System and Method for Generating Forces Using Asymmetrical Electrostatic Pressure (continuation)

Abstract

A system and method for generating one or more electrostatic pressure forces or one or more divergence in electric field forces, or both, acting on at least one surface of an object. Asymmetries in the resulting force vectors result in a net resulting force acting on the object. The magnitude of the net resulting force may be a function of the geometry of the object surfaces, the amount of electric charge present on the surfaces, and the dielectric constant(s) of materials present in a gap between the object surfaces. The invention may be produced on a nanoscale using nanostructures such as carbon nanotubes. The invention may be utilized to provide a motivating force to an object. A non-limiting exemplary use case example is the use of electrostatic pressure force apparatus as a propellantless thruster to propel a spacecraft through a vacuum.

Reference

This non-provisional patent application is a continuation in part of U.S. patent application Ser. No. 18/070,428, entitled “SYSTEM AND METHOD FOR GENERATING FORCES USING ASYMMETRICAL ELECTROSTATIC PRESSURE”, filed in the United States Patent and Trademark Office (USPTO) on Nov. 28, 2022, which published as US 2023-0121805, which is incorporated herein by reference in its entirety; Ser. No. 18/070,428 is a continuation in part of U.S. patent application Ser. No. 16/688,619, entitled “SYSTEM AND METHOD FOR GENERATING FORCES USING ASYMMETRICAL ELECTROSTATIC PRESSURE”, filed in the United States Patent and Trademark Office (USPTO) on Nov. 19, 2019, which published from the USPTO as U.S. Patent Publication No. US 2020-0255167 A1 on Aug. 13, 2020, and which issued as U.S. Pat. No. 11,511,891 on Nov. 29, 2022, which is incorporated by reference herein in its entirety; U.S. patent application Ser. No. 16/688,619 is a non-provisional of, and claims the benefit of priority to, U.S. provisional patent application Ser. No. 62/769,415 titled A PROPELLANTLESS PROPULSION CONCEPT FOR SPACECRAFT BASED ON ELECTROSTATIC FIELD MOMENTUM TRANSFER, filed in the United States Patent and Trademark Office (USPTO) on Nov. 19, 2018, which is also incorporated herein by reference in its entirety.

Statement regarding federally sponsored research or development: not applicable.

Background of the invention

1. Field of the invention

The field of the invention relates generally to systems and methods for providing forces on objects in which such forces are generated by voltages, or voltage differences, when such voltages or voltage differences are applied to electrically conductive surfaces in such a way as to generate electrostatic pressure forces on an object. In embodiments, the field of the invention relates to systems and methods that make use of such forces in specific applications or use cases. An exemplary use case, which is but one of many use cases, is the case in which it is desired to provide a motivating force on an object in the case which the object is disposed in a vacuum. The field of the invention further relates to engines for vehicles that operate on principles of applied electric charge or field, for example, but not limited to, engines and thrusters for space vehicles.

2. Background art

The elimination of complex systems, such as, for example, machinery, utilized for the conversion of energy to motion has the potential to provide a great cost savings over, and greatly reduced weight and volume, over the systems of the prior art. The elimination of complex systems for converting energy to motion is especially desirable, for example, in the case of self-propelled vehicles such as spacecraft, aircraft and watercraft. For example, the mass of a body or object to be accelerated is the single largest driving parameter of spacecraft design. For example, in order to motivate a spacecraft through space (i.e., through a vacuum) or maintain its location against external influence such as gravitational forces, spacecraft must carry within themselves all the propellant mass, excitation energy, and mechanical structure to generate physical thrust. As regarding the systems of the prior art, it is only through exhausting high velocity gas that physical momentum may be transferred to a spacecraft. This momentum over time is what accelerates the spacecraft and achieves a desired motion, or motivation, of the spacecraft. Again, as an example, commercial satellites typically reserve 85% or more of their total mass per volume budget for propulsion related activities. That is to say, due to the low efficiency of chemical and/or electrically enhanced chemical propulsion systems, 85% or more of the total weight per volume of a spacecraft is expended in propulsion related activities. A spacecraft’s mission capability is therefore determined in large part by the amount of physical thrust that can be extracted from the stored propellant. The total amount of physical thrust available to a spacecraft is determined by the efficiency of the propulsion system and the total amount of propellant stored on the spacecraft. When a spacecraft’s stored propellant is expended, the ability to control the path, or maintain precise location, of the spacecraft is brought to an end. Without the ability to react to external forces, the spacecraft ceases to be an asset and becomes a liability. Simply put, spacecraft become space junk when their stored propellant is exhausted.

Since any conversion of energy from one form to another is accompanied by losses due to friction, radiation or conduction of heat, hysteresis, and the like, it is needful that advances in the state of the art be developed that increase the efficiency of producing forces which may be used to motivate an object. It is especially desirable that such advances in the state of the art be in a form that eliminates the need for the use of stored propellant so that vehicles such as, for example and not by way of limitation, spacecraft using such a systems and method could greatly reduce, or even eliminate, their dependency on stored propellant and propellant based propulsion systems. Such advances, if realized, would greatly enhance the present ability to motivate payloads, increase the lifetime of spacecraft and other devices and systems, and thereby enable entirely new uses for such systems. Such advances would enable new systems and methods for providing applied forces for any number of use cases, one example of many, being the motivation of an object. It is an object of the present invention to utilize the energy stored in an electric field, or fields, to provide such applied forces.

The notion of using electric fields as a method of propulsion was previously explored as far back as the 1920’s by, for example, Thomas Townsend Brown (“Brown”). Brown discovered that a force was developed on a Coolidge tube when the tube was subjected to a high voltage. His electric field force effect is an electrical phenomenon, which employs an electric field for generating applied forces, which could be used, for example, to motivate a spacecraft without exhausting propellant. As disclosed in U.S. Pat. No. 2,949,550 [Brown 1957] and U.S. Pat. No. 3,187,206 [Brown 1958], as an “electrokinetic” phenomenon, electrical energy can be converted to mechanical energy which is then used to provide a force for providing movement to a structure. There were several patents describing propellentless propulsion devices based on this effect coined the “Biefeld-Brown Effect” named after Brown and his graduate school advisor, Dr. Paul Alfred Biefeld. Brown and Biefeld were U.S. Pat. No. 2,949,550 [Brown 1957], U.S. Pat. No. 3,018,394 [Brown 1957a], and U.S. Pat. No. 3,187,206 [Brown 1958] for devices based on utilization of the effect. Brown’s colleague A. H. Bahnson was similarly issued U.S. Pat. No. 2,958,790 [Bahnson 1958], U.S. Pat. No. 3,223,038 [Bahnson 1965], and U.S. Pat. No. 3,227,901 [Bahnson 1966] utilizing the effect.

There has been recurring interest in these devices since the work of Brown. In one configuration, two asymmetrical capacitors are arranged to rotate about a vertical axis, termed Asymmetrical Capacitor Thruster (ACT). Another common configuration involves one capacitor plate of a capacitor plate pair being disposed above its mate, arranged so the device can lift off of the ground. This device is called a lifter. Alexander de Seversky investigated lifters during the 1960’s with his “Ionocraft” and received a U.S. patent [Seversky, 1964]. De Seversky’s craft combined a series of wires perpendicular to a mesh plate to lift the device. J. L. Naudin and others have constructed devices similar to the original Brown patent, and then assembled multiple devices into larger designs to create “lifters” that perform similarly to de Seversky’s craft. These designs vary greatly in size and shape; some are comprised of multiple cells, or comprise stacked layers of cells, to create more efficient and more powerful devices. Other such devices are disclosed in U.S. Pat. No. 6,492,784 to Hector Serrano [Serrano 2002], which generates the Biefeld-Brown Effect using stacked-disc asymmetrical capacitors.

NASA also has investigated the use of Brown’s discovery. Jonathan Campbell of NASA’s Marshall Space Flight Center has designed and tested ACTs that use dielectrics to increase their thrust, receiving U.S. patents for this work in 2001 and 2002 as disclosed in U.S. Pat. Nos. 6,317,310, 6,411,493, and 6,775,123 [Campbell 2001, 2002, and 2003].

Thomas Bahder and Chris Fazi [Bahder and Fazi 2002] of the Army Research Lab (ARL) in Adelphi, MD have also reported work on the subject. They constructed multiple devices, both original and reproductions of designs found on the internet and made qualitative observations. Bahder and Fazi’s paper includes a brief history and an attempt at an explanation of the cause of the force observed. However, they conclude that “At present, the physical basis for the Biefeld-Brown effect is not understood.”

An early test of this effect in vacuum was performed by Robert Talley [Talley et al., 1991] of Veritay Technology performed in the late 1980’s under an Air Force contract. Talley suspended a sphere-disk ACT from a suspension wire and measured torsion forces on it. This gave him the sensitivity to be able to measure small forces. This lengthy report is one of only two written on this effect describing a measurement of a force while in a vacuum chamber. Talley ultimately attributed the force that he observed to the electrostatic interaction between the chamber and the device. Talley wrote, “Direct experimental results show that under high vacuum conditions . . . no detectable propulsive force was electrostatically induced by applying a static potential difference . . . between test device electrodes . . .” Talley concluded (page 91 of his report), “If such a force still exists and lies below the threshold of measurements in this program, then the force may be too small to be attractive for many, if not most, space propulsion applications.” While this work makes a strong case against the ability of these devices to produce a force in a vacuum, it did not address the use of asymmetrical capacitors in the atmosphere.

Follow-on work was performed by NASA to evaluate the technology. A comprehensive review of the current state of the art can be obtained from Canning, Francis X., Melcher, Cory, and Winet, Edwin, Asymmetrical Capacitors for Propulsion, Glenn Research Center of NASA (NASA/CR-2004-213312), Institute for Scientific Research, October, 2004. Canning [2004] showed that a majority of asymmetrical capacitors (ACTs) exhibit a null thrust unless there is an accompanying ion wind. They performed tests on cylindrical-disk geometries under applied voltage in a vacuum bell jar and concluded that there were no forces produced in a vacuum. They find that their operation is “fully explained by a very simple theory that uses only electrostatic forces and the transfer of momentum by multiple collisions”.

Nearly all patents described above include an electrode at a high voltage in air, the consequence of which is that the air is ionized as electrons are stripped from its gas molecules. Once the gas ions are charged, they will traverse toward the electrode of the opposite polarity as directed by the field. This current is known as corona current. These gas ions bombard other neutral gas ions which in turns produces a net movement on the gas which is normally about 1 m/s. Since these thrusters are comprised of an asymmetry of the electrical field there is only one direction of gas movement emanating from the sharp electrode to the dull electrode. The sharp electrode creates a higher electric field locally which ionizes the gas whereas the dull electrode does ionize the gas. This asymmetry gives rise to the direction of the wind regardless of the polarity of the electrodes. In all cases, momentum is conserved by having a net ion wind in one direction, and the momentum on the asymmetrical capacitor in the opposite direction. There are applications that take advantage of this effect, such, for example, devices such as lifters. In 2018, Professor Steven Barrett of MIT made headlines by building a horizontal aircraft fly across a gym with no moving parts using ion wind thrust [Xu et al., 2018] and spoke at a recent Electrostatics Society of America conference on the subject.

Many of the above patents make no reference to ion-wind effects; and, experimenters, including Brown, do not mention methods to mitigate this well-known ion-wind effect. As a result, many authors who test asymmetrical capacitors believe the force they observe will have some use either in space or for large aircraft, both of which are impossible for ion-wind versions. Therefore, the current state of the art of the use of electrical energy for the direct production of linear force and motion is through ion wind propulsion or one of the two technologies mentioned below.

The most current example of a propellantless field propulsion system is an electromagnetic drive system as disclosed in British Patents GB2229865, GB2334761, GB2399601 and UK Patent Application GB2537119 to Shawyer, as well as U.S. Pat. Appl. No. 20140013724 to Fetta. This system includes an axially-asymmetric resonant cavity with a conductive inner surface adapted to support a standing electromagnetic (EM) wave. The resonating cavity lacks second-axis axial symmetry, thereby causing the standing EM wave to induce a net unidirectional force on the resonant cavity, thus generating thrust without reaction mass. Experimental versions of these EM devices have reportedly produced thrust levels of micro-newtons up to milli-newtons from several kilowatts of input power (AIAA Journal of Propulsion and Power, op. cit.).

Field modification approaches to propellantless propulsion include apparent reductions in gravitational mass or inertial mass. U.S. Pat. No. 3,626,605 to Wallace discloses a method and apparatus for generating a time-variant non-electromagnetic force field due to the relative motion of moving bodies constituted of elements whose nuclei have half integral “spin” values, with said force field exhibiting itself in the form of an induced secondary gravitational force. U.S. Pat. No. 5,280,864 to Woodward in 1994 discloses a method for producing transient fluctuations in the inertial masses of material objects by employing an effect that is a consequence of relativistic theories of gravitation. This patent is a continuation in part of application Ser. No. 07/521,992 filed in 1990 as CIP of U.S. application Ser. No. 07/031,157 filed in 1987 as CIP of application 6/919,647 filed in 1986, now all abandoned. The patent basically uses high frequency vibrating piezoelectric force transducers to accelerate a capacitor array while applying high frequency AC to electrically oscillate ions in the dielectrics. The relativistic Mach Effect was predicted to produce unidirectional forces.

In subsequent U.S. Pat. Nos. 6,098,924, 6,347,766 and 9,287,840, Woodward disclosed various improvements to the device of U.S. Pat. No. 5,280,864 for producing propellantless thrust by using piezoelectric force transducers attached to resonant mechanical structures, in accordance with Mach’s principle and local Lorentz-invariance predictions of transient rest mass fluctuations in accelerated objects. The device was designated the “Mach Effect Thruster”. The latest U.S. Pat. No. 9,287,840 in 2016 incorporates acceleration and temperature feedback sensors in the electronics control system, uses a DC bias voltage superimposed on the high frequency the AC voltages to activate transducers, and applies pulsed AC waveforms. With these improvements, the device produced 6-7 micro-newtons of thrust with a 100 W power input, which is approximately 14 megawatts/Nt. The disclosure admits that the device is not scalable and that arrays of multiple small devices would be necessary to generate larger thrusts.

In U.S. Patent Application Publication No. 2006/0065789, Woodward introduced his “flux capacitor” which proposed modifications to the devices of U.S. Pat. Nos. 5,280,864, 6,098,924, and 6,347,766 to overcome a serious internal propagation speed problem. The force transducers were eliminated, and the capacitor arrays were either enclosed within induction coils or external induction coils were aligned with axes perpendicular to the displacement fields in the capacitor. The objective was to replace transducer accelerations by using induction coils to generate perpendicular magnetic field oscillations of the dielectric ions.

None of the above described systems or methods satisfy the stated need in the art.

Brief summary of the invention

The present invention comprises an apparatus and method that have one or more of the following features and/or steps, which alone or in any combination may comprise patentable subject matter.

Generally, the system and method of the invention satisfies the stated need in the art by generating a force usable for any purpose, such as, by way of example and not by limitation, thrust, motivating force or actuation, without the use of any expelled propellant, or any propellant at all. The system and method of the invention takes advantage of an aspect of the conservation of momentum for electromagnetic systems in a novel way, in which a net force is generated on a system or object by imbalances of electrostatic pressure. This “Electrostatic Pressure Force” (EPF) has been thoroughly tested by the inventors and has been verified repeatedly in a laboratory environment using a variety of independent configurations for the system of the invention.

In accordance with one embodiment of the present invention, the invention comprises an apparatus for generating a force on an object, comprising an object that comprises at least one surface, wherein an electric charge or electric field, or both, is/are applied to said at least one surface, or to at least one region of the at least one surface. The application of the electric charge or electric field to the at least one surface or at least one region of the at least one surface may give rise to an electrostatic pressure acting on the at least one surface or at least one region of the at least one surface of the object, thereby generating an electrostatic pressure force on the at least one surface or at least one region, or both. The electrostatic pressure force acting on the at least one surface, or at least one region of the at least one surface, may be characterized by a net resulting electrostatic pressure force acting on the object. In embodiments, the at least one surface, or the at least one region of the at least one surface, may be further defined as a plurality of surfaces, each surface possibly having one or a plurality of regions, each surface and/or region experiencing an electrostatic pressure force proportional to the amount of electric charge on the surface or region, or the magnitude of the applied electric field to each surface or region, or both; the electrostatic pressure force acting on the surface or region having a vector that may also be determined by the three-dimensional shape and size of the surface or region. The vector sum of each of the electrostatic pressure forces on each of the surfaces and/or regions may result in at least one net resulting electrostatic pressure force acting on the object.

The magnitude and direction of the electrostatic pressure force acting on any surface or region of the invention may be achieved by determining one or more parameters selected from the group consisting of: 1) the amount of electric charge on the surface or region; 2) the magnitude and direction of any electric field acting on the surface or region; 3) the three-dimensional shape of the surface or region; or 4) the size of the surface or region. The foregoing parameters may be determined in any combination in order. Thus these parameters may be determined by the user, in accordance with the inventive principles set forth herein, such that at least one desired electrostatic pressure force acting on a surface or region of the invention is achieved, and when the object comprises a plurality of surfaces or regions of surfaces, at least one net resulting force acting on the object is achieved.

In embodiments, the net resulting pressure force may be characterized as acting on a center of mass of the object, thus propelling the object along a desired vector. In any of the embodiments, the net resulting pressure force may not act on or through a center of mass of the object. In such cases, the net resulting pressure force may impart a rotational force on said object, having components in any or all of the axes of a three-dimensional coordinate space, thus steering the object.

(The remainder of the brief summary, the brief description of the drawings, and the definitions and exemplary embodiments at paragraphs 0023 to 0114 and 0135 to 0153 are omitted for length; the complete text is at the source.)

Detailed description of the invention

Theory of operation of the invention

In embodiments, the present invention may make use of Conservation of Energy for a center-of-mass (CM) system in which the total energy (kinetic plus potential) is zero. The kinetic energy of a system is comprised of an object with mass M, velocity v with potential energy U is written as:

0 = ½Mv² + U (Equation 1)

What follows is a method to determine the conservation of momentum similar to the formalisms of Kirk McDonald [McDonald 2002] where one simply solves for momentum to give:

Mv = −2U/v (Equation 2)

Now we simply turn the velocity in the denominator of (2) into its operator dx/dt:

Mv = 2U dt/dx (Equation 3)

The next step is to note that d(Ut) = U dt + t dU and solving for U dt = d(Ut) − t dU. The differential of the product of energy and time is akin to the differential of the energy-time action integral S = ∫L dt of the Lagrangian. Nature chooses the path of least action which is found by setting the differential to zero, δS = δ∫L dt = 0. Here we make the claim that the differential of the energy-time product should also be set to zero, d(Ut) = δ(Ut) = 0, meaning:

U dt = −t dU (Equation 4)

Putting this back in to (3) becomes:

Mv = +2t dU/dx (Equation 5)

There are other ways to derive this equation but it is well known that Force is the time rate of change of momentum and is also the spatial derivative of energy with distance.

The next step is to fill in the potential energy of the system. Conventionally one uses an external field as a source of the potential. However, we use a more generic form of energy, the energy stored in the field. In particular the energy stored in the electric field given by

U = (ε₀/2) ∫E² dτ (Equation 6)

a well-known equation. The placement of (6) into (5) along the x direction gives

Mv = ε₀t (d/dx) ∭ E² dx dy dz (Equation 7)

= ε₀t (d/dx) (∬ E² dy dz) (Equation 8)

= ε₀t Δ(E²A) (Equation 9)

which can be written as

P(t) = Mv = ε₀t [E₂²A₂ − E₁²A₁] (Equation 10)

Equation (10) shows a linear time dependence on the momentum with a corresponding force of

F = dP/dt = ε₀[E₂²A₂ − E₁²A₁] (Equation 11)

if the electric field does not have a time dependence (electrostatic). Equation (11) is remarkable because it shows that a system (or object) can experience a net resulting electrostatic pressure force F if there are asymmetries in the electrostatic pressure experienced by (i.e. acting on) the surfaces of the object, for instance, such that the vector sum of the electrostatic pressure force acting on the surfaces of the system (or object) is non-zero. The determination of the electric field strength at any point along the surfaces of the system (or object), the resulting electrostatic pressure and electrostatic pressure force acting on the surfaces of the object, and the net resulting electrostatic pressure force acting on the system (or object) as a function of the geometric arrangement of the surfaces of the object and the applied voltage or voltage differential giving rise to the electric field may be accomplished by computational methods.

The ε₀E² relation is well known to science. It is the electrostatic pressure on the surface of an object. The permittivity of free space ε₀ is 8.85 × 10⁻¹² F/m and the maximum allowed electric field in air before breakdown is about 10⁶ V/m. This gives an electrostatic pressure on the order of about 1 Pa or one Pascal. Since air is approximately 101.3 kPa, electrostatic pressure is about five orders of magnitude less. It is important to note that electrostatic pressure force is not the force or pressure due to Coulomb attraction on a surface. For example, if one surface is positive and the other surface is negative, there will be a strong Coulomb force of attraction between both surfaces which is on the order of kq₁q₂/r², where k = 1/(4πε₀) = 9 × 10⁹ N·m²/C².

Although the electric field is well defined in the region between the two surfaces and consists of a known direction, the direction of the electrostatic pressure force is not dependent upon the direction of the electric field; rather, it is a function of the square of the electric field. Thus, in the example in which the invention comprises a first electrode and a second opposing electrode, the two electrode surfaces will have a strong force of attraction due to the Coulomb coupling constant, but the electrostatic pressure between the two surfaces will push the two surfaces away from each other, albeit a much weaker force than the Coulomb force due to the electrostatic pressure force being linearly dependent on the free space permittivity constant while Coulomb’s constant is inversely proportional to that same constant. Thus, in embodiments of the invention that comprise opposing electrodes, the electrodes comprising electrically conductive surfaces of the invention may be attached by a non-electrically conductive structure in order to prevent them from collapsing together due to the Coulomb force. In embodiments, the structure for securing the electrodes may be non-conductive. In embodiments, the reactive force provided by the structure exactly equals the attractive Coulomb force tending to cause the electrodes to come together, allowing the novel net electrostatic pressure force described below, which results from an asymmetry of electrostatic pressure forces acting on the electrodes, to be observed and to be utilized in a net electrostatic pressure force apparatus of the invention.

A novel inventive scheme of the invention makes use of electrostatic pressure force, which, in general, is the product of an electrostatic pressure and the surface area upon which the electrostatic pressure acts. In accordance with the above relationships, depending upon the geometric arrangement of the conductive surfaces (i.e., electrode surfaces) of an object, and the intensity of an applied electric field having a divergence (which may be continuous or non-continuous), the surface or surfaces of an object may be subjected to differing levels of electrostatic pressure resulting from the applied electric field such that, when all electrostatic pressure forces acting on the surfaces of the object are vector summed, a net non-zero resulting electrostatic pressure force acts on the object. When the electrostatic pressure forces on the object are of different vectors such that their sum is a net electrostatic pressure force vector that is non-zero, the electrostatic pressure forces on the object may be described as being “asymmetric”.

A desired resulting net electrostatic pressure force may be produced by the inventive method steps disclosed and claimed herein, which steps may include defining, in three dimensional space, the size, three-dimensional shape, and arrangement of the electrically conductive surfaces of an object such that, when the object is subjected to an electric field, or when the object is subjected to a divergent electric field, a desired resulting net electrostatic pressure force is produced from the summation of the electrostatic pressure forces resulting from electrostatic pressures acting on the electrically conductive surfaces of the object. Such computational means may, for example, run iterative computations, such as in a Monte Carlo analysis, varying the geometric arrangement of the electrically conductive surfaces and varying the applied voltage or voltage difference, until the desired net resulting electrostatic pressure force is achieved. Using the apparatus and method of the invention, it is possible to achieve a desired net resulting electrostatic pressure force acting on a body or object by determining the geometric arrangement of the conductive surfaces of the body or system such that the net electrostatic pressure force is maximized by maximizing the electrostatic pressure on one or more surfaces of the body or system, and by minimizing the electrostatic pressure on other surfaces of the body or system. Said another way, by creative manipulation of the conductive surfaces on one of the surfaces, or by the presence of a plurality of dielectric materials of differing permittivities in the electric field, there may be created regions of lower electrostatic pressure which may be crafted into a surface that experiences lower electrostatic pressure, therefore having an imbalance of electrostatic pressure acting on it. The surface that has the least electrostatic pressure acting on its surface is subject to less electrostatic pressure force. This may be visualized as one surface making more thrust in a vector direction than the other surface does in the opposite vector direction.

In embodiments, the asymmetric electrostatic pressure forces acting on the object may be established by the size, geometric three-dimensional shape and three-dimensional arrangement of the electrically conductive surfaces of the object as acted upon by an electric field; or, by the plurality of dielectric materials of differing permittivities in the electric field to establish a divergent electric field acting upon the electrically conductive surfaces of the object; or a combination of both.

Differentiation from other theories of operation

The present invention does not require the use of an ion wind to generate the force. Interestingly, if ion wind is generated using geometries described herein, the electrostatic pressure force is in the same direction of the wind. [Imagine a rocket moving in the direction of its exhaust]. In embodiments, the invention may be encapsulated in an enclosure to remove ion wind effects. The proof of concept and reduction to practice tests mentioned herein were generally performed within an enclosed box to nullify ion wind effects.

Force measurements are performed on the box itself which removes all doubt that the forces observed are contained within the box and not due to outside effects such as ion wind and Coulomb attraction to exterior surfaces (walls, chambers, etc.). The Coulombic attraction to other surfaces is prevented by sufficiently grounding the test chamber box.

Many of the measurements performed on the test devices described herein make use of direct current (DC), or non-time-varying applied voltages, which eliminates magnetic effects. Magnetic effects are well known to occur if a system uses strong currents which can interact with the Earth’s magnetic field via Lorentz Law forces, resulting in unwanted forces and torques on that system. Magnetic fields can also be generated by constant currents (Ampere’s Law) or changing electric fields (Faraday’s Law) which can interact with the Earth’s magnetic field as well. The present invention has proven to work in DC, i.e. non-time-varying voltage, mode which eradicates all magnetic components for explaining the phenomenon.

Without the presence of a magnetic field, the present invention does not generate field momentum. Classical electrodynamic fields possess momentum, as was first realized by Poynting [1884] and discovered independently by Heaviside [1885], who found that a finite cross-product of E×B is proportional to a momentum density. The fact that this momentum occurs for every frequency including zero frequency, as in the case of static fields, has troubled scientists since the beginning of the formulation of electrodynamics and has only recently been widely accepted and appreciated. The notion that fields carry momentum similar to the way in which particles do has led scientists to resolve paradoxes that question whether electrodynamics obeys Newton’s laws. One famous example involves two charged particles moving at right angles towards one another. The electrical force between them is repulsive but the magnetic force is not equal and opposite [Page and Adams, 1945]. This seems to violate Newton’s third law. Only when the field momentum of the charges is taken into account does the conservation-of-momentum laws hold.

It is possible to use angular field momentum to impart mechanical momentum onto a system. The famous Feynman disk paradox shows how stored angular field momentum can be converted into mechanical rotational momentum [Feynman 1965]. This has been verified experimentally by Graham and Lahoz [1980]. As a result of the insight provided by Dr. Feynman many researchers have proposed the use of linear field momentum as a tool for propellentless propulsion. The idea first arose more than 50 years ago when Dr. Joseph Slepian theorized that a craft can be propelled by “a means of propulsion which does not require any material medium upon which the propelling thrust is exerted” [Slepian 1949]. Work continues into the 21st century to investigate the possibility that field momentum (E×B) could provide forces on objects without expelling propellants [Corum, et al. 2001]. The Electromagnetic Momentum Generator (EMMG) developed by Brito [Brito 1999, 2001 and 2003] is a toroid geometry used to generate field momentum in the x-direction that supposedly generates a very small mechanical force in that direction. It uses a parallel-plate ring configuration to generate the electric field in the radial direction encompassed by a current-carrying coil to create the circumferential magnetic field. Their belief was that having the field momentum present itself was enough to generate a force.

However, the consensus of NASA’s Breakthrough Propulsion Project (BPP) in 2003 was to independently verify any net thrust claim in the area of field momentum, a task given to the Astronautics department at the United States Air Force Academy. Experiments by Bulmer and Lawrence [2003] aimed to monitor any change in the momentum of a laser beam as it passed through a volume containing linear field momentum. A laser beam was placed within this volume parallel to the electrodes whose DC offset was monitored. The belief was that any change in the DC offset would suggest an acceleration of space where the field momentum existed. However none was ever detected.

Although there are many researchers trying to use field momentum as a means to produce a linear force as an analog to the Feynman disk, none have been successful. This is most likely as a result of not addressing the hidden momentum.

The invention is not subject to the recently discovered “hidden momentum”, a momentum commonly used to cancel field momentum. This additional momentum, which is a relativistic effect, derives from internal stresses of the system, was not formally introduced until 1967 by Shockley and James [1967]. They considered a system of two counter-rotating oppositely charged flat disks in the presence of the field of a charged particle. As the disks slow, the changing electric field creates a magnetic field that acts on both the particle and the disks. This appears to give the system a total net force, thus requiring an internal equal and opposite force if the system is to remain stationary. This paradox was resolved a year later by Coleman and Van Vleck [1968], who used the Darwin Lagrangian to solve for the equations of motion (a more complete discussion was provided by Furry [1969]). They found that the electric field of the charged test particle does exhibit a force on the magnet due to relativistic effects. This can be explained using a simple model developed by Haus and Penfield [1968].

Multi-blade test cases

An example of a test article of an embodiment of the electrostatic pressure force apparatus of the invention used to verify functionality of the invention as herein described is shown in FIG. 21. An embodiment comprising nine blades 100 arranged as depicted, each blade being substantially 0.25 inches in height, spaced 0.25 inches apart with each blade being substantially four inches in length, was fabricated. The gap between surfaces 100a and 102a (see FIG. 13) was 0.25 inches. The 0.05 inch thick blades 100 and the back plane electrode 101 were coated with a conductive paint to create the conductive electrode surfaces. A wire carrying V+ was connected to the painted surface through the back of the device and attached using epoxy. The entire structure was then filled with high voltage epoxy dielectric which was subsequently cured. An initial ground plane was created using copper tape that only covered the electrode area of 4 in × 2 in = 8 in² on the top outside of the surface (not shown). The test article was tested by placing it onto a foam test stand that was connected using a high-tension string to a force meter (Omega model DGF155-0.12). The test stand itself was hung from a structure using a string in a pendulum configuration. Any forces on the stand were monitored in real time. The applied voltage difference ΔV was supplied to the device as herein described using a high voltage power supply capable of providing up to ±40 kVDC. The V−, or ground, side of the applied voltage difference ΔV from the power supply was connected to the copper tape. The force meter and power supplies were monitored using a LabView program.

Still referring to FIG. 21, other test configurations included replacing the foam test stand with a transparent box lined with ITO-coated PET film that was grounded. This eliminated Coulomb forces as well as ion wind forces. Forces on the box were monitored directly. Tests on the foam stand were repeated in both tension and compression mode by flipping the device 180 degrees to ensure there was no Coulomb attraction to the walls. Flipping the device ensures the forces are as described herein. Ion wind was prevented by placing the foam test stand inside a plastic bag.

Still referring to the test setup as depicted in FIG. 21, an example of the resulting force is shown in FIG. 22. The raw force is shown in red with 0.1 mN resolution. The thick dark red line is a smooth fit to the data. The black line is the applied DC voltage to the test device. Clearly there is a force in the positive direction (compression) when the voltage is applied. At +25 kV, the net average force for these two tests is approximately 237 μN. Similar tests to the one shown were repeated dozens of times. One striking verification of the theory was to increase the ground area to see if the force increased linearly. Increasing the ground area was performed by adding more copper tape to the back side which increased the surface area from 8 in² to 15 in² by coating the entire backside of the 3 in × 5 in area. Using the computational methods of the invention, this was expected to increase the force by approximately 1.8. Measurements after the application of copper tape to the full backside gave an average over several runs of 421 μN which is an increase of 1.77. Thus this test result correlated with the expected result, which was produced using the computational methods of the invention, very closely.

Several additional tests were shown to be consistent with the theory. The electrostatic pressure force has been shown to be a function of the square of the applied voltage difference. This was expected theoretically but is also observed experimentally (as well as computationally, using the computational method of the invention) as shown in FIG. 23A. Using this same test article, tests were performed at a variety of different voltages and the corresponding averages were measured.

Other test articles using a variety of different dielectrics 600, coatings, electrodes, and geometric arrangements of the electrically conductive surfaces were also shown to be consistent with the claimed invention. Test results for styrofoam EPF devices is shown in FIG. 23B. The force’s squared dependence on voltage has been observed repeatedly over a variety of shape and geometries tested by the inventors.

Referring now to FIG. 24, the invention may comprise a plurality of blades 100 which affect a larger area increasing the net resulting electrostatic pressure force. The net resulting electrostatic pressure force grows as the number of blades 100 increases which affects a larger surface area on the ground plane depending on the spacing between blades 100, length of blades 100, the gap between electrodes, etc. There are many parameters of the geometric arrangement of the invention which may be optimized to achieve a desired net resulting electrostatic pressure using the computational methods of the invention.

Referring now to FIG. 25, it may be seen that COMSOL is a very useful tool for performing the computations required to achieve a desired net resulting electrostatic pressure force. For example, using such computational techniques, it is shown that there is little benefit in increasing the length of the blades 100 once it exceeds the spacing between the blades. There is little, or no, electric field reaching the electrode surface(s) 101a of electrode 101 which is Faraday shielded by the larger electrode blade 100, all at the same voltage.

Other aspects of the geometric arrangement of the electrostatic pressure force apparatus of the invention can be modeled by the computational techniques of the invention as well such as, for example, the thickness of the blades 100. As the blades get thicker, the area of them increases and the resulting pressure on the V+ side starts to compete with the pressure on the ground side. At some point, the pressure on the V+ side increases enough to overcome the EPF on the ground side and the force switches directions. Switching of the direction of the force based on the geometry alone has been observed by our team.

In any embodiment of the invention, gas breakdown can be prevented using an optional dielectric medium 600 in between the electrodes. The dielectric 600 can possess high dielectric strengths to reach high local electric fields depending on the dielectric used. Polyimide, PTFE, Styrofoam, epoxy, RTV and high voltage putty have all been used to increase the voltage on the electrodes limiting breakdown effects. For example, the test article of FIG. 23A was filled with high voltage epoxy while the test articles of FIG. 23B were filled with polyimide and foam.

Referring now to FIGS. 26 and 27, in addition to optimizing the geometric arrangement of second electrode 102 and first electrode 101 by minimizing the pressure area product, one can easily maximize the pressure area product using the computational method of the invention. FIG. 26 shows a method for increasing the electrostatic pressure force for a constant non-time-varying electric field source. Here, the electric fields on the object surfaces were calculated using computation methods provided by a free software called FEMM (Finite Element Method Magnetics) for a given ground plane geometry. These field plus their geometry was given as input to MatLab (by MathWorks) which calculated the electrostatic pressure force. Matlab can then be used to then generate a new script that can be read by FEMM, calculate the electric fields, and then again monitor the resulting pressure force in an optimization scheme. An example is shown in FIG. 26 using triangles as the chosen feature to provide an optimal ground which increases the effective area.

Referring now to FIG. 27, the results of this case show that as a flat electrode 102 is replaced with an electrode comprising triangular shaped features comprising electrically conductive surfaces, the electrostatic pressure force will initially be reduced for less than five such features. However, as the number of equally spaced triangle features is increased, the electrostatic pressure force increases and will eventually surpass the simple flat surface. As the number of triangles increases for the given area, the net electrostatic pressure force grows until a maximum at about 23 triangle features before the net electrostatic pressure force decreases. The benefit of the triangular V− electrode seems to suggest a factor of 6× in the strength available purely by geometrical arrangement considerations alone for a given potential. As the number of triangular electrode features grows larger, the benefit of the additional electrically conductive surface area is lost as the electric field can no longer penetrate into the grooves between the triangular features due to the Faraday shielding effect. Eventually, as the number approaches infinity, the force will be the same as the original flat plane as expected. We have also studied half circles, domes of various radii and other ground shapes for optimization purposes.

Embodiments comprising time varying applied voltage

The invention, in embodiments, may comprise an applied voltage difference that is a time-varying voltage difference. A more general solution to Equation (10) includes this time dependence:

P(t) = Mv = ε₀t [E₂²(t)A₂ − E₁²(t)A₁] (Equation 12)

Equation (12) shows a non-linear time dependence of the momentum with a corresponding force given by:

F(t) = dP(t)/dt = ε₀t [2E₂(dE₂/dt)A₂ − 2E₁(dE₁/dt)A₁] + ε₀[E₂²A₂ − E₁²A₁] (Equation 13)

Several non-limiting, exemplary cases of a time dependent force are now discussed. The most common case would be that of a sinusoidal time dependence such that E(t) = C sin(ωt + φ). We note that

dE/dt = Cω cos(ωt + φ) (Equation 14)

t dE²/dt = C²ωt sin(ωt + φ) cos(ωt + φ) (Equation 15)

The average of (15) is non-zero with the extra factor of time t over a full period. The second term is identical to Equation (11) and has a nonzero average as well. For a phase shift of zero, the time dependent part (15) is negative and subtracts from the overall force. Interestingly, the force would be greatly enhanced if the phase shift φ is nonzero and the two terms would add to a greater force. For example, with an amplitude of 100 V/m, the second term averages to be C²/2 = 5000 (V/m)². With a zero phase shift, the contribution for the time dependent term (15) is −2500 giving a total amount of 2500. On the other hand, if there’s a phase shift of 90 degrees, then the time dependent term is +2500 giving a net of 7500 (V/m)². In general, the force scales as C²/2 and is either increased or decreased by an amount C²/4 depending on the phase of the signal.

It is important to note that a frequency component of the time varying applied voltage plays no part in the resulting net electrostatic pressure force. Analysis of the average of the above terms shows that the frequency component cancels out. The amplitude component however, remains and thus the net electrostatic pressure force is strongly correlated to the square of the amplitude.

There are other time-dependent terms that can be utilized such as exponential decays, hyperbolic decays as well as square waves, triangle waveforms, etc. As to which is the best form to use we do not know at this time. Experimentally square waves work best but that is most likely due to overshoot since it is impossible to achieve changes in the high and low state instantaneously which would require infinite bandwidth. Such transients are known to give stronger forces [see Woodwards’ MET] but their affects tend to cancel on the opposite cycle.

Thus, the applied voltage difference ΔV between opposing electrodes, in any embodiment, may comprise a time varying voltage difference that is independent of frequency.

Scalability

Referring now to FIG. 28, the ultimate goal is to have a nanoscale version of this thrust technology. FIG. 28 shows a COMSOL computational result of the force as a function of gap distance for a three-bladed EPF device (figure insert). As one moves the ground closer to the electrodes the force increases as expected for a given voltage. As long as electrical breakdown is prevented, the blade electrodes and the ground can be as close as possible.

There is no reason as to why systems comprising embodiments of the invention cannot be made on the nanoscale. The technology already exists to generate small vertical arrays called field emission arrays (FEAs). These FEAs are used not only for television displays and related devices, they are also used for Field Emission Electric Propulsion (FEEP). FEEP rely on strong electric fields to accelerate atomic ions from the surface of a metal (cathode) toward a grounded plate. A replacement for current FEAs is the use of carbon nanotubes (CNT) which are more robust and possess superior electrical properties. CNTs can be made to conform not only to the geometries of FEAs but also small nanowires at the microscopic scales.

In further embodiments, the invention may comprise nanostructures. Referring now to FIG. 29, in further embodiments of the invention, known fabrication techniques may be utilized to fabricate any physical embodiment of the invention that comprises a first electrode with at least one proximal electrode surface 100a, at least one structure 700, and, in embodiments, a plurality of structures 700, for disposing proximal electrically conductive surface 100a a distance from distal electrically conductive surface 101a, and at least one opposing electrode surface 102a as hereinbefore described. In this embodiment, wires made of several CNTs may be synthesized using chemical vapor deposition and grown vertically on an Si wafer array. The transfer of the CNTs onto an Al₂O₃ substrate preprinted with silver paste is shown in FIG. 29. The purpose of the research was to develop better CNTs with enhanced field emission properties. The result is that CNTs can be generated in a small parallel wire-like pattern on the microscopic scale.

Further embodiments of the claimed invention

One exciting attribute is the possibility of making the electrodes and the ground system transparent. Indium Tin Oxide (ITO) used for touch screens, cell phones, etc. has widely been used as a successful transparent conductor for decades. Since the EPF device does not require high currents, the lower resistivity of conventional non-transparent conductive materials such as copper, silver, gold, etc. is not necessary. Thus the entire EPF system can be made transparent similar to glass. One application of this technology would be to use it as a propulsive thrust for spacecraft as a glass cover on top of the required solar panels. The skin of a spacecraft can be used for station keeping or thrust maneuvers. This application will save volume and mass but also extends the life of the spacecraft which to date is solely limited by propellant availability.

In a traditional chemical or electric enhanced chemical rocket propulsion system the velocity added to the propulsive mass fraction comes from the heating of material or accelerating the mass fraction in some kind of electromagnetic field. In all cases, the propulsive mass fraction is expelled from the spacecraft. The change in velocity of the expelled mass times the propulsive mass fraction is the propulsive momentum available to be transferred to the spacecraft. Specifically, in chemical rocketry, the mass fraction acceleration energy comes from the breaking of high energy chemical bonds in the propellant. In ion/plasma chemical rocketry the delta velocity comes from accelerating ionized gas in an electromagnetic field. In solar sailing, low mass/high energy solar wind is collected on a massive scale to provide the physical momentum needed to accelerate the spacecraft. No matter the chemical or electrical enhancement, all rocket propulsion systems rely on action/reaction physics to achieve motion. To move the spacecraft, high velocity mass must transfer its physical momentum to the spacecraft prior to being ejected. EPF propulsion is not like these other forms of propulsion in that no mass is consumed or expelled in the conversion of Electromagnetic Potential into Physical Momentum. Electrical potential is converted into physical momentum via a unique application of electrostatic physics and unique reactor design.

In all classical or electrically-enhanced chemical rocketry propulsion systems, once the propellant is exhausted the propulsion system becomes useless. In all cases, the amount of energy that can be packed into the propellant is a function of how chemically or electrically unstable the material is. The trade between safety and economy tends to make spacecraft large and expensive with very small payload mass fractions. These propulsion systems all have life spans and efficiencies that are directly dependent on the propellant they consume. Once the propellant is exhausted, the propulsion system shuts down and its mass fraction of the spacecraft becomes waste. The mass fraction of the space vehicle devoted to conventional chemical or electrical/chemical propulsion including fuel, oxidizer, storage tanks, pumps, rocket motors, and structure to hold all this together is upwards of 98% of the total mass of the spacecraft. Unique to EPF propulsion, the mass fraction devoted to propulsion can be as little as 2% of the total mass of the spacecraft. As no mass is consumed or expelled in the production of thrust, no spacecraft mass fraction need be reserved for propulsion. As the propulsion system need never be turned off, the mass fraction dedicated to making thrust is never wasted.

In direct contrast to chemical rocketry, an EPF propulsion system does not require any fuel or oxidizer or mechanical systems or propellant mass to be consumed or expelled in any way. EPF creates physical momentum from stored electrical energy in a hermetically sealed reactor, and over time, that created physical momentum is realized as physical force. The spacecraft is accelerated by the application of this physical force. As no mass fraction of the spacecraft is expended to create thrust, the lifespan of the EPF thruster, and thereby the spacecraft housing them, are near limitless. Realistic mass fractions of the spacecraft devoted to propulsion could be as little as 2% of the total mass of the spacecraft. This projected low mass fraction is in direct contrast to the 98% mass fractions currently accepted for chemical/electric spacecraft propulsion systems. Low propulsion mass fraction, very high efficiency, and never having to turn off the propulsion will bring about a revolution in the exploration of space. Travel times to the planets will be measured in days as opposed to months and years. Greater mass fractions of the spacecraft will be used for the payloads.

In chemical/electric rocketry propulsion, the physical momentum available to the spacecraft is limited by the exit velocity of the expelled mass. All chemical/electric forms of spacecraft propulsion are limited to accelerating the expelled mass at some small fraction of the speed of light. As a result of this restriction, the maximum velocity any chemical rocket propulsion system can achieve is a very small fraction of the speed of light. EPF propulsion does not require the expulsion of mass to transfer physical momentum and therefore has the capability of propelling a spacecraft to a significant fraction of the speed of light.

In embodiments, the invention may achieve not only asymmetrical electrostatic pressure forces, or EPF, but may also achieve an additional force termed the “Divergence in E-field” or “DIV-E” force(s) as described below.

The divergence in E-field (DIV-E) force

The theory defining the generation of DIV-E forces of embodiments of the invention is now described.

The present invention makes use of conservation of energy for a system or an object, such as, for example, a center-of-mass (CM) system or object, in which the total energy (kinetic energy plus potential energy) is zero. The kinetic energy of a system may be comprised of an object with mass M, velocity v with potential energy U is written, setting the total energy to zero, as:

0 = ½Mv² + U (Equation 1)

What follows is a method to determine the conservation of momentum where one solves for momentum to give:

Mv = −2U/v (Equation 2)

Now we turn the velocity in the denominator of (2) into its operator dx/dt to give

Mv = 2U dt/dx (Equation 3)

The next step is to note that d(Ut) = U dt + t dU and solve for U dt = d(Ut) − t dU. The differential of the product of energy and time is akin to the differential of the energy-time action integral S = ∫L dt of the Lagrangian. Nature chooses the path of least action which is found by setting the differential to zero, δS = δ∫L dt = 0. Here the invention utilizes the concept that the differential of the energy-time product should also be set to zero, d(Ut) = δ(Ut) = 0, meaning:

U dt = −t dU (Equation 4)

Putting this back in to Equation (3) results in:

Mv = +2t dU/dx (Equation 5)

It is understood that force, generally, is the time rate of change of momentum and is also the spatial derivative of energy with distance.

The next step is to fill in the potential energy of the system. Conventionally one would use an external field as a source of the potential. However, the invention uses a more generic form of energy, the energy stored in the electric field. In particular, the energy stored in the electric field is given by

U = (ε₀/2) ∫E² dτ (Equation 6)

where ∫dτ is the integral over the volume. The placement of Equation (6) into Equation (5) along the x direction gives:

Mv = ε₀t (d/dx) ∭ E² dx dy dz (Equation 7)

An important aspect of the derivative is noting that it operates on both the electric field squared and the volume elements via the chain rule. Thus:

Mv = ε₀t [ (d/dx)(∬ E² dy dz) + ∭ (dE²/dx) dx dy dz ] (Equation 8)

Mv = ε₀t [ Δ(E²A) + 2∇E∇E ] (Equation 9)

which can be written as:

P(t) = Mv = ε₀t [(E₂²A₂ − E₁²A₁) + 2∇E∇E] (Equation 10)

Equation (10) shows a linear time dependence on the momentum with a corresponding force of:

F = dP/dt = ε₀[(E₂²A₂ − E₁²A₁) + 2∇E∇E] (Equation 11)

if the electric field between the electrodes does not have a time dependence (i.e., if the electric field between the electrodes is electrostatic). Thus, it is a discovery and inventive concept for the structure claimed that the resulting force contains a surface effect (first term of Equation 11) as well as a volumetric effect (second term of Equation 11). The term ε₀E² is the electrostatic pressure on the surface. This pressure, when applied to an area, results in a force; and, if there is an uneven, or asymmetric, amount of electrostatic pressure on the two opposing surfaces of the electrodes, the system will experience a net force on its center of mass.

Additionally, the second term is a volumetric force on the system, and is present provided there is a divergence in the electric field within the volume between the electrodes. Thus, we refer to the surface effects (first term of Equation 11) as the electrostatic pressure force (EPF) while the volumetric effect (second term of Equation 11) is referred to as the “divergence in E-field force” (also may be referred to as “divergent electric field force” or “DIV-E” force). A DIV-E force is experienced on an object in the case in which the electric field between the electrodes of the object is characterized as having a non-zero divergence; i.e., when the electric field between the electrodes is divergent. The DIV-E field may be caused to be divergent if, for example, a plurality of dielectric materials having differing permittivities are disposed in the electric field between the electrodes. In embodiments, these dielectric materials may be disposed in the gap, or volume, between the electrodes where they are within the electric field which may be created by the application of voltages of different levels to the electrodes, or may be an externally applied electric field from man-made or natural sources. The divergence in E-field force, or DIV-E force, may be characterized as volumetric because it operates on all points of the three-dimensional volume of the dielectric materials subject to the divergent electric field.

One of the discoveries made in the present invention is that this asymmetry of the electrostatic pressure results in a net electrostatic pressure force on a system or object comprising the apparatus of the invention. This may be accomplished by maximizing the force on one electrode surface and minimizing the force on another electrode surface. Usually the high voltage electrode surface experiences minimized electrostatic pressure while the ground, or negative voltage electrode surface, experiences the maximum amount of electrostatic pressure. It is not important which surface is which.

Additionally, the second term of Equation 11 shows that a net divergence in E-field force on an object can be generated internally provided that a divergent electric field exists in the volume between the electrodes, and at least one dielectric material is disposed within the divergent electric field. This can be a microscopic electric field or a macroscopic one, and may be achieved, for example, by the placement of one or more dielectric materials, such as dielectric material layers, having differing permittivities, in the volume or gap between electrodes, in the electric field between the electrodes of the invention.

In another example, a first dielectric material having a first permittivity, and a second dielectric material having a second permittivity, may be placed in the electric field between the electrodes. Because the first dielectric material and the second dielectric material have different permittivities, a divergent electric field is established between the first and second electrodes, resulting in a net divergent electric field (DIV-E) force acting on the dielectric materials. When the dielectric materials are attached to a structure that also is attached to the electrodes, such as an object body structure, the net DIV-E force acting on the dielectric materials also acts on the object body, and could be used, for example, as a motivating force. This arrangement may be extended to any configuration and any number of electrodes, and any configuration and any number of dielectric materials having differing permittivities.

The presence of the divergence in E-field force (DIV-E force) was also verified by testing. These tests involved changing the dielectric material in the electric field which allows the divergence of the field to play a stronger role in the force which in some cases creates the force in the opposite direction consistent with the theory. Hundreds of other test articles were devised in order to test and verify both the electrostatic pressure force as well as the divergence in e-field DIV-E force.

The divergent electric field (DIV-E) force(s) may be achieved by the use of materials, which may include but not be limited to metamaterials, having differing values of permittivity placed in the E-field between conductors of the system. A series of materials, including but not limited to metamaterials, may be placed in an arrangement between the electrodes as shown in non-limiting, exemplary fashion in FIG. 30. A first electrode 1000 may comprise a conductive surface 1003 which may comprise any electrically conductive material. Similarly, a second electrode 1001 may comprise a conductive surface 1006 which may comprise any electrically conductive material. Electrodes 1000, which may have electric potential V+, and 1001, which may have electric potential V− which may be a different potential than V+, may be separated by a physical gap 1002, and one or a plurality of dielectric material layers or structures of differing permittivity may be located between conductive surface 1003 and conductive surface 1006. In the non-limiting, exemplary embodiment shown in FIG. 30, two dielectric materials of differing permittivity, namely, a first dielectric material 1004 having a first permittivity ε1, and a second dielectric material 1005 having a second permittivity ε2, are shown as being located between electrically conductive (electrode) surface 1003 and electrically conductive (electrode) surface 1006. The dielectric materials 1004 and 1005 may have differing thickness T1 and T2, respectively, and they may take any three-dimensional shape desired to achieve a specific net resulting DIV-E force 1011. Electrodes 1000 and 1001, and dielectric materials 1004 and 1005, may be fixed relative to one another by a structure 1007 which may be electrically isolating, such that a DIV-E force 1010 acting on a dielectric material is translated to a net resulting DIV-E force 1011 acting on the apparatus, or object to which the apparatus is attached, tending to motivate the object along a thrust vector or force 1011. In embodiments, the electric field that gives rise to the volumetric DIV-E forces acting on first dielectric material 1004 having a first permittivity ε1, and a second dielectric material 1005 having a second permittivity ε2 may be generated or sourced by any external electric field source, which may be man-made or naturally occurring, or any combination of the two.

In still further embodiments of the system and method of the invention, the invention may comprise a plurality of embodiments of the apparatus depicted in FIG. 30 as shown in FIG. 31. A series of combinations of dielectric materials 1004 and 1005, and electrodes 1000 and 1001 which may have applied voltages V+ and V−, may be placed in an arrangement as seen in FIG. 31. Thrust, i.e. force, on the object results from the summation of the resulting divergence in E-field (DIV-E) forces and electrostatic pressure forces on the conductive surfaces 1003 and 1006 (depicted in FIG. 30 for the singular case). The net force 1021 acting on the structure is the vector sum of all of the net resulting DIV-E forces 1011 from each of the “cells” depicted in FIG. 30. In other words, the structure of FIG. 31 may be a plurality of the structures shown in FIG. 30 combined in such a way as to produce a desired net force 1021.

If the divergence in E-field force, or DIV-E force, is established using one or more dielectric materials in the electric field, the electric field magnitude(s) are reduced by the dielectric constant of the dielectric materials, and the overall force may be reduced accordingly. Interestingly, since the force is a function of the permittivity of the dielectric materials, one can tailor their effect by applying time-varying V+ and V− having a frequency component, since most dielectrics have strong frequency dependence. For example, at certain frequencies, the permittivity of one dielectric material could be low while the other dielectric material(s) could be high. Use can be made of the fact that the dielectric materials’ permittivity may vary with frequency. By modulating the excitation frequency of applied voltages V+ and V−, changes in the resulting forces on the object may be achieved. Thus, frequency could be used as a way to steer the resulting force(s) on the object as forces decrease on one electrode and increase on another. If thrusters comprising the invention were oriented along different axes of the object, the object could be steered in a desired direction in three-dimensional space by the modulation of frequency of the excitation voltages V+ and V− for the various thrusters.

In embodiments, the inventive apparatus and method of the invention may comprise any number, size, three-dimensional shape, and arrangement of electrodes and dielectric materials to achieve one or more electrostatic pressure force(s), one or more divergence in E-field forces, or combinations of electrostatic pressure force(s) and divergence in E-field force(s) as may be desired. Computational methods may be utilized to determine the number, size, three-dimensional shape, and three-dimensional (i.e. geometric) arrangement of electrodes and dielectric materials to achieve one or more electrostatic pressure force(s), one or more divergence in E-field force, or combinations of electrostatic pressure force(s) and divergence in E-field force(s) as may be desired. The applied electrode voltages, or the external electric fields, may be time varying, and may be modulated in any manner, for example in frequency and in amplitude.

The computational method

The method of the invention may also comprise the step of using a computational method to determine the size, three-dimensional shape and three-dimensional arrangement of said plurality of electrically conductive surfaces so as to achieve a desired net resulting electrostatic pressure force acting on said object; wherein the computational method comprises the steps of:

• a. defining a size, three-dimensional shape and three-dimensional arrangement of each of the electrically conductive surfaces;
• b. determining the electric field intensity at each point along said electrically conductive surfaces;
• c. determining the resulting electrostatic pressure force acting on surfaces of said object;
• d. summing, in vector fashion, all resulting electrostatic pressure forces acting on each of said surfaces of said object to determine a computed total net resulting electrostatic pressure force acting on said object;
• e. comparing said computed total net resulting electrostatic pressure force to a desired net resulting electrostatic pressure force for acting on said object; and
• f. iteratively changing the size, three-dimensional shape and geometric arrangement of each of the electrically conductive surfaces or the value of the at least one voltage and repeating steps a. to e. until the desired net resulting electrostatic pressure force acting on said object is achieved.

In embodiments, the voltages applied to the electrodes to establish the electric field may be time varying or electrostatic. If the electric field is externally applied such as by any man-made or environmental source, the electric field may be time-varying or may be electrostatic.

Embodiments of the invention may comprise an apparatus and method that is configured according to the inventive principles set forth herein such that an object may be subject to one or more electrostatic pressure forces, one or more DIV-E forces, or any combination of one or more electrostatic pressure forces and one or more DIV-E forces.

Claims

We claim:

1. An apparatus for generating a force, comprising: an object having at least one surface, wherein said at least one surface is subject to an electric field; wherein the electric field acting on the at least one surface gives rise to an electrostatic pressure acting on the at least one surface; wherein the electrostatic pressure acting on the at least one surface gives rise to an electrostatic pressure force acting on the least one surface; wherein the magnitude and direction of the electrostatic pressure force acting on the at least one surface is determined by one or more parameters selected from the group consisting of 1) the magnitude and direction of the electric field acting on the surface or region; 2) the three-dimensional shape of the surface; and 3) the size of the surface; wherein the one or more parameters are determined so as to produce a desired at least one net electrostatic pressure force acting on the object.

2. A system for motivating a structure, comprising: a plurality of apparatuses for generating a force, each apparatus comprising: at least one object having at least one surface, wherein said at least one surface is subject to an electric field; wherein the electric field acting on the at least one surface gives rise to an electrostatic pressure acting on the at least one surface; wherein the electrostatic pressure acting on the at least one surface gives rise to an electrostatic pressure force acting on the least one surface; wherein the magnitude and direction of the electrostatic pressure force acting on the at least one surface is determined by one or more parameters selected from the group consisting of 1) the magnitude and direction of the electric field acting on the surface or region; 2) the three-dimensional shape of the surface; and 3) the size of the surface; wherein the one or more parameters are determined so as to produce a desired at least one net electrostatic pressure force acting on the object; wherein each apparatus comprising the plurality of apparatuses is attached either directly or indirectly to a structure to be motivated; wherein at least one resulting motivating force is applied to the structure, the at least one motivating force being the vector sum of all of the at least one net electrostatic pressure forces acting on the surfaces of the apparatuses.

3. An apparatus for generating a force, comprising: a structure comprising a configuration of dielectric material disposed in an electric field, wherein the configuration of dielectric material is characterized as having a volume; wherein the electric field within the volume is a divergent electric field; and wherein the divergent electric field within the volume acting on the configuration of dielectric material gives rise to a net divergent electric field force acting volumetrically on the configuration of dielectric material; and wherein the configuration of dielectric material and the structure are adapted to transfer the net divergent electric force to the structure.

4. The apparatus of claim 30, wherein the configuration of dielectric material comprises a plurality of individual dielectric materials, each individual dielectric material having a different permittivity than the other individual dielectric materials; and wherein the divergence of the electric field within the volume is caused at least in part by the effect of the difference in permittivity of the individual dielectric materials on the electric field.

5. An apparatus for generating a force, comprising: an object having at least one surface, wherein said at least one surface is subject to an electric field; wherein the electric field acting on the at least one surface gives rise to an electrostatic pressure acting on the at least one surface; wherein the electrostatic pressure acting on the at least one surface gives rise to an electrostatic pressure force acting on the least one surface; wherein the magnitude and direction of the electrostatic pressure force acting on the at least one surface is determined by one or more parameters selected from the group consisting of 1) the magnitude and direction of the electric field acting on the surface; 2) the three-dimensional shape of the surface; and 3) the size of the surface; wherein the one or more parameters are determined so as to produce a desired at least one net electrostatic pressure force acting on the object; and wherein said object further comprises a configuration of dielectric material disposed in a divergent electric field; wherein the divergent electric field acting on the configuration of dielectric material gives rise to a net divergent electric field force acting volumetrically on the configuration of dielectric material; and wherein the configuration of dielectric material and the structure are adapted to transfer the net divergent electric force to the object, such that a total net force acting on the object is the vector sum of the at least one net electrostatic pressure force acting on the object and the net divergent electric force acting on the object.

(The dependent claims 2 to 19, 21 to 29, and 31 to 32 are omitted for length; the complete text is at the source.)