this is a post I made at www.overunityresearch.com (http://www.overunityresearch.com/index.php?topic=1489.msg24020#msg24020) today, but I'll let you guys in on this as well. (Formatting doesn't work so well on this forum, but that's ok)
Ladies and Gentlemen,
Today I performed a simulation on pendulum dynamics that I’ve been meaning to perform for some time, and it gave me a very surprising result! I was expecting MORE energy from a moving and swinging pendulum, when in fact I calculated LESS energy. Here’s my short write up so you understand what I did.
Abstract: Dynamic simulation of a simple pendulum shows that the energy delivered to a vertically moving pivot at constant velocity, by a swinging and falling pendulum attached to it, is LESS than the potential energy lost in the gravitational field. The motion starts from theta=0 deg to theta = 180 deg, where theta is the pendulum angle relative to the horizontal. The pivot and weight have the same vertical velocity at t=0 and at n*T/2, where T is the period of oscillation, and n = 1, 2, 3, ...
Graph Plot: The simulation results show the pendulum angle and the angular velocity as a function of time. For the simulation, the radius was set to 1 m. I also curve fit sinusoidal functions to these results, because I wanted to see if the pendulum motion was truly sinusoidal, but we can see it is not quite sinusoidal.
To calculate the energy supplied to the pivot, the following formula is used:
U_pivot = integral[ m * R * theta_dot^2 * sin(theta) * dy , from y_initial to y_final)
where ‘theta_dot’ is the derivative of ‘theta’ which is the instantaneous angle of the pendulum in radians. Note: F_radial = (m * R * theta_dot^2), and multiplying by sin(theta) picks out the vertical component of the radial force F_radial, so we are actually integrating Fy * dy, over the height that it traversed which gives us the work or energy that was produced by the falling pendulum.
On the other hand, the potential energy that the pendulum mass would have delivered without swinging, is calculated as:
U_potential = m * g * (y_initial - y_final) = m * g * h,
Where ‘g’ is the gravitational acceleration constant, and ‘h’ the height difference the pivot traversed while the pendulum perfomed a swing from theta = 0 to theta = pi.
From my simulation in MATLAB, I obtained these numbers, (for an arbitrary constant vertical velocity of the whole system):
U_pivot = 7.73 J
U_potential = 11.61 J
So because the mass was swinging on it's pendulum arm, it only delivered 66.6% of the potential energy that it lost in moving vertically in the gravitational field!
If the process is reversed, and the system is moving UPWARDS, it would gain an additional 50.2% more potential energy than is required as input. In other words, FREE ENERGY from the gravitational field of the earth!
Therefore, a simple gravitational energy generator would be a pendulum on a pivot that moves up and down, and the pendulum only swings on the way up, thus gaining energy on the upward stroke, and delivering that energy on the downward stroke when it is not swinging.
This result is very surprising, and not only because there is a difference between the two values, but the difference is backwards from what I expected. If anything, I thought that while the pendulum is swinging, obviously greater centripetal force needed to keep the pendulum in its swing is greater than m*g, so the energy should be larger when integrated over all angles, but it is actually LESS, so the system actually lost energy!
In retrospect I guess this makes sense. Intuitively we can say that as the pendulum starts to fall relative to the pivot, it begins from a weightless condition relative to the pivot, so the pivot does not see the mass weight, and the same happens as the pendulum approaches zero velocity close to theta = pi, but around theta = pi/2, where the angular velocity is max, the vertical force would be much greater than m*g. However, in the integration, the time spent here is actually lesser than the time spend around the START and END of the swing, where the pendulum does not produce much force on the pivot.
This is an amazing result, that shows what could be at work in the Bessler wheel. Any weight inside a rotating wheel, that swings on its pendulous pivot, will deliver less or more energy to the wheel depending on wheather the pivot is moving down or up. Of course, in a wheel, the pivot is not moving perfectly vertical except at two angular locations, but if the swing happens fast relative to the rotation of the wheel, perhaps within 10 deg, we can approximate it as vertical around these angular locations, and the results that I calculated apply.
Anyway, this is the secret that we’ve been looking for!
Share the blessings!
EM
I created another graph to better illustrate the secret.
I now show the vertical force F_y exerted on the pendulum pivot (mass 1 kg, R=1m)
If I integrate this force over one swing * dy, which is proportional to time since the frame of reference is moving with constant velocity, I basically calculate the energy delivered to a stationary frame of reference. This energy is proportional to AREA 1, shown, and is obviously less then the energy delivered by a NON swinging pendulum (AREA 2).
EM
PS. I added the second graphic to illustrate the problem analyzed.
Let me explain this in a step by step fashion, so everyone can be onboard. Please take a look at the figure below.
Step 1) Pre Release, t<0
Before t=0, both the carriage and the pendulum move together with the same constant vertical velocity, and the configuration is as shown in part a) of the figure. The weight of the pendulum is carried by the cable as F_y =m*g There is also a torque at the pivot, since the pendulum weight is displaced to the right of the pivot, but this is counteracted by the carriage which can only slide up and down. Imagine the pivot is welded so no rotation can occur.
Step 2) Release of Pendulum t=0
At time t=0, the pendulum is released and the pivot joint is free to move. The tension on the cable instantly drops to zero, since the pendulum is now in free fall relative to the pivot and is under the influence of gravity. The velocity of the pendulum is the same as the carriage at this instant but begins to accelerate downward. This instant is shown in part a) of the figure.
Step 3) Maximum tension in the cable
As the pendulum swings it eventually reaches a vertical attitude as shown in part c) of the figure. At this point the pendulum attains its maximum velocity relative to the pivot, and also generates the largest tension on the cable, which exceeds m*g.
Step 4) Maximum swing
In part e) of the figure, we see the pendulum has swung to it’s maximum angular displacement (theta = pi) and is now at rest relative to the pivot just as at t=0. Relative to a stationary frame of reference, both the pivot AND the pendulum have the velocity w*R, just as they had at t=0.
While the pendulum swung and dropped a distance delta h, it lost a certain amount of potential energy in the gravitational field (m*g*delta h), and also generated a force on the moving cable in the process. Integrating this force times an infitesimal dy displacement, produces the total energy that was delivered to the cable, and in turn, to the stationary frame of reference of the pulley. The amazing result is that these two energies are not the same thus violating conservation of energy. Is a gravitational field than not a conservative field? Calculations show that the energy delivered to the cable is actually LESS than the energy lost in potential due to the drop in height in the gravitational field.
It’s ok to get excited, this is an amazing result and reversable! Moving the carriage upwards, the pulley motor would supply less energy than is gained in potential energy. So FREE ENERGY from the gravitational field!
EM
Seems a similar principle to the following ?
http://en.wikipedia.org/wiki/Botafumeiro
http://www.youtube.com/watch?v=c6az7f1n_HU
IINM, when a pendulum is released from horizontal whilst pivoted to a sled moving downward at a constant velocity the pendulum never swings to horizontal again [relative to the sled & its starting orientation ] ?!
Is this what you found in your sims ?
Consider the fish that swims...
It produces asymmetric pressure gradients along it's body in precisely controlled undulating patterns. Such helps produce vortices which, due in part to friction and molecular adhesion, roll down the body, increasing in size and rotational velocity while naturally spinning in the preferred direction such that the fish is able to kick it's tail off of the spinning columns of water. Kicking nearly in direct opposition to the direction of spin of each alternating shed vortice. It seems that the universities are only beginning to toy with the concepts shared by the "crackpots" of yesteryear.
http://dabiri.caltech.edu/publications/RuWhDa_JFM11.pdf (http://dabiri.caltech.edu/publications/RuWhDa_JFM11.pdf)
Pay particular attention to the concept of "vortex added mass".
What is innately understood by even the simplest of creatures remains long hidden from the assumedly wise for profound reasons. After watching the otter swim on a nature show in the eighties, I have exploited the spinning vortex to enhance the efficiency by which I swim, cupping the palms together and pushing a spinning vortex of water down the body, feeling it spin toward the feet, then kicking both feet in unison, kicking off the ball of water for an easy push off the return side of the spinning vortex of water.
What this has to do with the wheel is fairly obvious to those with some experience. Of course, using the fish metaphor, one might substitute gravity as the medium or flow direction and arcuate inertial interactions as the "vortex enhanced mass". The fact that serious researchers often encounter stunningly "counterintuitive" principles in such endeavors, is, I believe, intentional. But I digress...
EM has hit the lever right on the sweet spot. It is, however, but one of many smaller answers in a growing flood of questions. Questions as to how mankind has arrived just where he has, at the point point in time he has, with the technology he has, in the condition he has.
While many are now asking the question: "Who is John Galt?" (or, "who will save us?" or "where can I escape what is happening around me?")
I would counter with the question: "Who is Yeshua, Jesus Christ?"
Quote from: TechStuf on July 19, 2012, 06:54:39 PM
I would counter with the question: "Who is Yeshua, Jesus Christ?"
your imaginary godfairy savior friend.
The drunken one, right on cue. He is nothing if not consistent. We all believe in something or someone. That is what separates us from some of the animals.
I believe I will ask God once again to bless wilby in such a way that he must face at least a few Truths.
God bless your heart, Wilby, in Christ Yeshua.
Hi EMdevices,
Very interesting and exciting simulations indeed!
BTW: Thanks also to TechStuf for his insights.
A little story:
"Perpetual Motion Toy - 12/14/97"
http://keelynet.com/energy/mptoy.htm (http://keelynet.com/energy/mptoy.htm)
<quote>
Note: the spiral ramp is in effect a vortex and it appears that vortexes
in some way add energy to things, they keep reappearing in many overunity ideas.
<end quote>
Very Best,
Yann