Electrical Energy, Generation of Electrical Energy

The Gravelectric Generator Fran de Aquino

To cite this version:

Fran de Aquino. The Gravelectric Generator: Conversion of Gravitational Energy directly into Elec- trical Energy. 2016. hal-01359690v5

HAL Id: hal-01359690 https://hal.archives-ouvertes.fr/hal-01359690v5 Preprint submitted on 30 Dec 2016

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The Gravelectric Generator Conversion of Gravitational Energy directly into Electrical Energy

The electrical current arises in a conductor when an outside force acts upon the free electrons of the conductor. This force is called, in a generic way, of electromotive force (EMF). Usually, it has electrical nature. Here, we show that it can have gravitational nature (Gravitational Electromotive Force). This fact led us to propose an unprecedented system to convert Gravitational Energy directly into Electrical Energy. This system, here called of Gravelectric Generator, can have individual outputs powers of several tens of kW or more. It is easy to be built, and can easily be transported from one place to another, on the contrary of the hydroelectric plants, which convert Gravitational Energy into Hydroelectric energy.

Key words: Gravitational Electromotive Force, Gravitational Energy, Electrical Energy, Generation of Electrical Energy.

1. Introduction The research for generate Gravitational there is a magnetic field through the iron core. If Electromotive Force (Gravelectric Effect) began the system is subject to a gravity acceleration g with Faraday [1]. He had a strong conviction that (See Fig.1), then the gravitational forces acting there was a correlation between gravity and on electrons (Fe ), protons (F ) and neutrons electricity, and carried out several experiments p trying to detect this Gravelectric Effect (Fp ) of the Iron core, are respectively expressed experimentally. Although he had failed several by the following relations [4] times, he was still convinced that gravity must be = = χ gmamF (1) related to electricity. Faraday felt he was on the eBeegee 0 brink of an extremely important discovery. His = = χ pBppgpp 0 gmamF (2) Diary on August 25, 1849 shows his enthusiastic = = χ gmamF (3) expectations: nBnngnn 0 “It was almost with a feeling of awe that I went to mge , mgp and mgn are respectively the work, for if the hope should prove well founded, how gravitational masses of the electrons, protons and great and mighty and sublime in its hitherto unchangeable character is the force I am trying to neutrons; me0 , me0 and me0 are respectively the deal with, and how large may be the new domain of inertial masses at rest of the electrons, protons knowledge that may be opened up to the mind of and neutrons. man.” Here we show how to generate Gravitational Electromotive Force, converting Gravitational Energy directly into electricity. r This theoretical discovery is very important B because leads to the possibility to build the Iron core Gravelectric Generator, which can have individual outputs powers of several tens of kW. r g 2. Theory Fig. 1 – An iron core of a coil subjected to a r In a previous paper, we have proposed a gravity acceleration gr and magnetic field B system to convert Gravitational Energy directly with frequency f . into Electrical Energy [2]. This system uses Gravity Control Cells (GCCs). These GCCs can be replaced by the recently discovered Quantum The expressions of the correlation Controllers of Gravity (QCGs) [3], which can factors χ , χ and χ are deduced in the produce similar effect. In this paper, we propose Be Bp Bn a simplification for this system, without using previously mentioned paper, and are given by GCCs or QCGs. ⎧ ⎡ 442 ⎤⎫ ⎪ 56.45 π Br rmse ⎪ Under these conditions, the system shown χBe ⎨ ⎢ 121 +−= − ⎥⎬ ()41 μ fcm 2222 in the previously mentioned paper reduces to a ⎩⎪ ⎣⎢ 0 e ⎦⎥⎭⎪ coil with iron core. Through the coil passes a electrical current i , with frequency f . Thus, 2

442 ⎧ ⎡ ⎤⎫ momentum: ΔxΔp ≳ , making Δ = vmp ee , ⎪ 56.45 π Br rmsp ⎪ h χ ⎢ 121 +−= − ⎥ 51 Bp ⎨ 2222 ⎬ () where v is the group velocity of the electrons, ⎢ μ fcm ⎥ e ⎩⎪ ⎣ 0 p ⎦⎭⎪ which is given by = h mkv eFe . Then, the ⎪⎧ ⎡ 56.45 π Br 442 ⎤⎪⎫ result is χ ⎢ 121 +−= rmsn − ⎥ ()61 Bn ⎨ 2222 ⎬ 11 ⎢ μ0 n fcm ⎥ h ⎩⎪ ⎣ ⎦⎭⎪ Δx≳ == 1 ()8 kvm 2 According to the free-electron model, Fee ()3π VN 3 the electric current is an electrons gas In the case of Iron, propagating through the conductor (free ( VN ×≅ 104.8 28 / melectrons 3 ), Eq.(8) gives electrons Fermi gas). If the conductor is Δx −10 made of Iron, then the free-electrons density re = ≳ ×101 m (9) 28 3 * 2 is VN ×≅ 104.8 / melectrons . Comparing with the value given by Eq. (7), we The theory tells us that the total energy of −10 can conclude that re ×≅ 104.1 m is a highly the electrons gas is given by where NEF 53 , plausible value for the electrons radii, when the 1 = 22 2mkE ; =(3π2 VNk )3(The Fermi sphere). electrons are inside the mentioned free electrons h eFF F Fermi gas. On the other hand, the radius of Consequently, the electrons gas is subjected to a protons inside the atoms (nuclei) is pressure − 53 = 52 VNEdVdEN . This −15 ()()F F r ×= 102.1 m, . Then, considering these † p ≅ rr pn gives a pressure of about 37GPa . This −10 enormous pressure puts the free-electrons very values and assuming re ×≅ 104.1 m, we obtain close among them, in such way that if there are from Eqs. (4) (5) and (6) the following expressions: 28 3 ×104.8 electrons inside 1m , then we can 4 ⎪⎧ ⎡ B ⎤⎪⎫ ⎢ 18 rms −×+−= ⎥ 1011046.1121 conclude that the each electron occupies a χBe ⎨ 2 ⎬ () − 329 4 3 ⎪ ⎢ f ⎥⎪ volume:Ve ×= 102.1 m . Assuming e = 3 πrV e , ⎩ ⎣ ⎦⎭ for the electron’s volume, then we get ⎪⎧ ⎡ B4 ⎤⎪⎫ −10 χχ ⎢ −9 rms −×+−=≅ ⎥ 1111035.2121 r ×≅ 104.1 m (7) BpBn ⎨ 2 ⎬ () e ⎪ ⎢ f ⎥⎪ It is known that the electron size depends ⎩ ⎣ ⎦⎭ of the place where the electron is, and that it can where Brms is the rms intensity of the magnetic vary from the Planck length field through the iron core and f is its oscillating 10 −35 m ( = cGl 10~ −353 m) up to10 −10 m , planck h frequency. Note that χBn and χ Bp are negligible which is the value of the spatial extent of the in respect to χ Be . electron wavefunction, Δx , in the free electrons It is known that, in some materials, called Fermi gas (the electron size in the Fermi gas is conductors, the free electrons are so loosely held ≡Δ 2rx e ). The value of Δx can be obtained by the atom and so close to the neighboring from the Uncertainty Principle for position and atoms that they tend to drift randomly from one atom to its neighboring atoms. This means that the electrons move in all directions by the same * = ρ ANVN ,; N ×= 26atoms/1002.6 kmole 0 ironiron 0 amount. However, if some outside force acts

is the Avogadro’s number; ρiron is the matter density of upon the free electrons their movement becomes 3 not random, and they move from atom to atom at the Iron (7,800 kg/m ) and A is the molar mass of the iron the same direction of the applied force. This flow Iron ( 55.845kg/kmole). † of electrons (their electric charge) through the The artificial production of diamond was first achieved by conductor produces the electrical current, which H.T Hall in 1955. He used a press capable of producing pressures above 10 GPa and temperatures above 2,000 °C is defined as a flow of electric charge through a [5]. Today, there are several methods to produce synthetic medium [6]. This charge is typically carried by diamond. The more widely utilized method uses high moving electrons in a conductor, but it can also pressure and high temperature (HPHT) of the order of be carried by ions in an electrolyte, or by both 10 GPa and 2500°C during many hours in order to produce a single diamond. ions and electrons in a plasma [7]. Thus, the electrical current arises in a conductor when an outside force acts upon its 3 free electrons. This force is called, in a generic amount of Gravitational Energy directly into way, of electromotive force (EMF). Usually, it is electrical energy. Basically, it consists in a Helmholtz coil placed into the core of a Toroidal of electrical nature (e = eEF ). However, if the nature of the electromotive force is gravitational coil. The current iH through the Helmholtz coil

( = gee gmF ) then, as the corresponding force of has frequency f H . The wire of the toroidal coil is made of pure iron (μ ≅ 4000 ) with electrical nature is e = eEF , we can write that r = eEgm (12) insulation paint. Thus, the nucleus of the ge Helmholtz coil is filled with iron wires, which According to Eq. (1) we can rewrite Eq. (12) as are subjected to a uniform magnetic field B follows H with frequency f H , produced by the Helmholtz χ eBe 0 = eEgm (13) coil. Then, according to Eq. (10), we have that Now consider a wire with length l ; cross-section ⎧ ⎡ 4 ⎤⎫ area S and electrical conductivity σ . When a ⎪ 18 B ()rmsH ⎪ χBe ⎨ ⎢ ×+−= 1046.1121 − ⎥⎬ ()181 voltage V is applied on its ends, the electrical ⎢ f 2 ⎥ current through the wire is i . Electrodynamics ⎩⎪ ⎣ H ⎦⎭⎪ tell us that the electric field, E , through the wire By substitution of Eq.(18) into Eq.(16), we obtain is uniform, and correlated with V and l by ⎧ ⎡ 4 ⎤⎫ ⎪ 18 B ()rmsH ⎪⎛m ⎞ means of the following expression [8] V ⎨ ⎢ ×+−= 1046.1121 −1⎥⎬⎜ e0 ⎟gl ()19 r r ⎢ f 2 ⎥ ⎝ e ⎠ ∫ == ElldEV (14) ⎩⎪ ⎣ H ⎦⎭⎪ Since the current i and the area S are If B = 8.0 T ‡ and = 2.0 Hzf , then Eq. r ()rmsH H constants, then the current density J is also (19) gives constant. Therefore, it follows that ≅ 43.0 lV (20) r r ∫ . === σσ ()SlVESSdJi (15) In order to obtain V = 220volts , the total length By substitution of E , given by Eq.(14), into l of the iron wire used in the Toroidal coil must Eq.(13) yields have 511.63m. On the other hand, the maximum = χ ()eBe 0 glemV (16) output current of the system (through the This is the voltage V between the ends of a wire, Toroidal coil ) (See Fig.3 (a)) will be given by when the wire with conductivityσ and cross- (Eq.17), i.e., section area S , is subjected to a uniform imax = 43.0 σS (21) magnetic field B with frequency f and a gravity Since the electrical conductivity of the iron is σ ×= 7 /1004.1 mS and, assuming that the g (as shown in Fig.(2)) (The expression of χ Be is diameter of the iron wire is 4mm, given by Eq. (4)). φironwire = 2 − 25 Substitution of Eq. (16) into Eq. (15), gives ( S = πφironwire ×= 1025.14 m ), then we get max = χ ()eBe 0 σgSemi (17) imax ≅ 56 Amperes (22) This is the maximum output current of the system This is therefore, the maximum output current of for a given value of χ Be . this Gravelectric Generator. Consequently, the S maximum output power of the generator is

max = ViP max ≅ 3.12 kW (23)

r Note that, here the Helmholtz coil has two turns B V only, both separated by the distance R (See Fig.3

wire (a)). By using only 2 turns, both separated by a

large distance, it is possible strongly to reduce the σ capacitive effect between the turns. This is highly gr Fig. 2 – The voltage V between the ends of a wire when it is subjected to a uniform magnetic field B ‡ The magnetic field at the midpoint between the coils with frequency f and gravity g (as shown above). is B = 71.0 μ μ RNi . Here μ ≅ 4000 (pure iron; H r 0 r Now consider the system shown in Fig.3. commercially called electrical pure iron (99.5% of It is an electricity generator (Gravelectric iron and less than 0.5% of impurities.) Generator). It was designed to convert a large 4

Wire spiral (Iron with insulation R R paint)

Helmholtz Coil GRAVITATIONAL R Electromotive Force

(a)

i Gravitational Electromotive Force

l (total length)

Wire spiral (in red)

(b)

Fig. 3 – Schematic Diagram of the Gravelectric Generator (Based on a gravity control process patented on 2008 (BR Patent number: PI0805046-5, July 31, 2008).

5 relevant in this case because the extremely-low that in this case, we must have d = 1.14 mmr . frequency = 2.0 Hzf would strongly increase the Thus, if the ferromagnetic tube is covered with capacitive reactance ( C = 21 πfCX ) associated insulation of 1mm thickness, then the outer to the inductor. radius of the ferromagnetic tube is

Let us now consider a new design for the = dout − mmrr = 1.131 mm. The area of the cross- Gravelectric Generator. It is based on the device section of the ferromagnetic tube, S , must be shown in Fig. 4 (a). It contains a central pin, ft which is involved by a ferromagnetic tube. When equal to the area of the pin cross-section, i.e., r 22 2 the device is subjected to gravity g and a ft π ( out inner ) =−= πrrrS pin (27) magnetic field with frequency f and H where rinner is the inner radius of the intensity BH (as shown in Fig. 4 (a)) the ferromagnetic tube. magnetic field lines are concentrated into the Therefore, if the pin is covered with ferromagnetic tube, and a Gravitational insulation of 0.5mm thickness, then we can

Electromotive Force is generated inside the tube, conclude that inner = pin + 5.0 mmrr . Consequently, propelling the free electrons through it. The pin is we obtain from Eq. (27) that made with diamagnetic material (Copper, Silver, = 9mmr (28) etc.,) in order to expel the magnetic field lines pin from the pin (preventing that be generated a Then, the area of the cross-section of the pin is 2 − 24 Gravitational Electromotive Force in the pin, pin πrS pin ×== 105.2 m (29) opposite to that generated in the ferromagnetic On the other hand, the maximum output tube). current of the Gravelectric Generator shown in Several similar devices (N devices) are Fig.4, according to Eq. 17, will be given by jointed into a cylinder with radius R and i = 43.0 σS (30) height R . The pin, the ferromagnetic tube and max pin the cylinder have length R (See Fig. 4 (a) and where σ is the electrical conductivity of the (b)). On the external surface of the cylinder there ferromagnetic tube. If the ferromagnetic tube is 6 § is a Helmholtz coil with two turns only. The made with Mumetal(σ ×= /101.2 mS ) , then current through the Helmholtz coil has frequency we get r i ≅ 7.225 Amperes (31) f H in order to generate the magnetic field BH . max The devices are connected as shown in Fig. 4 (c). This is therefore, the maximum output current of Since the pin and the ferromagnetic tube this Gravelectric Generator. Consequently, the have length R , then the total length of the maximum output power of this generator is conductor through the Gravelectric Generator, max = ViP max ≅ 6.49 kW (23) l , is given by = (2RNl ). Equation (20) tells us that in order to obtain V = 220volts (assuming 3. Conclusion the same value of χ = 43.0 given by Eq. (18)) These results show that the discovery of the Be Gravelectric Generators is very important, the total length l must have 511.63m. This because changes completely the design of the means that electricity generators, becoming cheaper the ()RN = 63.5112 m (24) electricity generation. They can have individual If the area of the cross-section of the cylinder outputs powers of several tens of kW or more. In 2 addition, they are easy to be built, and can easily above mentioned is = πRS , and the area of the be transported. 2 cross-section of the device is = πrS dd , then assuming that ≅ 2.1 NSS , we can write that d 2 ≅ 8.0 ()rRN d (25) Substitution of Eq. (25) into Eq. (24) gives 5.1 rd = 056.0 R (26 ) § Note that, if the ferromagnetic tube is made with Equation (24) tells us that for electrical pure iron (σ ×= 7 /1004.1 mS ), the N = 640 devices, the cylinder radius must be maximum current increases to i = 7.1117 A . ≅ 40.0 mR . On the other hand, Eq. (26) tells us max 6

BH , fH Magnetic field lines

Insulation 1mm thick Ferromagnetic tube Gravitational Electromotive Force Fundamental Device R i Insulation 0.5 mm thick Diamagnetic pin (Copper)

rpin

rinner

router

rd (a)

Cylinder R

Helmholtz Coil N devices R

(b)

(c)

Fig. 4 – Schematic Diagram of another type of Gravelectric Generator

APPENDIX ⎧ ⎡ 4 ⎤⎫ ⎪ 23 B ()rmsH ⎪⎛m ⎞ The Eq. (4) of this work is derived from V ⎨ ⎢ ×+−= 105.1121 −1⎥⎬⎜ e0 ⎟ ()IVgl ⎢ f 2 ⎥ ⎝ e ⎠ the general equation below (See Eq. (20) of ⎩⎪ ⎣ H ⎦⎭⎪ reference [9]). If B ()rmsH = 8.0 T and fH =60Hz, then Eq.(III)gives ⎧ ⎡ 4222 ⎤⎫ ⎪ 56.45 π Br rmsxe ⎪ χBe ⎨ ⎢ 121 +−= −1⎥⎬= ≅ 46.0 lV (V) μ frcm 218222 ⎩⎪ ⎣⎢ 0 ee ⎦⎥⎭⎪ Note that this equation is approximately equal to Eq. (20). Therefore, the only change is in the ⎧ ⎡ 44222 ⎤⎫ frequency of the voltage (and current); previously ⎪ 56.45 π Brk rmsexe ⎪ ⎨ ⎢ 121 +−= −1⎥⎬ ()I 0.2Hz and now 60Hz (See Fig.5). ⎢ μ fcm 2222 ⎥ ⎩⎪ ⎣ 0 e ⎦⎭⎪ , fi = fH

Therefore, Eq. (4) expresses χ Be in the particular ←iH, fH case of k = .1 However, the values obtained in r xe V l , fB Eqs. (7) and (8) led us to think that, in the Fermi HH f=fH gas, kxe >1. This conclusion is based on the following: while r ×≅ 104.1 −10m (See Eq.(7)), xe gr the value of re is given by Fig. 5 – The voltage (and current ) with −1 V i Δ≅ xr 2 1 3π 2 VN 3 ×1037.0 −10m, which e ≳ 2 ()≳ frequency equal to f H , now H = 60 Hzf . shows that, in the Fermi gas, r , is not smaller e The equations (5) and (6) are also similarly than ×1037.0 −10 m . Therefore, we can write that derived from the general expression, i.e., min −10 −10 4222 re ×≅ 1037.0 m. Since rxe ×≅ 104.1 m, then it ⎧ ⎡ ⎤⎫ ⎪ 56.45 π Br rmsxp ⎪ max min χ ⎢ 121 +−= −1⎥ = follows that rrk ≅= 7.3 . On the other hand, Bp ⎨ 218222 ⎬ exexe ⎪ ⎢ μ0 pp frcm ⎥⎪ max min max ⎩ ⎣ ⎦⎭ assuming that ≅ rr xee , we get rrk exexe ≅= 1. Thus, the value of k is in the interval ⎧ ⎡ 44222 ⎤⎫ xe ⎪ 56.45 π Brk rmspxp ⎪ ⎢ ⎥ min max ⎨ 121 +−= 2222 −1 ⎬ ()V << kkk xexexe .The geometric media for k xe ,i.e., ⎢ μ fcm ⎥ ⎩⎪ ⎣ 0 p ⎦⎭⎪ kkk maxmin ≅= 9.1 , produces a value that xexexe ⎧ ⎡ 4222 ⎤⎫ ⎪ 56.45 π Br rmsxn ⎪ possibly should be very close of the real value of χBn ⎨ ⎢ 121 +−= 218222 −1⎥⎬ = ⎪ ⎢ μ0 nn frcm ⎥⎪ k xe . Then, assuming that ≅ kk xexe and ⎩ ⎣ ⎦⎭ substituting this value into Eq. (I), we get an ⎧ ⎡ 44222 ⎤⎫ approximated value for χ , given by ⎪ 56.45 π Brk rmsnxn ⎪ Be ⎨ ⎢ 121 +−= −1⎥⎬ ()VI μ fcm 2222 ⎧ ⎡ 4 ⎤⎫ ⎩⎪ ⎣⎢ 0 n ⎦⎥⎭⎪ ⎪ 23 Brms ⎪ χBe ⎨ ⎢ −×+−≅ 1105.1121 ⎥⎬ ()II With the dimensions previously f 2 ⎩⎪ ⎣⎢ ⎦⎥⎭⎪ mentioned the free electrons, if the Fermi gas, Note that the numerical coefficient of the term have the size of atoms, and therefore they can not 24 5 cross the atoms of the conductor. Thus, passing fB of this equation is about×1002.1 times rms far from the atoms nuclei, they practically do not greater than the equivalent coefficient of Eq. (10). affect the structures of the protons which are in Making rms = BB (rmsH ) and = ff H (See Eq. the nuclei of these atoms. In this way, we have

(18)), then Eq. (II) can be rewritten as follows that ≅ rr pxp → k xp ≅ 1. Substitution of this ⎧ ⎡ 4 ⎤⎫ value into Eq. (V) leads to Eq. (5). ⎪ B ()rmsH ⎪ ⎢ 23 ⎥ In the case of the neutrons, due to its χBe ⎨ ×+−= 105.1121 2 −1 ⎬ ()III ⎢ f ⎥ electric charge be null, we obviously have ⎩⎪ ⎣ H ⎦⎭⎪ k = 1. Substitution of this value into Eq. (VI) Substitution of Eq. (III) into Eq. (16), xn yields leads to Eq. (6). 8

References

[1] Cantor, G. (1991) Faraday’s search for the Gravelectric effect, Phys. Ed. 26, 289.

[2] De Aquino, F. (2012). A System to convert Gravitational Energy directly into Electrical Energy. Available at http://vixra.org/abs/1205.0119

[3] De Aquino, F. (2016) Quantum Controller of Gravity. Available at https://hal.archives-ouvertes.fr/hal-01320459

[4] De Aquino, F. (2010) Mathematical Foundations of the Relativistic Theory of Quantum Gravity, Pacific Journal of Science and Technology, 11 (1), pp. 173-232. Available at https://hal.archives-ouvertes.fr/hal-01128520

[5] Hall, H. T. (1960). "Ultra-high pressure apparatus". Rev. Sci. Instr. 31 (2): 125.

[6] Valkengurg, V., (1992) Basic Electricity, Prompt Publications, 1-38.

[7] Fischer-Cripps, A., (2004) The electronics companion. CRC Press, p. 13, ISBN 9780750310123.

[8] Quevedo, C. P. (1977) Eletromagnetismo, McGraw- Hill, p. 107-108.

[9] De Aquino, F. (2012) Superconducting State generated by Cooper Pairs bound by Intensified Gravitational Interaction, Available at http://vixra.org/abs/1207.0008 , v2.