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Tuesday, April 26th, 2005
5:16p - Request for assistance -- smart people needed!
Well, now I'm working on the much harder problem of STL transit, since my FTL system requires good STL drives. Much to my annoyance, it turns out that Bussard ramjets don't actually work -- the drag will always be greater than the thrust. You *can* use one to decelerate, since drag actually *increases* your delta-V, but that still means you need all the fuel for the acceleration leg carried on board (I am assuming brachistochrone (continuous thrust) transit, as impulse trips are FAR too slow for interstellar journeys).

That is secondary, however, to the amount of math I don't know how to do. Here's the problem: I've got a colonized region roughly 18 lightyears on a side, containing thirteen inhabited systems, distributed roughly evenly, and with a fourteenth (Earth) at the center, but ships don't go there, or to one of the colonies (more on that later). I say "inhabited systems" because as much or more of the population lives off the colonized planet as on -- planets are used primarily for farming and reproduction, as most other tasks are more efficient in space (farming requires an elaborate ecosystem which cannot be maintained long-term in a spacecraft/station of less than ridiculous (planet-scale) size, and reproduction requires room). However, with one exception, none of the colonies is as yet fully terraformed, and so all require inputs of various substances, and occasionally of entire species, necessary to farming, that die out. Hence, the necessity of trade to keep these places going -- every few decades, Colony A needs a fresh supply of, say, earthworms, which are in plentiful supply on Colony B, which in turn needs periodic replenishing of its nitrogen-fixing bacteria... etc. Earth is ignored, because it no longer has the infrastructure necessary to supply ships, nor many of the needed organisms, and the one successfully terraformed colony (it simply required less than the others) has no need for anything any of the colonies can supply.

So, here's what I need to work out, which requires math I've either forgotten (anything beyond basic algebra) or never learned (anything beyond basic calculus): (1) Average distance between colonies. (2) Transit time (from the point of view of an observer on one of the colonies), assuming 1g constant acceleration (halfway there, and 1g deceleration back), from colony to colony. (3) Max velocity attained. If greater than .1 c, summary of relativistic effects (particularly subjective time for crew). (4) Delta-v needed for trip (this is easy if there are no relativistic effects; I need help if there are).

The answers to the first three determine whether this setting is at all feasible: if (2) is greater than about 40 years, the setting won't work at all, because it'll be as much as 60 years between the time a colony develops a need and the time help arrives. Also, if (3) is too low, the need for multi-generational crews develops, which tosses everything out the window, as I've already established you can't keep an ecology running on a spacecraft that long. (4) will determine if I can use a reasonable drive system, or need to do some handwaving, and whether it'll be fusion-based or MAM. But I have no idea how to answer any of these. Fortunately, I have smart friends. Anybody out there know how to calculate these things? Just give me some formulae I can drop numbers into, and I'll be very, very happy...

BTW, some technological assumptions:

Developments I'm assuming exist: Cheap ground-to-orbit flight (possibly space elevators); improved capacity for ecological predictions (i.e., "this species will probably be extinct in a century unless x"); whatever drive is necessary to achieve the required delta-Vs; cheap energy, probably some variant of tokamak fusion; extensive microgravity industry; improved power-storage or some mechanism for "beaming" power efficiently and safely; expanded library of genomes and resulting improvements in genetic engineering, but nothing magic.

Developments I'm assuming don't exist: Artificial wombs/seeds/eggs/cloning tanks; ability to culture anything other than micro-organisms and individual tissues; ftl travel (at first); gravity manipulation (simulation through centrifugal force/acceleration is commonplace); A.I., machine life, or any approximation thereof; magic (force fields, telepathy, making new species or recreating old ones from scratch, violating conservation laws)

Everything else is up for grabs. I'm going to toss out there, as a guess, that this period begins roughly 300 (establishment of colonies complete) and ends roughly 500 (FTL drive introduced) years into the future. During this time there is, by our standards, very little technological development -- I think most future histories extrapolate 19th/20th-century rates of development indefinitely into the future, while I lean more toward thinking of them as an anomaly akin to the Renaissance or the Ionian Revolution, soon to peter out.

Anyway, as I said, any help with the calculations would be MUCH appreciated. The one really good resource library for hard SF I've found (Atomic Rocket) unfortunately has a very strong exploring-the-solar-system bias, and therefore has little of use for these calculations (although it did have the formula for number of stars and number of borderline-habitable (terraformable) planets in a sphere of given radius around Earth, assuming that radius to be less than the distance to the galaxy's nearest edge (north, I believe)), and a nice section on plausible drives that includes delta-v capabilities, fuel requirements, efficiency, speed limitations, and basic workings.

current mood: annoyed

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