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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
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

first thoughts
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

geostationary orbit
Geostationary Orbit

r = 42,164 km = Earth’s radius + 35,786 km

elevator physics
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

strength of materials
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

strength of materials1
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

specific strength
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
theoretical strength limit
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
typical materials
Typical Materials

Stainless Steel – 2GPa

Quartz - 48MPa Tensile Strength (1GPa compressive)

Diamond – 60MPa Tensile Strength (but expensive)

orbital hybridization
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

orbital hybridization1
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

carbon nanotubes
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

elevator components
Elevator Components
  • Cable taper
  • Climber instead of moving ropes
  • Cable tilt
  • Counterweight
other considerations
Other Considerations
  • Climbing Time
  • Powering the climber
  • Radiation
  • Objects in orbit
  • Launching objects
references
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