the space elevator and what we need to built it photo source: ...
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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 KerznerPhysics 141A, UC Berkeley
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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
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Geostationary Orbit
r = 42,164 km = Earth’s radius + 35,786 km
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Elevator PhysicsForce 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
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Strength of Materials
Stress (σ) = Force / Cross-sectional Area
Stress (σ) = Young’s Modulus (E) * Strain (ε = ΔL/L) to proportionality limit
Yield strength - elasticvs. plastic deformation
Tensile StrengthBrittle vs ductile
http://en.wikipedia.org/wiki/Stress%E2%80%93strain _curve
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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
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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
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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
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Typical MaterialsStainless Steel – 2GPa
Quartz - 48MPa Tensile Strength (1GPa compressive)
Diamond – 60MPa Tensile Strength (but expensive)
Material Strength (Mpa)
Specific Strength (kY)
Breaking Length (km)
Glass 33 13 1.3
Micro-Melt 10 Tough Treated Tool Steel
5171(yield) 694 71
Kevlar 3620 2514 256
Diamond 60,000 observed
17045 1739
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Orbital Hybridization
Bond strengthCovalent>ionic>metallic
Bonding situationcauses excitation
New Schrodingerhas hybridized solutionsN(s + √3pσ)
Methane sp3 orbitals
Ethene sp2 orbitals(+ free pz )
mcdebeer.wordpress.com
en.citizendium.org
http://en.wikipedia.org/wiki/Orbital_hybridisation
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Orbital Hybridization
Graphene sp2 - sp2 overlap
sp2 and sp3 energy
Pi bonds for strength and conductivity
http://www.rkm.com.au/GRAPHENE/graphene-pi-orbitals.html
en.citizendium.org
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Carbon Nanotubes
SWNT, MWNT (n, m) indices1.4g/ccIndividual CNT shell 100,000 MPa48,000 kY 4900 km Breaking Length
Armchair SWNT theoretically up to 126 GPa
MWNT observed up to 150 GPa
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Elevator Components
Cable taper
Climber instead of moving ropes
Cable tilt
Counterweight
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Other Considerations
Climbing Time
Powering the climber
Radiation
Objects in orbit
Launching objects
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ReferencesSlide 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