(New?) Energy Parameter

[Doug Goncz]

Good morning, spr.

In my analyses of bicycle travel on actual terrain, pre- and post-
actual rides, I find the relationship between KE (kinetic energy) and
PE (potential energy) to be of great interest and importance. Of
course, in most analyses, energy is conserved, with E.t = KE + PE.

I have considered looking at KE/PE or PE/KE to emphasize forward motion
or energy storage, but neither seems fundamental. With the addition of
ultracapacitor energy storage on the MOEPED 3, there is PE + KE + EE.

It seems like for your garden variety kinematic problem
squareroot(KE*PE) might be fundamental. It has units of energy, and it
goes up in the right places and times and goes to zero at the right
times given an appropriate zero for PE. For my bicycle experiments,

E.p = cuberoot(KE * PE * EE) might be just the metric I need.

For other situations, with energy accountable in thermal, kinetic,
chemical, and other ways, the nth root of the product of n energy terms
would be the thing to use, having, of course, a maximum under the
equipartition condition. This seems to me quite tidy and useful!

I don't currently think a power product P.m = squareroot(P.m * P.e)
would be very relevant, but I am thinking dE.p / dt, which has the
units of power, would be relevant to some situations.

This is just a preliminary note...

There is a possiblity of putting an "E-meter" on the bicycle being
tested currently, using a Compact Flash instrumentation card, a Pocket
PC, and a few bits of instrumentation hardware.

I used to have a shunt-field AC power meter that would compute the
analog product of a reference voltage and a metered voltage to get a
reading. I think this is where I got the idea. I no longer have that
meter. I have also heard of "energy awareness" as a primary tactical
reality for jet fighter pilots, leading to success in dogfights.

Doug Goncz
Replikon Research
Falls Church, VA 22044-0394

[Doug Goncz]

Doug Goncz (I) wrote:
(snip)

> It seems like for your garden variety kinematic problem
> squareroot(KE*PE) might be fundamental. It has units of energy, and it
> goes up in the right places and times and goes to zero at the right
> times given an appropriate zero for PE. For my bicycle experiments,
>
> E.p = cuberoot(KE * PE * EE) might be just the metric I need.

Doh. I have reinvented the geometric mean. My bad.

I wonder if this is _why_ the equipartition condition is most probable.

I am having memory problems and can't remember the name of the fellow
who worked out the kinetic theory of gases. I read his book, too.

That is, I am wondering if in a system with n degrees of freedom, the
thermodynamic probability

p is proportional to nth root (product of E.1, E.2, ... E.n)

or perhaps rather than proportional, some other monotonically
increasing function of the geometric mean of the energies in the
various degrees of freedom.

I am planning a ride down Upton Hill nearby to collect data on my
ultracapacitor bicycle. Voltage on the ultracapacitors, and urrent into
and out of them, by time along the path down Wilson Boulevard to North
George Mason Drive. Ground speed and energy stored can be computed from
these readings. It's a long stretch with no lights. Perhaps some
morning, early. My legs are strong lately and knee pain is low.

I was going to use a Compact Flash 4-channel DAQ chip with 24-bit
resolution in the range +/- 5 V but it's unaffordable at the moment.
$600. A smaller DAQ with a serial interface is more likely.

Doug Goncz
Replikon Research
Falls Church, VA 22044-0394