Efficient TL10 and TL10^ reaction engines in GURPS Spaceships

Role-playing games Flat Black
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Which of the the TL10 and TL10^ (limited superscience) reaction engines in GURPS Spaceships are cost-effective and otherwise good for ground-to-orbit/orbital-to-ground cargo and passenger shuttles? Which are cost-efficient and good for orbital operations? Which are cost-efficient and good for interplanetary operations? I can do the calculations of course, but there’s no sense in re-inventing hot water is some else has done it already.

A winged shuttles the thing? Aerobraking?

I suspect that the cost multiple on ram-rockets is way too high at five times the cost of a rocket fed its reaction mass from tanks. For Flat Black I’m thinking of ruling that a ram-rocket has the cost of a reaction engine plus half that of a jet engine of the same size. Any thoughts?

I think the price for antimatter used in GURPS Spaceships is taken from Robert L. Forward’s Indistinguishable from Magic, and that was an estimate of the cost of making it using current (c. AD2000) methods in a purpose-built facility. Anyway, it is wince-inducingly expensive because the process is profligately wasteful. That technology is literally to make all possible particles at random and keep the ones that happen to be positrons. I’d like to assume that a limited-superscience method will be invented in the future that is at least one order of magnitude cheaper, and that (like all historical energy technologies) it becomes another order of magnitude cheaper as it develops to maturity, so that Tau Ceti is manufacturing antimatter in tiny quantities for G$100 billion (₢25 billion) per tonne. Antimatter-boosted propellant would then be available for $G120,000 per tonne.

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There’s a reason why Wives & Sweethearts moved from TL10 to TL11 lightly ^ during the planning stages, and that is that there’s no sensible engine for sub-week trips across solar systems until you get there. For plain surface to orbit it gets a bit easier.

External pulsed plasma has a fuel cost/dV ratio of 31,250, rather than the 100,000 of TL10 antimatter plasma rocket. (That ratio value is in $ / (mile/second per tank).) You also get 2G out of the single engine, while the higher-dV fusion drives are pumping out fractions of a G, and it’s efficient enough to get you off an Earthlike planet with a single tank of bombs.

If you don’t mind slightly lower efficiency, take a TL10^ fusion torch with water as reaction mass. Fuel is nearly free, two tanks of fuel get you to orbit, and 1.5G will get you off most worlds. Other reaction masses and high-thrust options let you tweak this.

You might also look at antimatter-thermal rockets. The TL10 version only gets you 0.2G per engine, but cost/dV is 11,111 and it’s four tanks to orbit. (High-thrust, 0.4G and 7 virtual tanks.) Having thrust less than planetary G means you rely on a runway, which may not be acceptable.

Other than that, TL9 HEDM at 2G and 12 virtual tanks, ratio 12,000.

(Virtual tanks = tanks before the adjustment from the Delta-V Increase table on Spaceships p. 17. 9 real tanks gets you a ×1.4 multiplier, which means they count as 12.6 virtual tanks. All these numbers are from the spreadsheet I wrote for So You Want To Build a Spaceship in Pyramid #3/94.)

Aerobraking isn’t really a consideration; getting from orbit to ground is nearly free anywhere with an atmosphere. Where the technique is useful is in interplanetary transits, which you’re not doing.

With these numbers of tanks, ram-rockets don’t seem to me to be worth the faff. If you’re scrimping every credit then there may be minor savings to be had, but it’s a tradeoff of capital cost against fuel cost.

Your basic nuclear drive is expelling its own energetic plasma, plus cold mass from the fuel tanks - which can be fed to it in a precisely measured manner. The ram-rocket needs to accept that cold mass at any speed from zero to hypersonic, while adjusting for local density and pressure. True, a Spaceships jet engine has to do the same thing, but it’s handling rather lower energy densities.

In Wives & Sweethearts I assumed that a normal bit of infrastructure for a civilised system is an antimatter factory in close solar orbit.

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I’d be happy enough with weeks-long trips to the asteroid mines if I didn’t then have to deal with players suggesting sub-dekasecond applications of the Eichberger Device.

What do you make of LACE and SABRE? LACE was a ramrocket that liquefied the oxygen from the intake, and SABRE is a hydrogen-burning ram-rocket that is supposed to be good to Mach 5.5 in air-breathing mode. I’d guess that SABRE ought to be plausible with high-tech materials.

Were you happy with Spaceships’ listed prices for antimatter fuels?

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Now, the unit of acceleration is the gee, which is 32.15 feet per second per second. And the unit of speed is the mile per second, where a mile is 5,280 feet. That means the the unit of time is 164.2 seconds and the unit of distance is 164.2 miles. The altitude of the edge of space is therefore 50/164.2 = 0.3045 distances. A rocket accelerating straight up at a-g will cover the distance in t, where ½(a-g)t²=0.3045, so t = √(0.609/(a-g)). In that time the amount of delta-vee expended is Δv= a√(0.609/(a-g)), and the upward velocity is v = (a-g)√(0.609/(a-g)) = √(0.609(a-g)). Never mind the changing mass ratio.

Adventures in good metrology!

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Huh. If I took the derivative correctly, and did the algebra correctly, I’m getting that the extremal value of delta-v expended is at a = 2g. And if a = g, then you have a zero divisor, which gives you infinite delta-v expended, so I’d guess that a = 2g is a minimum; it’s certainly going to be less than infinite!

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Okay.

I assumed an SM+7 launch vehicle to keep clear of scaling problems, but scale shouldn’t make a big difference.

The model is unstreamlined and unarmoured. It consists of 1–6 engines, an integer number of fuel tanks just sufficient for the mission, a control room, and enough payload systems to bring the total to twenty. A payload system could be a 15-ton cargo container or a 20-seat passenger compartment.

To account for losses to gravity drag I approximated a launch (which would actually consist of a vertical takeoff and a gradual pitch down as altitude and speed increased) by a vertical acceleration (at a-g) to the Kármán Line followed by a horizontal acceleration to orbital velocity (at sqrt(a²-g²)), and counting the vertical velocity at the peak of the climb towards orbital velocity. Any real trajectory would be more efficient.

For the time being I am considering brutal rocketry in both directions. A streamlined craft capable of a deadstick aerodynamic return from orbit would lose a bit of payload to armour and cost a trifle more owing to armour and wings, but would save half the fuel costs. I’ll look into it later.

A assumed 5% per year for amortisation and 0.02% per launch for maintenance, depreciation, insurance, and losses. All other prices were by the book.

Because I got lazy I used Tsiolkovsky’s equation for the propellant mass fraction rather than muck about with a lookup table and the “Delta-V Increase” table on p.17. I am not sorry.

For a typical example I chose a planet with 1.0 gee at the surface and a low-orbit velocity of 5 miles/sec, which is Earth-like, and a little bit pessimistic for Flat Black, where the typical world is a bit smaller and lighter.

If there are any problems with that please point them out to me.

I investigated a heavy duty cycle with 2,000 launches per year and a sporadic duty cycle with 250 launches per year. The differences weren’t very interesting.

The results I got are that

  • HEDM chemical is optimised for launch with 1 engine system and 9 tanks. Cost of launch is $110,838 per payload system (15 tons, 20 passengers).
  • Fusion torch is optimised for launch with 1 engine system and 3 tanks of water. High thrust engines are not indicated. Cost of launch is $115 per payload system (15 tons, 20 passengers).
  • antimatter thermal is optimised for launch with 6 engine systems and 4 tanks of antimatter-catalysed hydrogen. Cost of launch is $144,144 per payload system (15 tons, 20 passengers).
  • antimatter plasma torch is optimised for launch with 2 engine systems and one tank of antimatter-boosted hydrogen. Cost of launch is $541,352 per payload system (15 tons, 20 passengers).

Unless I make antimatter much cheaper it’s a clear win for fusion, and I’m pretty content with that. I don’t need access to space to be any cheaper that G$5.75 for a standby ticket to orbit, cattle class. $7.67 per tonne to orbit for ruggedised contain cargo is no problem at all.

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I modelled the trajectory to orbit as Γ-shaped as a very crude hack, and it doesn’t do to refine upon the parts. That expression is for the delta-vee expended in the vertical stem, but not all the vertical stems are equal. A ship doing 1 gee arrives at the top of the stem in infinite time with final velocity zero. A ship that does it at 2 gee arrives it with significant upwards velocity, which I count towards orbital velocity because I’m not worrying much about direction: this is a crude hack. A ship that does it at more than two gee spends more delta-vee in the notional vertical part, but it arrives at the Kármán line with a lot more velocity, so it spends less in the notional horizontal leg.

I have checked the total delta-vee expended as a function of acceleration from 1.1 gee to 20 gee in increments of 0.1 gee. It’s monotonically decreasing. 7.47 mi./sec at 1.1 gee, 5.78 at 2.0 gee, 5.26 at 10 gee, 5.18 at 20 gee.

EDITED TO ADD

I’ve checked a textbook, and it seems that I might be under-estimating v losses to gravity drag, which are 1.15 to 1.58 km/sec for various modern satellite launch trajectories. That’s what I get with 1.6 to 2.2 gee.

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I’ve re-done the optimisation considering Huang Di rather than Earth, meaning 1.58 gee at the surface and the low-orbit speed 7.65 mi/sec.

  • HEDM chemical is optimised for launch with 2 engine systems and 12 tanks. Cost of launch is $205,400 per payload system (15 tons, 20 passengers).
  • Fusion torch is optimised for launch with 1 high-thrust engine system and 4 tanks of water. Cost of launch is $174 per payload system (15 tons, 20 passengers).
  • antimatter thermal is optimised for launch with 6 high-thrust engine systems and 5 tanks of antimatter-catalysed hydrogen. Cost of launch is $473,000 per payload system (15 tons, 20 passengers).
  • antimatter plasma torch is optimised for launch with 3 engine systems and 1 tank of antimatter-boosted hydrogen. Cost of launch is $867,000 per payload system (15 tons, 20 passengers).

The middling sort of world has 0.81 gee and a low-orbit velocity of 4.15 miles/sec.

  • HEDM chemical is optimised for launch with 1 engine system and 8 tanks. Cost of launch is $67,900 per payload system (15 tons, 20 passengers).
  • Fusion torch is optimised for launch with 1 normal-thrust engine system and 1 tank of water. Cost of launch is $104 per payload system (15 tons, 20 passengers).
  • antimatter thermal is optimised for launch with 5 normal-thrust engine systems and 3 tanks of antimatter-catalysed hydrogen. Cost of launch is $78,700 per payload system (15 tons, 20 passengers).
  • antimatter plasma torch is optimised for launch with 2 normal-thrust engine systems and 1 tank of antimatter-boosted hydrogen. Cost of launch is $443,000 per payload system (15 tons, 20 passengers).

Conclusions

  1. Ground–orbit shuttles in Flat Black are pretty clearly powered by fusion torch motors using water as a propellant.
  2. The economic niche for non-rocket launch facilities seems to be pretty narrow. I doubt that they are reasonable.
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Prototypes of what the Spaceships jet engine is meant to represent, absolutely. But again we’re talking about chemical energy levels, not nuclear, being mixed with the outside air. In summary I’m not saying your approach is wrong but I don’t have a major problem with “5× cost” either.

Cost wasn’t as critical a concern most of the time because it was a military campaign, but broadly, yes – in particular it meant they were expensive enough that merchant shipping had to use antimatter-catalysed rather than antimatter-boosted hydrogen. (And therefore took multi-month trips across systems, which is interesting and leaves a niche for fast couriers.)

Let’s talk beanstalks. Because I like great fiery rockets, I am a recent convert to the idea. How does the beanstalk beat the fusion torch?

  • the individual capsule is cheaper to build (doesn’t need precise aerodynamic shaping, expensive fusion drive, etc.) and operate (solar electricity plus a share of beanstalk maintenance).
  • you can scale up the launch rate quite a long way without needing more runways, bold space pilots, traffic control, etc.

In W&S (GURPS TL11) a beanstalk is seen as the sign of a colony world that had “arrived”, that was a proper part of civilisation rather than somewhere primitive. But W&S doesn’t have divergent tech levels like Traveller, and every settled world is either part of or reasonably closely aligned with one of the eight or so big interstellar polities, so there’s some subsidy from the centre. Broadly I think the development stages might look like:

  • outpost - research station, you come in, do your job and go away again.
  • colony - this is your home, but it’s pretty basic. You have the high-tech gear that came on the colony ship, which includes a nanofac, so there’s plenty of stuff; but getting to and from orbit takes specialist hardware, messages off-world take a while to transmit, you probably don’t have a courier boat on station by the wormhole, and ships may not visit very often. Though I suspect the biggest part of feeling primitive is a low population: there’s nobody else to talk to about your obscure hobby.
  • more successful colony - you have a beanstalk, so orbit is a permanent part of your world rather than a place only visited by specialists. (There’s an obvious incentive to start doing this before it really makes direct financial sense, because like a public transport system it enables other productive things to happen.)
  • independent world - this is really only a financial shift, given the political realities imposed by large space navies, but it feels good.
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Stung by @whswhs’ skepticism, I have adopted a new, less crude, hack. My model is now that a shuttle upon launch first accelerates straight upwards at (a-g) until it has sufficient velocity to reach 164.2 miles altitude (that’s the bizarre unit of distance in the gravity-ton-milepersecond system, but it is also 264.2 km, a reasonable value for a low-orbit rendezvous). Then the angle of thrust is pitched down to arcsin(g/a), producing horizontal acceleration at √(a²-g²), which continues until the horizontal velocity is equal to low orbit velocity.

Total Δv expended (including the vertically-accelerating plus the horizontally-accelerating legs of the trajectory) is

  • Δv = √(2g).a/(a-g) + vorbit a/√(a²-g²)

That’s better, but I’m still not getting a job at JPL.

This approach gives much larger figures for the gravity losses, especially for low acceleration. And all the acceleration values here are a lot lower than a staged chemical rocket, so pretty brutal. Inasmuch as these figures don’t take into account that acceleration can be increased as fuel is spent, gravity losses are overestimated.

I’ve re-done the optimisations. Fusion torches using water as propellant are still the bomb.

  • HEDM chemical is optimised for launch with 3 engine systems and 10 tanks. Cost of launch is $147,700 per payload system (15 tons, 20 passengers).

  • Fusion torch is optimised for launch with 1 engine system and 3 tanks of water. Cost of launch is $140 per payload system (15 tons, 20 passengers).

  • AM thermal is optimised for launch with 5 high-thrust engine systems and 8 tanks of antimatter-catalysed hydrogen. Cost of launch is $463,000 per payload system (15 tons, 20 passengers).

  • AM plasma torch is optimised for launch with 3 engine systems and 1 tank of antimatter-boosted hydrogen. Cost of launch is $741,500 per payload system (15 tons, 20 passengers).

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The question remaining is whether that’s too ^ for your tech assumptions. As I understand it, this is a problem that nobody in the real world has any idea how to solve: there are all sorts of studies on fusion drives, but the combination of high thrust and high impulse just doesn’t seem to be available in current physics. Given that you have FTL, you’re obviously not being a purist. :slight_smile:

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Indeed not. But G$7 for a standby ticket to orbit might be too rich for my blood. Less than G$10 per ton ground to orbit. That’s going to be less than the hire of the shipping containers.

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You’ve accounted for fuel costs, but there may also be a per-launch cost element. Vehicle maintenance, pilot wages, air traffic control levy. And of course profit margin.

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I accounted for a return on capital at 5%, amortisation over a service life of 5,000 launches and 5,000 landings, 0.01% of ship price for servicing after each launch or landing…. But no hangaring, runaway and gate use charges, docking fees, safety inspection fees, booking fees, landing taxes, or, as you say, wages for the crew. Cargo and military shuttles probably don’t need a flight crew; the reassuring presence of a fiftyish-looking pilot and some thirtyish-looking flight stewards are probably the kind of labour service that keeps post-robotic GTL10 economies ticking over.

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Fair point, I did miss those bits.

I think the fusion torch is still best, but maybe by slightly fewer orders of magnitude. Especially when a government says “hey, people can fly to orbit for $10, let’s put a $10 tax on them and we still won’t strangle the orbital commerce boom.”

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That sounds as if you’re assuming that a couple of TLs in the future, the usual way that people support themselves will be by “labor.” I’m not sure that that assumption is justified.

In the broad sense, where “labor” means productive work, there have been eras when labor was not highly regarded, and when what people thought desirable was ownership of capital. Anywhere in the range of years from Jane Austen from P.G. Wodehouse will give you a look at such a culture. Of course, the Victorians had factory workers, and before them the Romans had slaves; but in an advanced economy, perhaps capital (in the form of AI) can provide the “slaves,” and the normal human condition will be to own capital and get income from it.

In the narrower sense, you could have humans who do “work,” but who do so using large amounts of capital—tools, equipment, plant, and so on—and who don’t get paid “wages” or “salary” for it.

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Sorry, I was being ironic.

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Ah, humor! I’m really bad at recognizing humor.

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And I at making it.

I’ve thought a lot about the post-labour economy; it’s important for Flat Black, and will begin in my lifetime, I think. I wrote about it on the SJGames forum once, but got such hostile reactions that I had to delete the posts. I’ll get something committed to electrons as part of this exercise, but not in the “space travel” section of the “technology” chapter.

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I repeated the exercise using winged shuttles and assuming a deadstick re-entry. That involved reducing the payload by one system, adding the cost of winged and one system of steel armour (steel!), and halving the fuel costs. (launches and landings are a join product with identical supply curves because of Kirchoff’s Junction Rule for vehicles; the fares and freight rates will not split into cheap landings and expensive launches, even though it seems that launches cost fuel and landings don’t.)

The optimisation was dull. Drive spec ended up not changing for any drive type except for fusion torch with normal thrust using hydrogen. Launch costs came down by 47% for the antimatter plasma torches, but went up 0.05% for AM thermal with high thrust and water propellant. Fusion torch with normal thrust using hydrogen is still the bomb, with its cost per system of payload down from G$140 to G$131. The difference is small enough that any per-launch cost that is structured like a docking charge or runway fee (i.e. independent of payload) and over G$150 would tip things back to the slightly more capacious wingless design.