Recent Trends in Aerospace Design and Optimization

8/9/2019 Recent Trends in Aerospace Design and Optimization

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SAROD-2005

1 PHYSICAL PRINCIPLES FORPROPULSION SYSTEMS*

All propulsion systems in use today are based onmomentum conservation and rely on fuel [1]. There is oneexception, namely gravity assist turns that use thegravitational fields of planets to accelerate a spacecraft.The only other long-range force known is theelectromagnetic force or Lorentz force, acting on chargedbodies or moving charges. Magnetic fields around planetsor in interstellar space are too weak to be used as a means

for propulsion. In the solar system and in the universe asknown today, large-scale electromagnetic fields thatcould accelerate a space vehicle do not seem to exist.

However, magnetic and electric fields can easily begenerated, and numerous mechanisms can be devised toproduce ions and electrons and to accelerate chargedparticles. The field of magnetohydrodynamics recentlyhas become again an area of intensive research, since

University of Applied Sciences and HPCC-Space GmbH,Salzgitter, Germany# IGW, Leopold-Franzens University, Innsbruck, Austria

Aerodynamisches Institut, RWTH Aachen, Germany

* ESA-ESTEC, Noordwijk, The Netherlands J. Huser, Walter DrscherSAROD-2005Published in 2005 by Tata McGraw-Hill

both high-performance computing, allowing thesimulation of these equations for realistic two- and three-dimensional configurations, and the progress ingenerating strong magnetic and electric fields havebecome a reality. Although the main physical ideas ofMHD were developed in the fifties of the last century, theactual design of efficient and effective propulsion systemsonly recently became possible.

One weakness that all concepts of propulsion have incommon today is their relatively low thrust. An analysisshows that only chemical propulsion can provide thenecessary thrust to launch a spacecraft. Neither fission

nor fusion propulsion will provide this capability. MHDpropulsion is superior for long mission durations, butdelivers only small amounts of thrust. Space flight withcurrent propulsion technology is highly complex, andseverely limited with respect to payload capability,reusability, maintainability. Above all it is noteconomical. In addition, flight speeds are marginal withrespect to the speed of light. Moreover, trying only to flya spacecraft of mass 105 kg at one per cent (non-relativistic) the speed of light is prohibitive with regard tothe kinetic energy to be supplied. To reach velocitiescomparable to the speed of light, special relativityimposes a heavy penalty in form of increasing mass ofthe spacecraft, and renders such an attempt completelyuneconomical.

The question therefore arises whether other forces(interactions) in physics exist, apart from the four known

Physical and Numerical Modeling forAdvanced Propulsion Systems

Jochem Hauser

#

Walter Drscher

#

Wuye Dai

Jean-Marie Muylaert

*

Abstract

The paper discusses the current status of space transportation and then presents an overview of the two mainresearch topics on advanced propulsion as pursued by the authors, namely the use of electromagnetic interaction(Lorentz force) as well as a novel concept, based on ideas of a unified theory by the late German physicist B.Heim, termed field propulsion. In general, electromagnetics is coupled to the Navier-Stokes equations and leadsto magnetohydrodynamics (MHD). Consequently, the ideal MHD equations and their numerical solution basedon an extended version of the HLLC (Harten-Lax-van Leer-Contact discontinuity) technique is presented. Inparticular, the phenomenon of waves in MHD is discussed, which is crucial for a successful numerical scheme.Furthermore, the important topic of a numerically divergence free magnetic induction field is addressed. Two-dimensional simulation examples are presented. In the second part, a brief discussion of field propulsion is given.

Based on Einstein's principle of geometrization of physical interactions, a theory is presented that shows thatthere should be six fundamental physical interactions instead of the four known ones. The additional interactions(gravitophoton force) would allow the conversion of electromagnetic energy into gravitational energy where thevacuum state provides the interaction particles. This kind of propulsion principle is not based on the momentumprinciple and would not require any fuel. The paper discusses the source of the two predicted interactions, theconcept of parallel space (in which the limiting speed of light is nc, n being an integer, c denoting vacuum speedof light), and presents a brief introduction of the physical model along with an experimental setup to measure andestimate the so called gravitophoton (Heim-Lorentz) force. Estimates for the magnitude of magnetic fields arepresented, and trip times for lunar and Mars missions are given.

Key Words: physical principles of advanced propulsion,electromagnetic propulsion, numerical solution of the MHDequations; field propulsion, six fundamental physical interactions, conversion of electromagnetic energy intogravitational energy, Heim-Lorentz force.


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2 Jochem Hauser, Walter Drscher, Wuye Dai, and Jean-Marie Muylaert

interactions in Nature, namely long-range gravitationaland electromagnetic interactions, and on the nuclear scalethe weak (radioactive decay, neutron decay is anexample) and strong interactions (responsible for theexistence of nuclei)? It has long been surmised that,because of their similarity, electromagnetic fields can beconverted into gravitational fields. The limits ofmomentum based propulsion as enforced by governingphysical laws, are too severe, even for the more advancedconcepts like fusion and antimatter propulsion, photondrives and solar and magnetic sails. Current physics doesnot provide a propulsion principle that allows a lunarmission to be completed within hours or a mission toMars within days. Neither is there a possibility to reachrelativistic speeds (at reasonable cost and safety) nor aresuperluminal velocities conceivable. As mentioned byKrauss [2], general relativity (GR) allows metricengineering, including the so-called Warp Drive, butsuperluminal travel would require negative energydensities. However, in order to tell space to contract(warp), a signal is necessary that, in turn, can travel only

with the speed of light. GR therefore does not allow thiskind of travel.

On the other hand, current physics is far from providingfinal answers. First, there is no unified theory thatcombines general relativity (GR) and quantum theory(QT) [3-6]. Second, not even the question about thenumber of fundamental interactions can be answered.Currently, four interactions are known, but theory cannotmake any predictions on the number of existinginteractions. Quantum numbers, characterizingelementary particles (EP) are introduced ad hoc. Thenature of matter is unknown. In EP physics, EPs are

assumed to be point-like particles, which is in clearcontradiction to recent lopp quantum theory (LQT) [3, 4]that predicts a granular space, i.e., there exists a smallestelemental surface. This finding, however, is also incontradiction with string theory (ST) [5, 6] that uses

point-like particle in 4 but needs 6 or 7 additional real

dimensions that are compactified (invisible, Plancklength). Neither LQT nor ST predict measurable physicaleffects to verify the theory.

Most obvious in current physics is the failure to predicthighly organized structures. According to the second lawof thermodynamics these structures should not exist. Incosmology the big bang picture requires the universe to

be created form a point-like infinitely dense quantity thatdefies any logic. According to Penrose [7] the probabilityfor this to happen is zero. Neither the mass spectrum northe lifetimes of existing EPs can be predicted. It thereforecan be concluded that despite all the advances intheoretical physics, the major questions still cannot beanswered. Hence, the goal to find a unified field theory isa viable undertaking, because it might lead to novelphysics [8], which, in turn, might allow for a totallydifferent principle in space transportation.

2 MAGNETO-HDYRODYNAMICPROPULSION

Because of the inherent limitations of chemicalpropulsion to deliver a specific impulse better than 450 s,research concentrated on electromagnetic propulsion

already in the beginning of the space flight area, i.e., inthe fifties of the last century. Electric and plasmapropulsion systems were designed and tested some 35years ago, but until recently have not made a contributionto the problem of space transportation. Allowing for amuch higher specific impulse of up to 104 s, the totalthrust delivered by a plasma propulsion system istypically around 1 N and some 20 mN for ion propulsion.No payload can be lifted form the surface of the earthwith this kind of propulsion system. On the other hand,operation times can be weeks or even months, andinterplanetary travel time can be substantially reduced. Inaddition, spacecraft attitude control can be maintained foryears via electric propulsion.

2.1 MHD Equations

The MHD equations are derived from the combination offluid dynamics (mass, momentum, and energyconservation) and Maxwell equations. In addition,

generalized Ohm's law, j=evB, is used and

displacement current E/ t in Ampere's law is

neglected. The curl of E in farady's law is replaced bytaking the curl of j and inserting it into Faraday's law.

Making use of the identity B=2B, with

B=0, one obtains the equation for the B field.

Introducing the magnetic Reynolds number

Rem=vL/ m,m=1

0, which denotes the ratio of the

vB convection term and the m

2

B diffusion term, the ideal MHD equations are obtainedassuming an infinitely high conductivity of theplasma. The MHD equations can thus be written inconservative form

U t

F=0

(1)

U=[vE

B ] (2)

F=

[

v

v vPIB BEPvB vB

v BB v

](3)

where is mass density, v is velocity, andEdenotes totalenergy. P includes the magnetic pressureB2/2m.


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Physical and Numerical Modeling for Advanced Propulsion Systems 3

E=p/1u2v2w2/2

+Bx2By

2Bz2/2m

(4)

P=pBx2By

2Bz2 /2m . (5)

In additional to the above equations, the magnetic field

satisfies the divergence free constraint B=0 . This

is not an evolution equation and has to be satisfiednumerically at each iteration step for any kind of grid.Special care has to be taken to guarantee that thiscondition is satisfied, otherwise the solution may becomenon-physical. Due to the coupling of the inductionequation to the momentum and energy equations, thesequantities would also be modeled incorrectly.

2.2 Numerical Solution of the MHD Equations

The above ideal MHD equations constitute a non-strictlyhyperbolic partial differential system. From the analysisof the governing equations in one-dimensional spatio-temporal space, proper eigenvector and eigenvalues canbe found. The seven eigenvalues of the MHD equations

are (the details of the MHD waves are presented in [13]):

[u ,ucA, uc s,ucf] . All velocity component

are in the direction of propagation of the wave.

2.2.1 MHD-HLLC Algorithm

In order to approximate the flux function, the appropriate

Riemann problem is solved on the domain xl, xr and

integrated in time from 0 totf. A major task is the

evaluation of the wave propagation speeds.

q*=sM=

rqr srqrlq lslq lp lprBnl2 Bnr

2

r srqrlslq l

(6)

P*=slq q

*q PBn2Bn

* 2 . (7)

In order to evaluate the integrals, the (yet unknown)

signal speeds sland sr are considered, denoting the

fastest wave propagation in the negative and positive x-directions. It is assumed, however, that at the final time

tf , no information has reached the left, x l0, and

right, xr0 , boundaries of the spatial integration

interval that is, xlsltf and xrsrtf. Applying the

Rankine-Hugoniot jump conditions to the ideal MHD

equations and observing a conservation principle for theB field, eventually leads to

K* =K

SKqK

SKq*

u K*=u K

SKqK

SKq*

+

P*PKnxBnKBxKB

*Bx

*

SKq*

v K

*= v

K

SKqK

SKq*+

P*PKnyBnKByKB

*By

*

SKq*

EK

*=E

K

SKqK

SKq*+

P*q*PKqKBnKBv KB

*Bv

*

SKq*

(8)

(9)

Byl*=Byr

*=By

HLL, Bzl

* =Bzr* =Bz

HLL(10)

(11)

2.2.2 Wavespeed Computation

The eigenvalues reflect four different wave speeds for aperturbation propagating in a plasma field: the usualacoustic, the Alfven as well as the slow and fast plasmawaves

a2=

p

s

(12)

cA2=Bn

2/m (13)

2cs , f2 =a

2B

2

ma

2B

2

m2

4 a2cA

2 . (14)

FHLLC=

{F

lif0sl

Fl

*=FlslUl

*Ul if sl0q

*

Fr=F

rsrUr

*Ur* if q

*0srF

rif sr0 }

.

Bxl* =Bxr

* =BxHLL=

sr Bxrsl Bxlsrsl


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2.2.3 Divergence Free B Field

To obtain a divergence free induction field in time, anumerical scheme for the integration of the B filed has tobe constructed that inherenltly satisfies this constraintnumerically. The original equations should not bemodified, neither should an additional Poisson equationbe solved at each iteration step to enforce a divergence

free B field. For the lack of space we refer to Torrilhon[14] or to [13]. In 2D where the vector potentia lonly hasa z-component, the divergence ofB only depends oncomponents Bx and By. the magnetic field is defined attwo locations: at the center of the computational cells, andat the surfaces. In fact, only the normal component isdefined at the cell surfaces (the magnetic flux), for aCartesian grid. The evolution of the magnetic field at thecell surface is then obtained by directly solving the

Ampere equation. Defining =vB at cell vertices, itcan be shown [14] that the field at the cell surface centerscan be obtained in such a way that the divergence-free

condition is exactly satisfied.

bt

={bx t

=y

z

by t

=xz} (15) bx ,i1/2, j=

ty

[z ,i1/2, j1 /2z , i1 /2, j1/2]

by ,i , j1 /2=

- t

y[z ,i1/2, j1 /2z ,i1 /2, j1/2]

(16)

bdS=0y [bx ,i1/2, jbx , i1 /2, j]x[b

y , i , j1/2b

y ,i , j1/2]=0

(17)

Bxi , j=1

2[bx , i1 /2,jbx , i1 /2,j]

By i , j=1

2[by , i , j1 /2by ,i , j1 /2]

(18)

Figure 1: Schematic of staggered-grid variables used in theDai & Woodward scheme. For a non-orthogonalcoordinates a staggered grid does not seem to have anadvantage, since cell normal vectors do no longer point in acoordinate direction. A cell centered scheme seems to beadvantageous for curvilinear coordinates.

2.3 Simulation Results

2.3.1 Brio-Wu's shock tube

Initial conditions: =2.0, V=0,Bz=0,Bx=0.75

=1,p=1, by=1 for x0

=0.125,p=0.1,By=1 for x0

Computational domain is the rectangle [-1,1].

2.3.2 Supersonic Flow Past Circular Density Field

The solution domain is in the x-y plane [-1.5, 3.5; -4.0,

4.0], example first computed by M. Torrilhon.

Figure 2: 1D MHD solution at time t = 0.25s.


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Initial conditions: outside the density sphere, velocity

component vx=3, =1. Inside the density sphere:

=10, velocity vx=0. For all: B=(Bx=B0, 0), p = 1,

vy=0 and =5 /3 .

Figure 3: Supersonic flow past initial density field, shownpressure distributions: left: B0=0, right B0=1. The impactof the magnetic induction on the pressure distribution isclearly visible.

2.3.3 Classic 2D MHD Orszag-Tang Vortex

Computation domain is a square domain of size

[0, 2][0, 2].

Initial conditions are given by:

vx , vy =sin y , sinx

Bx, B

y=sin y , sin 2x

, p , vz, Bz=25 /9, 5 /3 ,0, 0 with =5 /3

This case uses periodic boundary conditions.

Figure 5: OrszagTang MHD turbulence problem with a384 384 uniform grid at t=2s.

3 FIELD PROPULSION

The above discussion has shown that current physicallaws severely limit spaceflight. The German physicist, B.Heim, in the fifties and sixties of the last centurydeveloped a unified field theory based on the

geometrization principle of Einstein 18 (see below)introducing the concept of a quantized spacetime butusing the equations of GR and introducing QMs. Aquantized spacetime has recently been used in quantumgravity. Heim went beyond general relativity and askedthe question: if the effects of the gravitational field can bedescribed by a connection (Christoffel symbols) inspacetime that describes the relative orientation betweenlocal coordinate frames in spacetime, can all other forcesof nature such as electromagnetism, the weak force, andthe strong force be associated with respective connectionsor an equivalent metric tensor. Clearly, this must lead to ahigher dimensional space, since in GR spacetime givesrise to only one interaction, which is gravity.

Figure 4: OrszagTang MHD turbulence problem with a384 384 uniform grid at t=2s.


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The fundamental difference to GR is the existence of

internal space H 8, and its influence on and steering ofevents in 4. In GR there exists only one metric leading

to gravity. All other interactions cannot be described by a

metric in 4. In contrast, since internal symmetry space is

steering events in 4, the following (double) mapping,

namely 4H84, has to replace the usual mapping

44 of GR. This double mapping is the source of the

polymetric describing all physical interactions that can

exist in Nature. The coordinate structure ofH8 is therefore

crucial for the physical character of the unified fieldtheory. This structure needs to be established from basicphysical features and follows directly from the physicalprinciples of Nature ( geometrization, optimization,

dualization (duality), and quantization). Once the

structure of H8 is known, a prediction of the number and

nature of all physical interactions is possible.

As long as quantization of spacetime is not considered,

both internal symmetry space, denoted as Heim space H8, and spacetime of GR can be conceived as manifoldswith metrics.

3.1 Six Fundamental Interactions

Einstein, in 1950 [9], emphasized the principle ofgeometrization of all physical interactions. Theimportance of GR is that there exists no backgroundcoordinate system. Therefore, conventional quantum fieldtheories that are relying on such a background space willnot be successful in constructing a quantum theory ofgravity. In how far string theory [5, 6], ST, that uses abackground metric will be able to recover background

independence is something that seems undecided atpresent. On the contrary, according to Einstein, oneshould start with GR and incorporate the quantumprinciple. This is the approach followed by Heim and alsoby Rovelli, Smolin and Ashtekar et al. [3, 4]. In addition,spacetime in these theories is discrete. It is known that thegeneral theory of relativity (GR) in a 4-dimensionalspacetime delivers one possible physical interaction,namely gravitation. Since Nature shows us that there existadditional interactions (EM, weak, strong), and becauseboth GR and the quantum principle are experimentallyverified, it seems logical to extend the geometricalprinciple to a discrete, higher-dimensional space.

Furthermore, the spontaneous order that has beenobserved in the universe is opposite to the laws ofthermodynamics, predicting the increase of disorder orgreater entropy. Everywhere highly evolved structurescan be seen, which is an enigma for the science of today.Consequently, the theory utilizes an entelechialdimension, x5, an aeonic dimension, x6 (see glossary), andcoordinates x7, x8 describing information, i.e., quantummechanics, resulting in an 8-dimensional discrete space inwhich a smallest elemental surface, the so-called metron,

exists. H8 comprises real fields, the hermetry forms,

producing real physical effects. One of these hermetryforms, H1, is responsible for gravity, but there are 11

other hermetry forms (partial metric) plus 3 degeneratedhermetry forms, part of them listed in Table 2. Thephysics in Heim theory (HT) is therefore determined bythe polymetric of the hermetry forms. This kind of poly-

metric is currently not included in quantum field theory,loop quantum gravity, or string theory.

3.2 Hermetry Forms and Physical Interactions

In this paper we present the physical ideas of thegeometrization concept underlying Heim theory in 8Dspace using a series of pictures, see Figs. 6-8. The

mathematical derivation for hermetry forms was given in[10-12]. As described in [10] there is a general coordinate

transformation xmi from 4H

84 resulting

in the metric tensor

gi k=xm

ixm

k(19)

where indices , = 1,...,8 and i, m, k = 1,...,4. The

Einstein summation convention is used, that is, indicesoccurring twice are summed over.

gi k=: ,=1

8

gi k

(20)

gi k

=x

m

i

xm

k.

(21)

Twelve hermetry forms can be generated having directphysical meaning, by constructing specific combinationsfrom the four subspaces. The following denotation for the

metric describing hermetry form H with =1,...,12 isused:

gi kH=: ,H

gi k

(22)

where summation indices are obtained from the definition

of the hermetry forms. The expressions gi kH are

interpreted as different physical interaction potentials

caused by hermetry form H, extending the interpretation

of metric employed in GR to the poly-metric ofH8. Itshould be noted that any valid hermetry form either must

contain space S

2

or I

2

.Each individual hermetry form is equivalent to a physicalpotential or a messenger particle. It should be noted that

spaces S2I2 describe gravitophotons and S2I2T1 are

responsible for photons. There are three, so calleddegenerated hermetry form describing neutrinos and socalled conversions fields. Thus a total of 15 hermetryforms exists.


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In Heim space there are four additional internalcoordinates with timelike (negative) signature, giving rise

to two additional subspaces S2 and I2. Hence, H8

comprises four subspaces, namely 3, T1, S2, and I2. The

picture shows the kind of metric-subspace that can beconstructed, where each element is denoted as a hermetryform. Each hermetry form has a direct physical meaning,see Table 3. In order to construct a hermetry form, eitherinternal space S2 or I2 must be present. In addition, thereare two degenerated hermetry forms that describe partialforms of the photon and the quintessence potential. Theyallow the conversion of photons into gravitophotons aswell as of gravitophotons and gravitons intoquintessence particles.

There are two equations describing the conversion of

photons into pairs of gravitophotons, Eqs. (23), for detailssee [10-12]. The first equation describes the production of

N2 gravitophoton particles from photons.

wphrwph=Nwgpwphrwph=Awph .

(23)

This equation is obtained from Heim's theory in 8D spacein combination with considerations from number theory,and predicts the conversion of photons into gravitophotonparticles. The second equation is taken from Landau's

radiation correction. Conversion amplitude:The physical

meaning of Eqs. (23) is that an electromagnetic potential(photon) containing probability amplitude Awph can be

converted into a gravitophoton potential with amplitudeNwgp,, see Eq. (24).

Nwgp=Awph . (24)

In the rotating torus, see Fig. 9, virtual electrons areproduced by the vacuum, partially shielding the protoncharge of the nuclei. At a distance smaller than theCompton wavelength of the electron away from thenucleus, the proton charge increases, since it is lessshielded. According to Eq. (24) a value of A larger than 0is needed for gravitophoton production. As was shown in[10], however, a smaller value of A is needed to startconverting photons into gravitophotons to make the

photon metric vanish, termed A=vkvkT /c21011

where v is the velocity of the electrons in the current loopand vT is the circumferential speed of the torus. From thevanishing photon metric, the metric of the gravitophoton

Figure 6: Einstein's goal was the unification of allphysical interactions based on his principle ofgeometrization, i.e., having a metric that is responsible forthe interaction. This principle is termed Einstein'sgeometrization principle of physics (EGP). To this end,

Heim and Drscher introduced the concept of an internalspace, denoted as Heim space H8, having 8 dimensions.

Although H8 is not a physical space, the signature of the

additional coordinates being timelike (negative), theseinvisible internal coordinates govern events in spacetime .Therefore, a mapping from manifold M (curvilinear

coordinates l)in spacetime 4 to internal space H8 and

back to 4 .

M H8 N

4H

8 4

l 1,. . . , 4

curvilinear

1,. . . , 8

Heim space Euclidean

m 1,. . . , 4

l xm

g ik

Heim Polymetric

gik

Figure 8: There should be three gravitational particles,namely the graviton (attractive), the gravitophoton(attractive and repulsive), and the quintessenece orvacuum particle (repulsive), represented by hermetryforms H1, H5, and H9, see Table 2.

conversion

Figure 7: The picture shows the 12 hermetry forms thatcan be constructed from the four subspaces, nalely

namely 3, T1, S2, and I2 (see text).

H8

S2

S2

I2

I2

gik

9

3

gik

10

T1

gik

11

3T

1

gik

12gik

1

3

gik

2

T1

gik

3

3T

1

gik

4 gik

5

3

gik

6

T1

gik

7

3T

1

gik

8

Heim Space

In H8, there exists 12 subspaces, whose metric gives6 fundamental interactions

(+ + + - - - - -)signature of H8


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pairs is generated, replacing the value of A by the LHS ofEq. (6) and inserting it into the equation for thegravitophoton metric. This value is then increased to thevalue of A in Eq.(6). Experimentally this is achieved bythe current loop (magnetic coil) that generates themagnetic vector and the tensor potential at the location ofthe virtual electron in the rotating torus, producing a highenough product v vT, see Eq. 32 in [12]. The couplingconstants of the two gravitophoton particles are different,and only the negative (attractive) gravitophotons areabsorbed by protons and neutrons, while absorption byelectrons can be neglected. This is plausible since thenegative (attractive) gravitophoton contains the metric ofthe graviton, while the positive repulsive gravitophotoncontains the metric of the quintessence particle that doesonly interact extremely weakly with matter. Through theinteraction of the attractive gravitophoton with matter it

becomes a real particle and thus a measurable force isgenerated (see upper part of the picture).

3.3 Gravitational Heim-Lorentz Force

The Heim-Lorentz force derived in [10-12] is the basisfor the field propulsion mechanism. In this section adescription of the physical processes for the generationof the Heim-Lorentz force is presented along with theexperimental setup. It turns out that several conditionsneed to be satisfied. In particular, very high magneticfield strengths are required.

In Table 1, the magnitude of the Heim-Lorentz force is

given. The current density is 600 A/mm2. The value is

the relative change with respect to earth accelerationg=9.81 m/s2 that can be achieved at the corresponding

magnetic field strength. The value 0H is the magnetic

induction generate by the superconductor at the locationof the rotating torus, D is the major diameter of the torus,while d is the minor diameter. In stands for the product ofcurrent and times the number of turns of the magneticcoil. The velocity of the torus was assumed to be 700 m/s.Total wire length would be some 106 m. Assuming a

reduction in voltage of 1V/cm for a superconductor, athermal power of some 8 kW has to be managed. Ingeneral, a factor of 500 needs to be applied at 4.2 K tocalculate the cooling power that amounts to some 4 MW.

32

3 Nwgpewph 2

Nwgpa4 mp c

2

d

d03

Z.

(25)

d

[m]

D

[m]

I n

[An] N wgpe 0

(T)

0.2 2 6.6 106 1.4 10-7 13 710-16

0.3 3 1.3 107 7.4 10-6 18 210-5

0.4 4 2.7 107 210-5 27 1.110-2

0.5 5 4 107 3.910-5 33 0.72

0.6 6 1.5 107 4.810-5 38 3

Table 1: From the Heim-Lorentz force the following

values are obtained. A mass of 1,000 kg of the torus isassumed, filled with 5 kg of hydrogen.

3.4 Transition into Parallel Space

Under the assumption that the gravitational potential ofthe spacecraft can be reduced by the production ofquintessence particles as discussed in Sec.1., a transitioninto parallel space is postulated to avoid a potential

conflict with relativity theory. A parallel space 4(n), in

which covariant physical laws with respect to 4 exist, is

characterized by the scaling transformation

xin=1

n2x1 , i=1,2,3; tn=

1

n3t 1

v n =n v 1 ; cn =n c1

Gn=1

nG ; n =; n.

(26)

The fact that n must be an integer stems from therequirement inHQTandLQTfor a smallest length scale.Hence only discrete and no continuous transformationsare possible. The Lorentz transformation is invariant withregard to the transformations of Eqs. (26) 1. In otherwords, physical laws should be covariant under discrete(quantized) spacetime dilatations (contractions). There are

1 It is straightforward to show that Einstein's fieldequations as well as the Friedmann equations are alsoinvariant under dilatations.

Figure 9: This picture shows the experimental setup tomeasuring the Heim-Lorentz force. The current loop(blue) provides an inhomogeneous magnetic field at thelocation of the rotating torus (red). The radial fieldcomponent causes a gradient in the z-direction (vertical).The red ring is a rotating torus. The experimental setupalso would serve as the field propulsion system, ifappropriately dimensioned. For very high magnetic fieldsover 30 T, the current loop or solenoid must bemechanically reinforced because of the Lorentz forceacting on the moving electrons in the solenoid, forcingthem toward the center of the loop.

I

N

Br

B I

r


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two important questions to be addressed, namely how thevalue n can be influenced by experimental parameters,

and how the back-transformation from 4(n) 4 is

working. The result of the back-transformation must notdepend on the choice of the origin of the coordinate

system in4. As a result of the two mappings from 4

4(n)4 , the spacecraft has moved a distance n vt

when reentering 4. The value t denotes the timedifference between leaving and reentering 4, as

measured by an observer in 4. This mapping for the

transformation of distance, time and velocity differencescannot be the identity matrix that is, the secondtransformation is not the inverse of the first one. A

quantity v(n)=nv(1), obtained from a quantity of 4, is

not transformed again when going back from 4(n) to4.

This is in contrast to a quantity liket(n) that transforms

intoT. The reason for this non-symmetric behavior is

that t(n) is a quantity from 4(n) and thus is being

transformed. The spacecraft is assumed to be leaving4

with velocity v. Since energy needs to be conserved in

4, the kinetic energy of the spacecraft remains

unchanged upon reentry.

The value of n is obtained from the following formula,Eq. (27), relating the field strength of the gravitophotonfield, g+gp, with the gravitational field strength, gg,produced by the spacecraft itself,

n=ggp

+

gg

Ggp

G. (27)

For the transition into parallel space, a material withhigher atomic number is needed, here magnesium Mgwith Z=12 is considered, which follows from theconversion equation for gravitophotons and gravitons intoquintessence particles (stated without proof). Assuming avalue ofgg= GM/R

2 = 10-7 m/s2 for a mass of 105 kg and a

radius of 10 m, a value of gg= 2 10-5 m/s2 is needed

according to Eq. (27). provided that Mg as a material is

used, a value of (see Table 1) I n =1.3107 is needed. If

hydrogen was used, a magnetic induction of some 61 Twould be needed, which hardly can be reached withpresent day technology.

3.5 Mission Analysis Results

From the numbers provided, it is clear that gravitophotonfield propulsion, is far superior compared to chemical

propulsion, or any other currently conceived propulsionsystem. For instance, an acceleration of 1g could besustained during a lunar mission. For such a mission onlythe acceleration phase is needed. A launch from thesurface of the earth is foreseen with a spacecraft of a mass

of some 1.5 105 kg. With a magnetic induction of 20 T,

compare Table 1 a rotational speed of the torus ofvT= 103

m/s, and a torus mass of 2103 kg, an acceleration larger

than 1g is produced and thus the first half of the distance,

dM, to the moon is covered in some 2 hours, whichfollows from t=2dM/g, resulting in a total flight timeof 4 hours. A Mars mission, under the same assumptions

as a flight to the moon, would achieve a final velocity of

v= gt = 1.49106 m/s. The total flight time to Mars with

acceleration and deceleration is 3.4 days. Enteringparallel space, a transition is possible at a speed of some

3104 m/s that will be reached after approximately 1

hour at a constant acceleration of 1g. In parallel space thevelocity increases to 0.4 c, reducing total flight time to

some 2.5 hours [10-12].

4 CONCLUSION

In GR the geometrization of spacetime gives rise togravitation. Einstein's geometrization principle wasextended to construct a poly-metric that describes allknown physical interactions and also predicts twoadditional like gravitational forces that may be bothattractive and repulsive. In an extended unified theorybased on the ideas of Heim four additional internalcoordinates are introduced that affect events in ourspacetime. Four subspaces can be discerned in this 8D

world. From these four subspaces 12 partial metrictensors, termed hermetry forms, can be constructed thathave direct physical meaning. Six of these hermetryforms are identified to be described by Lagrangiandensities and represent fundamental physicalinteractions. The theory predicts the conversion of photons into gravitophotons, denoted as the fifthfundamental interaction. The sixth fundamentalinteraction allows the conversion of gravitophotonsand gravitons (spacecraft) into the repulsive vacuum orquintessence particles. Because of their repulsivecharacter, the gravitational potential of the spacecraftis being reduced, requiring either a reduction of the

gravitational constant or a speed of light larger than thevacuum speed of light. Both possibilities must be ruledout if the predictions ofLQT and Heim theory areaccepted, concerning the existence of a minimalsurface. That is, spacetime is a quantized (discrete)field and not continuous. A lower value of G or ahigher value ofc clearly violate the concept of minimalsurface. Therefore, in order to resolve thiscontradiction, the existence of a parallel space ispostulated in which covariant laws of physics hold, butfundamental constants are different, see Eq. (11). Theconditions for a transition in such a parallel space aregiven in Eq. (12).

It is most interesting to see that the consequentgeometrization of physics, as suggested by Einstein in1950 [9] starting from GR and incorporating quantumtheory along with the concept of spacetime as aquantized field as used by Heim and recently in LQT,leads to major changes in fundamental physics andwould allow to construct a completely different spacepropulsion system.

Acknowledgments

The first author is grateful to M. Torrilhon, SAM, ETH

Zurich, Switzerland for discussions concerning both theimplementation of a numerically divergence freemagnetic induction field and of boundary conditions.This work was partly funded by Arbeitsgruppe Innovative


12/12


Projekte (AGIP) and Ministry of Science, Hanover,Germany under Efre contract.

REFERENCES

[1] Zaehringer, A., Rocket Science, Apogee Books,2004, Chap 7.

[2] Krauss, L.M., Propellantless Propulsion: The MostInefficient Way to Fly?, in M. Millis (ed.) NASA

Breakthrough Propulsion Physics Workshop Proceedings, NASA/CP-1999-208694, January1999.

[3] Rovelli, C., Loop Quantum Gravity, PhysicsWorld, IoP, November 2003.

[4] Smolin, L., Atoms of Space and Time,ScientificAmerican, January 2004.

[5] Zwiebach, R., Introduction to String Theory,Cambridge Univ. Press, 2004.

[6] Lawrie, I. D., A Unified Grand Tour of TheoreticalPhysics, 2nd ed., IoP 2002.

[7] Penrose, R., The Road to Reality, Chaps. 30-32,Vintage, 2004.

[8] Heim, B., Vorschlag eines Weges einereinheitlichen Beschreibung der Elementarteilchen,Z. fr Naturforschung, 32a, 1977, pp. 233-243.

[9] Einstein, On the Generalized Theory of Gravitation,Scientific American, April 1950, Vol 182, NO.4.

[10] Drscher, W., J. Hauser, AIAA 2004-3700, 40th

AIAA/ASME/SAE/ASE, Joint PropulsionConference & Exhibit, Ft. Lauderdale, FL, 7-10July, 2004, 21 pp., see www.hpcc-space.com .

[11] Drscher, W., J. Hauser,Heim Quantum Theory forSpace Propulsion Physics, 2nd Symposium on NewFrontiers and Future Concepts, STAIF, American

Institute of Physics, CP 746, Ed. M.S. El-Genk 0-7354-0230-2/05, 12 pp. 1430-1441, www.hpcc-space.com .

[12] Drscher, W., J. Hauser, AIAA 2005-4321, 41th

AIAA/ASME/SAE/ASE, Joint PropulsionConference & Exhibit, Tuscon, AZ, 7-10 July, 2005,12pp., see www.hpcc-space.com .

[13] Hauser, J, W. Dai: Plasma Solver (PS-JUST) forMagnetohydrodynamic Flow-Java Ultra SimulatorTechnology, ESTEC/Contract no 18732/04/NL/DC,2005.

[14] M. Torrilhon, Locally Divergence-PreservingUpwind Finite Volume Schemes forMagnetohydrodynamic Equations, SIAM J. Sci.Comput. Vol. 26, No. 4, pp. 1166-1191, 2005.

Table 2: The hermetry forms for the six fundamental physical interactions.

Subspace Hermetry form

Lagrange density

Messenger particle Symmetrygroup

Physicalinteraction

S2

H1S

2

, LGgraviton U(1) gravity +

S2I

2H5S

2I2, Lgp neutralthree types of

gravitophotons

U(1) U(1) gravitation +

vacuum field

S

2

I2

3

H6S2

I2

3

, Lew Z0

boson

SU(2) electroweak

S2I2T1 H7S

2I2T1, Lemphoton U(1) electromagnetic

S2I23T1 H8S

2I23T1 W bosons

SU(2) electroweak

S2I

2

3T

1H9I

2, Lq

quintessence U(1) gravitation

vacuum field

H10 I23, Ls

gluons SU(3) strong
http://www.uibk.ac.at/c/cb/cb26http://www.hpcc-space.com/http://www.hpcc-space.com/http://www.hpcc-space.com/http://www.uibk.ac.at/c/cb/cb26http://www.uibk.ac.at/c/cb/cb26http://www.hpcc-space.com/http://www.hpcc-space.com/http://www.uibk.ac.at/c/cb/cb26

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