Mars spins nearly the same rate as earth (about a 24.62 hour day). Mars has about 1/9 earth's mass. At 17,000 kilometers, altitude of Mars synchronous orbit is less than half the altitude of geosynchronous orbit (about 36,000 kilometers).
These considerations have led some Mars enthusiasts to claim a Mars elevator made of conventional materials is possible. No bucky tubes or other science fiction material is needed, Kevlar will do. Is this true? I will take a look using Chris Wolfe's spreadsheet.
Safety Factor
In earlier blog posts using Wolfe's spreadsheet I used a safety factor of 1, a razor thin margin. The slightest scrape or nick will make the tether break. This is like drawing a pentagram to summon the demon Murphy's Law. No sensible entity would risk expensive payloads on such a narrow margin. Much less human lives. I hope to revise my earlier blog posts to include more sensible safety margins.
In later blog posts I looked at scenarios using a safety factor of 3. With this margin a portion of tether can lose up to 2/3 of it's mass without breaking.
In this post I'll use tables looking at a range of safety factors. With a safety factor of 2, I cut tensile strength in half. A safety factor of 3 cuts tensile strength to a third. Which is a lot like cutting exhaust velocity in the rocket equation. Increasing an exponent can make tether thickness sky rocket.
Mars Equator to Mars Synchronous Orbit
This is the lower part of a Mars elevator. It exerts downward newtons that need to be balanced with upward newtons from elevator mass above Mars synchronous orbit.
Safety
Factor

Zylon
Taper
Ratio

Tether to
Payload
Mass Ratio

1

13

154

2

162

3191

3

2016

51824

Payload is mass of elevator car as well as elevator car's contents. The elevator car will need to include motors and power source.
Mars Synchronous to Sub Deimos Elevator Top
Elevator top is set 50 kilometers below Deimos' periapsis. This is to avoid collision. The counterweight and tether above Mars synchronous orbit must counterbalance the downward force of the lower elevator.
Mars Synchronous to Sub Deimos Elevator Top
Elevator top is set 50 kilometers below Deimos' periapsis. This is to avoid collision. The counterweight and tether above Mars synchronous orbit must counterbalance the downward force of the lower elevator.
Safety
Factor

Zylon
Taper
Ratio

Tether to
Payload
Mass Ratio

Counterweight
to Payload
Mass Ratio

1

1.02

38

1200

2

1.03

955

14800

3

1.05

1761

180000

The Whole Shebang
Safety Factor 1
Safety Factor 2
Benefits
Obstacles
Comparison to Phobos Elevator
Assuming lifting a 10 tonne elevator car and contents from Mars' surface and given a safety factor of 1, we'd need 10 * (38 + 154) tonnes of tether material. That'd be 1,920 tonnes of Zylon. Perhaps worthwhile if the elevator had a vigorous through put. I think these are the numbers Mars enthusiasts are talking about when they talk about Mars beanstalks made of Kevlar.
Also needed would be a 12,000 tonne counterweight. That's about thirty times the mass of the I.S.S.. This to lift a 10 tonne elevator car from Mars' surface? The need for a stud hoss counterweight sinks the argument for a Mars elevator, in my opinion.
10 * (162 + 955) = 11170. About 11 thousand tonnes of Zylon to lift a 10 tonne elevator car and contents.
We'd need a nearly 150,000 tonne counterweight.
I think it's pretty obvious a Zylon Mars elevator with a safety factor of two isn't worthwhile. I'm not going to bother looking at a safety factor of 3.
The elevator top is moving at about 1.7 km/s. It needs another 1.6 km/s to achieve Trans Earth Insertion (TEI). From the surface of Mars it takes about 6 km/s for TEI. So the elevator cuts saves about 4.4 km/s off of trips to earth.
Given a sensible safety factor, a Zylon tether would need to be much more massive than the payload. The counterweight mass would dwarf the payload mass.
Mars neighbors the main asteroid belt. Some rocks from the belt make their way to Mars neighborhood. Collision with asteroidal debris could cut the tether. Given this elevator's 20,000 km length and healthy taper ratio, there is a large cross sectional area. This increases likelihood of an impact.
Also there is a chunk of Debris named Phobos which crosses the elevator's path every 10 hours or so.
A Phobos elevator dropping to Mars' upper atmosphere and extending to Trans Ceres insertion is about 13,700 km. This about 6,000 km shorter than the Mars elevator described above. It also has a smaller taper ratio. This makes for a smaller cross sectional area to intercept debris. Being anchored at Phobos, this elevator won't collide with Phobos. The top is well below Deimos. orbit.
This tether can provide Trans Ceres Insertion as well as Trans Earth Insertion.
It takes about a .6 km/s suborbital hop for a Mars ascent vehicle to rendezvous with this tether foot.
Using a safety factor of 1, the upper Phobos tether has a 3.21 payload to mass ratio. The lower Phobos tether has a tether to payload mass ratio of about 16.1. So from top to bottom, about twenty times the payload mass is needed in Zylon.
The Phobos takes about 1/10 of the Zylon mass for a mars elevator with a safety factor of one.
A sub Deimos Mars elevator can't throw payloads above Mars escape velocity.
But with higher taper ratio, it'd take ten times as much zylon mass than a Phobos elevator.
This is with a safety factor of 1.
A Zylon Mars elevator with better safety factors is impractical.
I hope to revisit the upper Phobos tether and lower Phobos tether pages and include safety factors of 2 and 3. I suspect with a higher safety factor that a Zylon tether from Phobos to Mars upper atmosphere may not be feasible.
8 comments:
What about a tether that is built gradually?
You run a very thin tether down from your spaceship. It can carry a few dozen kg at most. The first step is to run a second line up, and add mass to the spaceship.
After a few weeks, you'll have the massive propellant depot needed as counterweight, and the large bundle of tether strands needed to provide the tensile strength.
The propellant depot/counterweight can fuel spaceships to complete their journey and artificially increase the throughput of the tether to increase its usefulness.
Matter Beam, let's say average speed of elevator car is about 260 miles per hour. It'd take two days to ascend and two days to descend the elevator. The elevator and contents can be about .5% of the tether mass even if you're daring and optimistic and use the safety factor of 1. The elevator engines and power source are going to take some mass so let's say the contents of the elevator car contain .3% of the elevator mass in Zylon. 1.003^230 is about 2. So it would take 230 4 day trips to double elevator mass. And that's using some very optimistic assumptions.
Is there any merit in an exceptionally slowly rotating rotovator? Where the only real purpose of the rotation is to transport material from point A to point B without the need for a elevator car?
Hollister David:
I'm sorry, but how did you get the 0.5% figure?
Matter Beam, go to The Whole Shebang section. For the lower part of the elevator as well as the upper part to counterblance, you will need 1,920 tonnes of zylon to accommodate a 10 tonne payload. 10/1920 = .00521. About 5%.
And that's with a safety factor of one.
I see.
So for every 1kg of climber, you'd need 192kg of Zylon and 1200kg of counterweight?
You know, the situation can be flipped around if we consider much faster travel times. A free wheeling mass pulled up by a secondary cable attached to the tether and travelling through vacuum is unlikely to limit itself to 260mph. 1km/s can easily be achieved. After all, the tether is very straight and after the initial boost, you'd only need to counter gravity drag. You can also just drop the empty bucket once it reaches the top. It could be completely used up instead: a spool unrolling as it travels with the remains adding to the counterweight mass.
The elevator is 19700km long or 17000km? That's a travel time of 5.5 to 4.7 hours and not having to travel back down would mean the elevator can double its mass in 24 trips using a factor 1.03, or about 5.5 to 4.7 days. Within a year... well, it adds up extremely quickly.
Matter Beam, Secondary cable? What's the mass of this secondary cable? Do you imagine a loop with a pulley on each end? How much mass is the pulley? How many newtons of stress can the junctures with pulleys withstand? Going around a pulley would induce bending and flexing thus wear and tear on the tether.
A straight line isn't a valid assumption. Elevator cars going up or down will have Coriolis force pushing the tether sideways inducing oscillations.
Also how much horse power will the elevator cars have? Or how much horse power would the engines driving the pulleys have? How many kilograms are the engines and power source?
1 km/s can easily be achieved if you use lots of hand wavium.
Bumblebee,
"Is there any merit in an exceptionally slowly rotating rotovator?"
Long thin objects want to hang vertically in a gravity field due to tidal effects.
The slower it is rotating, the quicker it will stabilise, hence the more energy will be required for keep it turning against this tidal braking.
That said, if most of your mass is moving downhill  for example, supplies from Earth for the colonists, fuel from Phobos for ships, etc  then a rotovator tether below Phobos' orbit will have net positive momentum which will raise its orbit. Using moving masses along the tether, synced to the tether's rotation, it might be possible to harvest that extra momentum and convert it to rotation.
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