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Fate of a Broken Space Elevator Blaise Gassend. Space Exploration 2005 — April 3-6 2005 Blaise Gassend — Computer Science and Artificial Intelligence.

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Presentation on theme: "Fate of a Broken Space Elevator Blaise Gassend. Space Exploration 2005 — April 3-6 2005 Blaise Gassend — Computer Science and Artificial Intelligence."— Presentation transcript:

1 Fate of a Broken Space Elevator Blaise Gassend

2 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Some Previous Work Tower of BabelTower of Babel –Don't mix inches and meters. Kim Stanley Robinson's Red MarsKim Stanley Robinson's Red Mars –Falling space elevator is a cataclysmic event. –Wraps around Mars multiple times. –Hits hard, with destructive violence. Dr. Bradley EdwardsDr. Bradley Edwards –Broken ribbon flutters to the ground or burns up. –Top fragment might be reattachable.

3 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Single Break Model We consider a failure where the elevator breaks at a single place.We consider a failure where the elevator breaks at a single place. Two fragments result, we study each one independently.Two fragments result, we study each one independently. Top fragmentBottom fragment

4 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory The Simulator Ribbon: strength 130 GPa, Young’s modulus 1 TPa, density 1300 kg/m 2, uniform stress of 65 GPa.Ribbon: strength 130 GPa, Young’s modulus 1 TPa, density 1300 kg/m 2, uniform stress of 65 GPa. Breaks: if strength exceeded or reenters too fast.Breaks: if strength exceeded or reenters too fast. Simulation: written in C, rotating reference frame, 100 masses and springs, forward Euler integration, 1 s time step, heavy longitudinal damping.Simulation: written in C, rotating reference frame, 100 masses and springs, forward Euler integration, 1 s time step, heavy longitudinal damping.

5 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Outline Introduction Introduction Top Fragment Top Fragment Bottom Fragment Bottom Fragment Simulations Reentry Modeling Effect on Ground-Based Assets Collisions in Space Collisions in Space

6 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory The Top Portion Escapes The top fragment of the elevator always escapes from the Earth. The top fragment of the elevator always escapes from the Earth. Recovery seems very improbable. Recovery seems very improbable.

7 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Effect of a Climber Even with a climber at its base, the top fragment escapes.Even with a climber at its base, the top fragment escapes. Moving climbers around will not help.Moving climbers around will not help. Without ClimberWith Climber

8 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Stability of Unanchored Space Elevator Arnold and Lorenzini (1987): A long enough dumbbell tether has positive orbital energy and is unstable.Arnold and Lorenzini (1987): A long enough dumbbell tether has positive orbital energy and is unstable. Steindl and Troger (2005): A geo-synchronous sky hook is unstable.Steindl and Troger (2005): A geo-synchronous sky hook is unstable. Impact for space elevator:Impact for space elevator: –When elevator is anchored, there is no stability problem. –Risk of stability problems when you are finished deploying but before you anchor? –Deployment increases stability. –How fast do you need to deploy to be stable?

9 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Outline Introduction Introduction Top Fragment Top Fragment Bottom Fragment Bottom Fragment Simulations Reentry Modeling Effect on Ground-Based Assets Collisions in Space Collisions in Space

10 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Low Breaks Most likely case (LEO).Most likely case (LEO). Minimal Coriolis effect. Falls straight down.Minimal Coriolis effect. Falls straight down. Some burnup on reentry.Some burnup on reentry. Cut 10% upCut 20% up

11 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Significant wrapping around Earth.Significant wrapping around Earth. Burn-up can cause fragments to be flung away.Burn-up can cause fragments to be flung away. Example of long lived fragment in 30% case.Example of long lived fragment in 30% case. Breaks near GEO Cut 30% upCut 40% up

12 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Higher… Centrifugal force causes first break now.Centrifugal force causes first break now. Tip of ribbon whips around sporadically.Tip of ribbon whips around sporadically. Cut 50% upCut 60% up

13 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Near the tip Wraps all the way around the Earth.Wraps all the way around the Earth. Overall small fraction of ribbon burns upOverall small fraction of ribbon burns up –Worst case for break 30% up ribbon. Cut 80% upCut 100% up

14 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Reentry Modeling Based on models for meteoroids.Based on models for meteoroids. –Jones and Kaiser (1966) Ribbon threads are very thin (10 μm).Ribbon threads are very thin (10 μm). –No thermal mass –Uniform thread temperature No ablation for slow enough reentry.No ablation for slow enough reentry. –Assume ribbon ablates at 600 K. –Limit velocity  5 km/s. Atmospheric Friction Radiation Velocity

15 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Terminal Velocity Simulation shows situ- ation at start of reentry.Simulation shows situ- ation at start of reentry. After initial reentry, slows to terminal velocity.After initial reentry, slows to terminal velocity. –10 m/s at 43 km –0.5m/s at ground level  Impact of elevator is leisurely. GravityCurvature Atmospheric Friction Tension

16 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Force on Ground Object Once ribbon reaches ground, only curvature force can be large.Once ribbon reaches ground, only curvature force can be large. –Worst case for large building with clear path to horizon. –Force arises from change in direction of tension. –For 20 T elevator: What about slipping/ sawing?What about slipping/ sawing? Tension BuildingHeightForceForce/Width 1 m 1.1 kN 1 kN/m 100 m 11 kN 10 kN/m

17 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Outline Introduction Introduction Top Fragment Top Fragment Bottom Fragment Bottom Fragment Simulations Reentry Modeling Effect on Ground-Based Assets Collisions in Space Collisions in Space

18 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Collisions in Space Fragment with SatelliteFragment with Satellite –Small collision cross- section. –Comparable risk to normal operations except GEO satellites. Fragment with ElevatorFragment with Elevator –Large collision cross- section. –Significant risk during limited period of time. Assume any collision is bad.Assume any collision is bad. Usually small risk windowUsually small risk window –A few hours for top fragment. –A day for bottom fragment. θ

19 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Limiting Risk to Elevators Only ever deploy a single space elevatorOnly ever deploy a single space elevator –Allows rolled up elevators to be in space for recovery. –Not a very compelling solution in the long term. Space out elevators by 90 degrees of longitudeSpace out elevators by 90 degrees of longitude –Works for low-altitude breaks. –At most 4 elevators. Move off equator if break occursMove off equator if break occurs –Needs detailed study to confirm reliability.

20 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Conclusion Confirms Brad Edwards’ reassuring views.Confirms Brad Edwards’ reassuring views. –Falling ribbon poses no mechanical threat at ground level. –Smaller risk of elevator fratricide than feared. Some surprisesSome surprises –Recovery of top fragment is not an option. –Less ribbon than expected burns up. Future workFuture work –Look into stability issues for unanchored ribbon. –Better models for the simulation.

21 Space Exploration 2005 — April Blaise Gassend — Computer Science and Artificial Intelligence Laboratory Questions? Contacting me: Telephone (617) Telephone (617)


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