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The Space Elevator and what we need to built it

The Space Elevator and what we need to built it. Photo source: http :// www.gizmodo.com.au /2011/02/how-to-build-a-space-elevator-and-become-an-interplanetary-civilization/. Skylar Kerzner Physics 141A, UC Berkeley. First Thoughts.

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The Space Elevator and what we need to built it

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  1. The Space Elevatorand what we need to built it • Photo source: http://www.gizmodo.com.au/2011/02/how-to-build-a-space-elevator-and-become-an-interplanetary-civilization/ Skylar Kerzner Physics 141A, UC Berkeley

  2. First Thoughts • 1895 – Konstantin Tsiolkovsky proposes a tower up to geostationary orbit • 1959 – Artsutanov suggests a geostationary base that lowers a cable • 1966 – Isaacs, Vine, Bradner, Bachus determine that the strength required is at least twice that of any existing material Faculty.randolphcollege.edu

  3. Geostationary Orbit r = 42,164 km = Earth’s radius + 35,786 km

  4. Elevator Physics • Force is downward below geostationary,upward above it • Geostationary point experiences greatesttension • Orbital velocity at 2/3 to Geostationary • $100/lb instead of $11k/lb http://en.wikipedia.org/wiki/File:Space_elevator_structural_ diagram--corrected_for_scale%2BCM%2Betc.TIF

  5. Strength of Materials Stress (σ) = Force / Cross-sectional Area Stress (σ) = Young’s Modulus (E) * Strain (ε = ΔL/L) to proportionality limit Yield strength - elastic vs. plastic deformation Tensile Strength Brittle vs ductile http://en.wikipedia.org/wiki/Stress%E2%80%93strain _curve

  6. Strength of Materials A: Engineering Stress = Force / Original Area B: True Stress = Force / Area http://en.wikipedia.org/wiki/File:Stress_v_strain_brittle_2.png http://en.wikipedia.org/wiki/File:Stress_v_strain_A36_2.svg

  7. Specific Strength • Specific Strength = Strength / density [N * m / kg] • Cable Material needs 30-100MN*m/kg • Breaking Length – Can suspend its own weight under Earth’s gravity = Specific Strength / g • Required breaking length: 4960km

  8. Theoretical Strength Limit • Atoms are in a harmonic potential well of depth Eb= 10eV • Interatomic distance d = width of well = 0.2nm • Eb = kd2 / 2  k = 2Eb / d2 • Pushing on a slab: F = kΔd * A/ d2 • Δd/d = ΔL/L • F = E*A*ΔL/L • Result: E = 2Eb / d3 • If Δd can  d then T ~ E = 300Gpa

  9. Typical Materials Stainless Steel – 2GPa Quartz - 48MPa Tensile Strength (1GPa compressive) Diamond – 60MPa Tensile Strength (but expensive)

  10. Orbital Hybridization • Bond strengthCovalent>ionic>metallic • Bonding situationcauses excitation • New Schrodingerhas hybridized solutionsN(s + √3pσ) • Methanesp3 orbitalsEthene sp2 orbitals(+ free pz) en.citizendium.org http://en.wikipedia.org/wiki/Orbital_hybridisation mcdebeer.wordpress.com

  11. Orbital Hybridization • Graphenesp2- sp2 overlap • sp2 andsp3 energy • Pi bonds for strength and conductivity en.citizendium.org http://www.rkm.com.au/GRAPHENE/graphene-pi-orbitals.html

  12. Carbon Nanotubes SWNT, MWNT (n, m) indices 1.4g/cc Individual CNT shell 100,000 MPa48,000 kY 4900 km Breaking Length Armchair SWNT theoretically up to 126 GPa MWNT observed up to 150 GPa

  13. Elevator Components • Cable taper • Climber instead of moving ropes • Cable tilt • Counterweight

  14. Other Considerations • Climbing Time • Powering the climber • Radiation • Objects in orbit • Launching objects

  15. References • Slide 7: http://en.wikipedia.org/wiki/Specific_strengthhttp://en.wikipedia.org/wiki/Space_elevator • Slide 8: Atomic Physics: An Exploration Through Problems and Solutions 2nd Edition - Budker • Slide 9: http://en.wikipedia.org/wiki/Tensile_strength#Ductile_materialshttp://en.wikipedia.org/wiki/Material_properties_of_diamondhttp://en.wikipedia.org/wiki/Kevlar • Slide 12: http://en.wikipedia.org/wiki/Carbon_nanotube#Strengthhttp://www.sciencedirect.com/science/article/pii/S092150930101807X • Slide 13: http://en.wikipedia.org/wiki/File:Space_elevator_balance_of_forces.svg • Slide 14: http://en.wikipedia.org/wiki/File:SpaceElevatorInClouds.jpghttp://en.wikipedia.org/wiki/File:Space_elevator_balance_of_forces.svg

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