Johann Bessler's Perpetual Motion Wheels Part III

Professor 'sGravesande's letter to Newton

Probably the most important written account that we have from a very well-qualified contemporary "hands-on" witness of one of Bessler's wheels (the Weissenstein wheel), is the letter written by Professor Willem Jacob van 'sGravesande of Leiden University to Sir Isaac Newton. This letter was published in 'sGravesande's Oeuvres philosophiques et mathématiques, which is now available on-line, e.g. at http://cerebro.xu.edu/math/Sources/sGravesande/gravesande.html. The letter is in Vol I, p303.

Up to now, English-language writers all seem to have relied on the translation of this letter that appeared in the Annual Register, for the year 1763, Vol 6, p126-128 (reprinted in Henry Dircks' Perpetuum Mobile..., 1861, p38.) This translation is generally accurate, but it does have one error and two omissions. Since I'm still reasonably fluent in reading French, I've made my own unabridged, more literal translation below (with the main corrections highlighted in bold type):—

Translation:—

Letter to Mr. Neuwton (sic) On a Machine invented by Orffyreus.

Doctor Desaguliers has doubtless shown you a letter, which Baron Fischer wrote to him a while ago, about the Wheel of Orffyreus, which the inventor claims to be a perpetual motion. The Landgrave wished that I also should examine the machine. This Prince who loves the Sciences and the Fine Arts, and who by the help that he gives to all those who follow them with some success, doesn't neglect any opportunity to render the inventions which are presented to him useful to the public, wished to see that machine made known everywhere, and put into the hands of people more skilful than the inventor, so as not to lose the benefits that would naturally attend such a singular invention.

I thought, Sir, that you would not be displeased to have a rather detailed account of what can be seen from an external examination of a machine concerning which sentiments are so divided, and which is opposed by almost all the accomplished mathematicians. A majority maintain the impossibility of perpetual motion, whence comes the scant attention that has been paid to the machine of Orffyreus. I know I am inferior to those who have given demonstrations of the impossibility of this motion, nevertheless to explain to you the sentiments with which I examined this machine, I have the honour to tell you that about seven years ago I believe I discovered the paralogism of these demonstrations, in that they could not be applicable to all possible machines; and since then I have always been convinced that one could demonstrate that perpetual motion was not contradictory; and it seemed to me that Mr. Leibnitz was wrong to regard as an axiom the impossibility of perpetual motion; which was nevertheless at the basis of part of his philosophy. Notwithstanding this conviction, I was very far from believing that Orffyreus was accomplished enough to discover perpetual motion. I considered that perpetual motion would not be discovered until after many other inventions, if ever. But since I have examined the machine, I don't know how to express my astonishment.

The inventor has a genius for mechanics, but is not in the least a profound mathematician, however that machine has something surprising about it, even if it be fraudulent. The following is about the machine itself, the interior of which the inventor will not permit to be seen, lest anyone should steal his secret from him. It is a drum about 14 inches thick by 12 feet diameter; it is very light, being made of several wooden boards assembled with other pieces of wood, in such a way that the interior could be seen from all sides if not for an oilcloth which covers all of the drum. This drum is traversed by an axle of about six inches diameter, terminated at its ends by three-quarter inch iron journals, on which the machine turns. I examined these journals, and I am convinced that nothing from outside contributes to the movement of the machine. I turned the drum very slowly, and it stood still as soon as I took my hand away; I made it make a turn or two in that way. Then I made it move slightly more quickly; again I made it make a turn or two; but then I was obliged to hold it back continually; for having let it go, it reached in less than two turns its maximum velocity, so that it made twenty-five or twenty-six turns per minute. It kept up this motion some time ago for two months in a sealed room, in which it was impossible that there could have been any fraud. His Serene Highness had the room opened and had the machine stopped after that time, because, as it was only a prototype, the materials might not be strong enough to stand a long period of running.

The Landgrave was present at the examination which I made of the machine. I took the liberty of asking His Serene Highness who has seen the interior of the drum, if something might change in its interior after a certain period of running; also if there might be some components in which fraud could be suspected; His Serene Highness assured me that this was not so, and that the machine was very simple.

You see Sir, that I have not seen enough of it to assure myself that the principle of motion which is certainly in the drum, has really been demonstrated to be a perpetual motion, but I still believe my strong presumption in favour of the inventor should not be denied.

The Landgrave in his generosity gave a worthy present to Orffyreus, to be let into the secret of the machine, with a promise never to part with it, or to reveal it until the inventor had derived other rewards for making his invention public. I know very well Sir, it is only in England that the sciences flourish sufficiently to find the inventor a worthy reward for his invention. It is simply a matter of assuring him of it if his machine proves to be a true perpetual motion. The inventor does not ask to touch the money until after the machine has been internally examined; such an examination could not reasonably be demanded before the reward had been assured. Since it is a matter of usefulness to the public, and of the advancement of science, to discover whether the invention is real or a fraud, I thought that you might like to have this account. I am, etc.

Comment:—

In the 1763 translation,  'sGravesande's remark "I made it make a turn or two" (which he says twice) has been omitted. The importance of this remark is that it removes any possible doubt that a slowly-turned wheel might still have been able to start running if turned through a sufficiently large angle. (I think that this was precisely what he was trying to find out).

The interesting and somewhat puzzling fact that  'sGravesande makes clear is that the wheel never, ever, tried to "run away" when turned slowly, and yet that large, high-inertia wheel accelerated to its maximum velocity in less than two revolutions when started off with only slightly more external energy. That implies the expenditure of quite a lot of internal energy. But then it would never go beyond its characteristic rotational speed of 26 rpm!

Johann Bessler's Perpetual Motion Wheels Part II

A silux model of MT-18.

One of Johann Bessler's more interesting examples in the book named (by John Collins) as "Maschinen Tractate" is number 18. In his notes on this example, Bessler says "...the principle is not to be scorned or disregarded, for it tells more than it shows."

I decided to make a silux model of this, just to see what would happen.

A silux model of Maschinen Tractate No. 18, as first prepared

Here is a screenshot of my model as I first prepared it, corresponding to the configuration as originally drawn by Bessler. See p23 of Maschinen Tractate as edited and published by John Collins.

The wheel is 1 meter diameter, with a large mass of 2000kg, which gives it a rotational inertia of 242kg-m². (A lighter wheel risks failing to complete a cycle of operation).
The four weights are 15kg each.

Each of the cantilever springs is fabricated from 13 segments, with each 1.5 milligram segment connected to its neighbour with a torsion link of 100N-m/rad. Torsion links of 250N-m/rad connect the springs to the wheel hub.

The model is turned to this configuration to start the simulation

Simulation results

I suspected, correctly, that the original configuration (or anything much like it) would not occur during continuous running of the simulation. Instead, I turned the wheel to the configuration shown, which does occur during continuous running, and so is a suitable starting point. 

The wheel is started at 1.05 rad/sec. The start is "smooth" with all components moving at their correct velocities — having been run up from a zero-velocity start. This includes, of course, the highest weight, which has begun its "flip" over to the descending side.

Even such a heavy wheel drops its rotational speed to 0.89 rad/sec just before the highest weight hits its wheel-rest on the descending side. Even with impacts set to a realistic elastic/plastic ratio of 10%/90%, the weight bounces at least 25 times against the wheel-rest, wasting energy with each bounce.

The simulation is finished after one cycle, i.e. after the wheel has turned through exactly 90 degrees, and so is once again approximately at its starting configuration. By then, its rotational speed has dropped to 0.655 rad/sec, and it has lost rotational energy (½Iω²) of 133.4 - 51.9 = 81.5J, a very large amount.

I suspect that not all of the "lost" energy is lost from the device as a whole — a fair amount of it has probably gone into greater deformation of the springs. (The wheel's already-reducing speed could easily cause a further significant energy exchange from the wheel to the springs). If I thought it was worthwhile, I would integrate a full torque vs angle graph for a wheel forced to turn at a constant speed, which had been settled down as far as possible to steady-state operation. I would also do that for various combinations of weight magnitudes and spring strengths. But I have already done enough work on this model to be fully convinced that it cannot deliver any net energy.

Even if the wheel is started from rest at the unrealistic original configuration, it doesn't turn far enough for the first weight to entirely "flip" over. The wheel accelerates at first, but then decelerates to rest again, and starts to turn back before the weight is able to reach the point of unstable equilibrium where it could complete its flip.

Johann Bessler's Perpetual Motion Wheels Part I

If asked to name the best-ever example of a mechanical perpetual motion wheel, most people would probably cite the wheels of the German inventor Johann Bessler (1680-1745), also known as Orffyreus. While many visitors here will know a lot about Bessler's work, I'll give a summary below for others who may not be so familiar with it.

John Collins' book (top left), and his re-publications of Bessler's works (which include English translations)

Summary

British author John Collins, who has a website at http://www.free-energy.co.uk/, has worked tirelessly to bring as much as possible of Bessler's surviving work to modern public attention. From his own book, and his re-publications of Bessler's books, we learn that on the 6th of June 1712 Bessler first demonstrated what he always insisted was a genuine, stand-alone mechanical perpetual motion machine, in the town of Gera. Over the next four years he built at least three more machines, which have become known by the names of the locations where they were exhibited. The 3 ft diameter Gera Wheel was followed by the 5 ft diameter Draschwitz Wheel, then the Merseburg Wheel, and finally the Kassel, or Weissenstein Wheel. While the Gera and Draschwitz Wheels could rotate only in one direction, the latter two, both of about 12 ft diameter, were bi-directional. That is, after being given a gentle push in the desired direction of rotation, they would then undergo rotational acceleration up to a steady state speed which they would maintain until forcibly stopped. The wheels could do mechanical work such as driving stampers (as used in papermaking), turning an Archimedean screw for raising water, or lifting a 70 pound box of bricks. 

The Weissenstein Wheel successfully completed an impressive fifty-four day period of continuous operation, from 12 November 1717 to 4 January 1718, in a locked, sealed and guarded room in Weissenstein castle, arranged by Prince Karl, the Landgrave of Hesse-Kassel. Karl, the only person besides Bessler who is known to have seen the wheel's internal mechanism, promising never to reveal its details, stated that it was "... so simple that a carpenter's boy could understand and make it after having seen the inside of the wheel ... "

Johann Bessler's Weissenstein perpetual motion wheel

Sale price: 100,000 Reichsthalers

Bessler always kept the internal mechanism of his wheels concealed. His single condition for revealing the mechanism was that a purchaser should first pay his asking price of 100,000 Reichsthalers. He had sufficient faith in his machine to state that if it was found to be fraudulent, he would gladly forfeit not only the purchase price, but also his life! And that would almost certainly have happened if he had tried to defraud one of the absolute rulers of the time. Of course from a viewpoint in the often corrupt modern world, Bessler should have added some safeguard against a corrupt, powerful purchaser who might have insisted on initial secrecy, subsequently installing a fraudulent mechanism in order to get the invention, and Bessler's permanent silence, at no cost. But in his day, the most likely purchasers were always princes and kings, men of honour and integrity.

Although Bessler's wheels passed the tests demanded of them, and were subjected to the most minute external examinations, often by persons specially chosen for their theoretical and practical competence, Bessler was never able to obtain the 100,000 Reichsthalers for his wheel. He came very close on one occasion, when Czar Peter the Great of Russia decided to purchase it. Unfortunately, the Czar died shortly before the deal could be concluded.

Another false "explanation"

Earlier in this blog, on 26 April 2014, I showed how a description that originally applied (and was only ever intended to apply) to a non-working wheel has been used in modern times to "explain", erroneously, how the Marquis of Worcester's perpetual motion wheel was supposed to work.

A very similar situation has also occurred with Bessler's wheel. Two years after the Czar's death, Bessler's maid Anne Mauersbergerin signed a statement saying that all his wheels had been fraudulent, and had been turned manually either by herself, or Bessler, or his brother Gottfried. Shortly thereafter, Bessler was arrested, examined and released without charges being laid.

The maid claimed that the wheel's support posts had been hollowed out, and contained a long thin piece of iron which turned the wheel by applying force to the axle journals. Even ignoring the fact that the bearing surfaces of the support posts were repeatedly examined, sometimes with the wheel shifted (and again operating) on other supports, with nothing suspicious being found; to anyone with any practical experience the maid's explanation is ridiculous. Assuming she had been coached by some of Bessler's numerous enemies, it's curious that such a poor explanation was chosen, when more plausible false explanations could have been made.

Where did the maid's "explanation" come from?

I strongly suspect that this erroneous "explanation" originated with Bessler himself, once again specifically to describe an imaginary non-genuine wheel. In his Apologische Poësie Part I section XXXVIII he recounts firstly a purely hypothetical conversation with one of his major critics (Gärtner) who claims that the wheel is driven through a hollowed-out support post, and secondly how he (Bessler) would then correct him (saying that he would have revealed "more than he could ever have wished" to Gärtner, if only his behaviour towards Bessler had been better).

Bessler would never have intended his comment about driving through a hollowed-out support to be taken seriously, for the perpetual motion wheels he actually built, yet that is what has happened.

Disinformation

Perhaps we have here an early example of the use of an implausible explanation to render legitimate information inert, a disinformation technique I may have more to say about later. In any case, the maid's statement and the subsequent arrest proved quite sufficient to discredit Bessler for the rest of his life. He died in poverty on 30 November 1745, possibly by suicide.

My next several blog posts will be about aspects of Bessler's work.

Deriving Gravity from Electromagnetism

A "wider issues" post

As I warned (or should that be "threatened"!) in my very first post to this blog, I'll occasionally post something on what I'll call "wider issues". This is the first one, and by comparison with others that I may do in future, it's a fairly small and innocuous one.

Gravity?

So, what is gravity? Everyone will have their own ideas and theories, and I'm no exception. For a long time, I have been attracted to the idea that there is a deep connection, not yet well understood, between gravity and electromagnetism. I'll present an idea below that seems, to me, to make a step forward in this direction.

I am an amateur student of the history of electrical technology. Anyone who delves into this will soon become aware of the shaky foundations of that subject, which persist today.

Early on, I had read Electromagnetic Theory by Alfred O'Rahilly (a must-have book for serious students of this subject), and moved on from that to more recent works by Peter and Neal Graneau, and by Andre Assis. In his paper titled Gravitation as a Fourth Order Electromagnetic Effect, Prof. Assis questions Grassmann's expression for the force between current elements, which is, as he says, the only one which appears in the textbooks nowadays. He implies that we would have done better to use and develop Weber's force law (an opinion I agree with). He points out that:—

"Weber succeeded in unifying electrodynamics and induction with electrostatics with his generalization of Coulomb's force. The next step would then be the unification of these interactions with gravitation. The natural path along Weber's procedure is to generalize even more Coulomb's law in order to derive gravitation. The forces of Ampère and Faraday were derived from second order terms and so the suspicion is that gravitation might be due to fourth order terms."

Prof. Assis then goes on to generalise Weber's Law, and to show that gravitation can indeed be derived from electromagnetism, as an interaction between neutral dipoles. His paper can be found at:—
http://www.ifi.unicamp.br/~assis/gravitation-4th-order-p314-331(1995).pdf

Further reading

For further reading, I'd recommend Prof. Assis' book Relational Mechanics, but with the warning that it probably isn't suitable for some of the more sheeplike followers of Albert Einstein.

Leonardo da Vinci's Perpetual Motion Wheels Part II

Leonardo's "J-tube" wheel

Here is the second of Leonardo da Vinci's perpetual motion machines to be analysed, again from Codex Forster II.

An animation has been made of this machine, at http://www.youtube.com/watch?v=GhR-K10UjnY, but obviously not in a "true" way. The falling weights don't accelerate correctly, and the wheel's rotational speed seems to remain unchanged, even though energy must be lost from the weight impacts. So, let's make the silux model:—

Silux model of Leonardo's "J-tube" machine, at start of simulation

I decided to make the model as the minimum necessary for testing. The circular part of the wheel is 1m diameter, of mass 10kg. In the model, it is made as Positive, Functional in the Edit Object box, whereas the J-shaped tubular part that carries the weight is made as Neutral, Functional, so that it cannot influence the wheel balance. The spherical weight is 4kg. Gravity is active; friction is negligible.

Results

Model at maximum wheel angle reached, with graph of wheel angle vs time

As expected, the weight falls at its maximum radius while the wheel turns through the first 90 degrees. Then it rises at a lesser, generally diminishing radius in the curved part of the tube, while the wheel turns another 147.94 degrees, to a maximum angle of 4.153 radians, i.e. 237.94 degrees, in 1.848 seconds. Thus it doesn't quite reach the 240 degrees necessary to complete a cycle, and so it fails to deliver any net energy. I tried a few variations, e.g. varying the wheel mass, which for some values allows a moderate exchange of energy between the wheel and the weight. The weight then oscillates slightly, as it rises in the curved part of the tube. But none of these variations could complete a cycle of operation.

Reference, and miscellaneous remarks

This completes my comments on Leonardo da Vinci's wheels. For more on his work, check out http://www.leonardodigitale.com/index.php?lang=ENG  (thanks to Ed, for the reference).

I should mention that I currently regard my gmail as a "read-only" inbox for emails. I'll read anything posted there, but I'll reply if necessary in this blog.

Recently I've been making a new blog post every five days, so I'll try to keep to that schedule, for a while anyway. Next time: a "wider issues" post.

Leonardo da Vinci's Perpetual Motion Wheels Part I

A great inventor

Many people regard Leonardo da Vinci as the greatest inventor of all time. Yet, while he is praised for being far ahead of his time for his many inventions of technologies that now exist overtly in the 21st century, some commentators seem a bit embarrassed by his inventions in the field of perpetual motion, which does not yet exist overtly. They assure us that he didn't spend much time on it; that he quickly saw how impossible it was, that he labelled his wheels "for studies on the impossibility of perpetual motion" and so on. 

This view tends to overlook what an inventor really does — to visualise something that is not actually realised (i.e. built) yet, and which won't be built until some future time. Usually the time interval between visualisation and realisation is only a few years at most, but for a few exceptionally far-seeing inventors like Leonardo, it can extend to centuries. Perhaps we just have to wait a bit longer for mechanical perpetual motion to appear?

However, other commentators (and I'm one of them) would say that Leonardo's basic and admittedly undeveloped idea of a weight-driven perpetual motion machine has already been realised, if not by the Marquis of Worcester in around 1639, then, to a very high degree of probability, by Johann Bessler in 1712.

Some of Leonardo da Vinci's perpetual motion drawings

I found the above image at http://www.leonardodavincisinventions.com, and decided to make silux models of two of Leonardo's machines. The two devices I chose are those drawn again by Leonardo side by side in the document now known as "Codex Forster II", in the section he labelled in clear Latin as Mechanica Potissimum, i.e. "Highest-Power Engineering". See http://www.vam.ac.uk/content/articles/e/leonardo-da-vinci-explore-the-forster-codices/ Volume 2, pages 90 verso and 91 recto. Leonardo wrote fourteen lines of script in his Italian shorthand mirror-writing (which I cannot read) under each of these drawings. Although some of his writing in Codex Forster II has been translated at the vam.ac.uk website, unfortunately these two pages have not been, so far.

On the page shown above, Leonardo obviously wasn't concerned about having gravity oriented in the same direction for all his drawings. The uppermost drawing has gravity oriented along the centerline he has drawn at 60 degrees from the vertical. The drawing furthest to the left has gravity oriented along the horizontal centerline.

It's pretty obvious that neither of these machines will deliver any net energy, but let's see what happens anyway.

Leonardo's "ratchet wheel" with pawl, and internal arms and weights

This drawing, from Codex Forster II, clearly shows the ratchet pawl, which is almost invisible in Leonardo's first drawing of this machine, at the top of this page. So the wheel must be intended to rotate anti-clockwise.

When the weights fall over-center on the descending (left) side, the first drawing shows them falling against the curved teeth of the wheel's rim, where they are held at a radial position. The geometry doesn't really permit that, and even at the lowest position where a weight could just have fallen against a wheel tooth, the impact will be an undesirable "glancing" one, for the round weights shown.

In my model, to get good perpendicular impacts at radial positions for the weights, I used separate wheel-rests (although they are incorporated into the wheel, all as one object). More wheel-rests are used for the arms, to keep the weights positioned as drawn on the ascending side. (A "wheel-rest" is a component of the wheel which is interacted with, i.e. "hit" by other objects).

Silux model of Leonardo's "ratchet wheel" machine, at start of simulation

Data: Wheel: diameter approx 1 meter; mass 20kg
           Weights: 4kg each
           Arms: 0.1kg each
           Gravity active, friction negligible.
           Weight to wheel impacts: 10% elastic/90% plastic.

There are two ways of running the model: 1) with the pawl always able to engage the ratchet teeth, and 2) with the pawl always disengaged.

Results

1) With pawl. For this version, I didn't bother to model the pawl. I just held the wheel stationary (i.e. "Simulation Member" was unchecked in the Edit Object box) until just before the falling weight on the left side had fallen far enough to hit its wheel-rest. The wheel was then activated, and the results recorded.

Wheel angle vs time with pawl active

The weight in unstable equilibrium on the left side was initially given a very light push of 0.01N for 0.1s, to start its fall. It fell down onto its wheel-rest at 1.436 seconds, bouncing three or four times. This, and the slight bouncing of other weights, accounts for the somewhat noisy wheel angle graph at first. The wheel reaches a maximum angle of only 0.0812 radians at 1.83 seconds, not enough to turn the wheel by even one ratchet tooth, let alone the four teeth needed to cause another weight to start its fall. The wheel angle returns to zero at 2.22 seconds, where the pawl would once again engage the original wheel tooth.

2) Pawl disengaged. For this version, the wheel is always active.

Wheel angle vs time with pawl disengaged

Because there is initially excess weight on the right-hand side of the wheel, it accelerates clockwise at first. This causes the weight in unstable equilibrium on the left side to fall down onto its wheel-rest, which occurs at 0.699 seconds. It bounces (noticeably) only twice. The wheel then decelerates to zero rotational speed at 1.840 seconds; then it starts to turn anticlockwise, but never enough to cause another weight to fall. It just oscillates at a slowly diminishing amplitude, as shown.