Go Small or Go Home

Just how big can you feasibly make a spacecraft? The size of an aircraft carrier? The size of an asteroid? How about the size of a small moon? Today we will look at scalability of spacecrafts and the systems within.

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A large (190 m) capital ship compared against the Space Shuttle Orbiter (37 m).

When designing a spacecraft, certain questions inevitably arise concerning how it should be sized. Crewed spacecrafts very obviously have a lower size bound, since you can’t really miniaturize people like you can lasers or rocket engines. At the very least, your spacecraft needs to be able to fit people. However, there is no clear upper size bound. With missiles and drones, there is no obvious lower size bound either.

Let’s take a look at size limits of subsystems.

Power usage is more or less the primary way to increase effectiveness of systems, and size is generally the way to reduce thermal and mechanical stresses caused by this power use. But these laws are almost never linear, and often hit ultimate limits.

Take lasers, for instance. As outlined in The Photon Lance, scaling a laser up or down in size produces very little difference in power output. However, scaling it up in size reduces the power per volume and power per area so it won’t melt when activated.

This means you often want to keep your weapons and subsystems as small as possible, but it’s physical limits that force them to grow larger.

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A Nuclear Thermal Rocket (NTR) next to a Magnetoplasmadynamic (MPD) Thruster at the bottom of the image. The NTR is roughly 60 times as long, and masses 6000 times as much. Much of that difference is in the NTR’s enormous nozzle.

A trend with sizing of subsystems is that systems tend to work more efficiently when larger. A single 200 kN rocket thruster, for example, will perform more efficiently and be less massive than ten 20 kN thrusters. Larger singular systems distribute mass better and require fewer complex parts than many smaller systems.

On the other hand, those ten lower efficiency thrusters would probably be preferred in combat to the single high efficiency thruster because of redundancy. Compare a stray shot taking out all of your thrust versus taking out only one-tenth of your thrust. Clearly, there is a balance to be struck, between redundancy and efficiency.

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The Saturn V used five rockets for its first stage. If one rocket failed unexpectedly, they still had 80% of their thrust remaining. This actually happened on the Apollo 13 mission, and they were able to continue their mission (until later failures).

Similarly, crew modules come with significant overhead, such as the plumbing for the sewage and air recirculators. As a crew module expands in size, this overhead reduces proportionally to the number of people within. However, bunching all of your crew together in a single module is a major liability in combat.

Alternatively, rather than making a single large spacecraft with highly redundant systems, some playtesters went the route of smaller spacecraft with no redundant systems. In that case, the redundancy is with the spacecrafts themselves, rather than with the subsystems.

Another consideration is that smaller subsystems can be manufactured more cheaply on assembly lines compared to single large subsystems. In the era of widespread, highly advanced Additive Manufacturing, these benefits are less pronounced, however.

There are certain minimum size limits that show up with drones and missiles, too. For instance, nuclear warheads have a minimum size. The smallest nuclear device ever made was the W54 at about 20 kg and the size of a large suitcase. This lower limit is due to Critical Mass needed for fission. Thus, for missiles, their warhead tends to determine just how small you can make the missile. If your missile has no warhead, their lower size limit is based on the rocket motor generally.

For drones, it is similarly the mass and volume of the weapons on that drone which limit the size of them.

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A small drone compared to the size of a human. The majority of the drone is reaction mass to offset the mass of the weapon and radiators.

But these are all lower limits. What about upper limits?

Generally, lower limits are all the rage because you want to make everything small, compact, and low mass. The smaller (volumetrically) you can make everything, the less armor you’ll need. The less massive you make everything, the greater the delta-v and thrust you’ll have.

There is actually very little stopping you from making enormous lasers or railguns, but simply making them bigger doesn’t actually improve their effectiveness or power, it only makes them deal with thermal and mechanical stress better. Essentially, you make things big because you have to, not because you want to.

But suppose you don’t care about making the most effective spacecraft, you just want to go big.

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A large civilian craft compared to a human. The human is the small black dot in the lower right.

At this point the Square-Cube Law begins to rear its head, and that is that volume scales cubically, while surface area scales quadratically. This is why large animals are built very differently than small ones. Without gravity, these issues are not quite as severe, but they still appear.

For instance, on the positive side, larger spacecraft are more efficient about their armor-to-everything-else ratio, because armor scales by surface area, and everything else scales by volume. Large capital ships tend to be armored like tanks while smaller ships run much lighter.

But on the negative side, acceleration suffers badly. Attaching thrusters to a spacecraft scales by surface area, and the mass of spacecraft scales by volume. Thus, the larger a spacecraft becomes, the lower and lower its acceleration inevitably becomes. As found in Burn Rockets Burn, thrust is hugely important, which is why only Nuclear Thermal Rockets and Combustion Rockets see major use in combat.

A ship that can’t dodge is a sitting duck to all manner of weapons. Most capital ships in Children of a Dead Earth range from hundreds of milli-g’s to full g’s of acceleration, and even that affords only partial dodging usually. Dropping that acceleration further is often fatal in combat.

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The smallest and largest capital ships in game. Roughly a 8x difference in mass, but only a roughly 4x difference in length (219 m vs 60 m).

Another negative aspect of growing in size is that the the cross sectional area of the spacecraft grows accordingly. And having a fat targetable cross section vastly increases enemy projectile ranges against you.

For combat spacecrafts, then, miniaturizing your spacecrafts is often the most ideal choice. But what about civilian crafts? Civilian crafts make a lot more sense to balloon up in size, especially for the sanity of the passengers.

The acceleration is still a problem, as if it’s too low, the spacecraft will have difficulty getting anywhere taking enormous amounts of time. But the other issues are gone. If travel time is not an issue, such as with a multi-generational colony ship, then you could try scaling up to truly enormous sizes.

theship
Maybe you could hollow out a small moon to make a colony ship.

When you start hitting small moon or asteroid sizes, though, then you begin to have to worry about gravitational stresses collapsing your ship into itself! But that’s far beyond the scope of what you’ll find in Children of a Dead Earth.

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38 thoughts on “Go Small or Go Home

  1. Can capturing other vessels be a thing?

    Because now I’m imagining ships with espatiers from Nation A pirating humongous, very slow(MPD thrusters) ore haulers from Nation B.

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    1. Capturing vessels is done in a few particular levels, actually, though only against military crafts! First you have to disarm a ship’s drives and weapons, and then you have free reign to capture their derelict vessel.

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      1. Is it possible to capture a vessel with the ability to maneuver at all, in universe? Say, by closing in, getting a ‘close enough’ velocity match, and then connecting the two vessels with some species of grapple hook?

        This would only be for targets that you need to maneuver afterwards(the ore haulers), of course.

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    1. Range scales with aperture size (in a way), however with a disk shaped aperture, the targetable area of your laser mirror increases very quickly. Since projectile weapon accuracy is primarily determined by targetable area, range against lasers tends to increase faster than the range of lasers.

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      1. It does? This is true, but as laser range rises, projectile travel time increases. And wouldn’t every round fired be guided with micro-thrusters, even rounds fired from weapons comparable to present day cannons and machine guns? I mean, your game has molecular additive manufacturing, which means that the manufacturing cost to add a feature like that wouldn’t be much. It’s basically a tungsten bullet with microthruster pits drilled into it and some kind of crude IR seeker on the nose or a course update receiver sensor on the back.

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        1. Ah, molecular additive manufacturing? In the backstory? Where’d you hear that?

          And I doubt it’d be worth it regardless, seeing as in the footage shown so far rounds in the 1-10mm range are expended by the thousands.

          Also- qswitched, was this determined experimentally ingame? Does the increased travel time come into this at all?

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          1. This very blog post mentions additive manufacturing with respect to engines. I know from outside knowledge that you can’t make rocket engines with additive manufacturing without essentially atomic scale precision. The reason you can’t is because that if you try to make them using techniques right now, involving lasers and metal powder, the metal crystalline structure isn’t good and you have about half the effective strength you get from casting and then proper chemical and heat treatment.

            So if you can do that, you can make every bullet be guided. You would expect that space warships would be very expensive even in a world that has the capability to make big ones, so you would also expect that the marginal cost would be worth it.

            If the bullets are guided, projectile range is basically either infinite if a shot is possible (aka the gun shooting them has enough muzzle velocity for an intercept – 10 kilometer/second railguns are feasible so you could fire shots across the solar system that would hit a non maneuvering target) or as far as you can expect the inefficient rocket motors in a bullet to chase a maneuvering target. (solid fuel microthruster pits would have poor ISP)

            Bullets would be pinpoint accurate – the only reason they would miss is either the enemy ship runs far or long enough that the bullet runs out of rocket fuel or the batteries on it die, or if the bullet is damaged by a defensive weapon like a PD laser.

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            1. Some note on additive manufacturing. SpaceX’s SuperDraco rocket’s thrust chamber was fully 3D printed in Inconel via laser sintering. It has been tested 80+ times at full thrust with full success.

              http://www.spacex.com/news/2014/07/31/spacex-launches-3d-printed-part-space-creates-printed-engine-chamber-crewed

              Also the article notes that the Falcon rocket already flown uses several more additively manufactured parts.

              NASA’s trying to catch up. They’ve made 75% of the rocket engine via additive manufacturing (via a breadboard rocket), and these pieces have all individually passed ultrahot, cryogenic, and vibration tested.

              http://www.nasa.gov/centers/marshall/news/news/releases/2015/piece-by-piece-nasa-team-moves-closer-to-building-a-3-d-printed-rocket-engine.html

              Seems thus far, however, only SpaceX has achieved a additively manufactured thrust chamber at 100% thrust.

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              1. I know about the SuperDraco. As I understand it, the problems with metal strength weren’t actually solved, rather, they used more metal and some 3d printed reinforcing structures to overcome them. When you’re talking about the mechanical parts in a monster NERVA engine, these are flaws you probably cannot afford.

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            2. “You would expect that space warships would be very expensive even in a world that has the capability to make big ones, so you would also expect that the marginal cost would be worth it.”

              I’m not sure that follows, especially in the presence of laser weapons.

              Warships are complex, but large pieces of machinery that are expected to take relatively small accelerations. They need large shipyards and are quite expensive, yes, but you don’t need to aggressively miniaturize the individual components. In fact, you probably want the components large enough that they can be quickly swapped out to give damage control and repair an easier time.

              Whereas unguided bullets are small, very simple, and can take high acceleration-there’s obviously some more complexities for AP rounds and the like, but when you get down to it they’re stamped out pieces of metal, thus very cheaply mass manufactured. They’re cheap enough that, as indicated in the videos shown so far, they can be expended by the thousands in a single engagement, and can overwhelm laser point defense by sheer weight of fire.

              Missiles occupy a sort of middle ground between bullets and warships. On one hand, they can independently maneuver, can carry armor to tank PD, and take relatively low acceleration, though higher than a warship. On the other hand, they are expendable munitions, but not to the same degree as bullets-because of their complexity of manufacture, they can’t be expended by the thousands per engagement like bullets can.(Hence why the extra expense in armor, to tank laser and PD fire.)

              Your guided bullet concept seems to combine the problems of both bullets and missiles-they would be complex, small devices that would have to take high acceleration.
              You would have to manufacture sensors sensitive enough to receive course corrections or see the enemy, electronics capable of reading them, a battery capable of powering both for the flight time, and dozens of solid rocket motors-all of which must fit within a 1mm-10mm round, and be capable of taking forces equivalent to getting hit with a truck on launch without breaking(or in the case of the motors, exploding).
              They would be very limited in their ability to maneuver to follow a target, limiting their range depending on how much the target can displace themselves.
              They wouldn’t be able to carry an effective anti-ship warhead or lots of armor to tank lasers. So you would still have to manufacture these rounds in the thousands to swamp point defense and cause cumulative damage.

              If we were observing two fleets of equal cost going at it- one that invested in these guided bullets as their primary anti-ship weapon, and one that invested in more missiles, conventional bullets, and lasers-I would bet on the second, because they would be able to hit the first fleet from beyond their effective range, covered by lasers that couldn’t be economically swamped by guided bullets at any range, and then wade in and finish the job with conventional guns that CAN economically swamp the first fleet’s point defense once they have been sufficiently reduced.

              Now, they might be wonderful long range PD against missiles, who have lower deltaV to maneuver with and little to no point defense. But I wouldn’t load them into every gun, or expect to use them against proper warships.

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              1. The electronics would be a single chip solution. The thrusters would be tiny cylindrical pits in the bullet filled with solid rocket propellant. They would use one of the methods that allows you to precisely pulse the solid rocket motors.

                The battery and wires and everything would ideally be fused into the metal of the projectile itself. Obviously this would be much easier to do with 3d printing – you’d print the bullet by laser sintering the metal powder around the guidance package.

                If you were really amazing with the engineering, you could make the receiver for course updates actually power the electronics that decode the message from the light energy exciting photocells embedded in the projectile. So the electronics would be cold when not receiving course updates and the range would be incredible because the battery energy is only used to provide the electric arc needed to trigger the solid rocket propellant. The battery would be just large enough for the bullet to consume all it’s fuel.

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                1. Oh, I’m not saying it can’t be done. (Though I personally doubt the reciever-power trick would work as well as you think it would-see Sensors and Countermeasures.)

                  What I’m asking is, can you mass manufacture enough of them to keep up with expenditures of thousands per engagement? You can’t armor the round like you can a missile-the mass budget just isn’t there-so the only way to penetrate point defense is by the thousands, like regular unguided bullets. And what you’re describing is still a pretty complex device compared to regular bullets.

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                  1. It’s more a matter of whether it’s worth the cost. The thing is, as qswitched has mentioned, each ship in combat had to throw away 1 or even several entire nuclear powered “tanker” ships to even reach that point. For every kilogram of payload, there are many kilograms of fuel that had to be expended, with that fuel obtained from mining moons and asteroids or even launched from Earth. There has to be a crew and all their supplies and shielding. And so on and so forth, space warships are ruinously expensive by modern day economics and even in a future world you’d expect for them to be very expensive.

                    Anyways, yes, you could possibly end up in a scenario where only dumb bullets are worth it. On the other hand, if you have self replicating factories or even mostly self replicating plants, making every bullet smart is trivial.

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                  2. Ok, look at it this way. Can’t edit posts, so here’s a refined version of my thoughts.

                    First, you’re asking the wrong question. The question isn’t “can you mass manufacture fast enough”. The question is, “can you afford enough 3d printer bullet maker machines to make the thousands of rounds you need, manufactured in parallel”.

                    And the easiest way to answer that is to imagine a few thousand of these machines, running in parallel, each one the side of a vending machine or so, and then ask what ELSE you need to even be making space warships like this.

                    And, that question is obvious. Either you have a massive launch system on earth to cheaply put the parts of a ship into orbit, like an electromagnetic track or a gigantic array of lasers or even a skyhook or space elevator. Whatever you use, this dwarfs the cost of smart bullet makers.

                    Or you already invented self replicating factories and put 1 of those factories on the Moon. It self replicated and now you have thousands or millions of factories, and the bullets are the same cost whether dumb or smart.

                    If you don’t have self replicating factories OR a large volume launch system, you probably got your space pwnwagon into orbit using a method similar to the new SpaceX booster recovery system, a tiny piece at a time. If that’s how you did it, every kilogram of hardware costs hundreds of dollars, and so the % difference between smart and dumb bullets is very small.

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                    1. Oh, and one final note : that’s on the cost side of the equation. If smart bullets have 10 times the chance to hit but cost 5 times as much in total costs (manufacturing costs PLUS the cost of the ship to deploy them, including launch costs) they are worth it.

                      And the cost difference would probably be small even if they had to be manufactured by white gloved workers by hand in a factory. The reason is that the costs are:

                      Dumb bullets = cost of bullet + fractional cost of ship (ship cost/total rounds carried) + cost of launch ($100+ per kg)

                      Smart bullets = cost of bullet + fractional cost of ship (ship cost/total rounds carried) + cost of launch ($100+ per kg)

                      So if you compare the ratio of smart/dumb, as you can see, even if the bullets are handmade the actual ratio is numerically pretty close when factoring in all costs. The smart rounds just have to be a little bit more effective to be worth it.

                      And they’d be immensely more effective. A miss is wasting a bullet. Being able to begin firing from greater range is almost priceless as a tactical advantage.

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          2. Yes, in game. I never could get lasers to be competitive with ‘dumb’ projectile weapons. The key issue is that while lasers are great for disabling complex systems, ‘dumb’ projectiles are way too hard to melt through with a laser, especially when you have thousands coming at you.

            I definitely welcome anyone trying to prove me wrong though. There’ll be plenty of opportunity for that when the game ships.

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      2. So… I ask, now, because I’m helping my wife with some far-future scifi books she’s writing, so this is not directly related to CoaDE. If you could generate an incorporeal lens, let’s say by manipulating gravity or somesuch, you could achieve far greater ranges without being vulnerable to projectile weapons? Generate a several-kilometer gravitational lens alongside your ship, emit the light at it, and get light-second scale ranges?

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        1. Interesting idea. I admit I haven’t studied spacetime that much, but the concept seems reasonable. In practice, as long as you could bend light, you can focus your beam.

          If you’re thinking of a straight up gravity lens though (https://en.wikipedia.org/wiki/Gravitational_lens), that would not do the trick, however, as it would cause the beam to diverge rather than focus. Normal gravity lenses are strongest in the center and weakest on the outside, which is the opposite of what you need to get a focusing point. You need to form something with gravity weakest in the center and strongest on the outside to mimic a convex lens, so it would be a bit more complex than generating a simple gravity well.

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          1. Right, that was a concern I hadn’t thought of. But I think that should fit with the brand of unobtainium she uses in her work, there’s already toroidal fields used for things like traffic control and so forth – a lensing field like this ought to be within capabilities. Thanks for the info!

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            1. Would you be able to use such a lens to bend as well as focus the beam? If some then you have the possibility of indirect-fire laser artilery.

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  2. You mention how linear acceleration suffers, but it’s far worse for angular acceleration. The moment of inertia scales up to the square of dimension and linearly with mass – which, if density is held constant, is a function of volume or cube of dimension – so you can think of it as scaling up to the fifth power of dimension. On the other hand, your moment arm is only increasing linearly, and your thruster’s output (assuming you scale it up with the ship) is only scaling up to the square power. Fifth versus third, your ship is becoming far less responsive, and spinning becomes increasingly expensive in terms of relative amount of propellant used. Granted, you can’t go that fast either, as you also become increasingly limited in what angular velocities and accelerations you can tolerate, seeing as these translate to larger tangential and normal accelerations, enough to throw around your crew. Move too fast and the edges of your ship start suffering under centrifugal gravity. To use the 190 meter capital ship displayed here as an example, the extremities experience 1 g outwards at 3 rpm, which would take 20 seconds to turn the ship around – and that’s not accounting for the time needed to get to this speed. By comparison, the space shuttle orbiter could manage nearly 7 rpm, which would take 8.5 seconds to turn the ship around, for the same effect.

    In terms of design implications, I would think larger ships would thus tend towards larger number of weapons for increased coverage and turreted guns over stationary mounts, seeing as it’s difficult to re-orient the ship to face its targets, while smaller ships could go the other way for exactly the same reason, that they can turn around and point their guns as necessary. This would probably have happened anyway, for quite a number of other reasons you’ve already outlined…

    An interesting side effect of these physics is that CMG’s become more useful at these sizes, since they rely on their own moment of inertia which can be scaled up in the same manner, and angular velocity, which is limited by the stresses caused at the edge of the disc that scale to the square of radius and angular velocity. To maintain the same stress at the edge of the disc then, you must decrease angular velocity by the same factor radius is increased; however, actual angular momentum scales proportionally to angular velocity, rather than to the square, so CMG performance suffers only to the first power rather than to the second as do thrusters.

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    1. Correct, angular acceleration plummets with size.

      And while the centripetal acceleration on the outer parts of a large spacecraft would start to become a problem for any crew, crew modules tend to be placed closer to the center if this is expected to be an issue anyways. This is done in game anyways, as enemy munitions can cause nasty spins in your ships which can be fatal for your crew.

      While CMG performance increases with size, as mentioned in prior posts, their effectiveness is so abysmal for combat purposes that they would still never become that effective in large spacecraft situations.

      For spacecrafts of enormous size, it’s far cheaper and easier to never rotate, and simply strap main thrusters in every direction.

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  3. One comment : you mention larger lasers not being more effective. Don’t larger focusing mirrors or lenses become significantly more effective by making the spot size at long distances smaller? Obviously like any other scaling law, this relationship would cease once the range is so great that the speed of light lag between the firing ship and the target is significant, but before that point, bigger mirrors should be immensely better.

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  4. “Crewed spacecrafts very obviously have a lower size bound, since you can’t really miniaturize people like you can lasers or rocket engines.”

    This is actually the second though I had, when watching The Borrower Arrietty, on what would happen if said Borrowers were discovered by humans. (Also, they would probably resist higher acceleration, as they clearly took advantage of the Square-Cube Law.)

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  5. Thin and long spacecraft are terrible at turning but can mount longer spinal weapons and less complex arrangements of broadside weapons, whilst having a smaller profile. Short and fat craft would be able to turn quicker with less centripedal stress, whilst also having less room for spinal mounts and a more vulnerable cross section.

    Furthermore, a short and fat craft can manoeuvre more quickly to meet a mission elsewhere, even if it means getting to a destination that is days away and taking a few minutes less to do so- and every second might count for policy makers at home.

    The largest and most powerful craft like battleships* might thus be long and thin. Cruisers*, even if they are a similar tonnage/mass, might be shorter, as befitting their role as rapid response craft. The wider open spaces on a short and craft might also hep the crew on long endurance ‘cruise-type’ missions.

    Should you wish to divide your escorts into ‘carries as much firepower as possible on a small/slim destroyer*-type platform’ and ‘extremely manoeuvrable frigate* that covers up holes in a formation’ then this also would help.

    Nonetheless, the square-cube law means that whichever craft type needs the highest acceleration to move around formations will be reasonably thin. You might therefore end up with multiple short/thin and short/fat craft types and classes depending on their specified mission.
    Does it need high acceleration and manoeuvrability to go around a formation quickly? Thin/short: Frigate and light cruiser. Does it need comfortable long-endurance crew modules and reasonable manoeuvrability? Fat/short: Heavy/patrol cruiser.

    You can get alot of world-building mileage out of just the sizes and lengths!

    *Replace with spacecraft types that fits your own worldbuilding as you see fit.

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    1. Sigh… What I wrote was utter rubbish. I wasn’t thinking straight. My apologies for this. Turning speed will not determine class at all. Ignore this.

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  6. Just discovered your blog and game, looks like a really cool thought experiment.

    Have you tried using your remass as armor? Most of the mass of the ship will be fuel/remass so why not put it to good use… like ice?

    I imagine a system like this; your remass is water, which is stored as ice in many hexagonal or square compartmentalized blocks/tanks around the surface of the ship. Under thrust your waste heat would be used to melt the ice before it is ejected out the back allowing you to perhaps retract your radiators from damage when your under fire, and could also be used as an emergency heat sink as well. Water has a pretty high heat capacity and will have two high-energy phase changes to absorb energy with.

    Perhaps the water-steam phase change could act as a reactive armor almost to some projectiles?

    Whipple shield> Outer armor> vacuum/insulator> Ice tank> vacuum/insulator> inner armor

    The outer armor would be the same shape as the ice tank so if it get blown out it does so cleanly and limits the damage to that compartment.

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    1. I did actually consider using ice as armor at one point. The biggest problem with ice is that it’s extremely weak, even in bulk.

      Ice has a tensile strength of about 3 MPa and a density of very roughly 900 kg/m^3.
      Boron Carbide, a high strength armor ceramic, has a tensile strength of almost 600 MPa and a density of about 2500 kg/m^3.
      Martensitic Steel, a high strength armor steel, has a tensile strength of about 2000 MPa and a density of 7700 kg/m^3.

      From a strictly strength standpoint, ice is 200x weaker than the ceramic and 667x weaker than the steel. From a strength per mass standpoint, ice is still 72x weaker than the ceramic, and 78x weaker than the steel.

      That sort of strength difference means that ice is essentially unusable as an armor against projectile damage.

      Some other issues with it include the low melting/boiling point. While not the only property for countering against lasers, the melting/boiling point is very important. Ice has a melting point of 273 K, whereas that steel, 1856 K, and that ceramic, 3036 K. That’s 7x and 11x higher than ice’s melting point, respectively. Lasers will vaporize entire segments of your ice armor without breaking a sweat.

      I tried other mass types, frozen methane, frozen hydrogen, etc., but these issues all exist with all of these propellants. Propellant is just really bad as armor, and not really worth the effort.

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  7. Simple question. You say “…Attaching thrusters to a spacecraft scales by surface area, and the mass of spacecraft scales by volume. Thus, the larger a spacecraft becomes, the lower and lower its acceleration inevitably becomes.” Isn’t that only true if you are using the “multiple small thrusters” approach? If you are using the “one big thruster” on your ship then doesn’t the thrust scale with volume?

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    1. Thrust of a rocket engine is dependent on the mass flow rate of the propellant, or how quickly you can move propellant from your tanks to your rocket engine. Assuming you have maxed out material stresses, the mass flow rate is limited by the areal cross section of your engine.

      This means that no matter how big your thrusters, your limit is the surface area of your spacecraft. One big thruster will have a better surface area of exhaust than many smaller ones, but it still scales up quadratically.

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