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HAL Id: hal-03231614

https://hal.archives-ouvertes.fr/hal-03231614v2

Preprint submitted on 27 May 2021 (v2), last revised 29 Jul 2021 (v3)

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A New Design for the Gravelectric Generator

Fran de Aquino

To cite this version:

(2)

A New Design for the Gravelectric Generator

Fran De Aquino

Professor Emeritus of Physics, Maranhao State University, UEMA. Titular Researcher (R) of National Institute for Space Research, INPE

Copyright © 2021 by Fran De Aquino. All Rights Reserved.

www.frandeaquino.org deaquino@elo ternet.com.br in

In a previous paper, we have proposed a system called Gravelectric Generator to convert

Gravitational Energy directly into Electrical Energy [1]. Here we show a new design for the

Gravelectric Generator. This system can have individual outputs powers of several tens of kW. It

is easy to be built, and can easily be transported.

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

INTRODUCTION

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. In a previous paper we have

shown that this force can have gravitational nature (Gravitational Electromotive Force), and we have proposed a system to produce Gravitational Electromotive Force, called Gravelectric

Generator, which converts Gravitational Energy

directly into Electrical Energy [1].

A new design for the Gravelectric Generator is shown in this paper. This system can have individual outputs powers of several tens of kW. It is easy to be built, and can easily be transported.

THEORY

Consider a coil with iron core. Through the coil passes a electrical current i, with frequency . Thus, there is a magnetic field with frequency through the iron core. If the system is subject to a gravity acceleration , then the gravitational

forces acting on electrons H

f

H

f

g

( )

F

e , protons

( )

Fp and

neutrons

( )

Fp of the Iron core, are respectively expressed by the following relations

[

2]

( )

1

0

g

m

a

m

F

e

=

ge e

=

χ

Be e

( )

2 0g m a m Fp = gp p =

χ

Bp p

( )

3 0g m a m Fn = gn n =

χ

Bn n ge

m , and are respectively the

gravitational masses of the electrons, protons and

neutrons; , and are respectively the

inertial masses at rest of the electrons, protons and

neutrons. gp m mgn 0 e

m

m

e0

m

e0

The expressions of the correlation

factors

χ

Be,

χ

Bp and

χ

Bn are deduced in the paper [3] and Appendix of [1], and are given by

( )

4 1 10 5 . 1 1 2 1 1 56 . 45 1 2 1 2 4 23 2 2 2 2 0 4 4 22 2 ⎪⎭ ⎪ ⎬ ⎫ ⎪⎩ ⎪ ⎨ ⎧ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − × + − = = ⎪⎭ ⎪ ⎬ ⎫ ⎪⎩ ⎪ ⎨ ⎧ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − + − = f B f c m B r k rms e rms e xe Be

μ

π

χ

( )

5

1

56

.

45

1

2

1

2 2 2 2 0 4 4 2

⎪⎭

⎪⎩

+

=

f

c

m

B

r

p rms p Bp

μ

π

χ

( )

6

1

56

.

45

1

2

1

2 2 2 2 0 4 4 2

⎪⎭

⎪⎩

+

=

f

c

m

B

r

n rms n Bn

μ

π

χ

where

k

xe

1

.

9

(See Appendix [1]) ; ;

m

re≅1.4×10−10

r

p

=

1

.

2

×

10

−15

m

,rnrp. [1]. Note that

χ

Bn and

χ

Bpare negligible in respect to

Be

χ

.

It is known that, in some materials, called

conductors, the free electrons are so loosely held

by the atom and so close to the neighboring 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 amount. However, if some outside force acts upon the free electrons their movement becomes not random, and they move from atom to atom at the same direction of the applied force. This flow of electrons (their electric charge) through the conductor produces the electrical current, which is defined as a flow of electric charge through a medium

[

4

].

This charge is typically carried by moving electrons in a conductor, but it can also be carried by ions in an electrolyte, or by both ions and electrons in a plasma

[

5

].

(3)

2

)

way, of electromotive force (EMF). Usually, it is

of electrical nature . However, if the

nature of the electromotive force is gravitational

(

F

e

=

eE

(

Fe =mgeg

)

then, as the corresponding force of

electrical nature is

F

e

=

eE

, we can write that

( )

7

eE g mge =

According to Eq. (1) we can rewrite Eq. (7) as follows

( )

8

0

g

eE

m

e Be

=

χ

Now consider a wire with length

l

; cross-section area

S

and electrical conductivity

σ

. When a voltage is applied on its ends, the electrical current through the wire is i. Electrodynamics tell us that the electric field,

V

E, through the wire is uniform, and correlated with

V

and by means of the following expression

[

l

6

]

( )

9 ∫ = = Edl El V r r

Since the current

i

and the area

are

constants, then the current density

S

J

r

is also

constant. Therefore, it follows that

( )

( )

10 .

∫ = =

= JdS ES V l S

i r r

σ

σ

By substitution of E, given by Eq.(9), into Eq.(8) yields

(

m

0

e

)

gl

( )

11

V

=

χ

Be e

This is the voltage

V

between the ends of a metallic cylinder, when it has conductivity

σ

and cross-section area , and it is subjected to a uniform magnetic field with frequency ,

and a gravity (as shown in Fig.(1)) (The

expression of

S

H

B

f

H g Be

χ

is given by Eq. (4)).

Substitution of Eq. (11) into Eq. (10), gives

(

m0 e

)

gS

( )

12 i =

χ

Be e

σ

i f = fH ←iH, fH V l f=fH

Fig. 1 – The voltage V between the ends of a metallic cylinder when it is subjected to a uniform magnetic field BH with frequency fH,and gravity

g(as shown above).

g

r

H

H

f

B ,

r

Substitution of Eq. (4) into Eq. (11) and Eq.(12) yields respectively

( )

13 1 10 5 . 1 1 2 1 2 0 4 23 gl e m f B V rms e ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎪⎭ ⎪ ⎬ ⎫ ⎪⎩ ⎪ ⎨ ⎧ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − × + − = and

( )

14 1 10 5 . 1 1 2 1 0 2 4 23 gS e m f B i rms e

σ

⎠ ⎞ ⎜ ⎝ ⎛ ⎪⎭ ⎪ ⎬ ⎫ ⎪⎩ ⎪ ⎨ ⎧ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − × + − = If Brms =BH(rms) =1.2T and

f

=

f

H

=

60

Hz

, then Eq. (13) and (14) give, respectively

( )

15

03

.

1

l

V

( )

16

03

.

1

S

i

=

σ

For iron wire # 12 BWG,

(

φ

=2.77mm; ), with length

(See Fig. 2) given by

m S / 10 04 . 1 × 7 =

σ

l

(

)

[

]

(

)

m

l

2

.

214

4

.

1

8

.

212

15

.

0

55

.

0

2

15

.

0

2

55

.

0

2

76

2

=

+

=

×

×

+

×

+

×

+

=

=

the Eq. (15) and Eq. (16) give, respectively

( )

17

220volts

V

and ( ) 8.4 106 2 64.4

( )

18 max A i theoretical = ×

φ

=

However, the maximum current supported by an

iron wire # 12 BWG,

φ

=2.77mm is

approximately13 A, i.e., imax(real) =13A.

Consequently, in this case, the maximum output power of the Gravelectric Generator is *

( ) max( ) 2.8 3.7

( )

19

max Vi kW HP

P real = real ≅ ≅

Note that, if the diameter of the iron wire increases up to

φ

=13mm the value of

increases up to (See Eq.

(18)) and the power would increase up to . However, the maximum current supported by an iron wire with diameter

is approximately 360A. Thus,

(theoretical imax )

1419

.

6

A

kW

312

mm

13

( ) 220 360 79.2 106

( )

20 max V A kW HP P real = × = ≅ .

This power is sufficient to feed the electric motor

of most electric cars.

*

(4)

(b) Top view

(5)

4

(b) Top view

(6)
(7)

6

References

[1] De Aquino, F. (2016).The Gravelectric Generator: Conversion of Gravitational Energy Directly Into

Electrical Energy, Bulletin of Pure & Applied

Sciences- Physics Year : 2016, Volume : 35d, Issue : 1and2 First page : ( 55) last page : ( 64) Print ISSN : 0970-6569. Online ISSN : 2320- 3218. DOI : 10.5958/2320-3218.2016.00008.7 [2] 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

[3] De Aquino, F. (2012). Superconducting State

generated by Cooper Pairs bound by Intensified Gravitational Interaction.

Available at http://vixra.org/abs/1207.0008 , v2. [4] Valkengurg, V., (1992) Basic Electricity, Prompt Publications, 1-38.

[5] Fischer-Cripps, A., (2004). The electronics

companion. CRC Press, p. 13,

ISBN 9780750310123.

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

[7] U.S. Energy Information Administration (2013)

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