By James Cowan Ludden: Beene III

3rd July, 2000

CONCLUSION: All over-unity systems must employ their elements so that the interaction occurs through a non-linear inter-relationship of those elements.


From 1979 until his death in 1988, Professor Stanley Ashby and the author collaborated in a study to consider the answer to seeming problems in chemistry and physics and to approach the study of physics prospective from a different prospective. The basis of this study was the mystical (kabbalah) understanding of the scriptures, which contains all knowledge and the use of arithmetic homiletics, which is the mystical understanding of the use of mathematics. The reader may object to the manner or instruments used in the study but unless one engages in the depth of such a study, it is foolish to make any judgments. Consider all the technology of today that we take for granted and just remember the resistance to new ideas in the past. The depth of this study is much more involved than this paper permits here and will be presented as a special paper at a later date.

The following theory was revealed to me, as is often the case of inspiration, which occurred without plan or fore-thought reading a magazine. The graphic vortex of a tornado was pictured in an advertisement caused me to consider the source of energy for such a phenomena. Where did all this energy come from? Could the shape of the funnel vortex itself in any way contribute to the energy of the system? The funnel shape of the tornado is essentially a non-linear vortex. Previous studies into three dimensional shapes and their effect/significance on the interchange and transfer of energy was a subject of years of work and study with my dear friend and colleague, Professor Stan Ashby (1923-1988). It was now necessary to examine this non-linear energy system and determine whether or not it responded to the previous studies.

If this was true, then there might be various natural sources or examples of such energy systems. The first thought that I had where the energy might be analyzed and would be the same shape as the tornado vortex, would be the musical instrument, the trumpet. Its shape is non-linear and indeed similar to the shape of the funnel cloud of a tornado. I considered the vibrational source of a trumpet, which are the vibrating lips of the musician, and the level of sound being emitted from the bell of the instrument. A simple acoustic measurement of sound IN versus sound OUT, revealed that the gain was well above unity! This test measured a gain of 4.7 and I realized that the manufacturers of the trumpet could indeed control the sound level generated and in this case had designed the trumpet to be rather quiet, for it was a child's instrument. Indeed, the manufacturer was being kind to the parents.

Just sit in front of a full orchestra and consider that all of the "brass" and "reed" sound of the music is coming from the lips of the musicians! Not so, all the instruments that employ non-linear surfaces along which the sound waves travel are over-unity devices!

The application of this theory can be extended from sound to heat (examples available), light (including lasers), electrical devices, etc., and to virtually any energy system. All over-unity systems today employ this procedure without the inventor realizing that he/she has done so, and I have examples of these at the end of this paper.

A great deal of the theory on which the Professor and I worked is very voluminous and it was difficult to apply the theory to many engineering situations but it seems that there is a "key", which relates the application to the theory. This "key" can usually be described though sometimes this key is very difficult, if not impossible to understand or imagine. At the present time, one has to apply a sense of artist expression or quiet imagination to gain an insight to solving a specific application.

Hence, I consider that this theory is a "Scientific Key" because it will allow very practical engineering applications to problems of over-unity. My assistance to gain insights or applications to various problems is available upon request.

The information is not patented for obvious reasons and I have the establishment of origin. This information is being offered to the public domain in order to enhance the livelihood of mankind, may all mankind use this information in peace.

The Trumpet Theory

For the moment, I shall just name this study "Trumpet Theory" for lack of a better name. We begin this study by considering the shape of a long trumpet, not like Harry James might have used, but one that we might have found in the times of King Arthur. This instrument was metallic, straight and without finger keys and with the end of the trumpet flaring in the usual manner of a bell as we observe in brass instruments. It would be difficult to determine the exact mathematical equation expressing the shape of the surface of this instrument, but we can approximate the shape with an empirical transfer function that is quite close to the surface shape and indeed, we could use several different transfer functions for this shape but a simple one will suffice. Keep in mind that the transfer function must be non-linear due to the shape encountered.

To begin, let us first think of a simple circumstance such as a sound wave traveling along a straight pipe (Parallel-piped) and assuming zero air velocity, the pressure wave moving in the pipe will be normal to the walls of the pipe. If the pipe ends, the sound waves will no longer be confined and will become nearly spherical in shape as they expand into the surrounding environment. So we see that the sound wave inside the pipe has a constant relationship to the wall of the pipe and the function is linear and constant. If the sound waves are traveling along a pipe where the walls of the pipe are increasing in diameter at a rate exceeding the spherical curvature of the sound wave, then the time rate of change causes a stress in the space-time continuum and the time component becomes negative, which is the necessary mechanism for the "gate" to open and for the transfer of energy. Fun huh? (There's a better way to explain this but the theory and required language would take considerable time to explain. That discussion will be in a following paper.) Consider a pipe shaped as a trumpet. Now, as the sound wave travels down a pipe with a non-linear surface, the sound wave does not diminish in intensity but rather increases in intensity due to the space-time stress. Thus there is an energy gain in any non-linear system employing such a transfer function. We can see this in the following figure.

The wave front, WFl, is the wave front having an extremely large radius (R1), since the pressure wave of this wave front is normal to the walls of the trumpet. Now as the sound wave continues to travel down the ever expanding-radius pipe, the sound wave front remains normal to the walls, but the effective radius of the sound wave is getting smaller (R2). As the sound wave continues into the bell, the radius reaches some minimum value, and from that point the wave radius begins to increase as the sound wave leaves the bell and moves into the environment. It is this reversal of the normally expected sound wave radius first being large (almost infinite but not really) and then becoming smaller as though the sound wave was returning to its source, that reverses the time function of the wave and allows an energy transfer. This all happens due to the shape of the pipe (trumpet).

The following examples are intended to present three possible situations of sound traveling down pipes of different types.

CASE#1: A long parallel-piped pipe of constant radius transmits a sound wave. The beginning wave front WF1 has a very large radius and as the wave front moves along through the pipe, the wave continues with constant radius and energy is very slowly lost through the interaction of the wave front and the air within the pipe. This method used to be used aboard ships to communicate between the bridge and the engine room and in some cases the pipes where several hundreds of feet long. Let W be the energy in the system, then

The energy density in the wave at WF1 = W1/2pR1 = E1, and the energy density in wave at WF2 = W2/2pR1 = E2 where the ratio E2/E1 = energy density change = R1/R2, so assuming no frictional loses, then W2 = W1 and there is no energy change.

CASE#2: Let's look at a pipe with fixed flared sides, such as a megaphone. Here the sides are linear and straight, and the sound wave originates from the apex or where the month opening is located. The sound wave is normal to the sides and the radius of the sound wave increases at a constant rate in normal sound propagation according to the inverse square law.

The curve for the side of the megaphone is given Y=mX+1 (a straight line) and the first derivative of Y is

Y'(X) = m and Y"(X) = 0. So the radius R = f (X)/sin (f) = Y/sin (f) and

R' (X)=dY/dX * sin (f)-f (X) * dsin (f)/dX * sin2 (f) and since dsin (f)/dX = cos (f) * d (f)/dX

[See "Calculus" Stan Grossman 1977 page 732] where d (f)/dX = f"(Y)/[1+[f' (Y)]2 ].Since f"(X) = 0, this implies that dsin (f)/dX = 0, or R' (X) = m/sin (f), and since m and f are constants then the radius changes with X at a constant rate. The energy density is E = R1/R2 and is constantly, linearly decreasing, regardless of the angle f !! Of course, the megaphone captures most all the sound and directs the sound in the direction in which the megaphone is aimed; so there is only a "gathering" of sound in one direction.


Part A: For the third case, that of the non-linear surface of a pipe, we consider a shape similar to that of a trumpet. The exact transfer function of the curvature of the surface may be very difficult to determine but an approximation to this surface as long as it is non-linear will suffice quite nicely. So, we empirically define

Y = f (X) = A+B*X+C*exp (kX), where A, B, & C are constant coefficients.

To help with some of the math, let's present some ideas about how to work with curve functions. Assume that we have a curve C that represents some functional curve. It is to be noted that C is the absolute value of the rate of change of direction with respect to arc length, in parametric form, so

K (t) = | df/ds | = |(dx/dt) * (d2y/dx2) - (dy/dt) * (d2x/dt2)| / [ (dx/dt)2 + (dy/dt)2]3/2 and the radius of this

curvature is p (t) = 1/ k (t)

For the Cartesian form, k (x) = | df/ds | = | d2y/dx2 | / [1+ (dy/dx)2]3/2

Thus, if y = f (x) = A+B*x+C*exp (kx),

then y' = f' (x) = B+C*k*exp (kx)

and y" = f"(x) = C*k2 *exp (kx)

Then, by substitution in k (x) above we have k (x) = | C*k2*exp (kx) | / [1+(B+ C*k*exp (kx))2 ]3/2

and by setting k = 0.05, A = 0.25, B = 0.0002 and C = 1, we would see a curve some similar to a trumpet. We don't need to accurately reproduce trumpet shapes, just explore non-linear device shapes. To determine the minimum value of k (x), we perform the first derivative of k (x) where k (x) = 0. I will let the reader work out the details, but the resulting equation is

1 + B2 + exp (kx)*(2BCk - 3BCk2) - 2*C2*k2*exp (2kx) = 0 and a solution by computer iteration reveals that x = 52.9857, the unit of which are the same as for A and C above, inches, centimeters, etc. This would be the outer rim of the trumpet bell which would be unreasonably large to be practical for a trumpet, but indicates there is a maximum for the size of the bell. Remember that x = 52.9857 is the value of x along the axis of the bell.

This analysis is presented here for the more mathematical among the readers.

Part B: From the same "Calculus" book mentioned earlier on page 733

K (t) = | dT/ds | = | dT/dx | |dx/ds | = (dT/dx) / (ds/dx), where ds/dx = (1+ (dy/dx)2 )1/2

Where T is the unit vector tangent to the curve which is in reality the radius vector, so we can treat this in a scalar sense in that dT/dx = dR/dx

Where the sin (f) = y/R = f (x)/R or R = f (x)/sin (f)

Thus R = (A+B*x+C*exp (kx))/sin (f) and dR/dx = [(df (x)/dx) / sin f) - (f (x)/sin2 f)(dsin f/dx)] and as we continue with this, we find that

R' = [(B+C*k*exp (kx))/sin f] -

[(A+B*x+C*exp (kx))/sin2 f]*(cos f)*[C*k2*exp (kx)/(1+(B+C*k*exp (kx))2)]

where f = tan-1 dy/dx = tan-1 (B+C*k*exp (kx)), so that if x is large, f becomes very small so that we can take that sin f = tan f = B

So, in the final analysis, we see that R' ~ B/sin f. This curve represents the rate of change of the radius of the sound wave front with respect to x (the distance / position along the length of the trumpet.

Energy of such a system.

We next have to calculate the energy transfer. Let W equal the total energy of the sound wave (the complete 360-degree circular wave). Then W1 is this energy at the center of the circular wave and the energy density along this wave is DEd1 = W1/2p*R1 in terms of watts/inch, for instance. Likewise, in the ending wave where R is some value considerably smaller, then DEd2 = W2/2p*R2 again in watts/inch. Since both of these are energy density, the gain of the system is simply

DEd = DEd2/DEd1 = (W2/R2)*(R1/W1), but now since the total energy of the system is constant (assuming negligible losses, then W1 = W2 = W. This implies that DEd = R1/R2. So, we can see that the gain of the system is simply the ratio of the sector of the two circles. Using the above empirical equation, the author has determined that the following parameters yield the optimum curve for this function, namely that

A = 0.07763, B = 0.001, C = 1, and k = 0.0038. ). We observe that this energy wave of very large radius does occur and the energy gain of the system is generated by the principle:

"Any phenomena in space-time (the category of "Matter" in InterCategorical Physics or ICP) that operates in a reverse manner or a manner contrary to normal observation, implies a shift in the time vector (the category of "Antimatter" in ICP) so as to cause energy to flow in to space-time (from no apparent source).

In summary, the longer one makes the trumpet, the larger the gain will be. Also, the shape of the curve will determine the gain of the system (as the parameters are adjusted). This is a relatively easy analysis of a somewhat familiar device and there are other samples that the author has discovered with varying degrees of explanation so as to define the "key". The "key" is the definition of the non-linear interface and this is not always very easy to see in a given device. The author would appreciate any thoughts by the readers of this paper and discussions by E-mail would also be appreciated and encouraged. The author, Jim Beene can be reached at wise@olympus.net.

General Principles

1. Over-Unity generation occurs as the result of a time reversal phenomena

2. Certain spacial configurations in "matter" space (3 dimensions of space and 1 dimension of time) seem to be "gate" devices.

Some working applications of this principle

Device #1: A gentleman by the name of Robert P. Freihage invented and designed a home heating furnace after his patent # 4,312,322 in 1980. He manufactured these furnaces until some manufacturing problems (there is a story here) caused him to experience a severe negative cash flow and put him out of business. A large university was engaged to conduct tests to establish the claims of this unit furnace. The university report does show that the system operates in the over-unity state except that the university refused to sign off on the report and in fact failed to operate the system according to the normal operating procedures. The normal operating conditions required that the furnace is cycled on-and-off and the university simply operated the furnace in a continuous ON state. Actually, the furnace design could be altered slightly and this operating condition problem of cycling could have been eliminated. I have the university report and the data and have written to Mr. Freihage years ago. At the time I could not raise the necessary operating funds to begin manufacturing, so the project was dropped.

I found out about this furnace in 1988 from a gentleman who was in the heating and air-conditioning business. He had sold these units as a standard part of his product line in a large northern US city where to this date as far as I know there are still a large number of units still operating. Looking at the patent will not show you the over-unity key. One would have to actually see one of these furnaces to determine why it performed as it did. Contact me if you have further interest.
Design Key: Fluid vortex
System Gain: 3.7

Device #2: Musical instruments of brass as described above, from trumpets to trombones, as well as many other exponentially shaped horns.
Design Key: Internal Shape
System Gain: varies, 3 to 6.5

Device #3: Life energy of various crustaceans and other lower forms where the shape of the shells or structure is exponential or spiral or any variation thereof.
Design Key: Internal/external Shape

Device #4: Another gentleman by the name of James F. Murray, released in his patent # 4,780,632 entitled "Alternator Having Improved Efficiency" in 1987, a device of his invention which looks a little strange and leads one to wonder why someone would go to the trouble of designing just another alternator. Just how many ways can one design an alternator? The patent is of course interesting from an engineering point of view, and while inclusive of all claims, leaves the reader with the feeling of waiting for the second shoe to drop. The most important document is a report that Jim Murray wrote in 1987 that explains the patent in terms of functionality. In order to patent his device and to distance himself from any ideas of over-unity, Jim Murray simply patented the design of the alternator without so much as a hint of over-unity. His paper of course does discuss this at length. The paper that Jim Murray wrote is essential to the full understanding of the device.

The only drawback of his device is that it is expensive to build with a good deal of CNC machine effort and much Dollars. However, from the study of this paper, it is an excellent exercise is looking for the key. It is hard to see and requires much insight and thought. It is there and it is very interesting.

Design key: This is left to the reader.

System Gain: Appears to be around 10, but the more interesting feature of the device is that there is no lag time when instantaneously shifting the load of the output. As George Gobel would say, "You can't get that kind no more!" This phenomenon happens because the output power doesn't come from the interaction between the rotor and the stator, but from the "gate" that is opened by the interaction of the rotor and the stator. The power that flows through the "gate" is instantaneous. What you need is what you get!

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