The huge multi-National oil companies employ tens of thousands of researchers whose sole function is to find new locations to drill oilwells. However, it is reasonably well established that, assuming that we find it all, we humans will manage to use it all up by around the year 2050, in less than 50 years. (That petroleum took hundreds of millions of years to form.) Actually, official government and industry records (presented in the first link at the end of this page) shows that at current usage rates, there appear to be around 43 years supply for the world, but frighteningly, only around FOUR years supply actually in or near the United States!
A natural side effect of the formation of that oil is that massive accumulations of natural gas (mostly methane) also exist underground, and we are using it all up at an amazing rate, too. It appears that the world may not use it all up for around 70 years or so, although the US figures to use up all the supplies in and near our country in around 8 years (at current usage rates).
We use these irreplaceable natural resources in some pretty disappointing and wasteful ways. Enormous numbers of barrels of oil get used up to make the plastic bags we bring everything home in (and then immediately throw away). Ditto for the packaging of almost every modern product. Our attitude seems to be "It's here, so why not use it all up. I won't be alive when it runs out!" But, hopefully, other people will be! "There will be smart people around. THEY will figure out what to do!"
Around 1990, I realized an interesting situation, which seems to show promise of being a source of electricity and mechanical energy billions and possibly trillions of times the total available energy in all existing oil, gas and coal! I am bemused that so many tens of thousands of researchers struggle to find oil supplies while exactly zero are even exploring this far more vast potential source of energy!
Technically, this concept is a "mechanism" or "coupling". There are countless such mechanisms that use shafts, pulleys, gears, levers, etc, to convert some form of energy into some other form. There are also mechanisms based on magnetism or electricity to do similar things. The premise described here is a "coupling" which is based on some peculiar aspects of how gyroscopes work. There does not seem to be any other mechanism that is capable of coupling this energy source with any usages, but this approach seems ideal for it.
We will refer back to this amount of energy soon!
Around 1990, it truly dawned on me that gyroscopes also maintain their orientation in space. I was "slow" on that since it was known for centuries! Certain applications of gyroscopes in navigation functions rely on this characteristic. So, it dawned on me then that, IF an (imaginary) million-ton, Ferris-wheel-type, gyroscope was built on the North Pole of the Earth, with the really, really good bearings that gyroscopes always have, an interesting possibility existed! Once a motor would be used to start the gyroscope spinning, it would then spin (forever, if the bearings were good enough and there was no air friction). Its spin axis would try to remain fixed in space, with the axis pointing to some specific star. But the Earth's rotation, and ground under the huge gyroscope, would constantly be turning, once a day. If the gyroscope axis was supported so it could stay pointed at a specific star, and the Earth able to slowly rotate beneath it, a TORQUE (or moment) would exist of the Earth trying to rotate the fixed axis of the gyroscope. A gear-train could then be driven by the differential motion of the Earth underneath to power a generator or other equipment. Essentially, the Earth's rotation would externally directly drive the gear train, using the gyroscope simply as a fixed object to push against!
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A different way of describing this is that the rotation of the Earth
necessary applies a TORQUE (or Moment) against the gyroscope's
axis, which drives the gear train.
The GYROSCOPE'S FIXED AXIS IN SPACE would represent
a structure to which the gear train could act to "load" the Earth's
rotation, to actually remove energy from the rotation of the Earth!
No other "fixed structure" is available for such
a use, except something like a pendulum or gyroscope that is
following Newton's Laws in trying to maintain its orientation in
space. We can even calculate how well this would work! We probably can never build a million-ton spinning gyroscope, but we DID launch 2,000 ton Saturn V rockets into space, and we make 150,000 ton oceangoing ships. So we will use the hypothetical example of a million (metric) tonne gyroscope (1,000,000,000 kg), 20 feet (6 meters) in diameter, turning at 2 revolutions per second or 120 rpm (so the outside surfaces would move at around 80 mph.) Once it was started (with a motor), if there was no friction it would continue to spin forever, at that constant 120 rpm speed, with no additional energy needed from any motor. The rotational inertia of such a gyroscope would be m * r2 or around 9 billion kilogram-meters-squared. It's (rotational) angular momentum would be this number times the rotational rate of 2 revs/sec (or 12.6 radians/sec) so it would be 115 billion kg-m2/second or 115 billion newton-meter-seconds. The (maximum) Moment (torque) that could be acting to drive the drive train on the gyroscope would then be this angular momentum times the rate of the applied rotation, which is one rotation per day. That is about one radian in 14000 seconds. Therefore the (maximum) applied Moment would be about 8 million newton-meters. This is the maximum amount of torque that could be available between the gyro axis (which is trying to remain in a constant line) and the base underneath it which is rotating with the Earth. If this Moment (torque) is multiplied by the rate of rotation (one radian in 14000 seconds), we get 600 newton-meters/second or 600 watts of energy. If there were no losses, this would be able to create about 1 horsepower of work, constantly and forever! That work would NOT require any input of any other energy source, and would forever come from removing a tiny amount of energy from the Earth's rotation. Such a machine would obviously eventually break down, but until then, it would forever be able to constantly produce that 600 watts of energy. Interesting? (It turns out that friction in the shaft bearings and air resistance in any real devices cause losses that can be significant, so the actual available power would be less than this. This particular example, with standard design bearings and surrounded by air, would have enough frictional losses to certainly eliminate generating any electricity to export!) People have pursued "perpetual motion" for centuries. Actual perpetual motion is impossible, because it would violate a number of scientific laws that are known not to be able to be violated. However, a mechanism such as this described would certainly give the APPEARANCE of perpetual motion! It would be able to run apparently forever, and even produce usable power in the process! It is NOT perpetual motion, though! What would be happening is that kinetic energy of the rotation of the Earth would just be converted into a different form of energy, such as electricity or shaft mechanical energy. No violation of any law would be happening! Actually, if the Earth ever stopped rotating, this device would stop working! My point here is that an unbelievably huge supply of energy is available to us (in addition to an even larger amount of solar energy constantly coming in from the Sun) and that there would be no pollution and no depletion of natural resources involved in using it. No global warming would result either! There are people today who keep pursuing "perpetual motion" but they rarely have a scientific background to understand how to calculate things like complex differential equations or to know what is possible and what is not. Such people would probably be interested to know that the device just described would qualify for their "perpetual motion" device, even though it actually isn't! After a million years of everyone on Earth using such devices, the Earth would have really slightly slowed down in rotation, by a fraction of a second longer day! But it turns out that the Moon's interaction with the Earth's ocean waters, as the tides, has a larger effect! In that million years, natural tidal effects will have slowed the Earth's rotation enough to make the day longer by around 22 seconds. In a few billion more years, the Moon's effect on the ocean tides will have slowed the Earth's rotation down to about 1/50 as fast as it is today (there will only be about seven, really long "days" in a year!)
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These two effects are actually quite different, but both are extremely interesting. The toy gyroscope, if it had absolutely perfect bearings and it operated in a perfect vacuum, should precess forever, without ever slowing down its spin. This represents an interesting subject, because there is the appearance of a NEW motion (the precession) which does not seem to be powered by anything. If you stop the precession with your finger, it will start up again, without the gyroscope rotor slowing down in the process! The initial impression is that it could represent some sort of "perpetual motion" (in that it seems to be creating new energy by starting up the precession motion without any apparent source of energy to do it!) although that is not actually the case. The mathematical understanding of that is fairly complex, though!
This specific effect is a theoretical example of "converting" the Earth's rotational energy into usable mechanical energy for us humans to use up. It also seems to resemble some sort of "perpetual motion" because the concept is that the giant gyroscope would not only keep spinning on its own but even be producing power in the process. But note that there is no "perpetual motion" at all here; that it is merely a conversion of one form of energy into another, from the kinetic energy of rotation of the earth into mechanical energy that could be used to generate electricity. There is no violation of Newton's Laws! However, the fact that the Earth's rotational energy could drive such a device for billions of years would certainly make it seem as though it WAS perpetual motion!
Now say that, over a period of 1,000 years, the Earth's rotation somehow SLOWED by 0.0007 SECOND per day. Instead of a day being the current 86164.09 seconds, it would then be 86164.0907 seconds long, an absolutely unnoticeable effect. (Especially if it only occurred so slowly that it took a thousand years!) The kinetic energy calculation above would be the same except we would now use 86164.0907 and the Earth's kinetic energy would be 2.145619292 * 1029 kg-m2/s2.
A basic law of Physics is that energy must be conserved. By gradually slowing down by just that fraction of a second, an unnoticeable effect, and one with no consequences whatever, the Earth would have had to have given up the difference in those two energy totals, or 3.6 * 1021 kg-m2/s2, or 3.6 * 1021 Joules. A Joule is a watt-second. To convert this into kWh, just divide by 3600 seconds/hour and 1000 watts/kW or 3.6 million, and get 1.0 * 1015 kWh.
This is identical to the total electric use of all Americans for one thousand years as calculated above! So, if we could just figure out how to insignificantly slow the Earth's rotation, to make the length of the day longer by less than a thousandth of a single second, we could have essentially limitless electricity for all of us for a thousand years! Interesting?
This amount of energy is the same as if a large 50-megawatt electric power generating plant operated constantly for 2 * 108 hours, or around 23,000 years! Or the total of the hundreds of such giant electric generating plants which operate continuously now (always using up conventional power sources such as oil, gas, coal, nuclear or hydroelectric).
See my reason for fascination? If someone could figure out how to SIMPLY tap into this enormous energy of rotation of the Earth, to somehow convert a tiny part of it into electricity, we could totally supply all the electricity needed for all American homes for a thousand years while only making the day 0.0007 second longer. No burning of any coal, oil or natural gas to deplete those supplies or pollute the atmosphere with their waste products and their global warming. There would also be no reason to use nuclear power generation to create electricity, and so there would not be all the environmental hazards there. Countries wouldn't even have political reasons to wage war over sources of petroleum or other energy supply natural resources! All the known supplies of oil, coal and natural gas together will probably be used up in well under 100 years. And then what? IF somebody can figure out how to convert that rotational energy of the Earth, WOW! Even a conservative view makes clear that there are billions of times as much energy present as we could ever hope to discover in all the coal and gas and oil and nuclear we will ever find.
This research also led me to investigate the immense amount of heat given off to the atmosphere by Electric Power Generating Plants and I have composed a separate essay on that at http://mb-soft.com/public2/powerplt.html. It is an astounding amount of wasted energy!
Actually, such a nearly unlimited source of electric power could provide power to drive electrolysis of water to create hydrogen, for possible fuel for future vehicles. (I personally feel that trying to produce enough hydrogen to be a commercially valid energy source is foolish, but it would be possible.) Even more interesting is that this energy capture process does not figure to have all the wastages of our conventional methods. Most people do not seem to realize that the actual energy in coal or oil or natural gas burned in our giant electric generation stations is nearly all wasted! Only something like 13% of it actually gets to our homes to be used as electricity! The rest goes into various forms of heat, dumped by "cooling towers" and assorted other methods of designed wastage. Most people do not realize that most modern cars are only around 21% efficient, regarding the energy that was in the gasoline, and even less when considering the original energy that was in the crude petroleum. (But that is a lot better than the average 15% automobile efficiency of the 1970s!)
This concept of simply converting a tiny portion of the Earth's rotational energy into mechanical energy, seems to have very little possible inefficiency or wastage. It IS true that then converting it into electricity would have some conversion losses, but they are still a lot better than 13% or 21% energy usage!
There is actually another aspect of this that seems even more attractive to me, for several reasons. Here is an example of the current "silly thinking". California has so many people that it is in urgent and even desperate need for electricity. As I understand it, they are funding research in North Dakota, around 1500 miles away, regarding generating electricity with giant windmills. That technology would have some environmental implications of its own, if really extensive use was made (wind patterns and weather patterns would be altered for everywhere east of the wind farms, for example), but that is not the silliest part. If you ask ANY knowledgeable Electrical Engineer, he can explain that the "power grid" that we rely on has a problem. Even when those high-tension power lines are operated at around 500,000 volts, they are designed so that roughly 10% of the electric power put in at one end of a 60 mile long stretch, gets lost as resistive heating (by the wires into the surrounding air). So, 60 miles away from ANY central electric generation station, only about 90% of that electricity is still available. (This is why virtually all such generating stations are pretty close to large cities where the electricity is needed.) So, go another 60 miles, and we lose 10% of that remaining electric power (or 9% of the original, so we have 81% still going. After 180 miles, there is only 72.9% left available.
If you continue with these "transmission line losses", which ALL Electrical Engineers can easily calculate, for a 1500 mile stretch to California, it is easy to see that only around 7% of the electricity created in North Dakota would actually get to California! And worse, the other 93% of it would go to heat up the air, contributing to global warming. A good idea? Who is doing this thinking?
I guess it sounds impressive to politicians and executives of giant corporations! They figure they are seen as "green" by spending money on researching such things! I do not argue that a MODERATE usage of wind power is a good idea, as long as the electricity created was to be used fairly locally. Maybe there should be a "Ministry of Common Sense" to oversee such things?
I admit that California seems to have an impossible situation. They keep needing to use more and more electricity, and they have started building electric power plants that will not be operational for ten years. California also relies very heavily on electricity generated by hydroelectric power plants at Hoover Dam and other dams, and drought has lowered the reservoirs more than a hundred feet below normal. They have spectacular problems. But spending money to research making wind electricity in North Dakota??? Wow!
Back to the issue here! Instead of a million-ton gyroscope at some central electrical generation plant, and then all the transmission losses and atmospheric heating, the idea seems extremely appealing that SMALL systems might be able to be installed for each house or building. Talk about "off the power grid!" This would be its own separate electric generation system. The idea of personal independence is a nice side benefit, should this concept be practical!
I happen to have a flywheel from an antique air conditioning refrigerator. It's radius is around 0.20 meter (8") and it weighs around 19 kilograms (42 pounds). Let's consider getting it to spin about as fast as a normal appliance motor, 1800 rpm. If we assume that all the mass is at the outer edge, the Rotational Inertia (I) is m * r 2 or 0.80 kg-m2. The Angular Momentum is I * w or 150 newton-meter-sec.
If the supporting shaft size is 4 cm (about 3/4") in diameter, then the shaft bearing velocity is 1.9 m/s. If standard ball bearings are used, which have a dynamic coefficient of friction of around 0.0015, the standard friction loss calculations show that the power loss due to friction in the bearings is 0.57 watt.
These are pretty good bearings. If the flywheel is spun up to 1800 rpm, it would coast for quite a while before stopping. Another way of looking at it is that IF a really tiny motor was placed on the gyroscope shaft, that provided just 0.57 watt of power, the frictional loss of the bearings would be overcome and the gyroscope would keep running at a constant speed of 1800 rpm. Notice that at this point, we need 0.57 watt of outside power!
Getting back to the gyroscope resisting having its axis changed, we now need that Angular Momentum times the rate of rotation of the Earth. Since the Earth rotates completely in 86,400 seconds (one day), it rotates one radian in around 14,000 seconds. So we just have 150 nt-m-s * 1/14000 /sec, which is around 0.01 nt-m of torque (moment) available. This torque is applied at a very slow rate (1radian/14000 sec), so we would only have less than one one-millionth watt of power generated. In this case, it is a really tiny amount of power and not nearly enough to overcome the frictional loss in the bearings. Yes, this was an example of what would NOT be useful, to show the general concepts involved!
Gyroscopes work better as their radius is increased. Let's consider a gyroscope of the same weight (19 kg) but ONE HUNDRED TIMES the diameter. This would be a really skinny rod curved into a giant circle with a 20 meter radius (over 120 feet in diameter, but extremely skinny. In fact, it would be much less than 1/4" in diameter if it was a steel rod. Also, let's slow down the rotation of the shaft, to 1/100 of before, so the actual speed of the outer parts is still around 80 mph, so we will use 18 rpm instead of 1800.
I = 7600 kg-m2. With the (slow) 18 rpm rotation, the Angular Momentum is 14,600 nt-m-s. When multiplied by the rotation rate of the Earth, we get more than 1 newton-meter of torque (moment) available. This would give about 1/14000 watt (0.00007) (one hundred times the output, with the same weight of material, but just a lot bigger).
Even better, the bearing velocity is only 1/100 as fast because the spin speed is that much slower. The result is that the bearing frictional loss is now only 1/100 of before, or 0.0057 watt.
Now, we're getting closer! If this giant Ferris Wheel type ring is made out of standard 2" diameter steel rod (ten times the previous diameter), (with a thicker supporting shaft and bigger bearings), the ring mass would be about 100 times as great 1900 kg (4200 pounds). These calculations show that it would then produce a continuous 0.007 watts of output power, with now about a watt wasted by bearing losses.
These calculations show that some power can be created but that it is difficult to overcome bearing friction. There are also two more complications that need to be considered. First, there would also be air resistance friction, and so the entire gyroscope would need to be enclosed inside a sealed chamber and the air removed so there was a good vacuum inside. Second, one must remember that the Earth rotates and causes the apparent axis of the gyroscope to change. So it would not remain standing up like a Ferris Wheel, but would need to (very slowly) rotate (the entire gyroscope) opposite the direction of the Earth's rotation. Astronomers say that it must revolve (precess) around a "polar axis" where the gyroscope would appear to completely tumble over once each day. So the room surrounding it would have to be REALLY big!
However, I also wanted these calculations to point out that the "crude" version described here is not very practical. For just a watt or two of power, the cost of building a really large gyroscope and making the supports, and then enclosing it in a sealed, evacuated room 140 feet high, wide, and long, is just not "cost effective" in business terms.
I am certain that a much more complex practical (mechanical) (low-speed) mechanism can be made. I believe that an enhanced version of my experimental "toys" can be made such that the entire device would fit into a normal room, and the low speeds eliminates the vacuum needs! It figures NOT to be inordinately complex.
I am also certain that Euler's Equations hold the key to maximizing the performance of the mechanism, but those equations become unbelievably complex for many situations. Most of the configurations that I have worked with wind up involving sets of 27 simultaneous differential equations in 27 unknowns! They are not much fun to try to solve! Whenever I can manage to complete those solutions, and then Integrate them, I will know how to maximize the device's performance regarding each of the many parameters, by Integrating the differential equations over each of the different variables.
In mathematics terms, the problem is called the Eigenvalue problem. However, it is an especially complex version of one! There are eigenvalues and eigenvectors all over the place! When I was still in College at the University of Chicago, I knew how to solve many such problems, but that was long ago and I seem to have forgotten much! Worse, it is commonly known that for the majority of practical cases, exact solutions to the eigenvalue problem for distributed systems is not possible. In general, efforts are made to try to find "approximate solutions". In this specific problem, many of the eigenvalues happen to be very complex equations based on the Euler Equations, and there are a LOT of them. I have pretty much given up on my ever being again able to solve such problems mathematically.
We all know that Newton's Laws of motion apply to all objects. His laws were refined by Euler into a set of three generalized differential equations for when an object is moving in a three-dimensional motion. The three equations are of the form:
with the usual symbols for angular velocities, rotational inertias, and such. The solution to this set of equations, for the complex initial conditions that I work with, will establish the energy (production?) conversion performance. So, in my opinion, we even already have the basic equations!
In my opinion, the idea of a truly huge spinning gyroscope to try to produce a few watts worth of power is impractical. But I believe that a "more sophisticated" mechanism of maybe eight or ten foot diameter, maybe in a basement, might be able to constantly produce 10 kW of electricity for that house.
This subject continues to fascinate me! For several years, I have believed that a rather complex variation of the concept above is very likely to be a very efficient converter of this one form of energy into a more useful form. My frustration is that each of my 27 variables would need to be maximized for performance. Setting up those rather complex Euler equations would be useful, establishing the eigenvalue problem for them, and then Integrating them over time and them partially differentiating them over a single variable, to determine a "best" dimension for that parameter. If this were done for each of the 27 parameters, then a realistically efficient conversion system might be possible. Without that math, just trying "best guesses" for all those parameters, may take many thousands of years!
I have also been very surprised that NO ONE seems to have ever become troubled by something in toy gyroscopes! Given that the rotor spin rate is not affected (which is true, except for friction and air resistance), even as a child I noticed that when the gyro is first released on its little pedestal, IT ACCELERATES up to some precessional speed! That energy had to come from somewhere! How come no one seems to have ever even thought about that? (It turns out that the Euler Equations show that that acceleration of the precession motion causes the entire gyroscope to lower a VERY small fraction of an inch . The (kinetic) energy of the precessional motion actually came from the (potential) energy of the height of the gyroscope weight in the Earth's gravitational field!) (I realize that was WAY more information than you wanted!) (However, that effect happens to cause a unique violation to Newton's Law of Conservation of Angular Momentum in the process, a troubling fact!)
The other response comment I want to make is that, should I actually find that my concept works, I would almost certainly "give it away" by providing full plans in some web-pages, much as I have done with the "free Air conditioning (since 2000)", or the "free Childhood Obesity/Precision Bodyfat analysis (since 2004)", the "beached whale saving concept (since 1997)", and many other things that I have chosen to give away in the past. I have noticed that immediately after I mention "giving it away" all those people seem to disappear! None of them seem that interested any more about helping people out, and I wonder if that is because they do not see how they could get disgustingly wealthy in the process. I realize that might be a cynical view, and they probably all just became extremely busy with more important things.
OK. I think I can give a vague idea of what the math problem is like that I need to solve, and which seems to now require Math that I had certainly learned in College but have since forgotten. In Physics or Engineering, there are Equations of Motion which describe (mathematically) the position, velocity and acceleration, in each of the three x, y, z directions, of an object at each instant of time. For something simple like throwing a baseball, this results in equations which describe a parabolic path, which a lot of people are familiar with. (For the record, the path is actually NOT a parabola! It is an ellipse! But it turns out that that part of the ellipse is SOOOOOOO close to being a parabola, that for any practical ball and thrower, it is never more than a millionth of an inch away from where it would be as a parabola. And the equations for a parabola happen to be simpler to solve. So it has long been called a "parabolic arc" even though it technically is not.) (Boy, are you learning a lot of worthless trivia here?)
But now consider a more complicated motion than just a simple ball in a uniform gravitational field. Imagine an ant, of some standard mass (weight) for an ant, walking in a constant circle an inch in diameter. I am going to ask something simple, just what the ant would weigh on a scale, at any instant. Ants seem to have sticky feet, and this one will need that! He is walking in his circles on one of the carriages of a small model Ferris Wheel which is both spinning and has its carriages separately spinning. Now, bolt the supporting structure of that model Ferris Wheel to the floor of a roller coaster car, and have that roller coaster constantly be following its complex (and fun) course. So now I want the equations of motion for the ant. The ant will always experience the effect of his weight, the attraction of the Earth's gravity, but he is forever tilting in every imaginable angle and position, and the effect of his weight, in regard to a "rest frame" of the surface he is walking on, is a moderately complicated problem, due to the combined effects of his own walking in that circle, the spinning of the main body of the Ferris Wheel, the spinning of that individual carriage in it, and the complex path of the roller coaster. However, the ant also experiences "inertia" due to the fact that he has weight. Just like when YOU are thrown toward one side when the roller coaster car turns to the other side, the ant has the same sensation of acceleration, but now in rather complex ways!
This turns out to be a fairly complex equation to just describe the POSITION of the ant. In three dimensions, of course, x, y, and z. Now, if that equation is processed by something in Calculus called Differentiation, we would have the differential equations (in x, y, and z) which describe the VELOCITY (like speed) of the ant in all three dimensions. THEN, if we differentiate them again, we can find the ACCELERATION of the ant in each of the three dimensions. These are actually what the Euler Equations are, in the usual form.
We are starting to get somewhere! Newton taught us that Force equals mass times acceleration. Since we would know the mass of the ant, and we just found the many individual accelerations (in x, y, and z), we could now do a vector addition to get the total resulting acceleration (in x, y, and z), and we could now determine the force sensation that the ant felt at ever instant, in all three dimensions. (All that sensation that you feel in a roller coaster of being thrown toward one side or the other, can actually be presented in mathematical equations like this, but actually a lot simpler ones than for our ant.
Now, sticking with our ant, if we now Integrate (more Calculus) each of these force components for an entire cycle of the roller coaster and Ferris wheel, we could calculate the TOTAL NET work which acted on the ant during that whole time. That number SHOULD total to ZERO for each of the three dimensions. You can think of this that you get thrown toward the left and toward the right an equal amount, actually an EXACTLY equal total amount in an entire roller coaster ride.
Unfortunately, MY mathematical problem is actually a little more complex than that of our ant! When I have come close to writing down the basic equations, it has always taken around six sheets of paper just to write the preliminaries down! The actual entire equations appear to require around 50 sheets of paper to just write down (although I have never fully written them all out yet!) Imagine WORKING with it, doing Calculus on it! (I am establishing that I am not as smart as I might have hoped!)
If my idea has merit, then one of those dimensions will wind up having a NON-ZERO net force. THAT would actually prove that my idea has validity, but I actually sort of already assume that it does! In fact, if I get an actual exact answer for this problem, I will know the theoretical maximum power output that a specific device might produce. What I really need is for those equations to essentially be solved for many different experiments where a single dimension of something is changed. Each time it is solved as above, a different net Work would be calculated. By using that Calculus Differentiation again, it is possible to determine the value of that dimension that gives the greatest possible value for the net Work, meaning that the dimension value is the best available dimension for that part of the mechanism.
That number would be plugged in and the whole works done again regarding altering some different dimension. Presto, again, etc, and a best dimension for that dimension would be calculated. Do this for every one of the mechanism dimensions, and a decent estimate for how it should be built should exist! (a FAR better guess than anything I can guess up to now!) As noted above, I have essentially had to simply make educated guesses regarding all those dimensions for the prototypes that I have made in the past, and they give evidence of having worked, but very minimally.
There are actually ways to carry this even farther, to get even better estimates, but you should get the point.
At whatever point when I can get access to or get someone to solve these things, I think I would then be able to build yet another prototype, and I would THEN be able to see if it can do what I think or not. There are probably some people who LOVE to do eigenvalue problems!
If it DOES, I am likely to say YIPPEE a few times and a few hours later, there are likely to be web-pages telling everyone else how to duplicate it, but bigger! I truly believe that a device between the size of a closet and a bathroom, may be able to constantly generate 3,000 to 5,000 watts of electricity, for a household, essentially forever (until it breaks). Of course, I could be wrong! Until I get some math problems solved, I will not know! I am pretty confident on this, and I can nearly taste it! Interestingly, if I am right, the device would NOT work at the Equator! Fortunately, human beings seem to like to live at around 40° Latitude, where it figures to work very well!
But for all those people who think they see a cash-train that they want to get on board, I really can't imagine that I would ever get dollar signs in my eyes and participate in anything like that! Sorry to disappoint!
The Earth's Rotation as a Source for Energy
Waste Nuclear Power For Making Electricity And Heat?
The Physics of Efficiency In Electric Power Plants
Individual Ways of Reducing Your Energy Usage
Methods of Storing Energy for Later
How Much Energy Comes From the Sun? And Why is there Global Warming?
How does the Sun create so much energy?
Inventions Which Might Help Deal With Coming Energy Catastrophes
An Invention to Efficiently Make Electricity from Solar
Enormous Heating of the Atmosphere by the Alaska Pipeline
Air Conditioning without Huge Electric Bills and without Freon
A Method of Storing Summer Heat to (Nearly) Entirely Heat a House all Winter
An Extremely Highly-Efficient (and Fast, 200.0 mph) Transportation System for People and Products
The Sophisticated Woodstove I Invented in 1973
The Physics of Wood as a Heating Fuel
Why is the North Pole Heating Faster than the rest of the Earth?
A Possible way to greatly reduce Aerodynamic Drag of Airplanes
( http://mb-soft.com/public/index.html )
C Johnson, Physicist, Physics Degree from Univ of Chicago