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