Jim Price said:Stevie D said:Quoted message said:shouldn't a higher CoG make it easier to balance?
I always thought a _lower_ centre of gravity gave you better balance.
Imagine a straight line between your front and rear wheels as your
balance line. You want to keep your COG above this line.
If your COG is 25cm above ground, and you lean 5 degrees, your COG is
2.2cm outside your balance line - but if your COG is 1m above ground,
and you lean 5 degrees, your COG moves to 8.8cm outside your balance
line. This means that you are inherently less stable - factor in the
leverage effect that a higher COG has and you get a much greater pull
downwards.
Try balancing a pencil on it's end on your finger, then try something
similar but about a metre long. I've tried this theory out on two
significantly different heights of unicycle - the taller one was much
easier to balance on as it seemed like you had much more time between
when you noticed it starting to topple and it getting beyond what you
could recover from.
It didn't just seem like you had more time to control a wobble, you did.
There are two distinct factors at work in height of CofG in
balancing. The first is that the lower the CofG the more stable the
thing is, in that a certain lean angle generates a smaller force
increasing the lean, so static balance is more easily achieved. The
second is that the higher the CofG the longer it takes to fall
over. Since we have a finite reaction time, there is a minimum height
of CofG below which it takes concentration and risk of failure to keep
balanced. So the lower the CofG the better the staic balance, but the
higher the CofG the easier the dynamic balance. So the optimum height
is as low as possible which is above an uncomfortably demanding
reaction time height.
I'm sure it won't surprise anyone to learn that evolution in her
wisdom has equipped us with reaction times well able to stop us
falling over when standing up :-)
--
Chris Malcolm [email hidden] DoD #205
IPAB, Informatics, JCMB, King's Buildings, Edinburgh, EH9 3JZ, UK
[http://www.dai.ed.ac.uk/homes/cam/]