Saturday, April 16, 2016

Liftport Lunar Tether

This is the fifth in a series of posts using Chris Wolfe's spreadsheet to look at various elevators.

274,000 km Lunar Tether

This is based on the Ladder PDF written by Liftport  founder Michael Laine and Marshall Eubanks.

Eubanks and Laine suggest the use of Zylon or M5. This is why I've been using Zylon through out these tether posts. These gentlemen have invested a lot of time and effort researching elevators and tethers. If they like Zylon, I'll follow suit.

They propose launching the tether to EML1. From EML1, the tether anchor would descend moonward towards Sinus Medii on the lunar surface, 0º, 0º. The spent upper stage would drop with the tether foot earthward.

If the mass were tethers alone, the 264,000 length would be inadequate to keep the tether from collapsing to the moon. But spent upper stage acts as a counterweight to maintain tension.

Ratios earthside of EML1

A spent Centaur upper stage is about 2250 kilograms. This is the quantity I used for foot station mass. These newtons subtract from newtons available for payload. The Ladder PDF calls for 11 tonnes of Zylon. By trial and error I entered payload quantities until tether mass in my spreadsheet came to 11 tonnes.

In addition to foot station mass of 2250 kg, I got a maximum foot payload mass of 1640 kg.

Zylon taper ratio: 1.61. Tether mass to payload mass ratio: 8.05

Given the extreme the extreme length of this elevator, I expected a higher number than 8. But the net acceleration at the tether foot is only .0274 newtons per kilogram. With this acceleration, a 10 tonne mass would exert as much force as when my 62 pound dog sits on my lap.

Ratios moonside of EML1

But what sort of payload can this elevator support moonside of EML1?

At the anchor in Sinus Medii, my tether model's cross sectional area is 1.64e-8 square meters. Multipying this times Zylon's tensile strength gives ~95.4 newtons the tether can support. Net acceleration at this point is 1.4 meters/s^2 (mostly moon's gravity). 95.4 newtons/(1.4 m/s^2) = 68 kilograms. For a payload just above the moon's surface, the elevator can support 68 kilograms.

Tether to payload mass ratio: 161.

Let's say we wanted a 1 tonne elevator car capable of carrying 9 tonnes of cargo. We'd need a 1,610 tonne tether.


Dropping a payload from 70,900 km earthward of EML1 would send a payload to to an atmosphere grazing orbit. Repeated perigee aerobraking passes could circularize the orbit. Shedding 3 km/s via repeated drag passes would require some thermal protection but not as much as the space shuttle which would shed 8 km/s over a very short time.

Thus lunar materials could be delivered to Low Earth Orbit (LEO) without using reaction mass.

Likewise, a 3 km/s LEO burn could deliver payloads to an apogee where orbit velocity matches tether velocity. Normal delta V from LEO to moon surface is about 6 km/s. So the elevator cuts about 3 km/s from the delta V budget for reaching the moon's surface. Cutting 3 km/s from delta V budget about doubles payload mass if using H/Lox bi-propellent.

Dropping a payload 160,000 km earth of EML1 would send a payload to an orbit with perigee as geosynchronous orbit altitude. At perigee the circularization burn is .95 km/s. Thus delta V between GSO and lunar surface is less than kilometer per second.

Some drawbacks

This is a very long tether. How fast can an elevator car move? Having copper wire along the length of the tether would boost taper ratio as well tether to payload mass ratio. For descent from EML1 to lunar surface, the tether to payload mass ratio is already 161.

So in addition to carrying gripping wheels and a motor, the elevator car must carry it's own power source. Photovoltaic arrays? There are solar powered golf carts. These aren't famous for their speed. There are Tesla cars whose lithium batteries can be charged by solar cells. These vehicles can move. It is also possible lithium batteries could be charged during an elevator cars down hill descent via regenerative braking. Downhill would be moonward or earthward from EML1. Movement towards EML1 would be uphill.

Batteries, solar arrays and/or regenerative brakes would boost elevator car mass and thus subtract from cargo mass.

Let's say the elevator car can move an average speed of 400 mph (644 kilometers/hour). A round trip along the length of this elevator and back would take about a month. If the elevator doubles payload mass delivered from LEO, it'd take about 160 months to recoup the investment of delivering tether mass from LEO.

And what justifies this investment? What are the benefits of a facility at Sinus Medii?

I'm a moon guy but it's the lunar poles I like. There are polar plateaus that enjoy near constant sunlight and very mild temperature swings. These plateaus neighbor permanently shadowed crater floors that might harbor rich volatile deposits. In situ CHON not only makes life support easier, but extra-terrestrial propellent could break the exponent in the rocket equation.

But Sinus Medii is at the equator. It's as far from the lunar poles as a lunar surface point can possibly be. We're stuck with two week nights, severe temperature swings and regolith drier than a bone.

Charles Radley has suggested mining He3.  I'm not holding my breath but what if we achieved fusion power? Here is John Schilling's take on fusion and lunar He3:
Helium-3 mining on the moon simply does not pass the arithmetic test. The highest 3He concentration ever recorded in lunar regolith is fifteen parts per billion, and the process by which it is deposited is inherently resistant to geologic concentration.
Assuming someone manages to invent a 3He fusion reactor that operates at 50% efficiency (giggle), that translates to net energy output of 4.5E6 joules per kilogram of high-grade regolith.
The energy output of a kilogram of the lowest grade of coal burned in a good 19th-century reciprocating steam engine, is about 4.5E6 joules per kilogram. And that doesn’t change if you substitute dried peat for the coal.
So, the proposal is to set up an enormous mining infrastructure on the Moon, and invent a fundamentally new kind of engine backed by fifty years of failed promises, for the sake of an energy source roughly as good as burning high-grade dirt in a type of engine obsolete for over a century.
And no, that analysis doesn’t change significantly if we include accessible reserves or environmental impact.
I understand that you want desperately to believe that there are immense riches to be had in space, as soon as the suits see the light and come up with the money. The good news is, this is probably true. But the list of great riches to be had in space, does not include lunar helium-3 (or helium-4, for that matter). The numbers do not add up, no matter what the glossy magazine articles say, and math trumps faith.

Other than fuel for fusion it is hard to imagine He3 markets that would justify the expense of a lunar tether and mine.

I admire Michael Laine. I believe tethers will play a part in making space transportation economical. I also like and admire Charles Radley as well as Marshall Eubanks. So it pains me to say this. At this point I am not enthusiastic about the Liftport Lunar elevator.

But there are other possible elevators in the moon's neighborhood.


Tony said...

With regards to powering the elevator car:
One application for a lunar tether will possibly (or even likely?) be to transport LH2 and LOX from lunar surface to Earth orbit – why not use part of the LH2/LOX payload to power the elevator car via a fuel-cell?

Tony said...

One more thing:

Do you think it would be possible to have *two* tethers (more or less parallel, with some distance between them) that share one foot station? So a car drives up on one tether, then on the foot station it leaves the tether (the car basically "parks" at the foot station). And once the loading/unloading of the car at the foot station is finished, it would attach to the *other* tether and drives down on that tether.

The cars obviously would need then to be transported from one tethers's anchor to the anchor of the other tether - but I imagine that to be trivial compared to the other challenges...

This way, the utilization might be better, I would imagine, as it would be possible to send a car up on one tether, while another car awaits unloading.

And I guess, if two tethers could be coupled like that, then this could be used to scale up the lunar lift over time...

Hop David said...

Tony, sure you could add to the tether to allow for two way traffic. But doubling the number of elevator cars means doubling tether mass. And tether mass is around 160 times that of an elevator car and its payload.

Unknown said...

I quite enjoyed this, but of course i have my own concept and so i'm looking for how to make this work with it. For that, i need to ponder.

It did occur to me though that power could be beamed from the counterweight to the elevator car as microwaves, in which case it only needs a relatively small rectenna and the electronics to convert the power. Putting large solar arrays on the counterweight is a help as it adds mass where you want it and the power can be used for other things as well, like station keeping.

Since the tether end that's above the lunar surface is going to wander around as the Moon librates and moves nearer and farther from Earth, there may regularly be times that this elevator would be near my favorite crater, Lalande, at 4.5 S by 8 E. My inclination then would be to put the counterweight a bit above EML1 and try to create a real space station there.

To keep the tether near the surface, it seems to me you are going to have to reel it in and out. That reel of material would also help beef up your counterweight / space station.

Michael Laine said...


Nice write up. THANK YOU for taking the time to do that. I'm not going to argue your math - although our numbers are different from yours in some important areas. Instead, I'd re-state a comment I've become a little famous for - "We don't even have all the questions, yet, let alone have all the answers..." So, to my mind, your critique is valid, and at this stage, it's to be expected that our numbers are different. We're almost certainly using different variables in our equations.

I've got three comments/responses:
1) NO ONE on our team thinks He3 for fusion is a viable market... Instead, look up Charles Radley's info on current, TERRESTRIAL markets for he3 - roughly $1M/liter for radiation detection, MRIs and a few other exotic uses. You noted in your research above that we can't carry very much cargo... so we need a small volume/small mass/high value product. H3 is ONE of several options. (There are others, but He3 seems to be the only one that people focus on, and they almost always point to fusion... I blame pop culture! ;-)

2) Tony - Adding another Ribbon will almost certainly tangle the two... thereby wasting a multi-billion dollar asset. It adds mass to a fragile system, and that weight penalty will ultimately decrease our cargo throughput. In short, it's a non-starter. Instead, imagine a v2.0 elevator that has Lifter cars that can bypass (robotic hand-offs) another car. Yes, that is a long time from now, but we've already got some interesting models. We're not even close to actually building those, yet. But they are in the plan.

3) Kim - Power beaming is assumed. Again, the mass of the required infrastructure to self-motivate each Lifter vehicle will kill cargo capacity and throughput. It's too slow and too heavy. We assume there will be power beaming elements at each of the three main nodes: The LiftPort (on the lunar surface), the PicoGravity Lab at the Lagrange point, and the Counterweight at the end of the Ribbon.

Thanks, ALL of you, for your interest in our project! FYI, we are rebuilding our website from scratch. The new site should be complete by the end of the month. On it, we'll have thousands of photos, hundreds if art images, and probably 50-100 technical pdfs. Hopefully, some of this stuff will answer many of the questions I didn't respond to, today.

Finally, we MIGHT have figured out something important. If so, there will likely be an announcement in the fall. (That's why we're rebuilding our site; we think there are going to be a lot of folks that want to independently check our math...)

Take care,
Michael Laine, President, LiftPort Group

Hop David said...

Michael Laine, thank you for the response! It is my belief the technologies Liftport is developing have a huge potential for making our solar system more accessible.

I am certainly fallible. I'd like to hear your numbers and the your methods. On several occasions hostile reviewers have exposed arithmetic errors on my part or flaws in the mathematical models I use. Although I hate eating crow, I wish more hostile reviewers would take the time to check my work.

Thank you for your response to Kim Holder. Interaction between commenters can make a post a lot more informative.

I recall plans for geosynchronous orbital power stations assumed beam power density a quarter of that for sunlight. Although those beams would have an atmosphere to penetrate and I think that quarter sunlight density was put out as P.R. against fears power beaming could be used a death ray. From EML1 to mid point of a moonward tether and base station to mid point is a distance comparable to geosynchronous. EML1 and counterweight distance to midpoint of earthward tether would be about 100,000 kilometers?

Orbital elevators and/or momentum exchange tethers are among my favorite day dreams. These smaller cousins to full blown Clarke towers don't suffer the big taper ratios their bigger cousins endure. Being shorter, they wouldn't have the through put issues of extremely long tethers. With much smaller taper ratios, it might be possible to have power cables along the length of the tether.

I hope to look at lunar sky hooks my next blog post. It is my belief there are lunar orbits low enough that earth's tidal influence won't wreck the orbits but high enough the orbits aren't vulnerable to lunar mascons. Such an orbit could have have a high inclination so polar as well as equatorial locations would be accessible.

Unknown said...

While the initial tether would go to the lunar equator. Additional tethers with an angular component can be established by dropping a tether and attaching it to vehicle to establish a new anchor point away from the lunar equator. These tethers would be longer and might have to carry reduced cargo but would save travel time on the lunar surface.

Charles F. Radley said...

Greetings, I wish to make several responses here:

1) Chris, you have misquoted me. I have never suggested using Helium-3 for fusion reactors. I have suggested selling Hleium-3 into the EXISTING market ... there is currently about $100 million per year demand for Helium-3 and it sells at one million dollars per ounce. It us used in a variety of industrial applications, e.g. neutron detectors for homeland security, oil and gas exploration and hospital MRIs. It is in short supply and high demand.

2) The velocity you quote for the climber is way too slow. You need to look at the study of the Technion University team in Israel [Jacobs Ladder] in 2010. They determined an optimized velocity of about 700 kilometers per second, taking only a few days to travel the length of the tether. We can probably go faster than this, but the limit is uncertain at this time.

3) Power source: the Technion team figured that a 25 KW PV solar array would suffice and easily be accommodated within the weight budget of the climber.

4) Poles versus equator: there is a lot of value to an equatorial bases, Oxygen can easily be extracted from any lunar regolith, and this can be shipped to LEO and sold to operators of geosynchronous communications satellites. It reduces the cost of propulsion from LEO to GEO by eight times, a market of around $1B per year. It would also greatly reduce the cost of mission to Mars and other solar system destinations. We can also obtain valuable rare-earth elements from the rich KREEP deposits at the crater Lalande, close to Sinus Medii.

5) We have a Facebook page at this link:

Charles Radley - Assoc Fellow AIAA

Robert Clark said...

Thanks for the insightful article. Note you are arguing the stumbling block is financial. This means it is technically feasible now.
About the financial question, you argue it would take 160 months to recoup the development cost, mostly the cost of getting the tether to the Moon, too long a time period for an investment of this magnitude.
But note this is highly dependent on the speed of the elevator cars. You give a speed of 640 km/hr. We might make a comparison to the Japanese bullet trains which have reached a max speed of 600 km. But the bullet trains have to use a large amount of power to magnetically levitate above the track and to fight air resistance, quite large when traveling at such high speed at sea level. Without these impediments, in vacuum in zero gravity, the elevator car should be able to travel much faster.
Another possibility might be to use the elevator car to carry the cargo to lunar orbit, but after that in zero gravity use electric propulsion (EP) to reach high speed. The thrust of EP is dependent on the power available. And higher thrust shortens travel time. So we might want to use the tether to carry high power to the EP thrusters.

Bob Clark

Anonymous said...

Does anyone know of somewhere on the web where someone has done the calcs for how much mass (fraction) it would take to tether and spin up a craft going to Mars.

Unknown said...

Hop, I think the reason most people specify Zylon while I stubbornly dream of Spectra is creep. A Spectra cable will continue to deform over time while under stress because its strength comes from Van der Waals forces between long molecule chains; these chains can slip past each other. Zylon experiences this effect to a much lesser degree in part because of its aromatic rings; they form a sort of ratchet that resists slipping. Another approach is to cross-link, forming chemical bonds between adjacent molecules; this can be done in PE with gamma radiation or electron beams, but with little information in the public domain about the effects on either creep or ultimate tensile strength.

LADDER as a science mission makes sense, both to validate tether / space elevator technology and to return new samples. It's a high risk approach, but someone has to be the first. It is not intended to be the first strand of a permanent structure, so long-term concerns about location and other design choices aren't terribly relevant.

Looking beyond the initial mission...

A suborbital hop from one of the poles to Sinus Medii base would cost 1.53km/s to accel and the same to decel (per 'travel on airless worlds'). Let's assume for the sake of argument that we have a reusable hydrolox rocket of 1 ton dry mass, 10 tons takeoff mass, 10% dV margins and Ve=4462 (~455 Isp). Further assume that we can manufacture abundant LOX at SM base, so the ship tops off after delivering cargo. An all-propulsive mission (launch, land at SM, unload payload, take on LOX, launch, land at pole) would deliver a bit over 3.5 tons of payload (35% payload fraction), a 'gear ratio' of 1.8kg fuel per kg payload. This is good enough to justify SM base as a place to accumulate material for shipment; the 'gear ratio' for direct surface to orbit is more like 3.3:1 so the tether ends up cutting transportation fuel costs by 45% even in the worst case. This is not without drawbacks as you mentioned, but it does have significant merits.

Expanding on that, a tether sling launch system at the pole to provide that initial 1.5km/s would drive the payload fraction to around 57%, or 0.75 kg fuel per kg payload. The launcher shaves off an additional ~32 percentage points of fuel costs, for a total fuel savings of 77% over direct to orbit. When added to the easy access to Earth return (3km/s or free with heatshield) and GEO (~1km/s), visions of giant GEO powersats start appearing.