Fate of a Broken Space Elevator

Blaise Gassend

Some Previous Work

Tower of Babel

Don't mix inches and meters.

Kim Stanley Robinson's Red Mars

Falling space elevator is a cataclysmic event.

Wraps around Mars multiple times.

Hits hard, with destructive violence.

Dr. Bradley Edwards

Broken ribbon flutters to the ground or burns up.

Top fragment might be reattachable.

Single Break Model

We consider a failure where the elevator breaks at a single place.

Two fragments result, we study each one independently.

Top fragment

Bottom fragment

The Simulator

Ribbon: strength 130 GPa, Young’s modulus 1 TPa, density 1300 kg/m2, uniform stress of 65 GPa.

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.

Outline

Introduction

Top Fragment

Bottom Fragment

Simulations

Reentry Modeling

Effect on Ground-Based Assets

Collisions in Space

The Top Portion Escapes

The top fragment of the elevator always escapes from the Earth.

Recovery seems very improbable.

Effect of a Climber

Even with a climber at its base, the top fragment escapes.

Moving climbers around will not help.

Without Climber

With Climber

Stability of Unanchored Space Elevator

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.

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?

Outline

Introduction

Top Fragment

Bottom Fragment

Simulations

Reentry Modeling

Effect on Ground-Based Assets

Collisions in Space

Low Breaks

Most likely case (LEO).

Minimal Coriolis effect. Falls straight down.

Some burnup on reentry.

Cut 10% up

Cut 20% up

Significant wrapping around Earth.

Burn-up can cause fragments to be flung away.

Example of long lived fragment in 30% case.

Breaks near GEO

Cut 30% up

Cut 40% up

Higher…

Centrifugal force causes first break now.

Tip of ribbon whips around sporadically.

Cut 50% up

Cut 60% up

Near the tip

Wraps all the way around the Earth.

Overall small fraction of ribbon burns up

Worst case for break 30% up ribbon.

Cut 80% up

Cut 100% up

Reentry Modeling

Based on models for meteoroids.

Jones and Kaiser (1966)

Ribbon threads are very thin
(10 μm).

No thermal mass

Uniform thread temperature

No ablation for slow enough reentry.

Assume ribbon ablates at 600 K.

Limit velocity  5 km/s.

Atmospheric
Friction

Radiation

Velocity

Terminal Velocity

Simulation shows situ-ation at start of reentry.

After initial reentry, slows to terminal velocity.

10 m/s at 43 km

0.5m/s at ground level

Impact of elevator is leisurely.

Gravity

Curvature

Atmospheric
Friction

Tension

Tension

Force on Ground Object

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?

Tension

Tension

Building

10 kN/m

1 kN/m

Force/Width

11 kN

100 m

1.1 kN

1 m

Force

Height

Outline

Introduction

Top Fragment

Bottom Fragment

Simulations

Reentry Modeling

Effect on Ground-Based Assets

Collisions in Space

Collisions in Space

Fragment with Satellite

Small collision cross-section.

Comparable risk to normal operations except GEO satellites.

Fragment with Elevator

Large collision cross-section.

Significant risk during limited period of time.

Assume any collision is bad.

Usually small risk window

A few hours for top fragment.

A day for bottom fragment.

θ

Limiting Risk to Elevators

Only 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 longitude

Works for low-altitude breaks.

At most 4 elevators.

Move off equator if break occurs

Needs detailed study to confirm reliability.

Conclusion

Confirms Brad Edwards’ reassuring views.

Falling ribbon poses no mechanical threat at ground level.

Smaller risk of elevator fratricide than feared.

Some surprises

Recovery of top fragment is not an option.

Less ribbon than expected burns up.

Future work

Look into stability issues for unanchored ribbon.

Better models for the simulation.

Questions?

Contacting me:

Email: gassend@mit.edu

Telephone (617) 253-4334

Fate of a Broken Space Elevator

Blaise Gassend

2005-04-07T17:54:57