The Space Elevator
and what we need to built it
Skylar Kerzner
Physics 141A, UC Berkeley
Photo source: http://www.gizmodo.com.au/2011/02/how-to-build-aspace-elevator-and-become-an-interplanetary-civilization/
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
Elevator Physics
Force is downward below geostationary,
upward above it
Geostationary point experiences greatest
tension
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 - elastic
vs. plastic deformation
Tensile Strength
Brittle vs ductile
http://en.wikipedia.org/wiki/
Stress%E2%80%93strain
_curve
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_str
ain_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 Materials
Specific
Breaking
Strength
Length (km)
(kY)(1GPa compressive)
Quartz - 48MPa Tensile Strength
Material
Stainless Steel Strength
– 2GPa
(Mpa)
Glass
33
13
1.3
Diamond – 60MPa Tensile Strength (but expensive)
Micro-Melt 10
Tough Treated
Tool Steel
5171(yield)
694
71
Kevlar
3620
2514
256
Diamond
60,000 observed
17045
1739
Orbital Hybridization
Bond strength
Covalent>ionic>metallic
Bonding situation
causes excitation
en.citizendium.org
New Schrodinger
has hybridized solutions
N(s + √3pσ)
Methane sp3 orbitals
Ethene sp2 orbitals
(+ free pz )
http://en.wikipedia.org/wiki/Orbit
al_hybridisation
mcdebeer.wordpress.com
Orbital Hybridization
Graphene sp2 - sp2 overlap
sp2 and sp3 energy
Pi bonds for strength and
conductivity
en.citizendium.org
http://www.rkm.com.au/GRAPHENE/g
raphene-pi-orbitals.html
Carbon Nanotubes
SWNT, MWNT
(n, m) indices
1.4g/cc
Individual CNT shell
100,000 MPa
48,000 kY
4900 km Breaking Length
Armchair SWNT
theoretically up to 126 GPa
MWNT observed up to
150 GPa
Other Considerations
Climbing Time
Powering the climber
Radiation
Objects in orbit
Launching objects
References
Slide 7: http://en.wikipedia.org/wiki/Specific_strength
http://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_materials
http://en.wikipedia.org/wiki/Material_properties_of_diamond
http://en.wikipedia.org/wiki/Kevlar
Slide 12: http://en.wikipedia.org/wiki/Carbon_nanotube#Strength
http://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.jpg
http://en.wikipedia.org/wiki/File:Space_elevator_balance_of_forces.svg