Re: Unicycling Theory


maestro8 wrote:
I've recently graduated with a degree in physics and, if anything, have
learned that there are some situations in which one's first-order
approximation is no where near what occurs in reality. We could argue
(and many have on this forum) about which formula is the best to
represent the physical situation and likely only achieve a crude
approximation; even then, we'd be at a loss as to which numbers we'd
plug into the formula.

In addition to the phenomena mentioned by yourself and tholub, there's
also that of slippage. I, too, have been down slopes significantly
greater than 23 degrees and have been able to stay in the saddle with a
combination of sliding, tacking, handle pressure and acceleration.
There are obviously many variables left out of your approximation that
renders it virtually meaningless.

Even if you're looking for a simple approximation, what are you going
to do with the number once you get it? Lay down a protractor and take
a grade measurement every time to come across a new hill? :p





Well, I tend to differ with you on this one Maestro. One thing I have
learned is that there is no point adding extra possibilities to
intentionally make a simply expressed problem difficult. RTFQ and
then ATFQ ! So K.I.S.S. and don't overengineer the problem.
Why add slippage, acceleration, tacking etc etc to the problem?
Reduce the problem to essential bare bones as per the post and it
really becomes very simple indeed, save for one factor not mentioned.

So for the laymen in here:

Adding in tyre slippage is way over the level at which Icon was asking
the question. Icon was on the right mathematical track in paragraph 4,
appropriate for the level at which the question was posed, and for
simple non slippy slopes it would give a pretty good answer too, *for a
stationary unicycle*.

However there is one major factor that does need adding. Once the
cranks are not horizontal they are less effective in keeping speed
constant (or in holding the unicycle stationary on the slope).

It is impossible to ride down a path having a uniform slope, at a
uniform speed. Speed varies throughout each revolution of the wheel.
To keep a constant overall speed , the moments when the pedals are near
horizontal have to be used to actually slow the unicycle down, because
in those times when the pedals are near vertical, you will not be able
to prevent some acceleration down the slope. So the maximum angle as
calculated in Icon's simple sin formula is inaccurate , in that it
would only apply to a stationary still stand situation.

You can stillstand on a much steeper slope than that which you can ride
down without increasing your overall speed.



Nao


--
Naomi

Convince me I am wrong about that? But *of course *you might convince
me I am wrong about that. But try an easier one first. Convince me
that 2 and 2 doesn't make 4.
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