History and Philosophy of Science

Donald Simanek's Pages

This museum is a celebration of fascinating devices that don't work. It houses diverse examples of the perverse genius of inventors who refused to let their thinking be intimidated by the laws of nature, remaining optimistic in the face of repeated failures. Watch and be amazed as we bring to life eccentric and even intricate perpetual motion machines that have remained steadfastly unmoving since their inception. Marvel at the ingenuity of the human mind, as it reinvents the square wheel in all of its possible variations. Exercise your mind to puzzle out exactly why they don't work as the inventors intended.

This, like many pages at this site, is a work in progress. Expect revisions and addition of new material. Since these pages are written in bits and pieces over a long period of time, there's bound to be some repetition of ideas. This may be annoying to those who read from beginning to end, and may be just fine for those who read these pages in bits and pieces.

Principles of
Unworkable Devices.
Perpetual motion machine inventors do have principles. Unfortunately the physical principles they assume are often ones not obeyed by nature. Let's examine just a few.
The principle of unlimited possibility. Anything is possible in nature.
The "heavier on one side" seduction.
The "more weight on one side" distraction.
The "unbalanced torque" deception.
The cyclic disappointment.
The elastic/inelastic dilemma.
Failure to isolate the system.
The static/dynamic trap.
The apples/oranges equation.
The artistic illusion.
Experimental "gotchas".
The "dog chasing its tail" principle.
Reinventing the square wheel.
Anything is possible
Inventors assume that since we haven't looked at every part of the universe nor have we looked at every possible mechanism or phenomena, we can't rule out anything. If one has faith in oneself, perseverance, and tinkers long enough with new and untested ideas, one may discover ways to thwart "known" laws of physics.
Those who think this way are much like the child who puts two blocks in a box, closes the box, shakes it, then opens it, hoping to find three blocks inside. The child hasn't yet had sufficient experience with how nature works to realize that nature doesn't work that way. Perpetual motion machine seekers hope that by using some new combination of well-known materials and well-known mechanisms, they just might make a machine that outputs more work than is required to run it.



The "heavier on one side" seduction.
The most naive level of perpetual motion seduction is the notion that if a system has more mass on one side of the axle, then that side must swing downward. That notion is quickly dispelled by consideration of this symmetric arrangement of three equal mass balls on equal length arms. Clearly there's more mass on the left side of the axle. But just as clearly, the device will not turn of its own accord. Even worse, if given a push, it will not turn continually. It will come to a stop from dissipative forces just as any wheel would. This wheel is as likely to come to rest in one position as in any other, for it is perfectly balanced in any position. Persons who have little experience with mechanisms may think it would prefer to come to rest with one ball directly above the axle, and the other two below. That is not true. Our naive expectations are not the way nature works.
We can test its stability by turning the wheel to any position whatever. No matter what position it happens to be in at rest, it has no tendency to turn in either direction, and will not initiate motion by itself.

The earliest unbalanced wheel of Villard de Honnecort underwent countless modifications and embellishments over the years. But the seductive principle that motivated the inventors was that "If you can keep the wheel heavier on one side as it rotates, then it will continue rotating forever." Their overbalanced wheels had weights that moved, and in the static picture at least, there were always more weights on one side of the wheel axle. But, when the system is analyzed, one finds that the torques are balanced (add to zero). A wheel will not initiate motion unless the torques are greater in one direction than the other. If the net torque about an axis are zero, the system will not start turning by itself.

The situation is worse than that. Newton's third law ensures that all internal forces in a system sum to zero, and all internal torques do also. If the system is to move, some external source must supply force or torque. A system with unbalanced torque from external sources moves toward a position where the torques will become zero. That's a position where the system will be in static equilibrium. Typically the system will oscillate around that position, slowing down gradually to rest as its initial stored energy dissipates and it comes to rest.


Critical readers will note that the above comments assumed a uniform gravitational field. Actually the gravitational field decreases with height, and the field direction diverges from the center of the earth. These effects are negligible for a machine that would fit in a laboratory. But they would cause a slight preference for some positions of this wheel. Still, they won't provide any force that would cause a consistently preferred direction of motion through many cycles.
The "more weight on one side" distraction.
Many people confuse 'mass' and 'weight'. To illustrate how this distracts some perpetual motion machine inventors, consider the simple example analyzed by Simon Stevin. A continuous chain of balls rests on an asymmetric ramp. Some persons naively assume that the chain will turn continuously because there is always more mass to the left of the vertex than on the right. But the chain doesn't budge.
The inventor may even test his assumptions by removing the two balls resting on the right ramp and weighing them on a balance. He does the same with the four balls on the left. The weights are not the same. He says, "I have tested this experimentally, and the weight of balls on the left of the vertex is twice as great as the weight of the balls on the right."


But this isn't a valid test. By removing balls for weighing, he's removing them from the parts of the system they interact with, and thereby changing the geometric and physical relation they had with each other and with the ramps.
So the inventor says "I'll prove my assertion that the left side is heavier by another method—experimentally." He places a fulcrum to support the system, directly beneath the top vertex of the triangle, so the fulcrum supports the entire system. The system tilts to the left. "See, the system is heavier on the left!", he says, triumphantly.
"And if you still are not convinced," the inventor says, "I'll prove my assertion with another independent experimental test. I will put an electronic scale under the left corner of the ramp, and another under the right corner, to see which weighs more. As you can plainly see, the left scale indicates greater weight, proving that the left side is heavier."


These last two tests are irrelevant to the inventor's purposes, for he is weighing the balls and the ramp. The mass of the ramp and the distribution of mass in the ramp is irrelevant to the operation of the machine, even the sort of operation that the inventor assumes.
"What about torques?", the skeptic asks. The inventor replies, "The loop at the bottom is obviously in balance, so we can ignore it." The balls on the left provide greater torque with respect to the vertex than do the ones on the right. There's an unbalanced counter-clockwise torque on the system, and that will produce counter-clockwise motion.
But, during all these tests on the actual system, the balls sit there unmoving. The inventor rationalizes: "If I could only get rid of that pesky friction, I'd have this thing working. Just a little more work, and we'll have it."

What's the error here? When analyzing a system or a part of a system, one must consider all of the forces and torques acting on that part of the system. Yes, the torques due to gravity acting on the balls are unbalanced about the upper vertex. But other forces also exert torques on the balls. The reaction forces of the ramps exert forces on the balls. The tension in the links joining the balls is a consideration, too. When all these things are considered, we find to our dismay that the net torque on any part of this system is zero. More to the point, the net forces and net torques on the ball-chain are zero. So the chain doesn't move by itself.

By the way, if you think that trick of balancing the system with a fulcrum, or with the two balance-scales, is absurdly blatant, let me tell you that a perpetual motion machine inventor very recently (in 2002) tried to pull that very trick on me. But he honestly and seriously thought it provided conclusive evidence in favor of his hypothesis. I provide another example below in the Experimental "gotchas" section.

Inventors have found many ingenious ways to make a wheel have more weight on one side of the axle, and to maintain that condition as the wheel is rotated. But as soon as it is left to its own devices the wheel finds an equilibrium position and just sits there unmoving. This happens when reaction forces reach just the right sizes to produce a net force of zero and a net torque of zero on the wheel.


The "unbalanced torque" deception.
Some inventors realized that it's not enough to have more mass on one side of the axle. So they sought some way to keep the torques unbalanced as the device rotated. Several possibilities occurred to the restless minds of diligent inventors:

Continually move mass from one side of the axle to the other just fast enough to replace mass lost elsewhere by the turning of the wheel, but accomplish those transfers without doing work on the mass from an external source.
Keep some part of the mass continually on one side of the axis, even as the wheel turns, so the wheel remains unbalanced.
Introduce some force that is always greater on one side of the axle than the other and provides torque that is continually greater in one direction.
Shield some portion of the machine from external forces.
Physicists and engineers today chuckle at the naiveté of such goals. They are all fundamentally impossible. But the perpetual motion machine inventor scoffs at such declarations of impossibility.
Attempts to transfer mass run up against a cruel fact of nature. It takes at least as much work to transfer mass from point A to point B as it does to transfer the same mass from point B to point A. Also, it takes the same amount of energy to transfer mass from A to B in a gravitational field no matter what path you choose between those points.

Consider the simple wheel shown. If it rotates clockwise, moving the light blue sector at the top to the right of the axis, the same size sector at the bottom moves to the left of the axis. The net result is that the mass distribution of the wheel remains the same as before.

The sector at the top has greater gravitational potential energy than the one at the bottom, so the inventor is encouraged. But then he discovers that the top sector loses exactly that amount of potential energy as the wheel rotates it to the bottom, while the sector at the bottom gains the same amount, for a net energy change of zero. Drat!

The nature of the gravitational field is at fault. Nature insists that the net amount of work done in carrying a mass around a closed loop be exactly zero. Such fields are called "conservative" meaning "energy-conserving". There are advanced mathematical ways of saying this, using vector calculus, but that goes beyond our present needs or purposes.


Pierre Richard (Engineer, Paris), 1858,
British patent No. 1870.
Dircks (1861), p. 482.
Some inventors took another approach. They tried to devise ways to supply excess torque in one direction.

The clever deception shown here looks like a deliberate satire/parody, a joke, and a challenge to discover the built-in jokes. But it was patented. Its essential idea is that the chain of heavy balls nest in cups attached to the outer wheel, but only on the right side, providing considerable clockwise torque. The vertical portion of the chain passes through the rotation axis, so those balls provide no torque about that axis.

The inventor has included a brake on the left. Some inventors included a brake as an obvious joke "to keep the machine from running so fast it would tear itself apart." This picture has an artistic deception. The two spokes at the top of the wheel are behind the solid frame of the machine, but the other spokes are in front of it. Therefore if anyone or anything tried to turn the wheel were, the spokes would hit the frame, preventing further motion.

The lower pulley has no obvious support. Also, it seems non-functional and could be omitted without compromise of the machine's performance. The upper pulley also has no apparent support, but a pillow block on the upper frame would fix that. The spokes should be behind the plane of the wheel so they don't interfere with the ball-chain, and the upper pulley could easily be supported by another frame on the near-side of the wheel. The cups should be designed with a slot to accommodate the links between the balls, and their tilt optimized so the balls won't slip out of the cups near the top, and so the balls will release without impediment at the bottom. Any competent mechanical engineer could fix all of this. All of these artistic "flaws" are mere window-dressing, and probably the fault of the artist, not the inventor.

It seems that there's always a net clockwise torque on the wheel of considerable size. But there's a hidden torque balancing that, provided by the weight of the vertical portion of the chain. This torque is exerted on the outer wheel just above the top pulley. It arises from the tension in the chain. The balls aren't supported entirely by the cups, but partly by the tension in the chain.

In order to keep a moving wheel unbalanced, some outside agent must do work on the wheel.

This is one of the most ingenious deceptions in the PMM literature.


The cyclic disappointment
Machines are cyclic. Wheels turn around an axle. Any process intended to produce power must move its components cyclically.
Many of the previously noted delusions about nature have the common feature that they are based on true observations about how something behaves over a finite time and distance (such as a ball rolling down an inclined plane) then assuming that such a process can also be worked into a wheel or other cyclic device. The trouble is, that with a cyclic device:

The weight that gains energy falling on one side of a wheel must lose the same amount of energy when being lifted up the other side;
The steel ball attracted to a magnet gains energy, but to return it to its original position and repeat the cycle requires just that much energy to be done on it;
The buoyant object rising in water gains energy, but it takes just that much work to return it back to its starting point at the bottom to repeat the cycle.
These observations hold no matter what the geometric path of the moving objects and no matter how quickly or slowly they move.
So, how about a non-cyclic machine? Can a ball roll down an incline forever? You'd need an infinite length incline, and a gravitational field of infinite spatial extent. All fields known in the universe have two features that make this impossible: (1) they have "sources" at a particular location in space, and (2) their strength decreases with distance from the source, becoming zero at infinity.

To make a gravitational field nearly uniform over a large region of space will require a distribution of mass over a volume of space as large as that region. To assemble and "nail down" that much mass requires a huge expenditure of energy. Finally, the energy available to any machine operating in that field is no greater than the energy you expended in assembling that mass to produce the field.

To increase the size of that uniform region to infinite extent requires an infinite amount of mass, and where do you put that mass? We are forced to make do with cyclic processes occurring in a relatively small finite region of space.

Ultimately the common feature underlying all of these natural limitations, and underlying all of physics, for that matter, is geometry of space and time.


The elastic/inelastic dilemma
When we analyze perpetual motion machines, it's useful to idealize the system by assuming zero friction. If the machine won't work as we hope without friction, it surely will perform worse with friction. But what about other energy-dissipative processes that convert mechanical energy irreversibly to thermal energy (heat)? Can we treat them the same way?
All real materials deform to some extent under application of force or pressure. In fact, one can argue that perfectly rigid bodies are a physical impossibility because then impacts between such bodies would give rise to infinite reaction forces for infinitesimal time durations.

In many materials, such as steel and glass, collisions can be over 95% elastic, that means that less than 5% of the impact energy is dissipated irreversibly. Can we assume elastic materials in our initial analysis, confident that this will set an upper limit on a machines efficiency?

If we do so, we encounter a severe dilemma. Consider any machine that has rolling balls, or shifting weights that suddenly change velocity due to impacts. Many classic perpetual motion machine designs have swinging hammers suddenly hitting pegs or "stops", as in the Honnecort wheel. Others have balls rolling down inclines and then stopped suddenly. Whenever there's such an impact, the hammer or ball will bounce or rebound. Invariably the inventor has not taken this fact into account, and it always decreases the assumed performance of the machine.

So can we redesign the machine for "softer" impacts? Perhaps we can put cushioning material at the impact point, or some sort of a catch or latch to prevent rebound. Alas, this is worse, for any such cushion or latch makes the impact inelastic, and dissipates energy as heat or sound. [In fact, chatter, clatter, whirring, humming, ticking or banging sounds from a machine are a sure sign of irreversible energy dissipation. The perfect perpetual motion machine would necessarily be perfectly silent.]

A collision between two nearly elastic objects is not necessarily an elastic collision.

It is not generally appreciated, even by some physicists and engineers, that a collision or impact can involve very nearly elastic materials and still be a significantly inelastic (energy-dissipating) impact. An elastic material is one that can be slowly deformed, then relax to its original state without energy loss due to the deformation. But during a rapid deformation due to collision or impact, energy is temporarily stored (as elastic or vibrational energy) within each body, and when the bodies separate, one or both of them may still retain some of that, which is subsequently slowly dissipated as sound or heat as it vibrates.

These phenomena are yet another "gotcha" nature springs on the over-optimistic perpetual motion machine inventor. Whenever the mechanism of a machine involves changing accelerations (and what mechanism doesn't?), mechanical energy will be dissipated irreversibly. But, as with friction, if we idealize these for analysis and the machine still won't work as we hope, then it will perform even more poorly with real materials and machinery. If we idealize everything and the machine's efficiency is still less than one, then we haven't achieved perpetual motion.



Generally we avoid bringing up classical thermodynamics, but here we can't resist mentioning the implications of what we've said above. One statement of the second law of thermodynamics tells us that the efficiency of an engine can never exceed that of a Carnot engine operating between the same two temperatures. The efficiency of a Carnot engine depends on its input and exhaust temperatures, according to the formula e = 1 - (Tc/Th), where Tc is the kelvin temperature of the cold reservoir and Th is the kelvin temperature of the hot reservoir. (The Kelvin temperature scale begins at absolute zero.) For real engines this is much less than one, only approaching a value of one when the temperature difference between output and input becomes infinite.
For example, the Carnot engine cycle is shown here for an ideal gas, on a pressure-volume-temperature graph. Everything about the Carnot engine is idealized, to properly represent the upper limit of what's attainable. The gas is an ideal gas, in which all gas particle collisions are perfectly elastic. The cycle has two portions during which the gas expands and contracts along isothermal (constant temperature) lines. It has two portions where, thanks to perfect insulation, the gas expands and contracts along two adiabatic lines (no thermal energy goes in or out). (T1 and T2 are the temperatures of the cold and hot reservoirs, while A1 and A2 are adiabats.) The changes occur infinitesimally slowly, to avoid inertial effects.

Real engines, if they are to be any use, must complete a cycle much faster, so inertial effects are unavoidable. Therefore the path (on this graph) of such a real engine will have "rounded corners" and will lie completely within the path of the Carnot engine. By the definition of work, it can be shown that the work done by engines is proportional to the area within their closed path on this graph. Therefore the real engine will do less work than the Carnot engine operating between the same temperatures, since its area is within that of the Carnot.

The Carnot engine's efficiency is proportional to the area within this boundary (the sum of the light blue and dark blue areas). Compare the diagram for a real heat engine (the smooth closed curve filled with light blue) operating between the same two temperatures, and you see that those sharp corners of the graph are rounded off, and the area within this curve is smaller. The efficiency of this engine is therefore smaller. While the ideal engine for other sets of variables will be different, the same general conclusions apply.

The Carnot engine has greater efficiency than any other engine operating between the same temperatures. If we idealize everything in a device and its efficiency still isn't greater than that of a Carnot engine operating between the same temperatures, then the second law of thermodynamics is still safe.

Textbooks always stress the point that the Carnot engine operates with strictly reversible processes. But sometimes they don't sufficiently emphasize that the operation of the Carnot engine requires infinitesimally slow operation, to avoid infinite accelerations of its material components. One method of analyzing the entropy changes in a real engine is to decompose its operating cycle into an infinite number of infinitessimal Carnot cycles. This is a valid method, but doesn't eliminate this problem—it only disguises it.

Even in the realm of smaller materials, atoms, molecules, and electrons, similar "gotchas" arise to thwart inventors' aspirations.

Failure to isolate the system
Freshman physics students are continually admonished to "isolate the system" when calculating the sums of torques and forces on a system, or some part of the system. Failure to do this leads to seriously wrong conclusions. The net force on a system is the sum of external forces acting on that system and only forces acting on that system. For purposes of analysis one may choose some portion of a machine as the "system", but must be careful always to keep in mind exactly what that portion is.

This simple machine has been constructed to illustrate such errors with a minimum of complicating details. In fact, this picture is the essence of the idea behind hundreds of perpetual motion machine proposals of the 17th and 18th centuries, which were often fantastically Baroque in their embellishment of mechanical details.

A wheel is free to turn on axle A. A heavy mass M is fastened to an L-shaped member MXY, hinged at pin X near the edge of the wheel. Point Y is linked to a member YZ that has the same effective length as AX.

The inventor points out that there's obviously more mass on the left side. Clearly if the machine were in this position and then released, the wheel would turn counter-clockwise as the mass M moves downward along the dotted line. The only path this mass can take is the dotted circle, which is entirely on the left of the axle A. So the mass always provides a counterclockwise torque anywhere on this circle. Also, wherever the mass is along this circle, the mass is greater on the left of the axle.

The inventor thinks he has solved the problem of keeping the mass and the torques unbalanced as the wheel turns.

This drawing is unlikely to deceive anyone, for the error is right out there for anyone to see. But the same fundamental deception is at the heart of many machines seen in the perpetual motion machine literature, but in those machines the deception is buried in a mechanic's nightmare of wheels, belts, linkages, springs, and other distractions.

The give-away here is the fact that the mass M must rise as high as it falls, so the net work done on it by gravity is zero around one cycle. But if the inventor focuses attention on the torques, some people may be seduced into thinking that the torques are unbalanced at any position of the wheel. How can that be?


John Haywood (Br. mechanic), 1790,
British patent No. 1750.
Dircks (1861) p. 66.
It can't. The loose language above failed to specify two things: (1) the body on which the torques act, and (2) the axis we choose to express those torques. We must choose a portion of the machine as our system, then carefully look at all external torques acting on that portion. It's the important principle that you must isolate the system before applying F = ma.

The torque due to gravity on the mass M, about the axle A, is always counter-clockwise in this machine. But that's not the only torque acting on the rigid combination of mass M and the member MXY. At point Y there's a force due to tension in member YZ, and it is clockwise around the axle A. There's also a force that the wheel exerts upward at joint X, and that also gives a clockwise torque around A. Now when the mass M is rising after it reaches its lowest point, the sense of these torques due to forces at X and Y changes sign. The net torque on MXY during the fall is counter-clockwise, while the net torque during the rise is clockwise. The torque analysis gets a bit messy, but the bottom line is that the net work done by all of these torques acting on member MXY is zero during each cycle.

The machine shown on the right was invented by John Haywood, a draftsman and mechanic. He obtained a British patent for it. The small rollers at the end of each spoke are supposed to be quite heavy, to provide the "overbalance". The error of physics that led him (and the patent examiners) to think it might work is the same as in our simpler machine described above.


The static/dynamic trap
Inventors who do appreciate the importance of torques will sometimes carefully analyze the torques in their proposals, concluding that the torques are unbalanced. This can result when they have drawn the picture in a manner that contradicts their assumptions. They draw, and analyze, a static picture of an unmoving wheel, and use the results to draw inferences about a rotating wheel. Sometimes they do it the other way around. If the wheel has shifting weights (as most have), their drawing shows at least one weight in a position it could not be in if the wheel were in the assumed state of motion.
The classic overbalanced wheel is such a case. As shown here it's easy to calculate the torques due to gravity acting on each of the balls. It's a correct static picture of one of the resting positions of the wheel. But is it a correct snapshot of the wheel in motion?