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Possible Mach Effects in Bodies Accelerated
by Non-Uniform Magnetic Fields
Current pulse
Coil
Final speed:
Ferrite block
vcl or vmf ?
Nembo Buldrini
Aerospace Engineering
FOTEC Forschungs- und Technologietransfer GmbH – Austria
[email protected]
Mach Effects
AM Spacecraft
AM
The possibility to transiently alter the mass of a body (in figure AM,
Active Mass) would enable the implementation of a unique
propulsion system, which wouldn’t require the ejection of propellant
in order to produce thrust, thus overcoming the limits of rocket
propulsion.
Mach Effects
Universe
In the so called “Mach effects”, this mass fluctuation would
originate from a radiative transaction between the body itself
and the rest of the mass of the universe.
Mach Effects
Universe
Any momentum gained by the body would be compensated by an equal amount of
momentum gained by the rest of the universe, which will move by an infinitesimal
distance in the opposite direction, thus satisfying the momentum conservation law.
One could say that, in a sense, the actual propellant is the universe itself.
Mach Effects
This is the final equation that describes the Mach effects:
2
2
2

1
1  E0  1   E0  
 
 

0 (t ) 
 
2
2
2  
4G   0 c t
  0 c   t  

this term is negligible
at low power
Integrating the equation over the volume of the body subjected to the
energy variation, one gets the simple relation:
 E
m0 (t )   2
 0 t
k
2
Bulk Acceleration
In order for the Mach effects to manifest, it was noticed that the
AM has to be subjected to a bulk acceleration (in addition to the
internal energy variation). This fact comes from first principles of
the derivation itself. How much is the magnitude of such
acceleration affecting the expression of mass fluctuation,
however, is not yet clear. At a first glance, the final equation:
2E
m0 (t )   2
 0 t
k
seems mute about this, but Woodward will bring some insights
about this issue during this forum...
Efficiency of Mach Effects
Given the last experimental results, the question why the magnitude of the
recorded effect is so low compared to the one predicted by the theoretical model
remains open.
As a first rough attempt to address this issue, it seems reasonable to insert into
the mass fluctuation equation an efficiency parameter, which, for explanatory
reasons, will be split in two different components, η1 and η2
k  E 1
m0 (t )   2 
2
0
t
2
The η1 parameter is the fraction of the energy injected into the active mass,
which is effectively contributing to a change of the internal energy.
The η2 parameter indicates the efficiency of the ME process itself, which could
depend on different factors (destructive interference, bulk acceleration
magnitude,…)
Mach effect devices: past and present
embodiments
Actuator
(piezoelectric material)
Active Mass:
Capacitor’s
dielectric
Thrust
Coil
Capacitor
~
Ballast
mass
Power
Supply
~
Power
Supply
Power Supply
~
Piezo-actuator type
Electric
Field
Force
Magnetic
Field
“Mach-Lorentz” device type
The experimental method used so far to investigate the existence of Mach effects is to
subject capacitors to charge and discharge cycles while they are accelerated.
Two main types of devices have been build, which differs from the method used to
accelerate the active mass (AM). In the piezo-actuator type, the capacitor is accelerated
mechanically by a piezoelectric actuator; in the “Mach-Lorentz” device, the acceleration
is provided by the Lorentz force, arising from the interaction of the electric field of the
capacitor with the B-field produced by an external coil
Mach effect devices: past and present
embodiments
Actuator
(piezoelectric material)
Active Mass:
Capacitor’s
dielectric
Thrust
Coil
Capacitor
~
Ballast
mass
Power
Supply
~
Power
Supply
Power Supply
~
Piezo-actuator type
Electric
Field
Force
Magnetic
Field
“Mach-Lorentz” device type
The advantages of using a dielectric in a capacitor as active mass are:
1) Large internal energy variations are easily obtainable
2) Fast internal energy variation are easily obtainable
On the other hand, both device types have challenges to getting the dielectric properly
accelerated. In the piezo-actuator type, for example, the reflection of shock waves on
the surfaces could impede an uniform acceleration. In the “Mach-Lorentz” type, the
magnitude of the Lorentz force produced is usually rather small.
A different experimental approach
In order to get easily both large internal energy variations and bulk
accelerations, ferromagnetic materials could be used as active mass
Placing a ferromagnetic active mass in a pulsed non-uniform
magnetic field, it will be subjected simultaneously to an internal
energy variation and a bulk acceleration.
If a mass fluctuation should take place, then the final speed should
be higher than classically calculated
Acceleration
Internal
energy
variation
AM
A different experimental approach
Let’s consider a simple device as the one here depicted…
S
P/S
C
D
(see next slide)
A power supply (P/S) charges a capacitor (C) up to the desired
voltage value. A switch (S) provides to transfer the energy of the
capacitor to a coil, in a form of a short and intense pulse. A cylinder of
ferromagnetic material constitutes the active mass (AM) which is
initially placed in the region where the B-field produced by the coil is
divergent. This setup is very similar to what is usually referred to as
electromagnetic pulse accelerator, or coilgun.
What happens during the discharge? (1)
During Phase 1 the current starts flowing into the coil
and the B-field rises. The mass fluctuation in the AM
(Active Mass) reaches its first positive peak.
But the magnetic force (F) acting on the AM is still
low: the mass fluctuation here hardly affects the
acceleration of the AM.
In this phase the force is
at its maximum
Phase 2: maximum force acting on the AM, mass
fluctuation reaches its negative peak. The AM
acceleration is higher (blue trace) than in the
“classical” case (yellow trace)
Phase 3 is similar to Phase 1: no much deviation
from the classical acceleration trace.
At the same time, the
mass is at its minimum
vmf
vcl
What happens during the discharge? (2)
COIL
The size of the AM
represents its mass
The displacement
during acceleration
is exaggerated
In this phase the force is
at its maximum
At the same time, the
mass is at its minimum
vmf
vcl
A rudimentary propellantless propulsion device
The active mass is accelerated as described in the previous slides,
but is then stopped inside the device. If Mach effects obtain, then
the final total momentum of the device should be <> 0.
pAM =pAM
pAA>=ppAAtot = 0
pAA
pAM
Active Mass
ptot <> 0
Accelerating
apparatus
pAM = Momentum of the active mass
pAA = Momentum of the accelerating
apparatus (coil + p/s + chassis)
ptot = Total momentum
A rudimentary propellantless propulsion device
Connecting the active mass to the device with a spring and
repeating the discharge process, it is easy to imagine the
following rudimentary propellantless propulsion device:
A rudimentary propellantless propulsion device
It has been calculated that the same effect obtains if the waveform of
the discharge is a damped sinusoid. In this case the the diode seen in
the previous circuit will be not necessary and a LC resonant – more
efficient – system can be used.
Behaviour of previously seen quantities in case of damped sinusoid current discharge
Frequency and magnitude are
not to scale!
Notice again that when the force (blue) is at a
maximum, the mass fluctuation (red) is at a
maximum negative. When the mass fluctuation is
at a maximum positive, the force is zero.
— Current
— Force
— Mass fluctuation
— Speed (classical)
— Speed (with m-f)
Quantitative Analisys
In order to make a preliminary quantitative analysis, a system
comprised of a coil and a ferrite cylinder (AM) has been modeled and
a finite element simulation has been carried out. This allowed to
calculate the forces acting on the ferrite cylinder and the change in its
internal energy during the discharge.
Simulation parameters:
Coil
Coil: 100 turn,  ext. 30mm
Ferrite
cylinder
 int. 22mm, length 23mm.
Peak Current: 50A
Ferrite Cylinder:  20mm, h 15mm
Inductance (coil + partially inserted
ferrite cylinder): 180uH
Quantitative Analisys
With the system previously described and modeled, and the
following parameters:
Natural frequency of the LC discharge circuit: 80 kHz
Efficiency parameter η1 = 0.1
Efficiency parameter η2 = 0.1
Pulse repetition rate: 130 Hz
It has been calculated that a thrust of
about 130 µN shall be produced
The problem is: we have no idea of the real magnitude of η1 and η2 …
Quantitative Analisys
Position = 0mm
(max energy)
1.40E-02
140
12
1.20E-02
120
1.20E-02
10
1.00E-02
100
1.00E-02
8
8.00E-03
80
8.00E-03
6
6.00E-03
60
6.00E-03
4
4.00E-03
40
4.00E-03
2
2.00E-03
20
2.00E-03
0.00E+00
0
0
0
5
10
15
Energy [J]
1.40E-02
0.00E+00
0
20
5
10
15
20
Position of the AM [mm]
Position of the AM [mm]
Position = 6.5mm
(max thrust)
Max thrust
Energy [J]
Force [N]
Thrust [uN], Force [N]
14
Energy [J]
The position of the AM is
critical in obtaining the
maximum thrust. Placing the
AM in the middle, maximum
energy variation is obtained,
but not force is exerted.
Placing the AM in the point
where max force is exerted,
the energy variation is quite
low. But there is a point
between this two positions
where thrust is maximized.
Force [N]
Thrust Maximization
Position = 10.9mm
(max force)
Position = 16.4mm
Force [N]
Thrust [uN]
Energy [J]
Material Selection
The ideal ferromagnetic material to be used as AM
should have the following characteristics:
• High response to applied magnetic fields
• High internal resistance (reduced eddy currents)
• High internal energy storing capacity
A candidate material, because of the high energy
storing capacity, could be Terfenol-D. It is a
conducting material, so it will be preferably laminated
in order to increase the internal resistance. Further
material characterization will be necessary in order to
assess the behaviour under pulsed magnetic fields.
Conclusions and Recomendation
• A new system has been described, which can be used to
investigate the existence of Mach effects
• The system relies on the interaction of ferromagnetic
materials with pulsed non-uniform magnetic fields
• The same system could be used for the construction of a
propellantless propulsion device
• A study aimed at finding and characterizing a suitable
material to be used as active mass in the described device
is required before starting the experimental activity
• An in depth analysis of the derivation of Mach effects, in
order to understand the role of bulk acceleration and to
help to estimate the magnitude to the described
“efficiency” factors, is highly desirable and recommended.
Possible Mach Effects in Bodies Accelerated
by Non-Uniform Magnetic Fields
Current pulse
Coil
Thank you for your attention!
Final speed:
Ferrite block
vcl or vmf ?
Nembo Buldrini
Aerospace Engineering
FOTEC Forschungs- und Technologietransfer GmbH – Austria
[email protected]