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DGoncz@aol.com
science forum Guru Wannabe

Joined: 25 Oct 2005
Posts: 122

Posted: Thu Jul 06, 2006 3:32 am    Post subject: Capacitance and mass

In my studies of the self-recharging ultracapcitor bicycle concept, I
have looked at partitioning of energy between PE, KE, and EE. The
bicycle has a motor/generator wheel in parallel with an ultracapacitor
pack, forming an "electric flywheel".

PE is essentially permanent. You can stay on a hille until your
supplies run out.
EE is temporary. Self-discharge depletes stored EE.
KE is transient. Friction dissipates KE without exception.

In an ealier post I considered the utility of an energy partitioning
measure

cuberoot (PE*EE*KE)

to represent the energy condition of such a bicycle.

I now am looking at KE and EE.

With knowledge of a motor constant k, for my bicycle 3/2 volt/mph, one
can reason through KE=EE to C = m/k^2, for my bicycle 10 F. I
speculated in the last post to spr thread "Collected 12 kj of sweat
energy today", which may not have appeared yet, that my C of 300 F was
10 times to high. OK, it's 30 times too high. That's where the draggy
feeling comes from.

The terminal speed of my bicycle on local hills is around 36 mph. That
would generate 54 V. One available D-cell sized ultracap is 350 F and
2.5 V. If I buy 20 of them, I will have 50 V of range at around 17.5 F
or about 12 kj. It's interesting how that 12 kj showed up in that
initial post. I can get rid of the existing pack and other 8 unused
ultracaps. They are more suitable to a velocar or truck project, which
I am not considering.

I would have saved the money if I had thought this through. That's how
it goes in R&D. You don't even know what the unknowns are until you
build something.

Here is the math:

g = 32.3 ft/sec/sec
F = 250 lbf weight of bike and rider
m = 250 / g
k = 3/2 volt / mph
KE = EE partitioning desired
1/2 m * v^2 = 1/2 *E (k*v)^2
m/k^2 = C result

Doug Goncz
Replikon Research
Seven Corners, VA 22044-0394
DGoncz@aol.com
science forum Guru Wannabe

Joined: 25 Oct 2005
Posts: 122

Posted: Sat Jul 08, 2006 2:37 pm    Post subject: Re: Capacitance and mass

Doug Goncz (I) wrote in my first post to this thread:

 Quote: 1/2 m * v^2 = 1/2 *E (k*v)^2 m/k^2 = C result

That should be:

1/2 * m * v^2 = 1/2 * C * (k*v)^2
m/k^2 = C

It would be useful for users to choose increments of capacitance, while
only one motor per bicycle can be fitted. (I have heard of a bushed
permanent magnet electric rear hub. It uses freewheels. I think it's
more important to have standard cogging and drive options, such as the
freehubs and the popular 3x7 Sachs hub, which is a hybrid gearing
system.)

To establish a unit of capacitance increment it seems that, with m now
equal to the the mass added to a bicycle with a retrofit:

j = weight specific energy
j = 20 pounds / 325 F (at 40 V capability)
m1 = 20 pound / motor (one motor hub weighs 20 pounds)
k2 = number of packs fitted, an integer
C1 = capacitance to make added KE = added stored EE

1/2 ( m1 + k2*j*C1 ) * v^2 = 1/2 C1 ( k * v )^2
C1 = m1 / ( k^2 - k2*j )

With C1 defined, it might be reasonable for a company to offer C1,
2*C1, 4*C1, etc as packs to be connected in parallel, assuming terminal
speed for all applications is the same, up to a C2 = the C from the
first line of this post for some standard bike and rider weight. At
that point, increments of C could be offered. The motor hub as a
generator is useful with C=0 but on hills, can overpower application
circuitry (lighs, a notebook computer, a cell 'phone, a Pocket PC, a
shaver). I have a regulator but it doesn't have the reliability I need.

for
j = 20 pounds / 325 F (at 40 V)
m1 = 20 pounds
k2 = 1 pack
C1 = 0.808 farad

for k2 = 2 packs
C1 = 0.81 farad

So it seems reasonable, for this motor and associated capacitor
technology, to offer 1, 2, and 4 farad packs that can be operated in
parallel at 40 V or some voltage based on terminal speed, and then
offer 10 F, 20 F, 40 F, etc sized packs.

Initially, one "reasonable" pack size could be selected, and
refinements offered later, but this will take some testing. A
"reasonable" pack size might be PE = 100 foot hill * 250 pound bicycle
and rider. That's what I used, more or less for my oversized pack. A
much smaller hill size might be used, say one the rider can just see
over, around 5 feet.

My neighbor tried the bicycle without the motor switched on. Tennis
playing high school kid; he goes like nobody's business. We had a good
ride on Brook Drive, nearby.

Any physics enthusiasts living in or visiting the Washington, DC are
welcome to call for a ride on a dry day.

Doug Goncz
Replikon Research
Falls Church, VA 22044-0394

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