A Modified Van de Graaff Generator Part I

Fig 1. The world's largest air-insulated Van de Graaff generator, built by Robert van de Graaff in 1931, now housed at the Boston Museum of Science. Image from http://en.wikipedia.org/wiki/Van_de_Graaff_generator.

Original Van de Graaff generator

The original Van de Graaff generator design is a good example of how electric charge continually brought onto the inside surface of an already charged spherical-shell conductor can be added to the shell for no additional energy penalty, hence increasing its voltage, no matter what voltage the shell has already reached. The charge is initially placed onto a motor-driven belt made of insulating material, at a location outside the shell. The belt transports the charge upwards into the shell, or "dome", where it is collected.

In a small to medium-sized laboratory Van de Graaff generator being charged by external excitation, charge would typically be sprayed onto the low-voltage end of the belt at say 10kV and 20μA. Ignoring losses, it would also be collected at the high-voltage end at 20μA, where the dome voltage can reach say 350kV. So if all energy losses could be eliminated, we would expend 0.00002 A × 10000 V = 0.2 W to get 0.00002 A × 350,000 V = 7 W, i.e. a 35 : 1 power gain.

A 7 watt output is of little practical use, and it's understandable in such a low-power device that not much attention would be paid to the possibility of generating excess energy. But if the current could be increased to say 200mA, still a very modest value in electromagnetic terms, the power output would be 70 kilowatts. That would certainly be a useful result, if it could be obtained without paying a full energy penalty to get it.

Even higher power gains would be possible for larger generators, able to operate with higher dome voltages.

Energy loss

For a Van de Graaff generator, the major energy loss associated with bringing charge onto the dome is obvious. Charge carriers on the belt have the same polarity as the charged dome, and so there is repulsion opposing the belt's movement towards the dome. The charge carriers have to be transported "exposed" against the entire voltage gradient between the dome and Earth.

Pelletron

Fig 2. Basic principle of the Pelletron. See http://www.pelletron.com/charging.htm for this image as an animated GIF.

This major energy loss also occurs in the "Pelletron" modification of the original Van de Graaff generator, which uses a chain of alternating insulating and conducting segments, instead of an insulated belt. (The conducting "pellets" can be conveniently charged/discharged by induction instead of by charge spraying or triboelectrification). In a Pelletron, not only are like charges repelling as the charged chain moves towards the dome, but unlike charges attract as it moves away, with a major energy loss in both cases.

Generation of charge within the dome

At first sight it would seem very easy to generate charge within the dome, rather than to generate it externally and then bring it in against the full voltage gradient. For example, simple metallic "comb" corona discharge generators could be connected directly to the inside of the charged dome (and would thus operate at its already high voltage). Or, a heated filament could be placed within the dome to generate electrons by thermionic emission, a method which can easily produce a current of 200mA or more.

Charge separation

However, we cannot produce any net charge by such methods, either within the dome, or elsewhere. Charge can only be separated, and the problem then arises of how to deal with the charges of unwanted polarity. A corona discharge will act on air molecules to create charges of the desired polarity; but also an equal quantity of charges of opposite polarity. These cannot be allowed to drift internally to the dome, where they would tend to neutralise the desired charge on it. Worse, if they are expelled outside of the dome, they will be attracted back to it, again tending to neutralise it. To get rid of them by neutralisation against Earth, they would have to be moved against the entire voltage gradient between the dome and Earth, thus destroying any possible net energy gain.

If a (negative) charge of electrons is expelled from a filament by thermionic emission, then the filament and whatever is energising it will develop an equal and opposite positive charge. This would soon cause a voltage breakdown (flashover) if the positive charge was not neutralised somehow, e.g. by connection to Earth. But electrons emitted from an earthed filament, no matter where it was positioned, would once again have to act against the entire voltage gradient between the dome and Earth, to reach the inside surface of the dome. This would again destroy any possible net energy gain.

So, charge separation within the dome certainly presents difficulties. Next time I'll look at the more promising method of bringing externally-generated shielded charge into the dome.

Comparing Electrical and Mechanical Quantities

Most students of physics will have seen the diagrams I've redrawn in Figure 1 below:—

Fig 1. Showing i) the exchange between kinetic energy of a mass and energy stored in a spring, in an oscillating mass-spring system; and ii) the exchange between energy stored in the magnetic field of an inductor and energy stored in the electric field of a capacitor, in an oscillating inductor-capacitor system.

Correspondences

By comparing the energy flow in an oscillating mass-spring system with that in an oscillating inductor-capacitor system, we see that there is a correspondence between certain electrical and mechanical quantities. For example:—

   charge corresponds to distance      (q corresponds to x)
   current corresponds to velocity      (i corresponds to v)
   capacitance corresponds to the      (C corresponds to 1/k)
      inverse of spring constant
   inductance corresponds to mass    (L corresponds to m)

Let's now look more closely at the correspondence between a stretched spring and a charged capacitor.

Fig 2. Energy added to a stretched spring, and to a charged capacitor

Energy triangles

In Figure 2A, a spring of spring constant k has been initially stretched over a distance x, by exerting an ever-increasing force F on it. The energy stored in the spring is given by the triangle (light blue) of base x and height kx  i.e. 

    U_S  =  ½ × x × kx  =  ½kx² 

Now, suppose we wish to stretch the spring a bit more, i.e. by Δx, and thus gain the extra energy represented by the darker blue area. The only possible way to do that is by increasing the exerted force F by ΔF, from an already high value to a new and higher one. Thus we have to pay a full energy penalty in terms of the force being exerted on the spring through the distance Δx, to gain our extra spring stored energy.

At first sight, the corresponding case with a capacitor seems to be exactly analogous. In Figure 2B, a capacitor of capacitance C has been initially charged with charge q, by subjecting it to an ever-increasing voltage V. The energy stored in the capacitor is given by the triangle (light red) of base q and height (1/C).q  i.e.

    U_E  =  ½ × q × (1/C).q  =  ½q²/C

Now, suppose we wish to add a bit more charge to the capacitor, i.e. Δq, and thus gain the extra energy represented by the darker red area. By analogy with the spring, we could do that by increasing the voltage V by ΔV, from an already high value to a new and higher one. Then we would once again pay a full energy penalty in terms of the voltage being applied across the capacitor to add the charge Δq, to gain our extra electrical energy.

Another way — but only for a capacitor

However, we could do something else, which as far as I know has no mechanical analogue. We could make our capacitor as a spherical conducting shell (or a major portion of one) which, by Gauss's Law, cannot retain any charge on its inner surface. Any net charge that is generated within the shell, or brought into it from outside, can then all be added to the shell at its inner surface for no added energy penalty, no matter what voltage the shell has already reached. Thus we might be able to obtain any desired increase in charge Δq without having to directly increase the applied voltage at all. That voltage increase, and the associated energy gain, would then occur incidentally, and automatically, as the charge was added.

Next time, I'll look further into the questions that I've now raised concerning a charged conducting shell:—

a) generating net charge within the shell

b) bringing an externally generated charge into the shell without paying the full expected energy penalty for doing so.

Interlude — and a Change in Direction

Mechanical devices — finished

Although there is more, I have now said all that I wish to say on mechanical devices, for the foreseeable future. I suppose it could be argued, correctly, that I haven't really contributed much to our existing knowledge of mechanical perpetual motion — although as I pointed out at the time, I think my ideas on the Casimir Effect Force Generator (posts of 2 to 17 September 2014) and the "Perpetual Force" Air Motor (posts of 22 November to 13 December 2014) could well be worth further investigation.

More support for the Casimir Effect Force Generator

As the years go by, I keep a look-out for support for my unorthodox technological ideas. On page 5 of its Issue 96, March/April 2011, Infinite Energy magazine published a letter from Wm. Scott Smith titled "Can We Make a Casimir-Cavity ZPE Thruster?" This letter, citing eleven peer-reviewed references from 1997 onwards, argued that an array of sufficiently small open-ended cavities would experience a net Casimir force. The only physical difference from the Casimir Effect Force Generator in my specification drawing of October 1994 was that the proposed open-ended cavities had straight rather than sloping sides. Although I found no-one who could make such a device in 1994, Smith claimed "A macroscopic array of nanoscopic cavities can be constructed quite easily with existing [2011] nanotechnology." If that's correct, I'd certainly agree that this would be an experiment well worth trying (for both straight and sloping-sided cavities).

This writer also said "Sometimes it is astonishingly difficult to reflect carefully enough on something we already know." I agree entirely with regard to Casimir force, and also, as will be seen, on some electrostatic matters, including Gauss's law.

Electrostatics

A modern electrostatic motor. Data: size 65 dia × 65 length; max rpm 10,000;
power 100W; weight 0.2kg; power-to-weight 500W/kg; efficiency 95%.
See http://www.shinsei-motor.com/English/techno

As mentioned at the outset of my very first post, I originally intended this blog to be mostly about my investigations into electromagnet/permanent magnet interactions. However, before getting into those, I'll first write up a few ideas on electrostatic devices.

In this series, I'll first discuss why electrostatics gives a wider scope than mechanics does for developing perpetual motion machines. There is at least one well-known technology which could in theory, and perhaps even in practice, be developed to give excess energy. There are also at least two other quite well-proven electrostatic perpetual motion machines that have already been built and demonstrated in the real world. These will all be discussed in due course.


A reminder about definitions

For now, I'll repeat the definition I first gave on 30 March 2014:—

       [quote begins]

Since this blog is titled "Perpetual Motion in the 21st Century", let's look at how "perpetual motion" is defined these days. In my opinion, the most authoritative English-language dictionary of all is the Oxford English Dictionary. Here is its definition:—

"Perpetual Motion: Motion that goes on for ever, spec. that of a hypothetical machine, which being once set in motion should go on for ever, or until stopped by some external force or the wearing out of the machine." 

(Reference: The Oxford English Dictionary, Second Edition, Clarendon Press, Oxford, Vol XI, p586).

This is the definition of Perpetual Motion to which I adhere.

There is an on-line version of the Oxford dictionary, at http://www.oxforddictionaries.com. It has this abbreviated definition:—

"the motion of a hypothetical machine which, once activated, would run forever unless subject to an external force or to wear: the age-old quest for the secret of perpetual motion"

The remarkable fact is that the Oxford dictionary is the only one that has not felt obliged to "modernise" the definition to incorporate some reference to energy, and thereby reduce it to an almost worthless banality (along the lines of "You can't get energy from nothing"). All other English-language dictionaries, and on-line sources such as Wikipedia have now done this, as far as I know.

       [quote ends]

I know I'm more or less a lone voice at present trying to preserve a valid and useful definition, but I've never been convinced that the appropriate response to the criticism that has been levelled at "perpetual motion" was to change its name (and to re-define the old name — badly). I'm reminded of the current fiasco concerning what was called "cold fusion" by Fleischmann and Pons. There are now well over a dozen different names for that topic, which generally only add confusion, rather than clarity.

However, it's true that in electrical technology there are cases where machines can deliver energy without needing any moving components. Unless the flow of electric charge carriers is being considered, "perpetual motion" is not a very appropriate term for such machines. So from now on, I'll probably use more modern terms like "excess energy" or "free energy" for these machines at least.

An electrostatic voltmeter (center) with two high-voltage power supplies:
a 2.5kV 12kHz supply for a corona-discharge ozone generator (right) and
a homemade 5kV 50Hz Cockroft-Walton voltage multiplier (left).

The "Laboratory" Frame Part IV

A part-inertial/part-laboratory experiment

Revisiting an earlier idea

When discussing the idea shown in the above figure, in my post of 25 April 2015, I assumed that the spring to be used to return the mass over portion B to C of the operating cycle would be a constant-force spring of force equal to twice the weight of the mass. Let's now look at this in more detail.

Does the mass-spring system act in full gravity?

First, recall that I have assumed that gravity always acts vertically, which it does, to an extremely close approximation, over the small time intervals of these experiments.

The value of the constant-force spring was calculated as:—

2W = 2mg = 2 × 10 × 9.80665 = 196.133 N.

Note that I used the same (standard) value for gravity, g = 9.80665 m/s² as I had used to calculate the behaviour of the mass between A and B. This is correct for a mass hanging freely from a suspension point and behaving fully "inertially", disconnected from Earth between B and C (as it was between A and B). However it would be possible to constrain the mass between B and C to radial movement only, e.g. in a vertical (radial) tube rigidly fastened to Earth. It could be argued that this should then modify the value to be used for gravity, to:—

g' = g - (Earth's centrifugal acceleration).

Hence, at the equator, g' = (9.80665 - 0.033916) m/s² , and the value of the constant-force spring becomes:—

2W = 2mg' = 2 × 10 × (9.80665 - 0.033916) = 195.45468 N.

So there would be a net gain of energy over the originally-calculated value, of:—

 (196.133 - 195.45468) × 0.271326 = 0.184046 joules, 

as the mass was returned from B to C, with the suspension point falling from B' to C' as before.

A net energy gain is calculated

This is a very low-power result, i.e. 0.184046J/10kg/8s  ≈  2.3 milliwatts of power per kilogram of active mass, over the operating cycle of 8 seconds. But nevertheless, it is a positive result as calculated.

I have set myself a simple "rule of thumb" — I will not even consider building any physical prototype machine that could not reach at least one watt of power per kilogram of active mass.

For now, I leave as an open question whether a gain like this could really be achieved in a system as discussed, where a mass is designed to behave truly "inertially" over part of its cycle, and is constrained into a laboratory frame for the rest of the cycle; or whether it just indicates some error, e.g. a breakdown of the assumption that gravity is always vertical. Two relevant points to bear in mind are:—

1. As soon as the mass is fired-off from Earth at point A, it no longer has any physical connection with Earth, and must act "inertially", albeit still under the influence of Earth's gravity.

2. The mass can certainly be constrained into a physical connection with Earth, forcing it to move radially in a laboratory frame over B to C, as discussed above. But gravity really acts radially, anyway! 

More experiments

There are obviously many more experiments that could be done, as developments of the ideas already discussed in this post and the three previous ones. I have done quite a few myself, including some that had a more clear-cut separation between "inertial" and "laboratory" behaviour than in the above introductory example. For example, a rotating-wheel gyroscope prefers to orient itself in an inertial frame as far as possible, rather than a laboratory frame. And the gyroscope can take other forms — such as the halter gyroscope, which many flying insects possess in some form. But to discuss these experiments further now would be to go too far out of order in what was always intended to be a roughly chronological-order blog.

Crane fly, with halteres visible behind the wings
Image from http://en.wikipedia.org/wiki/Halteres

The "Laboratory" Frame Part III

Once again we shall set up our inertial frame ABC, and this time we'll examine the behaviour of an unequal pair of masses in it (Fig 4).

Fig 4.  An unequal pair of masses

Centrifugal Force and Kinetic Energy data

The unequal mass-pair of Fig 4 is joined together by a rod (black) of negligible mass which pivots and rotates about the center of rotation as shown. For the values given we have:—

10kg mass:   Centrifugal Force = mv²/r  = 10 × 1² / 0.1 = 100 N
                          Kinetic Energy   = ½mv²  = ½ × 10 × 1² = 5 J

1kg mass:    Centrifugal Force = mv²/r   = 1 × 10² / 1    = 100 N
                         Kinetic Energy   = ½mv²  = ½ × 1 × 10² = 50 J

So we can have equal, balanced centrifugal forces, even though the masses have very different energies. By causing the mass-pair to travel along the inertial line ABC, we can achieve different start and finish velocities in the laboratory frame for both masses. Will that deliver any net energy?

Fig 5.  Mass-pair travelling along the (straight) inertial line ABC

Analysis

We shall assume that the mass-pair is "weightless", e.g. it has a constant-force spring to Earth (not shown) acting at the center of rotation, and neutralising its weight in the inertial frame. Since the spring is always active from A to C, and undergoes no net change in length, there can be no net energy change in it.

We start the mass-pair at point A, rotating as before, such that its center of gravity (at the center of rotation) is following the straight-line (purple) trajectory ABC in the inertial frame. For simplicity, we shall start it travelling downwards at Vy = -1m/s in the laboratory frame. Then, in that frame, we have:—

10kg mass:   Kinetic Energy = ½mv² = ½ × 10 × (1 + 1)² = 20 J

1kg mass:      Kinetic Energy = ½mv² = ½ × 1 × (10 - 1)²  = 40.5 J

When the mass-pair reaches point C, where its center of gravity is travelling upwards at Vy = 1m/s in the laboratory frame, we have:—

10kg mass:   Kinetic Energy = ½mv² = ½ × 10 × (1 - 1)²  = 0 J

1kg mass:      Kinetic Energy = ½mv² = ½ × 1 × (10 + 1)² = 60.5 J

So, although the masses each have quite different start and finish energies, there is no net energy loss or gain. More generally, in the inertial frame ABC, all we did was to take the rotating mass pair from a given energy environment at A, into another environment at C that had the same energy as A.