The Space Elevator and what we need to built it

1 / 15

# The Space Elevator and what we need to built it - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'The Space Elevator and what we need to built it' - binh

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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
• 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 Physics
• Force is downward below geostationary,upward above it
• Geostationary point experiences greatesttension
• Orbital velocity at 2/3 to Geostationary

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

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 Materials

Stainless Steel – 2GPa

Quartz - 48MPa Tensile Strength (1GPa compressive)

Diamond – 60MPa Tensile Strength (but expensive)

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 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

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
• Cable taper
• Climber instead of moving ropes
• Cable tilt
• Counterweight
Other Considerations
• Climbing Time
• Powering the climber