Hubble Telescope


Interstellar Trade:
A Primer

Page 2 of 2

More fun with starships.  How fast they go, how big they are, how many people are drinking at a space station bar, and -- oh, yes -- just a little about space battle fleets ...


Blue Band So far we have not said anything about how fast these ships go (in normal space, let alone FTL). In fact, we've said nothing about their technology except that it is for the builders what jetliner technology is for us. My intent was to handwave the technology and focus on the cold hard cash. Trade economics doesn't care about the actual technology - only how long cargo takes to reach its destination and how much it costs to get it there. Your favored technology is probably different from mine, anyway.  But having gotten this far, I'm tempted to at least glance at possible technology, and naturally I'll give into temptation.

The following assumes reaction drives (basically fancy rockets) operating in normal space at sublight speeds.Your FTL can be whatever you want it to be, so I'll ignore it, but you'll obviously need it to do much star-hopping. 

Given that on departure half the ship's mass is fuel (mass ratio = 2.0), we can estimate some possible speed ranges. For any reaction drive, this mass ratio corresponds to a delta v or potential ship speed of 0.69 times the drive engine's exhaust velocity. Since ships have to slow down at their destination - not just hurtle off into the void - their maximum normal-space transit speed must be about a third of exhaust velocity (or a little less in practice, to allow a fuel reserve). For a nuclear-ion drive this would be up to 100 kilometers per second or so; for a fusion drive, up to a few thousand km/sec; for matter-antimatter, about a third the speed of light or 100,000 km/sec. These normal-space speeds will of course be lower if the ship must also use fuel to enter or travel through FTL.

We can also estimate how far these ships go in normal space before making their FTL jump (or whatever they do). If a ship spends an average 27 days en route, all of it in normal space - FTL transit being an instantaneous pop-through - the outbound and inbound legs are each 13.5 days or about 1.17 million seconds. Assuming steady acceleration and deceleration, average normal-space speed is half of maximum speed reached. (In practice, acceleration increases as fuel is burned off, so it takes longer to reach peak speed than to slow back down.  We'll ignore this for simplicity.)

For a top service speed of 130 km/sec (exhaust velocity ~400 km/sec, typical of an advanced ion or early fusion drive), the outbound and inbound legs are each 75 million kilometers, or half the Earth-Sun distance ("astronomical unit," or AU). Acceleration/decleration will be a gentle 0.01 g. For an advanced fusion drive with top service speed of 5,000 km/sec, the outbound and inbound legs are each nearly 20 AU, Sun-Uranus distance, and acceleration is 0.44 g. For a matter-antimatter drive peaking at 0.3c, each leg is 350 AU - five times the diameter of Pluto's orbit - and acceleration is a bone-crushing 8 g.  Unless your ship has some kind of internal null-g field, forget about it.

All of these normal-space figures will be lower if the ships spend substantial time in FTL transit.  Indeed, if they make most of the passage in FTL the normal-space legs may be reduced to a piddly Earth-Moon distance, or even less.

Back in normal space, though, we can also estimate the rated power output of ships' drive engines. (I won't give the calculations, just the results.) These turn out to be impressive.  Take the giant freighter of 120,000 tons full-load mass. Since acceleration increases as fuel is burned, we'll suppose that the accelerations given above are at two-thirds fuel load, or a mass of 100,000 tons.

For the most primitive of the three propulsion examples above - exhaust velocity a mere 400 km/sec, and feeble acceleration of 0.011 g - rated engine power output is somewhat more than 2000 gigawatts (2 terawatts), more or less the electric power consumption of the United States. If you could somehow hook that ship's engines to the California power grid, brownouts would cease to be a concern. For the advanced fusion drive, exhaust velocity about 10,000 km/sec and acceleration of 0.44 g, the juice flows faster. In fact, rated power output goes up by just about a factor of a thousand, to 2 million gigawatts or 2000 terawatts. Turn on all the lights you want; the engine-room power gauges won't even flicker. Don't fool with the controls, though, unless you know what you're doing - one second of full-thrust operation puts out as much energy as a 500-kiloton bomb. Push the wrong button and you'll arrive at the Pearly Gates instead of Seychelle.

Do you even want to know the power output of the matter-antimatter drive? Well, here it is anyway: exhaust velocity of c, the speed of light, 300,000 km/sec; acceleration of 7.9 g; power output rather more than 10^9 gigawatts or a million terawatts. Trip the light fantastic! (To put things in another perspective, this is about three one-billionths of the power output of the Sun.)

From this excursion we'll now return to mundane operational issues. Having burned all that fuel with rather spectacular results, we might - belatedly - ask where the stuff comes from and how it gets into the tanks. (A starship's "fuel" may, in some technologies, be two different substances: A fairly small amount of energy source - U-235, deuterium-tritium, antimatter - the oomph of which is used to throw a whole lot of something else out the back at high speed to produce thrust. We'll just call it all fuel.) Presumably it is available somewhere cheaply at bulk rates, but it probably does not appear naturally in parking orbit around habitable planets, where starships fill their tanks.

The classic SF solution is to ship it in from somewhere else in space: the Moon, or the icy moons of outer planets (convenient sources of stuff like deuterium). This avoids the notoriously expensive surface-to-orbit lift. But we don't know whether all habitable planets will have a handy moon - I hope not, because if a large moon is required, as some theorists have suggested, habitable planets may be a good deal less common than otherwise. As for shipping in fuel from the outer planets (or ores from an asteroid belt, for shipbuilding), this has its own problems.

The economics of interplanetary transport are essentially the same as those of interstellar transport using FTL. (The whole point of FTL being to make the stars about as reachable as Solar System planets are.) If tankers are going to make a round-trip run of Earth-Jupiter distance in a few weeks, they will have to reach speeds on the order of 1000 km/sec. Unless your starships' normal-space technology is right up at the high end, the tankers will be as costly to build and operate as starships themselves. If instead the tankers move in low-energy transfer orbits their turnaround time will be a year or more; to bring in the fuel needed by the starship fleet they'll either have to be enormous or a large number will be needed.

Fuel delivered either way will not cheap by the time it reaches the pump. Nor is having the starships make fueling stops at the outer planets any solution; the extra transit legs added to every voyage will cost more than you save.

This leaves the alternative of shipping up fuel by shuttle from the habitable planet. Why not? Most of the freight the starships carry is going from planet surface to planet surface anyway. It's true that ideas like space mining and so on were developed in the first place to avoid hauling stuff up to orbit, which for us is horrendously costly - about $10 million/ton.  But for people to colonize space at all, the surface-to-orbit lift obviously has to become vastly cheaper. We have to get up there, after all. And if a civilization can build starships, it should be able to build a shuttle that can fly to orbit about as cheaply as a jetliner can get to Newark.

Suppose, then, that shuttle economics are equivalent to jetliner economics today. The round trip to low orbit and back - not counting loading and unloading time while up there - is about two hours, considerably less than a transcontinental jet flight.  With loading/unloading, maintenance downtime and so on, allow four flights a day.  A round trip passenger ticket, then, will run $250 dollars; round trip freight service is about $1000/ton - ten percent added on to the interstellar transit rate.

Fuel only goes up, but the shuttles obviously have to come back down for the next load. We can imagine that everything possible will be done to streamline the process. High-capacity pumps at each end minimize dwell time. Fuel shuttles might be pilotless, to save on life support and safety systems. (If a crewless shuttle crashes, it's lost money but no grieving loved ones unless it falls on someone, and they'll be routed over uninhabited areas. Also, it won't lead the news and trigger public hearings by the Planetary Council.) Altogether, it might be possible to squeeze fuel lift costs to $500/ton. If the starships carry a ton and a half of fuel for each ton of cargo, that adds another $750/ton to interstellar shipping costs. Total surface-to-orbit overhead is then $1750, or 17.5 percent - a nuisance, but not enough to demolish our cost and traffic estimates.

So much for shuttles; back now to the starships.  How big are they?

Take the present-day maritime tonnage rule; one registered ton = 100 cubic feet = ~3 cubic meters.  Assume it applies to fuel and hull (e.g., crew quarters, engineering spaces, etc.) as well as cargo. If the largest ship in service has a cargo capacity of 40,000 tons - twice that of the typical big freighter - her full load mass is 120,000 tons, and she has a total volume of 360,000 cubic meters.

A spherical ship of this size has a diameter of about 90 meters = 300 ft. If instead the hull is more or less cigar-shaped, with a length-diameter ratio of 6:1, this ship is 300 meters = 1000 ft long, with a diameter of 50 meters = 165 ft. At the other end of the spectrum, a 1500-ton capacity tramp trader, if spherical, has a diameter of about 30 meters = 100 ft. If cigar-shaped she is about 100 meters = 330 ft long. Modular ships would have dimensions in this same general range, but somewhat larger due to being assembled out of separate component pods.

Crew requirement:  This is difficult to estimate. Since crew members have about the same berthing requirements as passengers, each represents about one ton = $100,000/year in lost revenue capacity, so starship crews will be kept as small as practical. The operating crew need not be very large. Say, a pilot-navigator and engineer for each watch, plus life support specialist/medic, cargomaster, and the ship's captain, for a total of nine. Small ships would squeeze this down to four or five; the big ones might may double up the positions with assistants and trainees and have an operating crew of 20 or 25.

However, with ships enroute for a month or so at a time, maintenance technicians will be needed. Unlike aircraft, maintenance can't all be done during layovers, and since time is money you don't want to hold off departure because station techs haven't finished some routine servicing. Suppose, conservatively, one technician is embarked per $100 million in construction cost (i.e., stuff that has to be maintained). Small ships then have a maintenance crew of seven or eight, for a total of ten or twelve; the largest ship in service might have a crew of up to 250.

The scut work - swabbing decks and peeling potatoes, etc. - will of course be done by junior crew. Passenger-carrying ships, however, will need crew for hotel-type services - stewards, chefs, and the like. (Except for colony ships; colonists can do it themselves.) Coach class could make do with about one for every ten passengers. First class may get one for every two or three passengers; the first-class passengers also get larger cabins, and their ticket prices reflect it. If the typical ship has one percent of load given over to passengers, the required hotel staff would increase the crew by about a third. (Unhappily, they are likely to be looked down on by the operating and tech crew members.) On a passenger ship the hotel staff will vastly outnumber the rest of the crew, by some 30 to 1.

Before going on to the Cool Stuff, we can also say something about the orbital stations these ships travel between. These stations will host a variety of ancillary functions, but they exist primarily as starship ports and service bases. If at a given time three-fourths of the ships are en route, with the rest "in port," at stations orbiting one of the dozen colony worlds in the network, we might expect to see about fifteen starships docked up to an average station. One or two would be quite large ones, and a ship will arrive or depart about three times a day. Orbit-to-surface traffic is heavy; if each cargo shuttle can carry the load of a 747 jet freighter, about 100 arrive and depart each day. If starship fuel is shuttled up from the surface, some 150 daily tanker arrivals are needed as well. (At four daily flight for each shuttle, about 65 are required.) This is for a typical station;  the busiest in the trade network might have over twice the traffic volume.

At any one time we might expect to find 200 or 300 off-duty starship crew members in an average station; if seaport and airport experience is anything to go by, most will be in bars. Unlike airports, however, through passenger traffic is small; only about two hundred or so arrive or depart each day.   Passenger shuttles, however, also carry station crew, ships' crew members going downside to sightsee, etc., so there should be a few daily passenger flights.

A station is in effect a ship without a drive engine, so its general characteristics can be estimated much the same way. If ten percent of the overall cost of the merchant fleet goes to support the stations (reasonable, since the stations maintain the ships), the stations taken together will have about a tenth of the fleet's deadweight mass, or some 180,000 tons all told. A typical station would then have a mass of 15,000 tons - not counting cargo awaiting loading, fuel in storage tanks, etc. Stations, however, are likely to grow by accretion over the years and become great sprawling structures extending hundreds of meters in all directions.

The maintenance crew of the average station, using the same estimate as for ships, would be about 150. However, stations provide the major ship maintenance, so they probably have about as many technicians altogether as the ships themselves do. They alone will multiply the station population by tenfold; support staff and miscellaneous services might double it again, so that a typical station could have some 3000 workers. The largest might have two or three times as many. Living quarters will be nearly as expensive as ship quarters, but frequent shuttle fares also add up, so many people may live on board, even with their families - making the station a small but very cosmopolitan orbiting town.

The entire spacefaring population of the trade network, ship crews and stationers, comes to well over 50,000 people, perhaps as many as 100,000 (out of a total population on the dozen colonies of some 120 million). The space economy as a whole, however, employs many times more. If the merchant marine industry accounts for three percent of the economy it will also employ some three percent of the work force, perhaps 2 million people altogether, with a similar number employed in import/export industries.  


Guarding the Spaceways ...

Space science fiction wouldn't sell many books if people on these stellar colonies just traded peacefully with each other. Dramatic tension calls for a ruckus.  This is not unrealistic; judging from history a ruckus can usually be counted on.

Based on the estimates for the interstellar merchant marine, we can also make some guesses about space war fleets. People may fight each other even if they have no trade relations at all (not even rivalries), but historically the great navies have usually belonged to trading powers - Athens, Venice, Britain, etc. - and their primary mission was trade protection.

The expense of a trade-protection navy is basically an insurance premium charged against trade. Let's say that our 12-colony network is a trade federation, and its "insurance premium" for defense is ten percent of the total value of trade. (The setup could just as well be one planet monopolizing trade, in which case the navy protects the franchise; we'll delicately call it a federation anyway.) Since half the value of trade goes to support the merchant fleet - the other half being initial purchase cost of shipped goods - the cost of the war fleet will then be about 1/5 that of the merchant marine.

We may suppose that interstellar warships have roughly the same relationship to cargo ships as cruisers to ocean liners or jet bombers to airliners. Instead of cargo they carry weapons and sensors plus armor, more powerful engines, and greater fuel capacity. Ton for full-load ton they are doubtless more expensive than trade ships, maybe twice as much, but the cost per deadweight ton is about the same, since the technology going into it is similar. (Some present-day warplanes have a much higher cost-to-mass ratio than jetliners.  But that is due partly to "goldplating" of weapon systems and partly to false economies such as small orders that reduce production efficiencies.   We'll assume that our trade federation takes a businesslike approach to its fleet.)

For a first approximation we'll simply scale down the merchant marine by a factor of five to get the war fleet. Using the standard First World War jargon for space warships, we'll say one battlecruiser for each five heavy freighters,  one cruiser for each five medium freighters and one light combatant - call her a corvette, since destroyers were a specialized type for torpedo and antisubmarine warfare - for each five small freighters.

Thus the order of battle is

15 battlecruisers
60 cruisers
80 corvettes

This may or may not be a balanced fleet, depending on actual requirements. Substitute as needed. And in practice we'll probably have to replace some cruisers and corvettes with auxiliaries of various types. But cargo ships can also be requisitioned in wartime for auxiliary missions (such as, especially, tankers). Depending on the technology and threat level, it may also be feasible to fit cargo ships with weapon pods instead of cargo pods and use them as armed merchant cruisers. Contrariwise, warships may be fitted with cargo pods to serve as extremely well-armed transports.

The battlecruisers, let us say, have a full-load mass of 30,000 tons each; cruisers, 7500 tons; corvettes, 2000 tons. This comes out pretty close to the tonnages of naval ships c. 1916. (I swear I didn't plan that!) Because of their heavy fuel loads, however, their "Washington Treaty" mass - with all munitions and supplies aboard, but without fuel - would be about a third as much.  A battlecruiser will cost $10 billion (twice the cost of a present-day supercarrier); a corvette $700 million.

Assuming these ships are of the cigar-shaped configuration (Hollywood doesn't want fat warships), the battlecruisers are about 200 meters = 650 ft long ... about the same size as the ones at Jutland.  The little corvettes are about 75 meters = 250 ft long. This makes a corvette about the same size as a 747 or C-5, though larger in diameter and bulkier. Put another way, a corvette is rather close in size (and mass) to the Shuttle in launch configuration. If the corvettes have a surface-landing module - not unreasonable, for these workhorses of interstellar gunboat diplomacy - they might even have a fairly similar overall appearance.  (The express-mail courier ships would closely resemble corvettes, and might well be a civil version of the same design.)

Probably the war fleet has a somewhat lower peacetime operating tempo than the merchant marine - the warships spend about half their time docked up to stations, instead of a quarter or so as for the merchant ships. The savings in operating expenses allows for somewhat greater procurement, so they are replaced and retired from active duty after 20 years rather than 30. Most then go into a mothballed reserve force for another 20 years; hence the reserve is the same size as the active fleet. As with cargo ships, however, warships might instead undergo top-to-bottom overhauls and remain in service much longer.

Crews we can imagine will be larger in proportion than for cargo ships, but follow a similar pattern. The operating crew will be augmented with offensive and defensive weapon controllers, scan/ECM, and communications/intelligence; large ships will also have a command staff. Interstellar warships don't need hands to feed photons into lasers, much less shovel deuterium into the engines, but the crew of technicians will be larger per unit cost, since they may need to repair battle damage. Some warships may also carry a landing force of marines. Given the berthing cost and limited space (most of the ship is fuel) there won't be many of them, but they'll be highly trained elite troops comparable to SEALS. Overall, we might give a battlecruiser a crew of 300 and a corvette a crew of 20; rather more if a landing strike team is embarked.

This is not a huge force. The combined crews of all ships come to just over 10,000, with probably a similar number on "shore duty" at any given time.  Add in the marines and the total number wearing the uniform is still no more than about 25-30,000, with perhaps a similar number of civilian employees. Defense spending (at least for running the fleet, by far the largest item) is a modest $72 billion, 0.6 percent of the trade federation's combined GPP. In a prolonged, major war the fleet would expand greatly. However, it is supported by trade.  If the cost of trade protection - the "insurance premium" - approaches or even exceeds the value of trade itself there might be a general collapse of political support, with people dumping Rigellian green-fuming brandy out the airlocks or at least into a harbor.

Operations in a trade war will tend to be primarily in space. If large-scale planetary landings are required, however, cargo ships can be pressed into service as troop transports. Light infantry might be considered equivalent to civil passengers, one ton equivalent cargo capacity per soldier. However, some heavier equipment will doubtless be required, plus shuttles to carry troops, gear, and provisions to the surface, and other armed shuttles for close air support. All in all we might expect an invasion force to require perhaps three tons per soldier in spacelift, not counting the naval escort. If a tenth of the federation's entire merchant marine is gathered as an invasion force it can transport and land 120,000 light troops - considerably fewer, if much heavy equipment (e.g., tanks) is required. But 120,000 troops is a quite considerable force for invading a planet of some 10 million people.


The Star-road to Empire ...

All of the above is for a modest trade federation of a dozen colony planets, suitable to a fairly early era in interstellar history. At a later period the scale of things could get larger - very much larger. Suppose an interstellar empire of a thousand worlds, each having an average population of 100 million people. Everything above can then be multiplied by a factor of over 800. (!)

Ships would probably grow in size as well as numbers; by this time improved technology allows long-haul main trade routes. If a typical ship is now three times larger in linear dimensions she will be 27 times greater in mass, and the fleet can have thirty times as many of them. Large cargo ships will then be up to 300 meters = 1000 ft in diameter if spherical, or a kilometer long if cigar-shaped. Each has a cargo capacity of over a million tons, with a full-load mass of up to five million tons each. The empire's merchant marine will have about a thousand ships in this size range (and doubtless some that are much larger). In addition the merchant marine has perhaps fifty thousand (!) ships of 20,000-plus tons capacity each, plus of course hundreds of thousands of smaller vessels. The great hub-route stations are true celestial cities, with populations in the millions.

The Imperial Navy's capital ships are, let us say, also a kilometer long, with a full load mass of three million tons each. Here we've increased size more than numbers. Building cost of each: a cool $1 trillion, with a crew of 30,000 - as large as the entire force of the early trade federation.. The Imperial Grand Fleet comprises some 125 of these great dreadnoughts, and well upwards of a thousand cruisers, averaging a mere couple of hundred thousand tons each. As with the early trade federation this is by no means the largest force that could be afforded. The Imperial Senate holds down annual budgets firmly in the $60 trillion range;  it is a modest, economical trade-defense fleet.

Thus, a middle-period interstellar empire. For the Galactic Empire, allow perhaps 100,000 worlds with an average population of a few billion people each. The scaling factor this time is another 3000x or so. But I'll let you run the numbers for that one ....


-- Rick Robinson


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