# foot power

Alan Eliasen eliasen at mindspring.com
Fri Jan 28 02:17:06 EST 2011

```On 01/27/2011 08:18 PM, Nathaniel Theis wrote:
> On Thu, Jan 27, 2011 at 07:54:16PM -0700, Alan Eliasen wrote:
>
>>    Again, I will note that the only way to make the XO reasonably
>> powerable by a child (or an adult) is to reduce its power consumption.
>
> Well, this isn't entirely true. For example, something like a potter's
> wheel pedal could potentially generate sufficient (25+ W) amounts of power,
> given a reasonably efficient dynamo (and a reasonably efficient
> child!) However, the endurance problem is still *huge*.
>
> The XO-1 takes about 2-3 hours to charge from 10% battery level. If
> you have a foot-pedal system that generates 25 watts, you still need
> the child to do this for _several hours_.

I've seen a huge deal of confusion in the human-powered discussions
here and on the Wiki; there seems to be some sort of strange idea that
having a flywheel lets us get out more energy than we put in.  The
potter's wheel example above is one such example.  It seems to neglect
the idea that drawing off 25 watts of power from the flywheel's rotation
means that we have to put in (more than) 25 watts of power to keep it
from stopping.  Anyone who has ever used a generator on a bicycle knows
that you can *feel* the drag from the reverse electromotive force as
soon as you turn on the light.  It will stop you.  And those generate
maybe 3-6 watts.  The braking force from pulling off 25 watts of power
is huge.

> Alright, you may say, maybe you make it ultra-efficient and very easy
> to push the pedal down (repetitively, for hours on end!) But that's
> just the tip of the iceberg.

I'd never say such a thing, because I realize that if I'm going to be
getting 25 watts out, I need to be putting in more than 25 watts,
constantly, to keep the flywheel from stopping!  There's no such thing
as a free lunch, or a magical linkage that puts out more power than it
takes in.  It doesn't matter if it's a treadle, a kickwheel, a
playground carousel, or whatever... that kid has to be sustaining more
than 25 watts or the wheel will stop very rapidly due to the significant
drag from the generator.  No amount of magical efficiency will make it
"easy" to push the pedal down.  The kid has to be constantly putting out
an average of 25 watts (or significantly more, due to friction and
generator efficiency.)  Anything less and the wheel stops.  Rapidly.
Just how rapidly?  It's calculated below.

Let's analyze the above situation mathematically.  We're not doing
any justice to the cause of education if we can't analyze these
situations with basic physics and real calculations.

Let's take a pretty hefty potter's wheel.  I looked up some on the
web, and we'll use the figures of a 130 lb concrete kickwheel with
diameter 30 inches (radius 15 inches.)

I'm going to put the following equations in Frink notation, (
http://futureboy.us/frinkdocs/ )  Frink is a programming
language/calculating tool I've developed for just this sort of purpose.
It tracks units of measure through all calculations and ensures that
answers come out right, even when mixing units.

The moment of inertia, I, of the disc is given by:

I = 1/2 * 130 lb * (15 in)^2

Let's say that the kid is able to spin it to a rather high rotation
rate of 120 rpm.  (This is quite high for a foot-powered potter's wheel.)

omega = 120 rpm

The kinetic energy of the spinning wheel is given by:

E = 1/2 I omega^2

Which gives 338 joules of energy.

We're now going to draw this energy off with a generator.  Let's say
the generator produces 25 W of power and is, very generously, 60%
efficient.  (A bicycle hub generator that efficient is very expensive.)
The wheel will then come to a complete stop after:

E / (25 W / 0.6)

Or a dead stop after only 8.1 seconds if we stop adding power.  This
is significant braking.

Note also that the kid has to be putting in 41.6 watts of power for
the generator to produce 25 watts, due to its efficiency.  If the kid
lets it slow down at all, they'll have to put in more than 41.6 watts to
accelerate it back up!

We're also neglecting the significant amount of energy that was
needed to spin the wheel up to get it to this point, or any other
frictional or electrical losses.

A flywheel does *nothing* to reduce the amount of sustained power
that someone has to produce.  Especially if we can't posit some sort of
magic source of energy to spin it up in the first place.

If you disagree with any of this analysis, please respond with
physical equations.

"Engineering is done with numbers. Analysis without numbers is only
an opinion."  --Akin's Laws, #1