to compensate for
the fact that the turning wheel tends to push the frame forward. So
with the "right" amount of friction in the bearings to compensate for
air resistance at a certain speed, one would still be upright - apart
from other effects mentioned below.

Rolling resistance, however, acts in the tyre-wheel system and would
have no effect on the uprightness of the unicycle.

Celestial bodies, such as the moon, will attract you (gravitational
force), like they do attract ocean water and cause tides. In fact,
every body of mass will attract you: a mountain, a fellow unicyclist,
a mosquito. And density variations in the Earth, although this depends
on your definition of verticalness.

If there is more light coming from one side, e.g. if you are riding
towards a car's headlights, then the light falling upon you will tend
to push you off-vertical. If you have a headlight yourself, it will
exert a reaction force upon you.

If you are not riding exactly towards the North or the South, the
turning of the Earth will "push" you towards the equator.

If you breathe out, the reaction force will push you backwards. This
is different from air resistance, it also works in vacuum - though
breathing out would be a different experience there. A similar story
holds if you breathe in, except that this is not possible in vacuum.

I'd rather stop now :-)

Klaas Bil - Newsgroup Addict
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"dit dit diddle diddle dit dit did-it, dit dit diddle diddle dit dit did-it, *dit* diddle dit dit *dit* diddle dit dit, diddle-diddle-diddle-diddle-dit dit diddle diddle dit dit did-it,... - Spudman"