http://i136.photobucket.com/albums/q171 ... ecret2.jpg
The gun fixed to the earth fires at the vane and gives the disc and kinetic energy of 1/2 mv^2.
Consider next von Lieven's Figure 3. In this case the gun is also fixed to a similar disc and the gun plus disc has the same inertial characteristics as the vane plus disc.
http://i136.photobucket.com/albums/q171 ... ecret3.jpg
Action = reaction so the recoil of the gun provides the right hand disc with the same kinetic energy as the left hand disc.
To quote Hans.
When we now fire the gun both wheels spin in opposite directions with equal velocity. One wheel is driven by the impact, the other by recoil. We have just doubled our available energy output without further expenditure.
So with the right hand disc fixed and the left hand disk free we have 1/2 mv^2 of KE.
And with the right hand disc free and the left hand disk free we have another 1/2 mv^2 of KE.
So our total energy E = mv^2.
So if we fired our bullet at the velocity of light our total energy would be;
E = mc^2.

How interesting. But let's not get diverted from our task of understanding the Bessler wheel.
What happens if we fix the vane wheel to the earth instead of the gun? Now we only have 1/2.mv^2 and the gun shoots off like a rocket - or since in this case it is attached to a disc, like a Catherine wheel.
So the optimum arrangement for the maximum energy is to have both wheels free with 50% of the total energy available going to one wheel and 50% going to t'other - as one would expect from information theory.
So Kinetic Energy is not conserved. But if we neglect losses of energy going down into the materials in the form of heat, etc., and losses in the form of sound radiation, etc., then momentum is conserved. The left hand disc rotates clockwise and the earth to which the gun is attached rotates widdershins.
Th momentum imparted to the disc is mV. The momentum imparted to the earth is Mv.
Because M is very much bigger than m, v is very much smaller that V and escapes people's attention.
When I got to the point in von Lieven's brilliant paper where the energy available doubled, I recognised a similarity to a phenomena well know to structural engineers.
If you hang a weight on a cable and lower it onto a beam so that it just touches the beam without deflecting it. Then gradually slacken the string so that the weight is transferred ever so slowly to the beam, the deflection of the beam will be 1 inch say.
If on the other hand you suddenly cut the cable the deflection of the beam will be 2 inch. In short, there is twice as much energy available to deflect the beam with very fast (impact) loading than there is with very slow loading.
In an earlier post I made a reference to Archimedes. To get that reference I carried out a google search with the phrase "give me a lever" but when I looked at the wiki article I found the the original quote doesn't mention levers or fulcrums but is simply
"Give me a place to stand on, and I will move the Earth."
Since we seem to have many linguists on the forum here is the original in Greek.
δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω
And when you think about it that is all you need to move the earth, "a place to stand on".
If I push a weight up above my head I push down on the earth. I move the earth's centre of mass.
Indeed, if I lift my arm and command the earth to move, it does. Not, of course because I have commanded it but because the centre of mass of the earth has been moved by the raising of my arm.
So when I raise a weight up in the air and give it positive gravitational energy I push the earth down and give it negative terrestrial energy. When I let go of the weight and it falls down towards the earth the positive gravitational energy is released and the negative terrestrial energy is also released as the earth rises up to meet the ball.
The way energy is stored in material being raised up is vastly different from the way material energy is stored in free fall.
In the material lifted up the compressive and tensile strains are macro strains. In material in free-fall the strains are on an infinitesimal scale.
Also macro strain operates on external surface contact areas of the material whereas infinitesimal strains operate on the infinitesimal internal surface contact areas which are proportional to the volume of the material.
I briefly touched upon the subject of strains in this earlier post.
In the next post I will detail, inter alia, how we recognised that force (stress) was merely an alias for strain and that, as in the case of the gun and recoil, the energy available in a nominally closed system viewed from without can be up to twice that conventionally assumed.