Transcript v mf - Yimg
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 4G 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]