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Force Fields TAILORED FORCE FIELDS FOR SPACE-BASED CONSTRUCTION: KEY TO A SPACE-BASED ECONOMY Narayanan Komerath, Sam Wanis, Joseph Czechowski, Bala Ganesh, Waqar Zaidi, Joshua Hardy, Priya Gopalakrishnan School of Aerospace Engineering, Georgia Institute of Technology Source: www.nasa.gov School of Aerospace Engineering, Georgia Institute of Technology OUTLINE 1. Forces on objects in steady and unsteady potential fields 2. Generalization: Optical and other E-Mag fields; and acoustic fields 3. Application Horizons 4. Near term: Acoustic Shaping: results & applications 5. Far Horizon: Electromagnetic force fields 6. Middle Term – Magnetic Fields to demonstrate a particular solution -Sample Problem : the O’Neill Habitat - Architecture 7. Costing Using a Space-Based Economy Approach Source: www.nasa.gov School of Aerospace Engineering, Georgia Institute of Technology INTRODUCTION In space, minor forces exerted over long periods can achieve major results. Generation of forces by interaction with steady potential fields is well-known ESL: NASA MSFC/ LORAL NASA . Solar Sail: NASA M2P2: NASA / U. Wash. Here we consider: 1. Radiation Force due to unsteady interactions Laser/ Microwave Sail: JPL between beamed energy and matter – near & far term applications. 2. Quasi-steady magnetic fields: middle term architecture to get to the far horizon . Relevance: automatic construction of large/complex objects from random-shaped materials. School of Aerospace Engineering, Georgia Institute of Technology FORCES IN UNSTEADY POTENTIAL FIELDS 1. Radiation Force Due to Beamed Energy Radiation pressure due to plane wave on surface = k*E. ( E = Energy density) Absorbing surface: k =1. Reflective surface: k=2. Gradient forces: Beam waist acts as particle trap for transmitting particles, due to intensity gradient. Optical Tweezers: Particles are forced to the focus / waist of a CW laser beam -interpreted using geometric optics and refractive index for particles >> λ. -also works using Mie theory where particle size ~ λ -recently found to work for Rayleigh regime – nanoparticles << λ Satellite Positioning: Lapointe, NIAC study 2001. Ultrasonic beams - “Fingers of Sound / Space Drums” Used to hold and manipulate levitated/ suspended particles. R. Oeftering, NASA Radiation pressure on objects due to coherent beams is used in optics and acoustics. School of Aerospace Engineering, Georgia Institute of Technology FORCES IN UNSTEADY POTENTIAL FIELDS 2. STANDING WAVE FIELDS: Particles Drift into Stable “Traps”. •For particle size << λ, standing wave trap force ~ 103 times the single-beam force. •Trap stiffness in standing wave trap ~ 107 times the single-beam trapping stiffness. D ( z) 2 1 0 1 2 •Source only needs to provide small gain over losses - 0.02 0.04 Force 0.06 Potential z Trap regions can be of complex shape: Stable Trap Pressure distribution for a higher- order mode in a rectangular acoustic resonator. With standing waves in a low-loss resonator, small input intensity suffices to produce substantial forces on particles. Various mode shapes can be generated by varying frequency and resonator geometry. School of Aerospace Engineering, Georgia Institute of Technology CONSERVATION EQUATIONS ∂ ()()density of quantity + ∇ • flux of quantity = sources − sin ks ∂t General ∂ 1 1 B 2 E × B ε E 2 + + ∇ • = − ()J • E ∂ o µ µ t 2 2 o o Electromagnetic Poynting work done on energy density flux Particles by EM field Electromagnetic ∂ 1 p 2 1 + ρ u 2 + ∇ • ()pu = X • ()∇p ∂ ρ 2 o t 2 o c 2 Acoustic Work done on Acoustical potential Acoustical kinetic Acoustic Particles by acoustic Energy density, ep Energy density, ek Intensity flux, I field ep = potential energy that can be stored in the fluid by compressing it ek = kinetic energy due to acoustically energized fluid I = rate at which work is being done by unit area of fluid supporting an externally induced normal stress p and moving with velocity u is pu, i.e. rate (and direction) at which acoustic energy crosses unit area of space School of Aerospace Engineering, Georgia Institute of Technology IMPORTANT PARAMETERS & ORDERS OF MAGNITUDE Optics Acoustics z Maxwell’s stress tensor z Radiation stress tensor z Rayleigh regime diameters: z Rayleigh regime diameters: millimeters nanometers to centimeters z Mie regime: microns z Mie regime: meters z Refractive Index z Particle density vs. density of acoustic medium z Optical intensity z Sound intensity z From Zemanek (1998): z Wanis[1999]: GT acoustic chamber, 514.5 nm laser in water; beam waist 156 dB at 800 Hz (1 0 0) mode at of 8 wavelengths; glass sphere of 2mm radius rigid particles radius 5nm; refractive index 1.51; Force = 3.3 micro-newtons Force = 2.5 *10-22 N. School of Aerospace Engineering, Georgia Institute of Technology Tailored Force Fields (TFF): Time Line / Size / Application Map 1 – 5yrs 5-20 yrs 20-30yrs 30- 50 yrs. STANDING ULTRASONIC WAVE STEADY MAGNETIC 10-6m ACOUSTCS TELEPRESENCE LONG-WAVE ELECTROMAGNETIC STEADY BEAM ACOUSTICS 10-3m FORMATION FLIGHT ISS PARTS 100m HEAT SHIELDS : HABITAT PARTS/ FUEL TANKS 103m HABITAT CONSTRUCTION ASTEROID 105m RECONSTRUCTION School of Aerospace Engineering, Georgia Institute of Technology ACOUSTIC RADIATION FORCE: PRIOR APPLICATIONS •Rayleigh – proposed expression for radiation pressure in acoustic fields, analogous to Maxwell’s stress tensor. •King 1934: Theory for radiation force in acoustic fields – formation of dust striations in water tanks. Forces considered to be insignificant except with ultrasonic frequencies and neutrally-buoyant particles in water. •Levitation experiments: Ultrasonic levitators used to lift steel spheres – to demonstrate utility in non-contact melting and positioning within furnaces. •STS experiments: Holding molten drop of metal inside a container in micro-gravity. Problem: Radiation force lost when phase change / cooling occurred. Attributed to reversal of force due to formation of envelope of heated gas around the sphere. [Wang 1998] •Liquid manipulation using ultrasonics: NASA Glenn research •NASA Hybrid electrostatic levitator / ultrasonic manipulator facility. School of Aerospace Engineering, Georgia Institute of Technology ACOUSTIC SHAPING •GT extension: Extended the idea of positioning a single droplet, to the formation of entire walls in a chamber. Question: would particles migrate to point of minimum potential, or remain along entire surfaces of low potential? •KC-135 tests. Flight test proof that entire walls would be formed. Self-alignment seen. No particle spin. Acoustic chamber Ground test comparison between predicted Mode 110 Styrofoam walls formed in reduced gravity pressure contours and measured wall locations School of Aerospace Engineering, Georgia Institute of Technology ACOUSTIC SHAPING Wall formation process: KC-135 test. Frequency 800 Hz School of Aerospace Engineering, Georgia Institute of Technology SIMULATION: PREDICTED WALL SHAPES 2 2 0 1 1 0 3 2 0 1 0 0 + 0 2 0 2 3 0 + 1 0 0 1 1 0 + 2 2 0 School of Aerospace Engineering, Georgia Institute of Technology FAR HORIZON: ASTEROID RECONSTRUCTION? •Solar-powered radio resonators in the NEA region to reconstitute pulverized asteroids into specified shapes. •Formation-flown spacecraft to form desired resonator geometry. •Asteroids pulverized using directed beam energy or robots, •Solar energy converted to the appropriate frequencies. •Materials and structures for such an endeavor must come mostly from lunar or asteroidal sources. Example Point: Particle diameter: 0.1m Wavelength: 2m Particle acceleration: 10-5 g Resonator intensity: 170 MW/m2 Resonator Q-factor: 10,000 Active field time: 13 hrs Beam diameter = 100m Collector efficiency: 10% Collector area w/o storage: 1 sq.km School of Aerospace Engineering, Georgia Institute of Technology Can we generate radio waves intense enough? z In 1974, the Arecibo observatory transmitted a message into outer space z Power of transmission was 20 trillion watts Courtesy of the NAIC - Arecibo Observatory, a facility of the NSF. z Frequency 2380 MHz. Wavelength of ~12.6 cm David Parker / Science Photo Library z Signal duration: 169 seconds School of Aerospace Engineering, Georgia Institute of Technology Space Based Economy Self-sustaining Economy Support/Service Economy Space Habitats e Lunar Mining Lunar Manufacturing m i T Lunar Launcher Lunar Power Lunar Resources GEO Station Orbit transfer vehicles Maintenance Space Station Robotics Fuel Repair Com-sats Research Exploration Military Sensing GPS Earth Launch School of Aerospace Engineering, Georgia Institute of Technology Middle Term Test Case for Costing: ELECTROMAGNETIC CONSTRUCTION OF A 2KM DIAMETER, 2KM LONG RADIATION SHIELD At the 10-30 year horizon, force field tailoring can be used to build the first large human habitat at a Lagrangian point of the Earth-Moon system. Gerard O’Neill proposed such habitats and explored their construction in the 1970s. Features of the O’Neill [1975] habitat concepts: •Economic opportunities as motivator •Moon as first source for extraterrestrial resources, •L5 as the logical location for the settlement. • “Bernal sphere” + toroidal agriculture stations on either side. Near 1-g at equator •Shell made of aluminum and glass (to admit sunlight ) •Support structure made of aluminum ribs and/or steel cable •Projected earth-LEO launch costs of $110/lb •Lunar-based mass driver to send much of the required mass into Space Radiation shielding dominated mass of the settlement. School of Aerospace Engineering, Georgia Institute of Technology PRESENT APPROACH TO BUILDING HABITAT # 1975
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