Space Made Easy

Well, I previously posted about re-imagining the universe for Astrea Alexandra, my original dystopian science fiction.  Since that post, I’ve been busy crunching numbers with the help of the excellent Atomic Rockets resource for hard science fiction.  While I would not classify my story as “hard” science fiction (I use reactionless drives based on artificial gravity, which is nonsense by definition; I’m actually aiming for a 4 or 3.5 on Mohs Scale of Science Fiction Hardness), the site still has a lot of useful information.

So I crunched the numbers for the sort of warships and technologies I mentioned in my previous post.  Even with the idea that certain types of circular particle accelerators cause artificial gravity and that antimatter can be contained in quantities large enough to be useful, I expected to come across some problems that I would just have to invent other kinds of nonsense to surmount.  For instance, while I was using nuclear reaction-based thrusters as the primary in-universe propulsion, I had to overlook the fact that calculations showed my ships would require several times their own mass in hydrogen to run at full burn for a second.  I was basically trying out all the realistic equations so I would know where I needed to plug in additional applied phlebotinum to keep the plausibility of the universe I was building intact, to keep things working as easily as I wanted them to.

But, as it turns out, I actually need to concern myself with the opposite problem!  Having crunched the numbers, I see that I’ve made space perhaps too easy.  For instance, I wanted my 1 kilometer long antimatter-missile-slinging battleships to be able to slug it out with their opposites for hours at a time.  Given rough estimates of the effectiveness of point-defenses and their shield strengths, this came out to about 4 hours, which I thought was a good time, but I worried about whether or not a 1 kilometer battleship would have enough magazine space for sustaining that kind of barrage.  I worried about the ammunition problem and was even considering whether or not it would be plausible for munitions ships to reload battleships in combat, like a semi-automatic pistol changing clips.  Then, I crunched the numbers for the total volume of the missiles.  For anyone who’s curious, those numbers follow.  Battleships fire three kinds of missiles: long-range ship-to-ship offensive missiles (Sidewinders), medium-range offensive-defensive missiles with variable payload (Interceptors), and short-range defensive-only missiles (Beads).  Like the ships, missiles use “grav drives” to accelerate, so they’re cigar or pill shaped (for the purposes of my calculations I assumed they were cylinders with semi-spherical ends, though I used rectangular prisms for storage volume, as that would be bigger and more accurate).

What kind of missiles?

  • Sidewinder/600-series
    • 2m x 0.8m
    • 0.87m3 actual volume
    • 1.28m3 rectangular volume
    • 1.92 metric tons
    • 1.16kg of antimatter
  • Interceptor/400-series
    • 1m x 0.4m
    • 0.109m3 actual volume
    • 0.16m3 rectangular volume
    • 272kg
    • 0.465kg of antimatter
  • Bead/200-series
    • 0.5m x 0.2m
    • 0.0136m3 actual volume
    • 0.02m3 rectangular volume
    • 34kg
    • ???kg of antimatter

What is the rate of fire at the launcher?

  • Sidewinder=5.5 rpm, sustained
  • Interceptor=40 rpm, sustained, 6 missile-revolving launcher
  • Bead=900 rpm, sustained, 10-launcher assembly, 3 assemblies per emplacement

What is the maximum sustained rate of fire of a battleship in a classic dorsal-broadside engagement?

  • Sidewinder=132 rpm from 24 tubes
  • Interceptor=1120 rpm from 28 turrets
  • Bead=9600 rpm from 6 fully-facing emplacements and 14 edge-on emplacements

A battleship engagement could take an hour or more to resolve, over four hours for a full engagement between opposing walls of battle. If a battleship carries enough ammunition for a 6 hour engagement, how many missiles is that?

  • 47,520 Sidewinders
  • 403,200 Interceptors
  • 3,456,000 Beads

What is the volume and mass of these missiles?

  • Sidewinder
    • 47,520m3 actual volume
    • 60,825.6m3 rectangular volume
    • 91,238.4 metric tons
  • Interceptors
    • 43,948.8m3 actual volume
    • 64,512m3 rectangular volume
    • 109,670.4 metric tons
  • Beads
    • 47,001.6m3 actual volume
    • 69,120m3 rectangular volume
    • 117,504 metric tons

Assuming storage requires 2.1 times the space, how large are the magazines?

  • Sidewinder=127,734m3
  • Interceptor=135,476m3
  • Bead=145,152m3
  • ·Total=408,362m3

Dimensions of a battleship.

  • 1000m x 400m
  • 108,908,545m3
  • 21,781,709 metric tons
  • 0.37% volume and 1.46% of mass devoted to the magazines

As you can see, there is absolutely no reason why a battleship so designed should need to worry about magazine space.  In fact, I wound up going with a larger coefficient for storage (I think it was 4 or something) and giving the battleships 12 hours worth of munitions instead of 6, but the amount of internal volume devoted to magazines is still very small.  It comes out to about 1.4% of the internal volume and 3% of the battleship’s mass.  Making large portions of the interior and exterior of the ship unusable for magazine space made this more of a limiting factor, but I still don’t think it’s going to make sense for me to write a story where battleships start running out of ammunition, unless they’ve already been in several long battles without opportunity to resupply.  Now, frigates on the other hand are about a third the length of a battleship and only have 3.6% of its internal volume to play with.  Squeezing a magazine capable of sustaining the frigate through the course of an entire 4 hour engagement would be a challenge (but it can be done, I’ve crunched the numbers), and anything smaller need not apply–battleships will certainly be the queens of space (at least until they meet the 2-kilometer long heavy dreadnoughts, with double their firepower and 8 times the internal volume…then they’re just screwed).

But this does bring me to some of the problems I had to address by applying phlebotium to make things in universe harder, so that I could tell the story I wanted, without having the logical implications of my universe running away on me to make the story just plain silly.

  1. Reactionless drives are superweapons: “Jon’s Law” of hard scifi states that “Any interesting space drive is a weapon of mass destruction.  It only matters how long you want to wait for maximum damage.”  In terms of grav drives capable of imparting tens of kilogees of acceleration, that isn’t long at all.  At 3 kilometer’s per second a vehicle carries as much kinetic energy as its own mass in TNT, and a “slow” battleship that can only pull 10 kilogees reaches that speed in 3 hundredths of a second–and (assuming a density of 0.2 tons per cubic meter, which is comparable to the realistic figure David Weber was convinced to settle on) a battleship weighs in at over 21 megatons.  Of course that’s nothing compared to what happens once you allow these things to build up some steam.  Two-kilometer long bulk freighters have to pull speeds of 60 PLS (Percent Light Speed, which is 179,875 kilometers per second) in order to jump through a very short-lived wormhole for FTL travel.  At those speeds the freighter is a relativistic weapon carrying the kinetic energy of over 900 Petatons of TNT (3.9×10^27 Joules–assuming the same density as a battleship, which may or may not be realistic).  That’s ten percent of the total kinetic energy of Earth’s Moon, ten times the total wattage of the Sun!  Hitting a planet with one of those would be beyond a civilization ender–it would obliterate all life on the surface and probably seriously alter the planet’s rotation and orbit…and that’s what a freighter could do simply by failing to brake!  To avoid a story where planets got flattened by careless pilots, militaries threw unmanned freighters at one another, or battleships had to worry about being shredded by debris or their own spent missile sabots, I decided to make them impervious to kinetic weapons as long as their shields were up.  I had already decided that shields in universe would consist of circulating envelopes of exotic matter that had special properties that allowed it to protect a ship from harmful radiation, temperature, and kinetic impacts and had already decided it should be better at taking kinetic strikes than energy ones, to encourage the use of antimatter warheads.  When I ran the figures for the kinetic energy missiles and freighters would have, I decided that, in order to prevent a take-over of ramming attacks and kinetic-kill missiles, I needed to make the shields perfectly negate the energy from kinetic impacts.  Since the shields are already made of exotic matter that doesn’t play by our rules to start with, I felt like this was an acceptable break from reality.  It also explains why planetary sieges would require actual strategy as opposed to, say, just lobbing an asteroid at somebody from a safe distance (the planetary shield would casually destroy the asteroid and then whoever owned that planet would come looking for you in a battleship).
  2. Grav Drives Have No Top Speed: On Earth, your top speed is determined by friction.  The faster you go, the more friction you generate and the more energy you need to overcome the force of friction and keep accelerating–and the thicker your skin has to be in order to withstand the friction you’re generating.  Go fast enough, and friction has enough energy to set off nuclear fusion in the air in front of you, and then you are having a bad problem (and you will not go to space today).  In space, there is no friction, so there are only two traditional speed limits.  The first is how much fuel you have to accelerate.  The second is how long you have to accelerate.  For grav-drive ships, neither presents much of a problem.  A grav drive is basically a synchrotron (a circular particle accelerator that runs at relativistic speeds), and a small synchrotron (using the Large Hadron Collider as an example and scaling down) does not take too much power to run.  At a few tens of kilogees, it does not take too long to build up to ludicrous speeds either.  The only possible limit is the speed of light.  However, as I understand it, that top speed works by increasing the relativistic mass of the vehicle (though I could be wrong).  As a spacecraft approaches the speed of light, it’s apparent mass increases, meaning that it accelerates more and more slowly under the influence of the same amount of force.  While it never quite stops accelerating, its acceleration does slow down to the point that actually reaching or surpassing the speed of light is impossible.  But mass is irrelevant when dealing with acceleration due to gravity.  Two objects of differing mass exposed to the same gravitational field will accelerate downward at the same rate, since gravitational force increases proportionally to mass.  This is why, in-universe concern will be given to conserving shipboard volume rather than mass, because the amount of volume a ship has affects its acceleration (bigger volume=bigger grav drive=larger synchrotron radius=smaller radial acceleration of particles=smaller acceleration of ship) but the actual mass it carries does not (except for reaction-control thrusters, but those aren’t a huge concern).  So when the universal speed-limit comes along to increase the relativistic mass of a grav-drive ship and get its acceleration under control nothing happens.  The ship just continues to accelerate at a constant rate.  It’s relativistic mass could be billions of times greater than its rest mass and it would just keep going because the gravitational force would be billions of times greater as well.  I have two ideas for discouraging my reactionless drives from breaking the light-speed barrier (the only thing that’s supposed to travel faster than light in the stories is tachyons, and humans haven’t figured those out yet).  The first is to make acceleration uneven, such that something at the center of the artificial gravity bubble feels a small amount of additional forward acceleration and something near the edge feels a small amount less forward acceleration.  This would amount to about 0.01% of the overall acceleration, making for a +/-5 gee difference on a drive capable of 50 kilogees (which would still be enough to black out any crewmembers who were in the wrong place at the wrong time–or outright kill them if they weren’t buckled up).  At high enough speeds, I’m thinking the relativistic mass of the spaceship’s components would exert too much force on the spaceframe, causing the ship to break up.  Of course, I may need to cause this mysterious effect to increase dramatically in severity if I want to keep my ships top speeds in the 70-60 PLS range.  Since the behavior of the effect and its existence both have to do with the totally fictional science of artificial gravity, I feel like I can make up a plausible-enough solution.
  3. Battleships Have The Internal Volume of a Small Asteroid, Without All That Rock in the Way: The internal volume of a battleship is staggeringly huge, such that even her massive magazines occupy only about 1% of her internal volume.  This of course, raises the question of what to do with the rest of that space.  Part of the problem was solved using the unevenness of grav drive acceleration from before.  I could figure part of that volume being generally unsuitable for humans or acceleration sensitive systems during maneuvers (say as section 20 meters deep into the hull).  On a warship, this area would generally be composed of armor, with the necessary gaps for hangers, weapons system, cooling systems and a myriad of other things.  That accounts for roughly 20% of the ship’s volume.  Figuring power requirements to be roughly twice the amount necessary to sustain environmental artificial gravity (which is 1,000 times more energy intensive than the grav drive itself, which I did not expect) and giving the ship a 90 day cruise time, another 20% of the volume goes to fuel.  Then there’s the grav drive itself, which makes roughly 20% of the ship at the core nigh inaccessable.  The remaining 40% of the ship’s volume is roughly 43 million cubic meters, which falls comfortably in the range of volumes occupied by Star Destroyer classes from Star Wars.  That’s plenty of room for all the other systems, storage, crew quarters, and everything else the ship might need, plus giving it the luxury of some extra space (in this universe, high-ranking officers that command battleships are considered nobility and would expect to be accommodated as such).
  4. There is No Range Limitation on Jump Drives: In universe, the only thing capable of traveling faster than the speed of light is a tachyon, which humans can detect and cause as a secondary effect of some of their technologies, but cannot put to any useful purpose (yet).  In order to make interstellar travel feasible, I’ve given them the Jump Drive, an artificial-gravity based device that allows a ship to create and navigate a stable-but-transient (existing for 10 or 12 microseconds) wormhole as a shortcut to cross hundreds of light-days of normal space instantly.  The problem was putting limits on this thing once I created it.  The fact that I’d established that artificial gravity didn’t work too close too natural gravitational fields (otherwise, we’d have discovered it by now, since we have plenty of synchrotrons). gave me a reason for making jumping into or out of an area too close to a planet, moon, or star technically impossible.  Handwaving complicated jump calculations into existence (plus the need to “align” the drive to match said calculations) gave me a reason why starships couldn’t just jump whenever they felt like it (which would make for some pretty boring battles: “Whoops, we’re losing, everybody jump out now!”).  The fact that synchrotrons in real life need time to spin up gives me another reason to make jumps time-consuming.  All of that is very well and good for limiting warships in most situations, but in positing a universe where humans have struck out among the stars using this technology, I came to a very important question: why didn’t they go further?  A warship has a good reason never to venture too far from its home port, but exploration or colonization ships would just keep moving out there until they reached the edge of their range.  And what was that?  The only logical limit I can think of is fuel supply, and allowing the ships to use fusion reactors makes refueling even in unexplored space a matter of stopping by a gas giant and skimming off hydrogen with a magnetic ramscoop or something.  As long as you’ve got hydrogen, you’ve got fuel, and as long as you’ve got fuel, you’ve got power, and if power is all you need to keep a synchrotron running, well, then, you can practically jump forever (or at least until your food runs out, but a large colony ship could circumvent that problem by growing their own food).  While outright stopping a ship from doing something like this is impossible, I wanted to discourage it, so that most humans would settle down close enough to later require warships to shoot at each other with.  So far my best solution is giving jump drives a secondary fuel requirement.  Instead of hurtling around electrons, I have them accelerating positrons (antimatter).  Since positrons are charged and the other antimatter I’m using doesn’t have to be, I’m saying that we’ve invented some kind of neutral antimatter trap for collecting and containing large amounts of neutrally charged antimatter, but are stuck with lower-volume traps for charged positrons.  Throw in the idea that jump drives have to spike at insanely high relativistic speeds in order to cause their temporary hole in spacetime, and a limit comes out.  It might just be easier and safer to vent the super-relativistic positrons into space after a jump than try to slow them down and recapture them (in fact, early designs probably would have found the latter impossible, since the synchrotron would already be strained and overheating from accelerating the blasted things in the first place, and would burn out and explode–antimatter being antimatter–if someone tried to use the drive to decellerate the positrons again).  I’m not sure what the numbers will be on this, but I know they’ll be somewhat arbitrary.  The question will always be “so, they can store 5 jumps worth of positrons in so many traps–why don’t they just put more traps onto their ship and extend it’s range?”  However, since extremely long-range interstellar travel isn’t anything the protagonists would be interested in, I hope to keep that question on the fringes, out of sight, out of mind.

That’s about it!  Thoughts are welcome.  You’ll be hearing more about this universe and stories in it as they develop.  Thanks for reading!