the space elevator and what we need to built it photo source: ...
TRANSCRIPT
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
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
r = 42,164 km = Earth’s radius + 35,786 km
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
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
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 = 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
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 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
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
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
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
Elevator Components
Cable taper
Climber instead of moving ropes
Cable tilt
Counterweight
Other Considerations
Climbing Time
Powering the climber
Radiation
Objects in orbit
Launching objects
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