Building Things in Space

Construction in space, remarkably and wonderfully, is something we know that we can do, because we have done it. And it is worth saying something about, if only as a change from the distressingly popular subject of blowing things up in space.

To be sure, what we do now is only the final stage of assembly, and from kits. We all know how smoothly that can go. Like rendezvous and docking it might easily have been impractical, but it works about as well in real life as it did in Heinlein stories.

Thus we can build our ships in space, as big as we need them to be, instead of having to launch them all up from Earth. In this as in so much else, the ISS amounts to a training mission for deep space travel.

Actual fabrication of structures is another matter, but we are not likely to do it (other than as an experiment), or need to do it, for quite a long time to come. The reason lies in the odd economics of space travel, and Cobb's Law. If orbit lift is cheap, we can bring up the things we need. If it isn't cheap, we aren't up there either.

Cheap is a relative term when it comes to space travel, but I'll resort to my standard rule of thumb and say that with technical and economic maturity the major component parts of a spaceship - hab pods, tanks, drive units, radiator panels; some assembly required - might cost roughly a million dollars a ton, here on Earth at the factory gate. Launching them into space, along with assembly crews, might cost another $1 million a ton, making the on orbit flyaway cost $2 million per ton.

The good news is that this places deep space craft in the same broad range of cost, size for size and mass for mass, as jetliners, of which thousands are in regular service. The bad news is that the lunar spacecraft industry is strangled in the crib. It has no market unless its production cost at the factory cargo airlock can be brought down to twice Earth production cost at the factory gate. That is an awfully tough standard for a new industry on a new planet.

(If lift cost to orbit can be brought down to $100,000 per ton - which calls for the magic of heavy traffic demand, supporting regular flights by production vehicles - even food production is cast in doubt. $450/lb is a lot to pay for cornflakes. But cheap local produce from the ecohab is only cheap after someone has built the hab, and mastered space gardening techniques.)

More complete fabrication in space will grow partly out of special requirements for structures too big to lift and not suited to snap-together construction. But more than that it will evolve from the duct tape side of the equation. People will start modifying pods, authorized or otherwise. Over decades a boneyard of old structures and equipment will accumulate, begging to be repurposed. Orbital (or lunar, etc.) machine shops will appear to do this work.

And the machine shop is pretty much the basis for all industrial technology, a production line being simply a series of machine tools lined up and set up to run a standard job repeatedly.

Once space facilities can fabricate their own structures, the 'supply chain' economics changes. Now the lunar industry doesn't have to compete in the market for expensive prefabricated pods, but for much cheaper rolled aluminum and the like. Raw aluminum currently costs on order of $3000 per ton - even if the lunar cost were ten times greater, it would be cheaper than 'cheap' orbit lift.

A note of caution. As always in space economics there are some devils in the details. Inherently the trip from the lunar surface to lunar orbit and back, a round trip delta v of 3.2 km/s, is much cheaper than from Earth to LEO. A sensible, single stage vehicle can do it. But it will only be cheap when there is enough lunar traffic for frequent service, so that economies of scale can start to kick in.

So a lunar industry may have to start big - perhaps meaning for political reasons - to permit economies of scale in transportation, and likely in production as well. In the pristine world of economics there is no particular reason for this to happen, suggesting that politics might rear its ugly head.

Therein, presumably, would lie a tale.


Image from Atomic Rockets.

Related post: A Solar System For This Century.

Seas of Luna?

The lunar maria, 'seas,' are the only surface features on another astronomical body that we can easily recognize with the naked eye. But (so far as I know) no one ever thought to name them or map them till the telescope showed that they were indeed surface features on a world. And they had barely been named before it was realized that they were not seas at all, but dry plains.

The Moon has been getting dryer ever since. Until yesterday, when news came out that a research team using data from three spacecraft has shown that the Moon apparently does have water after all, in fact quite a bit of it, though very thinly dispersed as a nano-rime on surface rock grains. Moreover, the water seems to migrate toward the poles, suggesting that it might be in greater concentrations there.

I saw the story in yesterday's LA Times, dead tree edition. It is not up yet at Sky & Telescope, but it is up at the Bad Astronomy blog.

Of course there is already speculation about where the water comes from. Perhaps it is primordial, perhaps deposited by comet impacts over the eons. But coolness points for the theory that the solar wind is constantly breeding the stuff, hydrogen living up to its name by sometimes binding to oxygen atoms in the lunar surface.

But this is also one of those times when the March of Science can be exasperating. There wasn't a whole lot of hope for lunar water even back in the pre-Apollo books I read as a kid, and Apollo ended whatever prospects there were for anything like a subsurface permafrost layer. The possibility of ice hung on in a few perpetually shadowed craters, but my recollection is that even this hope had pretty much - so to speak - evaporated. Just back in May I blew off the Moon, largely for this reason.

Now, if these new findings hold up, lunar science is doing an Emily Latella on us: 'Oh. Never mind.'

But it gets better. Two of the three spacecraft whose data provided this information weren't even exploring the Moon; they just happened to pass through the neighborhood. (The third is Chandrayaan-1. I completely missed the news that India launched a moon probe; what a cool way to find out.) But just to add to the weirdness, one of the passers-by was Cassini, which hasn't been anywhere near the Earth-Moon system since it did a flyby in 1999, two years after it was launched. So that data was pretty much sitting on a hard drive somewhere, until someone decided to pull it up and look at it.

So the whole thing is wonderfully contrary and serendipitous. How much it affects the prospect of Doing Stuff on the Moon, I have no clue. On the one hand, 0.1 to 1 percent is quite a bit; at least a few glasses of water from every ton of moon rubble, and perhaps a couple of jugs of it. And baking it out of the rock, then freezing the vapor, doesn't seem hard to do on the Moon, given a pressure vessel. On the other hand, that is a lot of rock you'd have to bake to get a steady supply of water for, say, rocket fuel.

But in any case, the prospects for recoverable water on the Moon seem a lot better today than they did the day before yesterday. And much more important in the great scheme of things, even the prosaic, touched-already Moon has not lost its ability to surprise and enchant.

Three Stages to Orbit?

Back in the rocketpunk era, we all knew that reaching orbit called for a three stage rocket. Willy Ley, with an assist from Chesley Bonestall, showed us what it would look like. (Though thanks to Walt Disney I mostly remember a later version without the huge wings. It looked like a wine bottle with a little delta winged shuttle in place of the cork.)

As it turned out, we went into orbit on rockets that weren't even two stage, but 'one and a half' stages; the Vostok with strap on boosters, and the Atlas, even closer to one stage, dropping only booster engines, no tankage. This allowed all main engines to be started on the pad, a big consideration in the 1950s. Later orbital boosters have typically been two stage, sometimes with additional strap on solids.

The popular dream of orbital access is (reusable) single stage to orbit, SSTO, though no single-stage vehicle has gone into orbit. The required mass ratio is just too extreme for our fabrication technology - and building big rocket stages is a mature tech, over 50 year old. Maybe new material science, such as Super Nano Carbon Stuff, will change that equation, but not for sure and not yet.

Perhaps we should look back in the other direction, at some form of three stage orbit lift. With three stages to orbit, launch mass relative to payload typically grows, making it less efficient in hardware and fuel. The compensation is that stage mass ratios are less extreme, permitting more conservative, robust construction.


What got me thinking about this was commenter Jean's mention, last post, of Virgin Galactic's plans for an orbital SpaceShipThree. How would you go to orbit if you want to do it cheap, both development and subsequent missions? (I'm not trying to guess how Burt Rutan would do it, though I obviously had SpaceShipOne in mind.)

First I stole the idea of a subsonic air launch. The 'zeroth stage,' the release plane, can be any big transport type. According to this paper and a Bad Astronomy forum thread, air launch does not really save much delta v, but it means the vehicle doesn't need to take off itself either vertically or horizontally, adds operational flexibility, and permits a lighter vehicle. As it is I ended up with a release mass of 100 tons. (The Shuttle's dry mass is about 70 tons, and this was probably about what the Shuttle Enterprise weighed for its release-glide tests.)

The vehicle itself is a booster-orbiter combination rather than pure two stage. After release at high subsonic speed at about 10 km altitude (32,800 ft), the vehicle enters a steep supersonic climb, passing Mach 5 at about 30 km (~100,000 ft). It has left effective atmosphere behind at booster separation, at about 3 km/s and 50 km altitude. The orbiter continues to orbit; the booster glides back about 1500 km to its landing point.

The booster has a twin-body configuration, each body structure mostly fuel tankage. The orbiter has a similar body structure with shorter tankage and a payload bay. Propellants are good old kerosine and LOX, good for an Isp of 300-325 seconds. Combined thrust of all three engines is equal to launch mass, about 1 megaNewton.

The mass breakdown I came up with is:

100 tons release mass

66 tons boost stage propellant (mass ratio 3.0)
7 tons booster dry mass

21 tons orbiter propellant (mass ratio 4.5)
6 tons on orbit mass

0.5 tons OMS, etc.
4.5 tons orbiter dry mass (heat shield, 0.5 tons)

1 ton payload


Optimistically this is good for a total 8.3 km/s of delta v, before losses to drag and climbing against gravity; add the speed of the release plane for about 8.55 km/s. Low orbit speed is 7.8 km/s, so ascent losses have to be kept to about 0.75 km/s.

The vehicle dry mass is also optimistic. As a couple of comparison points, the Thor first stage of the Delta space launcher carries 95 tons of propellants and has thrust of 890 kN. Stage dry mass (plus some unused propellant) is 5.7 tons, so our twin booster can be about 80 percent heavier and sturdier than a Thor, relative to tank capacity. Like the Thor, a Cessna Citation III biz jet has a fuselage similar in diameter to our basic fuselage-tank and wing structure, is about 50 percent longer, and has a dry mass of 5.3 tons. So our vehicle can be about as solidly built as a corporate jet.

All of which is optimistic, but perhaps not grossly so - and most paper orbiters I've tried to come up with were grossly optimistic.

By my general rule of thumb, production versions 'should' cost $11.5 million each, but transatmospheric craft require a lot of specialized materials and equipment, so let us say an ideal production cost of $25 million. The handbuilt prototype will cost a good $250 million, the whole development program $1-2 billion. A small production run of 10 orbiters and boosters might be $750 million, plus conversion of a couple of jumbo jets; call it another $1 billion, so the whole front end is perhaps $3 billion.

Recouping this at 8 percent over a 25 year service life requires an annual charge of $280 million. If we fly 280 flights per year the development cost per flight is thus $1 million. Reportedly it costs about $1 million to fly the Shuttle back from Edwards AFB to Cape Canaveral. Let's - quite optimistically - say $2 million operating cost per mission, so total cost is $3 million per mission and per ton of payload, a third of typical present day cost. If the manned version can carry a pilot and two passengers, a passenger trip to orbit costs $1.5 million a pop.


But is there enough demand for the service? Are there enough multimillionaires willing to pay $1.5 million for a trip to orbit? Enough who will do it a second time?

A modified version of our vehicle, however, might find a commercial terrestrial use. If you replace a ton of fuel and the OMS system with another ton and a half of payload, the orbiter does not reach orbit, but has a ballistic trajectory of some 10,000 km, plus maybe 2000 km of glide. I don't know whether you'd get many passengers at $750,000 per ticket, but you can deliver 2-3 hour global express for $1200/kg, about $35 per ounce - and there is probably a market for it.

If there was ever a case of selling the sizzle, not the steak, this is it. Space access disguised as faster-than-overnight express.


Related links: I talked about orbit cost at my old website.

The Price of a Spaceship

Why assign a price to a spacecraft in, say, 2237? Whatever it costs will be quoted in rupees, florins, or some new unit, and the raw figure wouldn't mean a thing to us if we knew it. Which is just the point. We want to know how much a spaceship costs in context - how many people can afford a ticket, how many schools can be built for the cost of a gigawatt laser star.

In this ongoing discussion we're considering a recognizable future economy and technology. No Singularity, and not enough time for society to have evolved out of recognition. Perhaps the Industrial Revolution will reach maturity, in which further refinements are gradual. The first decades of aviation had Moore's Law style progress, but jetliners have had much the same performance and appearance for the last 50 years. A lot of low hanging fruit has already been picked.

In any case, we're dealing with a fairly recognizable future economy and technology, able to do a lot of things we can't, but doing many familiar things in familiar ways. In 2237, long distance air transport (the only kind likely to be common) will probably be at high subsonic speeds, in jetliners that mostly just look and fly like jetliners. They may have nanomaterial strips instead of flap actuators, but only geeks would notice.

Spacecraft will also be broadly recognizable, because we already build them. We've built many small robotic ones, and are starting to build big ones. The International Space Station is not unlike the forward end of an interplanetary ship, minus the main drive with its big propellant tanks and radiator fins or solar wings.

The ISS has a 'dry' mass - structure and equipment, minus all consumables - of 304 tons, about 10 percent more than the super jumbo Airbus A380 (277 tons). They are also roughly the same size, in overall dimensions (both having 'wings') and in bulk, with pressurized volume about 1200 cubic meters. The ISS has a crew of six as an exploratory craft, and about a third of the volume is living space, so if configured as a transport, so to speak, it might carry 20.

An improved and mature technology will surely improve on the ISS, but the most desirable improvement, better toilets aside, is making it cheaper. The ISS has cost something like $50 billion, about $170 million per ton. This is too much. We can't be getting around in spaceships that cost $50 billion just for the forward section, minus the parts that scoot it around.

As a comparison, the slightly smaller Airbus A380 can be yours for about $325 million, depending on options, or about $1.2 million per ton. 747 variants are comparably priced. In the broadest structural engineering sense they are all similar constructions: lightweight pressure tanks and trusses (e.g. wing spars), fitted with complex, lightweight equipment and electronics. So what accounts for the difference in cost?

The notorious Washington 'iron triangle' bears a share of the blame, from outright fraud to shameless overcharging, to subcontracting work out into 400 congressional districts. Throw in policy changes that can throw out years of design work.

Also the ISS is a prototype, in a fact a sort of meta-prototype. Skylab and Mir were caravels; the ISS is our first try at a galleon. The builders not only had to handbuild it, which makes any prototype costly; they had to work out all the design requirements. My rule of thumb is that a prototype costs about 10 times as much to build as a production item. It doesn't take too much squint to imagine that a comprehensive development program costs 10 times as much as handbuilding the prototype. Which pretty much gets you to the price differential between an Airbus A380 and the ISS.

A bit of bad news is that building satellites is an established, mature industry, and they also cost on order of $100 million per ton dry mass. One reason is a launch cost to LEO of $10 million/ton, with most satellites going to higher orbits, a strong motivation to cut weight to the extreme. Satellites squeeze a lot of sophisticated gadgetry into a very small mass. They are equivalent to the most expensive parts of a large spacecraft, minus the (relatively) cheaper large tanks and structures.


So I'll ignore satellites and repeat my round number guess, that future production spacecraft might, with some good luck, cost the equivalent of $1 million per ton of dry mass, more or less what commercial jets cost today. (Allowing for inflation, big jets of the 1950s and 1960s cost somewhat less, but still on the order of $1 million/ton.)

I think it is highly optimistic, given that it is a 100 to 1 cost reduction over current space practice. A lot of people think it is very conservative. A million a ton - $1000 per kilogram, $450/lb - is pricey, and it makes really big spacecraft horribly expensive, like the $50 billion laser star I outlined for Ferrell.

Modern naval ships cost only a tenth as much, ton for ton (carriers even less). But naval ships use thousands of tons of cheap shipbuilding steel. Lightweight materials are used extensively in superstructures, but the hull, where most of the mass is, is built of good old steel, and everything on all decks is massively braced against the heave of the sea. Seagoing ships are very strong, but they are not lightweight.

There is a loose analogy here to laptop versus desktop computers; it costs more to pack power into a lightweight container. Spacecraft don't need to be compact, and crew cabins and propellant tanks are inherently bulky, but they do need to be as lightly built as practical. This naturally pushes up cost per mass: you're hanging the expensive parts on a much lighter (and thus more expensive) chassis.


And after all, the cost of jetliners hasn't kept jet travel from becoming pervasive. For the adventure minded, third-hand deep space ships will in time be available for far less than their original sticker price, perhaps $10 million for Serenity.

Progress in space has been and will be slow, because up front costs are enormous, tens of billions, even hundreds of billions over a couple of decades, say to establish the first base on Mars.

But it we do it at all, eventually someone will come up with the DC-3 of deep space, or more likely a combination of basic drive, support, and habitat pods that can be configured to a variety of missions and turned out in production runs of scores, eventually hundreds.

Models might be in production for 50 years and in service for a hundred years, still serving outposts that don't rate modern ships. When they are finally gone they'll be remembered as the ships that opened up space.


Related link: On my old website I wrote about (FTL) interstellar trade.

The Return of Hubble

With only a few days' light lag, Rocketpunk Manifesto salutes the return of the Hubble Space Telescope, back in operation after recalibration of instruments following its May maintenance and upgrading service call from the Shuttle Atlantis.

See the link's comments thread, in which a member of the Hubble science team promised a spectacular September reprise debut. The promise has been duly kept, this showpiece image (via Sky & Telescope) being the Butterfly Nebula, the swan song of a dying red giant star some 3800 light years away in Cygnus. In spite of appearance the event was not an explosion; the nebula was formed by an eruption that lasted some 2200 years.

Astronomers have an advantage over most scientists, because their work produces such spectacular eye candy, and they certainly make the most of it.

Further Battles of the Spherical War Cows

In the comment thread to last week's post on lasers versus kinetics, Battle of the Spherical War Cows, I ventured a way to reduce that unending debate to a formula. Because calculus is above my math pay grade I worked it out using a spreadsheet, smashing up some lasers by throwing lots of kinetics at them. Among other things, I learned that the Killer Bus I proposed a couple of weeks ago is in fact a lousy way to deliver a kinetic punch.

As a service to bloodthirsty geekdom everywhere, I've refined the formula and now offer it to the world.

Suppose guided kinetics have faceplate armor of Super Nano Carbon Stuff (thermal properties like graphite, but strong), 1 meter thick. Mass of the faceplate depends on its shape, but as a broad guess this target seeker might have a ton of faceplate armor, plus another ton for the service module with guidance system, thrusters, and so on. The whole weapon is thus comparable in size and mass to a torpedo. It can be sent on its way by a rocket booster, a bus spacecraft (expendable or recoverable), or a mighty powerful coilgun.

The laser that engages it can be specified by average beam power (whether continuous or in pulses), wavelength, and size of the main mirror or other focusing optics. I use Luke's formula for continuous-beam heat damage, and follow Anthony Jackson's rule of thumb that drilling a laser hole becomes inefficient beyond a depth/diameter ratio of 50:1.

In ideal, spherical-cow conditions, how good a defense the laser puts up is given by this formula:


K = 1750 * P * D / (L * V)

Where

K = incoming kinetics destroyed

P = beam power (megawatts)
D = mirror diameter (meters)
L = wavelength (nanometers)
V = closing rate (km/s)


Example. A 25 MW, 1000 nm IR laser firing through a 3 meter mirror, against kinetics closing at 10 km/s:

1750 * 25 * 3 / (1000 * 10) = 13 (0.53 per MW)

So this laser will take out 13 target seekers with 1-meter faceplates before getting scragged by #14. The first incoming is taken out at nearly 1000 km range, half of them beyond 100 km.


Another example, higher techlevel. A 100 MW, 250 nm UV laser firing through a 10 meter mirror, against kinetics closing at 100 km/s:

1750 * 100 * 10 / (400 * 100) = 173 (1.73 per MW)

This powerful, long range laser will defeat an impressive 173 fast target seekers closing at 100 km/s. That is a lot, but dozens of aerial torpedoes were fired at Yamato and Musashi. This laser scores half its kills at ranges over 1400 km.


Now, a Ravening Beam of Death, a 1 gigawatt, 1 nanometer X-ray laser firing through a 1 meter telescope, against kinetics closing at 1000 km/s:

1750 * 1000 * 1 / (1 * 1000) = 1750 (1.75 per MW)

It seems that even kinetics thrown at Incredible Speed can't survive a Ravening Beam of Death, unless you throw a truly enormous number of them. A mere 1750 torpedoes aren't enough.


But all is not lost for kinetics. The key to successful kinetics turns out not to be huge ones, or even super duper fast ones, but lots and lots of small ones. Suppose that you can build a mini target seeker, with a face shield only 10 centimeters thick, but with the same proportions as the big ones. It might have a mass of a couple of kilograms, and be roughly the size and shape of a soft drink can ... a Soda Can of Death!

The number of these mini seekers you need to launch in a salvo goes up by a factor of 100 - but the total mass of your salvo goes down by a factor of 10.

To overwhelm the Ravening Beam of Death you need a staggering 175,000 Soda Cans of Death, but their combined mass of faceplate armor is now only 175 tons, for a total weight of ordnance of a few hundred tons. And if cost is proportional to mass - a fair first approximation, in most cases - the salvo will only cost a tenth as much as before. Is a few hundred tons of high-tech hardware, the equivalent of a single fairly small spaceship, too much to ask for taking out a Ravening Beam of Death?


A few lessons emerge from this. Unlike the World Wars image, laser defense against kinetics is not a task for 'secondary' armament - it is a job for your most powerful laser firing through your largest optics. The laser in our first example needed 5 minutes of steady zapping to defeat 13 target seekers. That same zap, directed against a single target, will burn through half a meter of Super Nano Carbon Stuff armor at 1000 km.

Kinetics should be fired in salvoes, enough to overwhelm the target. Launching them one at a time is like those bad guys who send in ninjas one at a time for the hero to defeat. (If you fire them sequentially from a coilgun, you'll need to bunch them up while enroute to the target.)

And if the salvo is enough to saturate a powerful laser defense, the target is unlikely to go staggering on its way from a few heavy hits. Overkill piles up quickly. If our second is attacked with a salvo of 200 target seekers, it will (ideally) stop the first 173 ... then get whacked by 26 tons of slugs, at least, hitting at 100 km/s. Kinetic salvoes almost always either fall short, or overkill the target.


As for the Purple-Green debate, the lesson is, it depends. If you want lasers to dominate the space battlefield, with kinetics not a factor, tweak laser performance so that no practical salvo can defeat it. (You can tweak the practical engineering as well as the physics; gigawatt lasers may just not be practical.) Vice versa if you want kinetics to dominate. If you want both beams and kinetics in play, tweak the factors so that the most powerful lasers can be defeated, but only by a massive and costly salvo.

So zap away or slug away as you please. Just make sure the parameters fit your desired result!


Related posts: Laser weapons, kinetic weapons (two parts), and my first on the battle of spherical war cows. Oh, and space fighters. And on all these subjects, always check out Nyrath the Nearly Wise's site about Atomic Rockets.

Working Stiffs in SPAAACE !!!

In North America this is Labor Day. I had vaguely assumed that it was ginned up early last century to keep May Day, with its lefty connotations, from catching on in 'Murrica. Good old Wikipedia set me straight. 'Our' Labor Day originated decades earlier, in Canada, while the call for a workers' holiday first arose in Australia.

If there are large numbers of humans in outer space, most of them will be workers. They will be working as researchers and assistants, engineers and technicians, administrators and support staff. Perhaps there will be Belters with singleships, but the great majority of people in space are likely to live in complex habitats, kept functional and alive by hundreds of specialized trades, professions, and crafts. And a great deal of plain hard work.

'Spacer' is, in essence, a skilled blue collar trade. Spacers (or whatever term emerges for them) operate heavy machinery, some of it very heavy and much of it exceedingly powerful and dangerous. They deal with precision devices, some of them exceedingly fine and delicate. On this blog I casually discuss large interplanetary spacecraft with plasma electric drives rated at a gigawatt, instruments that measure nanometers, and life support for hundreds of people. Someone builds and operates these fabulous and complex vehicles, and those someones are spacers: workers.

Given the high costs and resulting high automation there probably won't be full time potato peelers aboard spacecraft, but someone will end up peeling them. And once things get somewhat established, the necessary scut work won't get evenly distributed. Universities, the military, and big civil engineering contractors offer three different models of how things can get done, and none of them is the least bit egalitarian. Some sort of hierarchy of work is likely to emerge.

Science fiction has long been aware of this, and there have been a fair number of stories about labor unrest in space. Given 'Murrican political culture, in the rocketpunk era such commie stuff might be tucked well into the background. All those rebel colonists have to be rebelling over something, and it probably is not all abstractions about liberty and independence. At least not to start. More likely it begins with disputes over pay and working conditions, then spreads to the question of why someone who has never been to Ceres is making decisions instead of the people who live and work there.

Those who plan the human presence on Ceres, and those who pony up the money to get it built, also have their rightful claim. But since they generally appoint the decision makers, their claim rarely goes unheard. The working crews are expected to be content with their paychecks - not entirely unfair, presuming they signed on by choice, but not the whole of the story. They create a value above and beyond what they get paid for. (If they don't, why were they hired?)

The workers in space will have a stake in the work they do, and ultimately the biggest one, since they will build the human presence in space. And will be the human presence in space.


Image of space station workers from NASA, via RobiNZ Personal Blog.

Battle of the Spherical War Cows: Purple v Green

The stately orbit of this blog was disrupted when commenter Luke, posting at SFConsim-l, provided links to two nifty laser damage simulators at his site. Of course I started playing with it, spreading out to other calculations. Severe geekitude follows. You have been warned.

Suppose that in the midfuture, 2100 or 2200, we have a nuclear electric plasma drive. The largest drive engine units put out a gigawatt of power, and have a mass of about 1000 tons including shadow shield and radiators. Spacecraft structure and propellant tankage is about 1000 tons, and total payload is 1500 tons, for a total mass, less fuel, of 3500 tons. [Note: all numbers are shamelessly rounded off, and some are SWAGs.]

These largest class fast interplanetary craft carry about 6500 tons of hydrogen propellant, so full load departure mass is 10,000 tons. Exhaust velocity is about 30 km/s, specific impulse ~3000 seconds. Acceleration at half propellant consumption is about 1 milligee, putting on roughly 1 km/s per day, and maximum mission delta v is 30 km/s.

This is a big spacecraft. The hydrogen propellant tank has a volume of 100,000 m3, equivalent to a sphere 60 meters in diameter, or a cylinder 40 meters in diameter and 80 meters long. The radiator fins are the cool end of the reactor power cycle, so they can't be too hot if the reactor is to be efficient, including not melting. At 1500 K (~2250 F) you can shed about 250 kW per square meter, half a megawatt from the two sides of the fins. You're probably dumping 2 GW of waste heat, so you need 4000 square meters of radiator fins, say a pair of 50m x 40m fins.

The drive pylon is perhaps 100 meters long, so the whole spacecraft is about 200-250 meters long and 150 meters 'wingspan.' As a transport type it might carry several hundred people, say 300-700 crew and passengers. The habitat compartment could be a drum 40 meters in diameter and 20 meters long, volume 12,000 m3. Rotating at 5 rpm the rim spins at 10 m/s, and it provides half a g. (According to notes at Atomic Rockets, this spin rate may or may not be acceptable for comfort.)


But we are here to zap stuff, not travel comfortably through space. So we remove the hab compartment and replace it with 1000 tons of armor plus a 500 ton laser installation. The power plant supplies plug power for a 250 MW laser, zapping at 400 nanometers - the extreme visible violet - through a 10 meter mirror. Spot size is 1 meter diameter at 10,000 km, and it burns through about 2 mm per second of super nano carbon [TM] armor at that range.

Regarding armor, there's no neatly tucking these huge fins away, and if you did, 2.75 GW of waste heat would require expending a ton of water flashed to steam each second to carry it off. With your huge radiator fins and bulky propellant tank, your best bet is to turn end on and put the armor into a faceplate, including the forward edges of the radiator fins. Your minimum end-on cross section will be on order of 50 meters in diameter, 2000 square meters. Thus the faceplate can have 0.5 ton per square meter, and is about 0.3 meters thick.

At 10,000 km, the laser, held steady on a 1-meter spot with the trigger held down, will burn through this armor in about 150 seconds, or 2.5 minutes of steady zapping. At 25,000 km you're burning through 0.2 mm per second, and half an hour of steady zapping will burn though 30 cm armor.

But at 100,000 km your spot size is 10 meters, equal to mirror size - producing a burn rate insignificant against armor, but when aimed at the enemy mirror it is focused right down onto their laser. So once the zapping starts, the laser battle will probably be decided very quickly, by whose laser fails first. There's little advantage to keeping shuttered, since the enemy can then zap with impunity, and zap your mirror the moment your shutters begins opening.

So it seems to me that pure laser battles, even between large conventional lasers, are decided at very long range, the winner being whoever wins the mutual eyeball frying contest.


Now, as promised, purple versus green. Imagine a 'slow' armored target seeker, closing in at 10 km/s. The defending laser burns through the armor, gradually at long range, more quickly as the range closes approaches. I did a quick and dirty Excel spreadsheet. Opening fire at 25,000 km, at range 10,000 km the laser has burned through a meter of armor. By the time a target seeker has closed to 1000 km range, 100 seconds from impact, the laser has theoretically burned through about 18 meters (!) of armor. By the time a target seeker is 200 km from target, 20 seconds from impact, the laser has ideally burned through 100 meters of armor.

This ignores the aspect ratio of the burn hole, but a single big killer bus is not effective; it cannot carry deep enough armor to get decently close.

A swarm of small, lightly armored target seekers is also not effective; if they have 10 cm faceplates the laser can burn out hundreds of them.

But 'merely big' kinetics, say with a dry mass of 5 tons and armor plug 2.5 meters deep, strike a balance. If you fire a salvo of 50, 40 of them will be burned out before they reach 200 km and 20 seconds from the target, but ten of the salvo will reach that distance before they can be engaged and fried, and one will reach 150 km, 15 seconds from the target.

These big ships, with large lightweight fuel tanks, long drive engine pylons, and huge radiator wings, cannot be kicked sideways easily. Allow it, say, 50 milligees lateral thruster acceleration, comparable to a subway train leaving a station. In 20 seconds our ship can put on 10 meters per second, and displace itself laterally by about 100 meters. Evasion cross section is thus about 30,000 square meters, 15 times the cross section of the target, so when our big seeker fragments, 1/15 of its mass or about 300 kg are on collision course with the target. With ten target seekers reaching this range, total fragment mass on collision course is 3 tons.

The laser can put out 5 GW in 20 seconds, enough to vaporize 100 kg, or shatter and disperse a ton or so of dangerous fragments. But another 2 tons will hit, delivering the equivalent of 20 tons of TNT in explosive impact energy. So sorry to say sayonara. Large fragments of 100 kg will have an impact energy equal to a 1-ton bomb, while their momentum will be comparable to a major caliber naval shell, say 12" = 30.5 cm. Even with a (massive) Whipple layer, these will be hard to stop.

So it takes 50 heavy target seekers, of mass 5 tons each and deployed at a 'slow' closing rate of 10 km/s, to saturate the laser defense and batter the armor. Say a salvo of 70 to allow ample margin.


Civil aircraft today cost about $1 million or euros per ton. (We're doing order of magnitude estimates here, so ignore exchange rates.) Military and space hardware can easily be $10 million per ton. But since this is The Future, let's use a modest cost schedule, commercial-equivalent tech, and say our laser battlestar costs $3.5 billion, while a heavy armored target seeker costs $5 million. Thus a flight of 70 target seekers - enough to scrag the target with confidence - cost $350 million, a tenth the cost of the battlestar.

If the target seekers are thrown fast, our laser has less time to fry them, and the critical range, 20 seconds of flight time, is now 600 km. The laser can only burn through 12 meters of armor, so four target seekers will be fried beyond that range, but if 10 are launched, 6 reach 200 km, about 30 tons, putting 2 tons on target, with 1 ton penetrating the close-in defense. Now we need only about 15 target seekers costing $75 million, but also an expendable delivery craft. (Expendable because it uses its full delta v for a 30 km/s closing speed.) This craft is scaled down by 10 from the big ship, and costs about $350 million by itself, so the whole high speed delivery system costs $425 million, slightly more than the 'slow' kinetic force unit.


So who wins this battle of spherical cows? I rule it a draw. On the one hand, an orbital battery of target seekers can take out a laser battlestar costing 10 times as much as they do. On the other hand, the battlestar is impervious to anything but a massive strike, or a high speed strike of similar cost.

The technical balance is such that procurement mix will be chosen due to strategy and policy, not a no-brainer technical choice. The target seekers can be moved strategically in cheap canisters, and you can play a shell game with them, but you cannot brandish them the way you can brandish a laser battlestar. To use them is to lose them, while the battlestar can engage weaker targets at practically no cost, just wear and tear on the laser.

On balance this makes the laser battlestar a weapon of the strategic offensive, capable of probing operations, while kinetics are a weapon of strategic defense, making the targets they defend risky to attack.

Opinions welcome - error corrections, too.


Related links: Laser weapons, and a two parter on kinetics.