Tuesday, June 21, 2011

Interplanetary Flight Times.

Too often when we talk about future interplanetary flight we assume the trajectories used will be Hohman transfer orbits, elliptical orbits that intersect of both the orbit of departure and the destination tangentially, in the case of Mars this involves flight times of around 250 days. But even with todays chemical rockets the mass ratios for flight times of 150 days may be optimal for cost, and with thermal systems using hydrogen as the propellant flight times of just 70 days to Mars may not only be reasonable, but sensible, with hydrogen propellant and exhaust velocities of 10km/s a delta v of 6.5km/s is achievable with a mass ratio of only 2. All it requires is a thermal energy source to heat the propellant, aerobraking at Mars, and a propellant source on Mars for the return.

Sunday, June 19, 2011

Space Mirrors

I think mirrors are incredibly underrated by people theorizing about future space technology.

On Earth a mirror has to be heavily constructed to holds its form, in space with little or no gravity and no wind to contend with they can be as lightweight as soap bubbles.
The lightest mirrors that are now being studied are intended as solar sails, 3 grams a square meter has been achieved, if we round that down to 1 gram a square meter, how much light can be collected by 10 tonnes of mirrored material at various distances from the sun?
Well, 10 tonnes, at 1 gram a square meter, would give you an area of 10 square kilometers:

from sun___intensity___10km^2

1__________1.3_________13,000.0 (Earth)
2__________0.325________3,250.0 (Mars)
5__________0.052__________520.0 (Jupiter)
10_________0.013__________130.0 (Saturn approx)
20_________0.00325_________32.5 (Uranus)
30_________0.00144_________14.4 (Neptune)
40_________0.0008125________8.1 (Pluto)

So even at the distance of Pluto, just 10 tonnes of mirrored material gives us the ability to concentrate 8 megawatts of sunlight, if solar cells will give you 1KW/KG at Earths distance from the sun, using light-weight mirrors to concentrate the sunlight, they'll still give you about 0.44KW/KG even at Pluto's distance from the Sun.

Saturday, June 18, 2011

Blowing up asteroids

When we've gotten ourselves established in space throughout the Earth-Moon system the next place I'd like to see us target for exploitation are the Near Earth Objects (NEO's), asteroids that orbit the sun at about the same distance that the Earth does.

Because they're close, and because of their small size and low gravity, these objects hold the promise of resources within relatively easy reach, resources that even if not richer than those of the Moon, will in many respects be different to those offered by the Moon, and different and richer can mean the same thing.

Lets imaging our prospectors arriving at what they hope will be a gold mine of rich rare earth elements, water and other volatiles, heavy metals and whatever else that has a market value. Question: how to use the asteroid to shelter yourselves from the radiation of space, How to find out what's inside, and how to get out any resources that are there?

Here's an idea that I haven't come across than might solve all three problems at once - blow it up! No, not with explosives.

Small asteroids are not held together too well gravitationally, if they're loose rubble piles even kilometers inside them, even at their core, the pressure from the weight of material will be very small, so in principle it would be possible to drill a single hole, shove a balloon down it, blow air in, and spread the entire mass of the asteroid out over the balloons inflated surface. Then you move inside, hell, move the whole family inside!

OK, you still want solar reflectors to warm the interior, and you'll probably want more than just the balloon used to inflate the asteroid for accommodation.

If we take an asteroid that's a Kilometer in diameter, and inflate a balloon that's a kilometer in diameter inside it, if the material of the asteroid were spread out evenly, it would form a layer about 125 meters thick.

Friday, June 17, 2011

Rotovator assisted Aerial Propellant Transfer

In my post Aerial Propellant Transfer I concluded that with APT each flight could costs as little as "$1.5 million per flight plus the operators profit. Which comes to $75,000/tonne or $75/kg payload".

But by combining APT with hypersonic rotovators we can substantially improve even on that $75/tonne. Using a 600km long tether we can get the maximum velocity required from the orbiter spaceplane from orbital velocity of 7900m/s down to 4030m/s, a reduction in the required delta V of 3870m/s. We still have the ability to transfer 340 tonnes of propellant to the spaceplane from a tanker at 12,000meters, and because we've gone with APT rather than using the A380 (or similar aircraft) as a booster for air launch, we won't have the compatibility problems that would certainly have occurred in trying to mate a different spaceplane to the booster.

In my previous example post refueling the spaceplane needed a delta V of 8400m/s, by knocking 3870m/s off that requirement delta V comes down to 4530m/s, now we still separate from refueling with 340 tonnes of propellant, and our rocket engines are still H2/O2 with an exhaust velocity of 4500m/s so using the rocket equation a mass ratio of 2.75 gets us a delta V of 1.011 times exhaust velocity, ie. 4500 x 1.011 = 4550m/s. total mass to orbit is 1/2.75 of total separation mass which is 340/1.75 = 194.2tonnes, because total mass at separation has increased (from 400 tonnes to 534.2tonnes (33.6%) the unladen mass of the spaceplane will also have increased, working on a 33.6% increase, unladen mass goes from 40 to 53.4 tonnes, and payload increases from 20 to 140 tonnes. While we will have to increase the engine power of the spaceplane by 33%, the time those engines fire will also be reduced, the tanker requirements are unchanged ($500,000) allowing an increase of 33.6% in orbiter costs (servicing and capital) takes that to 1,336,000 total 1,836,000 divided by 140 tonnes brings cost/kg down to about $13.10, with rotovator energy costs of around $2.50/kg (the rotovator uses electric propulsion to maintain momentum, accelerating 1kg of payload by 4km/s 0.1kg of propellant is expelled at 40km/s, using E=1/2MV^2 that's 80 million joules or 22.2 KWh, at $0.1/KWh thats $2.22/kg of payload plus energy loses) totaling $15.60 plus the servicing and capital cost of the rotovator(?)

Thursday, June 16, 2011

The Stanford torus

Back in the '70's when dreamers were dreaming big dreams about Colonizing Space, one of the most popular colony designs was the Stanford Torus, named for it's torus design and its designers place of work.

The Stanford Torus is a tidy wheel design that spins at 1RPM, it's the shape of a bicycle inner tube 2km in diameter, and provides an artificial gravity as strong as that of Earth to its residents, who live in the inner tube with their heads pointed towards the axial, their feet planted on the inside of the outer circumference of the inner tube wall. The original design had a tube with a width of 130 meters which, with the tube circumference of 6.2 kilometers gave an area for the inhabitants of 832,000 m^2 or 83 hectares of living space.

The population of this colony was proposed to be 10,000 people, plus their pets and livestock, it was originally suggested that it be at L4 or L5, though it was later suggested that the ideal location would be at an orbit about Earth in 2:1 resonance with the moon so as to be positioned between the Moon - the source of raw material - and geosynchronous Earth orbit - the destination of its manufactured product - solar power satellites (SPS).
Being so deep in space the colony would be without the protection from the Earth's magnetic field that protects people and facilities in Low Earth Orbit, so the colony was to be protected by a several meters thick layer of slag or waste from the lunar regolith processing facility, this shield would weigh about ten million tonnes.

I like the Stanford Torus, it is easily the lightest of the various designs that the Stanford team studied, and unlike a cylinder design, it didn't have a pointless kilometers deep atmosphere, and the small diameter "inner tube" meant far lighter construction than a big diameter cylinder. it's an elegant design that's an efficient use of mass, and it caters for a population that I think is realistic, a smaller population would struggle to support a feeling of being a civic community, a much larger population would take time to build, and such a large colony would require a far bigger investment than would be necessary for a first step to establishing a community that was truly living in space.

I like the Stanford Torus, but I don't think colonizing space will be done on the back of a huge investment in mining the Moon, launching the mined regolith into space, catching and processing that regolith into solar panels, microwave emitters and girders, and then constructing SPS's tens of kilometers across which are then moved to GEO. It's all too big a hurdle, too much risk, too much investment all at once, every step of which has got to work.

The Stanford Torus I remember was a place I'd want to live, even if a small section cost ten million dollars, I imagined that there would be no shortage of super rich people, bored with the sterility of Beverly Hills, who'd jump at the opportunity to spend far more than ten million to live there, and I remember thinking that even if I couldn't live there, I'd sure want to visit it some day.

Wednesday, June 15, 2011

Aerial Propellant Transfer.

There are I guess four basic types of schemes for getting into orbit (putting aside the nuclear option which for political reasons and genuine safety reasons isn't worth wasting time discussing), there's the disintegrating totem poles we've always used (eg. Falcon, Shuttle), there's the really big capital investments schemes with banks of lasers, or banks of microwaves emitters to get the effective Isp of some tiny launch vehicle up enough to get it to orbit, thers's space elevators, and then there's some sort of fully reusable self-contained launch system (eg. Skylon).

If you want to see airline type operations into orbit forget Falcon, expendable or nominally re-usable - more like refurbishable - launch systems will never get the cost down low enough, they're like throwing 747's away after a single use.

Maybe one day we'll see the laser launcher or a space elevator, but if we do it'll only be after there's already lots of stuff going up via other means, people need to be realistic that big mind numbingly huge capital investments aren't going to get the ball rolling.

So we're left with the Single Stage To Orbit (SSTO) and Two Stage to orbit (TSTO)fully reusable options that have been proposed again and again over the last 40+ years.

Why hasn't one of the many variations on these methods ever been seen through?

SSTO has the problem with mass ratios, even with the most energy dense rocket propellant in use, 90% of your launch mass has to be propellant and the other 10% is structure, leaving ~0% as payload. You can look to improving that mass ratio with air breathing engines, and if jet engines could be built with the same thrust to weight ratios as rocket engines have, SSTO would be a done deal, but the reality is that the best jet engines only have T/W ratios of about 13:1 (verses about 50:1 for rocket engines), and you end up taking all the mass of those engines to orbit, and one tonne more of engine means one tonne less of payload.

TSTO has the problem of shear size, building a winged orbiter to carry 20 tonnes to orbit would in itself be a manageable financial expense, but to build the ~800 tonne winged booster for a twenty tonne payload isn't quite so manageable. When they were looking for a reusable system to replace expendable launch vehicles in the 70's the designs were often of two stage fully reusable vehicles, and Congress always said "no - too expensive".

If you've seen many of my comments on various blogs recently you probably know that I've become a bit obsessed with Aerial Propellant Transfer for spaceplanes. The reason is that I see it as a route to achieve today what could not be done 40 years ago. APT means you can dispense with that 20 or 30 billion dollar specialized booster and replace it with a $350 million dollar (plus modification) commercial aircraft.

Probably one of the first reactions to the suggestion of a "booster" that only goes to Mach 0.85 and 12,000 meters is that it's not enough to make a difference. But it actually counts for more than commonsense would suggest; when the orbiter begins its climb to orbit its engines are working with far less atmospheric back pressure and so are more efficient, the orbiter can take off from the ground with only enough propellant on board to reach the tanker, and so requires lighter landing gear and possibly smaller wings, and the atmospheric drag from 12,000 meters is far less than that from the ground half the atmosphere is below you.

That start from altitude is worth about 1km/s, it reduces the propellant mass ratio from about 90% to about 85%, and if 11% of your light-off mass is orbiter your payload goes from less than 0% to 4% of the orbiters total mass, even better, aircraft landing gear typically makes up about 2% of lift-off mass, if you're refueling in the air the weight of the landing gear can be halved - so you've increased payload by another 1% of the orbiters total mass to 5%.

If want to get a 20 tonne payload to orbit, how big does the orbiter need to be? 20 tonnes X 100/5 = 400 tonnes, of which 85%, or 340 tonnes is propellant and 40 tonnes orbiter.

So we need a tanker that can transfer up to 340 tonnes (minus any excess that the orbiter has carried up) to the orbiter at an altitude of 12,000 meters.

That's a lot of propellant, it's more than can be carried by a 747-8, and even the A380 freighter only has a take-off weight of 590 tonnes total, of which 250 tonnes is plane, which would leave only 340 tonnes for both rocket propellant and the A380's own fuel.

I've tried sounding aircraft engineers out on this, the A380 as a tanker has far more space in the fuselage than would be required, my thoughts are that perhaps a fuselage based on that of an A340 - some models of which are actually longer than the A380 - could be attached to the flight surfaces of the A380, that would shave about 80 tonnes off the total mass, but even doing this would still require that some of the rocket propellant (LOX) be carried in the tanker aircrafts modified inboard wing tanks as the structural payload (payload that can be carried in the fuselage, even with the lighter fuselage, would still only be 230 tonnes.

So while heavy lift to orbit using APT might be possible now, the aircraft to do it didn't exist just a few years ago, and even the A380 would need big modifications for a heavy lift orbiter.

Another point I want to emphasis is that using even the A380 as a booster for air launch wouldn't put anything like a 20 tonne payload into orbit, even with sticking on an A340 fuselage to reduce weight, the maximum weight of the fueled orbiter would be 230 tonnes and the increased drag and high center of gravity would bring in more complications, maybe 9 tonnes of payload could be carried to orbit.

ATP has an advantage over a system which uses a direct ascent from a runway, there are far more launch windows because the ascent from 12,000 meters can take place anywhere within perhaps a thousand kilometers of the runway.

So how much would each launch cost?
The cost of flying a jumbo on a long haul flight is around $500,000, a third of which is fuel, that's also about the cost of a USAF KC135 flight to refuel other aircraft a thousand km from base. So excluding the cost of the propellant transfered, that's probably a reasonable figure for the tanker.

The cost of the propellant LH2 and LOX will be around $250,000

The cost of the orbiter excluding propellant will be servicing and payback on capital invested, with the servicing aerospace engineers tell me that with the experience gained from the SSME's it's possible to build H2/O2 that can be turned around in with almost no servicing between flights if that applies to all of the orbiters systems, servicing of $450,000/flight seems reasonable (that's about 20 times the servicing cost/tonne of airliners).

With the payback on capital invested, the development of aerospace vehicles that don't require radically new technology is around a hundred million dollars a ton dry mass, the numbers quoted for Skylon are much higher than this, but everything about Skylon is new technology, from the engines, to the active thermal control system, to the truss frame construction. The ATP would weigh about 45 tonnes dry, so I'm putting development cost at $4.5 billion, if 10 are initially built and per unit manufacturing cost is $100 million that's $550 million each. If they're good for one thousand flights that's $550,000/flight.

Adding those all together works out at $1.5 million per flight plus the operators profit. Which comes to $75,000/tonne or $75/kg payload.

That seems ridiculously cheap compared to the SpaceX Falcon, but then they're still throwing hardware away with every flight.

It also seems ridiculously low compared to what REL are talking about for Skylon, by then Skylon is really pushing the envelope with new technology, and it's the last 10% that takes 90% of the effort, an ATP using the Skylon structural system would in theory weigh half as much dry and carry twice the payload.

Tuesday, June 14, 2011

The package deal. A comment I made at Nasaspaceflight

« Reply #79 on: 06/12/2011 09:58 PM »

1. Aerial propellant Transfer for spaceplanes. A modified A380 could refuel a reusable Lh2/LOX spaceplane large enough to put a 20 tonnes payload into LEO. With operations of airline efficiency, cost could be as low as $100/kg. APT hugely increases the number of launch windows compared to direct ascent from the ground.

2. Hypersonic rotovators. In sun synchonous orbits, combine this with APT spaceplanes and costs to orbit could be as low as $25/kg as payload /spaceplane quadruples.

3. Space tourism, a hotel in the polar dusk to dawn sun synchronous LEO orbit would be in  continuous sunshine.

4. Solar power satellites, these also go into sun synchronous orbit with microwave reflectors in equatorial orbit to send power to rectenna near population centers on the ground.

5. Stanford torus, again these go into sun synchronous orbit, they are a base for the crews building the Solar power satellites, a home for rich people wanting to move out of Beverly Hills and a destination for tourists.

6. Solar thermal rockets, I'm puzzled that these don't get more study for interplanetary flight, they only need light weight mirrors to collect sunlight and don't waste that sunlight energy the way solar sails do by just bouncing it away, at 1AU from it the sun provides 1 GW of power per square km, H2 propellant will give an Isp of about 1000s, H2O ~400s. Why would anyone even consider the weight cost and complexity of nuclear electric or solar electric?

7. Asteroid mining.

8. The lunar surface based rotating tether covered at the end of this paper:

Sunday, June 12, 2011

I'm a bit skeptical about Skylon.

After running through the mass numbers for Skylon that Reaction Engines offers, I'm left believing that they've got an engine that will theoretically get them to orbit in one stage, but only by them making unrealistic assumptions about the structural weight of the rest of the vehicle, total dry mass 53 tonnes, engine thrust 270 tonnes, engine T/W 14 therefore mass of engines ~19 tonnes, therefore mass of the rest of the vehicle ~34 tonnes. 34 tonnes for a winged vehicle that's 83 meters long, carries all its landing gear to orbit, it has a propellant volume around 1400^3 meters, it uses cryogenic propellants and it has to endure re-entry. I know they're promoting Skylon as having revolutionary construction materials and methods, but it seems to me they've had to make some excessively optimistic assumptions about the structural weight to get the numbers to come together  so they can continue with their pet project - the engines.

Looking at it another way: The combined propellant tank volume by my math (with a few assumptions on the current LH2:LOX ratio) would have enough volume to hold 500 tonnes of LH2/LOX at a 1:6 ratio, lets allow structural weight growth of 20% for the heavier take-off weight making structural wt 40.8 tonnes, 2 SSME's (or easily maintained equivalent) is + 6.4 tonnes, so total unladen weight is 47.2 tonnes, add a P/L of 15 tonnes and also the 500 tonnes LOX/LH2 and you get a take-off weight of 562.2 tonnes, at engine shut off weight is 62.2. Mo/M1 is 9.03, delta V at Ve 4500 m/s is 9907m/s.

9.2 km/s is about all you need to get into orbit.

Land transport without fossil fuels

When there are lots of people living on the moon or on Mars they'll probably like to have the same freedom to travel in their own personal vehicles that most of us in wealthier countries enjoy on Earth today, in fact, some sort of efficient transport across the surface of each planet is going to be crucial to development.

If we make the assumption that battery technology is never going to equal the energy density of petroleum fuels, and given the extra demands that are likely to be made on the energy systems of surface vehicle simply because of the environment they have to operate in, it would be useful to have a system that uses electricity but with which each vehicle would have a virtually unlimited electricity supply.

On the face of it that sounds impossible - without going nuclear - but it's actually pretty easy to do, all it requires is a roading system that has a reticulated power system that feeds each vehicle while it's traveling on longer journeys, and all that would require is a two rail fence down the middle of the major roads with the top rail being the positive, and the bottom rail the earth (think I'll stick with "earth" rather than try to be clever with "Lunar" or "Mars") each vehicle would be equipped with nothing more complicated than a couple of trolley poles to give unlimited range. To keep costs and hazards down, vehicles would still have batteries for emergency and just to cover the few tens of kilometers of unpowered minor roads, and the few kilometers of the driveway.

Thinking about it, it might even work on this planet.

Sunday, June 5, 2011

Shelter on Mars

There's huge optimism about the prospects of settling Mars amongst space cadets, you just have to look at the photos from the various probes to be drawn to the place, it just looks so benign, it even has a day of similar length to the Earth.
 What the pictures don't show, but we each know (at least on an intelectual level) is that it's bloody cold, there's almost no air, and what little there, even if concentrated, would kill you by asphyxiation in a couple of minutes, it looks so inviting, but it's more hostile to human life than any place on the surface of the Earth - that's not news - but do we really understand what that means?
 If I suggested to you that you could take a few tonnes of equipment and build a self-sustaining colony on the middle of the Antarctic icecap, or in death valley, you would probably find lots of reasons why it couldn't be done, easy to visit, but hard to stay without continual replenishment from outside.
  Having said all that, I think there is still reason for optimism, but that optimism has to be based on the reality of what's actually there, and the knowledge that life won't be easy, after all, people do live in cold and arid places on Earth.

What are the basics that our settlers will need? Lets list them:

Well, water is available on Mars, quite a lot of it if you know where to look, and to cut a long story short, growing food makes air (well, oxygen), and on Mars that food will also require shelter, so all we need is water, and a shelter under which we can grow food, which means it needs to be transparent, after all, we all ready have days of the right length.

We also need to recognize that to hold that air at the pressure we need, we have to have some way of containing it at at least 4 tonnes per square meter pressure with a 50:50 O2/N2 mix, or higher pressures if we want an air nitrogen content closer to that which we enjoy on Earth.

We could hold that pressure in one of two ways; either with a strong container with high tensile strength, which would either need to be brought from Earth or manufactured, or simply by trapping the air under a thick layer of non-permeable material and using gravity to hold it down. For a 40 kPa atmospheric pressure in our shelter we'd need 10.5 tonnes/ m^2 of material in Mars 0.38 gravity, if that material were transparent we could kill two birds with one stone, as, if we wanted to grow crops - and we need to grow crops - a transparent dome will save us having to either produce that light artificially, or else, if we want to use natural light, save us needing a complicated arrangement of mirrors to capture and channel the sunlight.

So what materials are available? Two spring to mind, glass is the obvious one, if we wanted to cover a hectare with glass though, we'd need to pour a sheet of it 4 metres thick with an area of 10,000m^2 thats just over one hundred thousand tonnes of very pure glass (high purity is necessary to allow the passage of light), the other option is water - or ice - we'd still need a hundred thousand tonnes of the stuff, and it would still need to be of high purity, but unlike glass, it doesn't require a great deal of energy and considerable manufacturing to produce, on Earth we manipulate water by the thousands of cubic meters with ease, it costs just a few cents a cubic meter if it's not bottled, I find fixing a broken window reasonably expensive in comparison.

So perhaps we could just inflate lightweight plastic domes which we could build ice domes over by slowly building up ice by simply spraying water on and letting it freeze, then, when we have our dome, putting a thin transparent sealing layer over the top to stop sublimation?

That would save transporting so much from Earth, and it would be the ultimate in ISRU.

It's also worth taking into account that such an ice dome only conducts 0.17 Watts/m^2 if the temperature gradient is 10K per meter through the thickness of the dome, so it's good insulation as well.

Friday, June 3, 2011

Fun in the water on Mars

Here's something that occurred to me the other day, If a soletta was used to warm Mars so that the ice melted, Mars would have enough water to cover its whole surface to a depth of 22 metres and only a fraction of that water would need to turn to vapor to give a high enough partial pressure to reach equilibrium.
Now, here's the fun part, while you still couldn't walk around on the surface of Mars without a space suit, it would only require scuba gear to swim in her seas!

Terraforming Venus

If Venus was put into permanent shadow, I wonder how long it would take for the CO2 in the atmosphere to freeze out, then if 2/3 of the nitrogen rained out you’d be left with a planet with 0.9 G and 1 atmosphere pressure.
If the dry ice and liquid N was at one pole, the other pole could be tropical without too steep a temperature gradient between them.

Bear in mind that we’re not talking about a natural planetary environment, but rather one in which radiation reaching the planet is strictly controlled for a given purpose.
While controlling the liquid N2 might be a challenge, I don’t see too many difficulties controlling the dry ice.
How about as the atmosphere is cooled the CO2 is controlled to form a ring of 15km high mountains at one of the poles, (though it could be made to happen at whatever location the geology dictates is most appropriate) the area enclosed by this ring is then cooled so that the excess N2 precipitates out there, N2 remains a liquid at 0.125 bar and -210C and the mountains isolate this N2 ocean enough from the bulk of the atmosphere so that the little heat that is brought in is radiated away to the eternal night experienced at this location without causing enough N2 evaporation to be a problem.
Whilst the mountains continually flow outwards as does the Antarctic ice cap on Earth, they are also continually replenished by atmospheric CO2.

When I fired this at Adam Crowl his maths suggested the atmosphere taking between 2 and 90 years to freeze out with a geometric mean of ~13 years. Not a very long wait for that much real estate.

Homes in a sunny orbit

I've always liked the idea of the Stanford torus, but such a facility really needs to be in sunlight continually, and if it's outside Earths magnetic protection it needs a radiation shell, I was recently reminded of dawn to dusk sun synchronous polar LEO's, an object in such an orbit is always above the day-night terminator, and so always in the sunlight.
If we could get cost to orbit as low as $100,000/tonne, just maybe we could see a Beverly Hills in space, a community for the super rich that the rest of us could at least visit.
Interestingly,  sun synchronous orbits are between 550 and 1000km high, a favorable altitude  from which to swing a rotovator:

Seen from the Earth, a 2km diameter colony at that altitude would appear to be about 1/4th the diameter of the Moon, orbiting at the terminator it would be easily and often seen.

a hammer-throw type surface based spinning tether lunar launcher

As a way to get stuff off the Moon, how about a hammer-throw type surface based spinning tether lunar launcher (suggested by "Robert" at Selenian Boondocks about a year ago), a 200km radius of rotation gets 50 tonne manned ship to escape velocity
with a centripetal acceleration of 28m/s (2.8g), rotation speed of 6.8 rpH, at 50GPa strength the tether weighs only about 15 tonnes.

To decrease the time between launches, you could have the
payloads travel down a permanently extended tether.
When you get to this radius of rotation, the possibility exists for the tether to catch
payloads from space, making low g rocket free transport available in
both directions.

Using the mass driver you face a major problem in power storage and
rate of discharge, the solution is usually to launch small
payloads, but using the "hammer-throw type surface based spinning tether
lunar launcher" the power storage issue disappears, the tethers rate of
rotation can be increased as slowly as power supply allows, and the high
payload/ tether mass ratio allows large individual payloads.

A tether with a radius of 4km located at Earth-Moon L2 would catch payloads arriving at
270m/s, subjecting them to a centripetal acceleration of 18ms^2, tether
rotation is at 3.86 degrees/sec. A carbon nanotube tether for a 50 tonne
payload/manned ship need only weigh about 200kg(!) at 50GPa strength,
so would need to rotate around something substantial, EML2, as you probably know,
is unstable, so the momentum of the arriving ship could probably be
used to maintain the receiver at EML2 if positioning at capture was
done with that in mind.

Energy costs for the tether option at 10c/KWhr are about $75/tonne assuming negligable losses, perhaps $100/tonne including losses.

Update 8th June: Well this idea has been looked at by the experts after all, it's covered towards the end of this document.