PROPULSIVE EFFECT ON A MASSIVE PLANE CAPACITOR
DRIVEN BY SLOPE-ASYMMETRIC PULSES
Stavros G. Dimitriou
Technological Education Institute, Dept. of Electronics Engineering
Ag. Spiridonos, 12243, Athens, Greece. E-mail : email@example.com
Abstract: A propulsive effect is observed on massive plane capacitors containing a metal slab between two thin dielectrics that separate their plates. The propulsive effect is first observed as rotation around a vertical axis, when two similar capacitors are placed at each end of a centrally suspended supporting beam and fed out-of phase with a medium-frequency waveform consisting of pulses with widely dissimilar rise and fall derivatives with respect to time.
1. MECHANICAL DESCRIPTION.
Each capacitor is made of two identical parts, connected in series through a copper slab, measuring 8x8x1 cm and inserted between two very thin sheets of dielectric, each one of the same area as the slab. The dielectric sheets are placed between and in contact with, the plates of the capacitor, which are made of bronze sheet with dimensions 8x8x0.05 cm., In this way, the 8x8 cm surfaces of the slab act as the opposite polarity plate to the external plate of the capacitor adjacent to them. The metal slab connects the two thin capacitors thus formed in series. The two massive capacitors are mounted vertically and alongside at the ends of a 38 cm - long beam of insulating material.
The beam is suspended essentially from its centre of gravity by an inverted -Y string suspension providing easy levelling of the beam plus minimum torsional resistance. In this arrangement then, the beam is free to rotate around the vertical axis. The total length of the suspension is 10 cm. The inverted "leg" of the suspending string is 13.5 cm long. The supply triplet of wires is led perpendicularly to the circuit from he suspension point in a somewhat loose manner, to allow for minimum torsion resistance. A sketch of the experimental assembly is shown in Fig. 1, at the end of this article.
2. ELECTRICAL DESCRIPTION
The two massive capacitors are driven so as to develop an exponentially rising / linear ramp decaying voltage waveform on them, generated by a modified CMOS 555 oscillator circuit placed at the centre of the supporting beam. The two massive capacitors are connected in parallel and form the timing capacitance of the oscillator. Power and control to the circuit are provided remotely by three thin ribbon-forming wires, Care has been taken to neutralise any torsional and magnetic forces on the suspension and on the wires connecting the massive capacitors to the oscillator. The circuit supply voltage is stabilises at 15 Volts nominally (14.66 V DC measured). The peak waveform voltage is 12.4 Volts.
The oscillator frequency is adjusted by a 22 kOhm rheostat in series with a 680 Ohm terminal resistor. Each massive capacitor was measured to be 360 pF nominally as the total series capacitance , with a tolerance better than 5%.
A differentiating circuit, providing as a DC output voltage the algebraic sum of the rise and fall derivatives with respect to time of the voltage waveform applied to both capacitors was used to peak the performance of the arrangement, by thus adjusting the timing resistor of the oscillator to 238 kHz.
The maximum performance of the thrust-generating phenomenon was verified by holding a 60-cm pendulum bob in front of the centre of each capacitor plate, at a distance of about 3 cm. Maximum horizontal attraction / repulsion of the bob per side coincided with the maximum of the derivative-reading indicator.
The wires carrying the waveform are connected to the geometrical centre of each plate of the capacitors, thus ensuring symmetrical current distribution in each capacitor. The polarity of connection is such that at each lateral side of the supporting beam there is one positive and one negative capacitor plate.
The polarity of the waveform fed to both capacitors is remotely controlled by the third (control) wire of the suspension, which operates a small polarity - inverting relay on the oscillator circuit.
3. PHYSICAL BEHAVIOUR.
The net value of the first derivative with respect to time of the current through the slab is found to generate a mechanical force on the mass m of the slab as given in  as:
where is a coupling constant.
The torsional pair of forces developed on the two capacitors is found to be proportional to the mass of the metal slab inserted in each capacitor, to the frequency of the waveform and to the peak voltage applied on the capacitors. For this particular waveform, the generated average thrust vector is given by  as
where and are constants is the ramp duration of the waveform. and is the timing resistance.
By keeping the thickness of the slab small (1 cm ) compared to its other dimensions ( 8x8 cm ) it is ensured that the slab will present negligible inductance at any waveform frequency of interest. This in turn minimises the skin effect on the slab and allows for uniform current distribution through it .
The direction of rotation and thus the generated pair of forces can be reversed by reversing the polarity of the waveform applied to the capacitors. The propulsive force developed can be deduced from the torsional parameters of the suspension system.
In the physical and electrical arrangement described above, the beam is displaced by 0.5 cm measured at a radius of 28.5 cm from its centre of gravity. This corresponds to 1.0 degree of rotation, clockwise or counterclockwise, as controlled by the above mentioned polarity inverting relay.
For the applied waveform which has a ramp decaying part of nominally 3% of the duration of the exponentially rising front, the generated thrust vectors push from the negative to the positive plate of each capacitor.
The generation of thrust vectors related to the algebraic sum of the first derivatives with respect to time of the electric current rise and fall slopes, acting upon a massive slab of copper has been described. The thrust vectors are made to appear as a torque pair over a set of massive plane capacitors, mounted at the ends of a wooden beam and supported from a vertical suspension as a revolving system
The author is indebted to Dr. David King and Prof. Costas. Xydeas of the University of Manchester for many helpful discussions. He is also most thankful to Dr.. John H. Schnurer for testing thrust generation and numerous discussions and to Dr. Anthony Leung for his suggestions.
 Dimitriou, S. G, "Radiation Phenomena of Specially Shaped Current Pulses," M.Sc. thesis, the University of Manchester (1994)  Jessop, G.R, "VHF UHF manual", 4th edition, Radio Society of Great Britain, 1985, pp. A2
Fig.1 Sketch of the experimental assembly. Suspension is shown half-scale.
This paper has been published on this web site, courtesy of Dimitriou Stavros
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