# Multi staged relativistic projectile usable in hard sci-fi space combat

Following this question, in the exact same setting

I'm making a world where sub-FTL interstellar travel is a thing, and so is interstellar war, but for the purpose of this question we'll assume the scale to be of a single system.

Spaceships have evolved quite a bit since our current era, and they range in size from several meters (something like 2 times larger than your average air superiority fighter, having a space-worthy manned vessel can't get any smaller than this in my universe) to up to 20 kilometers in the shape of a scaled-up space submarine.

Weapons comes in varying shape and size (proportional to the ship that bear them) and can be split in 3 categories:

• Missiles : Just your everyday payload carrying self propelled firestick, you could also call them torpedoes at this point, it doesn't really makes a difference as far a I know. They won't get bigger in size than an ICBM and the tech didn't evolve much aside from targeting and space-worthiness.

• Lasers: They are mainly used as a countermeasure and/or to mess with enemy targeting systems at close range (and occasionally to blind the enemy commander trough the window as a prank).

• Railguns: This is where R&D was the most successful, since those guns can get pretty big (remember the 20km ships?) and the biggest projectile to date is a whopping 100m long and can travel at 30Km/s. Picture throwing Saturn V at the enemy vessel). Please note that for smaller projectiles the speed can get up to 150km/s, but that is a very specialized gun and the average is less that 100km/s for a decent gun.

Concerning energy requirements, capacitors went a long way and are now extremely efficient, as well as cooling, even in space (firing a railgun more than once won't melt it for the first couple consecutive shots) and fusion is the go-to mean of energy production across the civilization. Dyson sphere project started in some systems, and the question of the access to the host star sparked the wars in the systems.

This time I want to ask you guys about the feasibility of a 3 stage relativistic projectile that would work as follow:

1. The first stage is a railgun that get the payload up to 150km/s over a 18km distance (hoping the acceleration doesn't destroy too much my payload)
2. Second stage comes when the projectile is at safe distance for ablative laser propulsion, the ship firing directly at the rear of the shell, further accelerating it to [calculations needed] km/s
3. Third and last stage is a mix of a HEAT charge and a casaba howitzer, and this is the last and only chance for the firing ship to make any trajectory correction by turning the shell around using tiny thrusters and detonating the nuclear charge, at a safe distance of course (maybe 1 A.U. or less, I don't exactly know what a safe distance is when 10,000km is considered point blank range in space).

Such a weapon isn't stealth-friendly in an already non stealth-friendry environment, so i'm looking to go really fast, really fast. Energy expenditure is out for simplicity's sake, and we shall consider the shell after the third stage to be going at relativistic speed (more than 1% of C), be hardly detectable and a pain to deflect (you don't want to create a relativistic could heading your way by destroying it... or do you?)

And now for the (somewhat) concise question: Would such a weapon system be realistically possible?

Please note the tech level to be several centuries ahead of today, so extrapolating current tech to the limit of physics is acceptable. Feel free to comment below for any missing info on the context if needs be (also feel free to edit for spelling, my previous question highlighted the fact that I utterly suck at it).

• @L.Dutch Thanks for editing! The "speeds per second" was meant as a joke but maybe it can lead to confusion... I guess I will leave it out – Alexcommil May 23 '18 at 8:56

First I want to say something about RailGuns in General

One of the sites you linked to talks about Children of a Dead Earth, which takes a common view of hard-science space combat, so I will talk about that.

For ships you have two ranges. At one range orbital mechanics are important. Ships are far away. However, you can easily figure out a ships acceleration, mass, ect because of all the heat it is dumping into space. You know where it is, and where it will be if it continues on its current track. You also know the limits of where it might be if it changes course. However, at this range, it takes awhile for your projectile to get there. Even at your "point blank range" of 10,000 km, it will take a 100 km/s projectile 100 seconds to reach its target. If the the target started a hard 5g burn right away, they would be 250km away from where you expected to find them. Small distance for space, but easily big enough to miss.

What about saturating the area with fire? Looking at the size of a submarine, best case for the shooter, your 20km ship has a cross sectional area of 20*1.4 = 168 km^2. The target zone has an area of 196,000 km^2. This gives a individual projectile a 0.08% chance of hitting. If you simultaneously launched about 70 of them, you would have about 50/50 odds of at least one hitting. (99.02)^70. Assuming the enemy rotates to present a smaller target zone to you, this can be significant worse (though doing so would probably mean any hit would be catastrophic, straight down the length of your ship).

The math gets much worse at longer ranges, though you can achieve saturation by firing a bunch of projectiles at once, but the ones you fire first go slower, so they all arrive at the same time. But ultimately, the target zone grows quadratically, with the additional distance the ship can put on, and that grows quadratically with projectile travel time.

NOTE: This is assuming you are already correcting for the fact your opponent is moving. This math is based on the fact that your opponent could start speeding up, or start slowing down (or just stop speeding up if they were already accelerating). The only concerns that the defender has is fuel, what impact they will have on their orbit. I suppose it could become an issue of attrition. Which ship's crew will not be able to handle the gees first, or which ship needs to burn to correct their orbit first.

My point being is that you really want your projectiles to be guided if used at any real range.

The other engagement range is suicide range where it becomes like a knife fight. Ships don't have time to dodge, and the battle (or at least each engagement) is over in seconds. Ships could easily have relative delta Vs 10km/s or more.

The one page you linked to seems to argue that the "inner engagement envelop" begins at 1 light second out, and rail guns come into serious play there. Honestly I don't see it. You are still look at travel times of close to an hour for rail gun projectiles. You could accelerate at a measly 1/10th gee and deviate nearly 500km from your expected position. You are still looking at a huge light cone.

At your knife fight range. What would knife fight range be? Usually people define it at about 1/10, or close to what you point blank range. Honestly, I have never seen a convincing argument for the use of traditional rail guns in realistic space combat (still does not mean they aren't cool).

Simplify it a bit. Rail gun launch your missiles. A railgun projectile, depending on how you do it, can be fairly stealthy. Once the missiles get within a "close distance" then they turn on and put on the steam and course correct as needed. I don't know why I don't see this proposed more often.

It also seems like overkill as written. Unless this is a WMD to be used against fixed targets (Which changes things ALOT).

But lets look at is as written.

First Stage 150 km/s in 18km. That gives you an acceleration of about 63,000 gees. That's a lot. A = V^2 / (2X)

Lets assume your projectile is made of a material on par with steel.

Let look at the compressive strength of steel, 250 MPa, this is the pressure it can withstand before breaking.

We multiply our accerlation by M, and the pressure by A, and we can get a ratio of mass to cross sectional area for our projectile. 396 km / m^2

The mass will be equal to the volume times the density. Volume will be area times length. So our ration of M/A becomes ALp / A or just L*p

The density of steel is 7.85 g/cm^3 or 7850 kg/m^3. So Lp = 396 . L*7850 = 396.

Your projectiles need to be shorter than 5 cm to avoid breaking up. So this is our first problem. Your launcher needs to be longer.

Second Stage

Laser Ablative Propulsion will take mass away from your projectile. It has a fairly high ISP, and you can get your delta V using the rocket equation V = 50,000*ln(mi / mf)

(The ISP can vary a lot from around 200 to up to 5000 ideally. I am going with the ideal materials, ect).

So if you use up half your mass, you will gain about 36km/s. IF you use up 9 tenths of your mass, you gain about 115 km/s. For a 150km/s gain, you need to ablate away all but 5% of your mass.

So even if we get up to 300 km/s total with the laser ablation, we are still only at a tenth of a percent of light speed (light is fast).

Also, because of light lag, you can't do a lot to adjust to distant targets in this phase.

What do we need to hit 1% light speed? We need to gain close to 3000 km/s during this phase (technically a bit less, but the rail guns contribution isnt really that much, only about 5%).

That gives us a mass ration of 1.14 x 10^26. OUCH!!!! Honestly Laser Ablation is good because you don't need to carry an energy source with you, but is not ideal for this application.

Third Phase

This is basically Nuclear Pulse propulsion which does not have a maximum ISP much better than the ablation (though the minimum is much higher). Once again, you need to loose mass to get faster. By loosing a similar amount of mass you need to loose about 95% of your mass again.

In Conclusion Not really possible. You could replace the final stage with some sort of photonic rocket (sort of like NPP). This is actually what project Daedalus proposed using. Using one (if they ever exist) could let you get to 1% light speed with only using half your mass. Much more feasible.

The other option is longer rail guns. Make your railgun 20x longer and now you hit 1% light speed. There are other problems of course. As the speed gets high friction is doing work faster, which will cause it to heat up like crazy, but it seems like you are already assuming they've got solutions to problems like that.

It looks highly complicated and unpractical.

First of all, you are stitching together multiple systems which are supposed to work one after the other, and an old motto among reliability engineers states that

What is not present cannot get broken

Let's then give a look at some basic physics equations.

The distance covered starting from still can be calculated via

$d = 1/2 a t^2$

while the velocity can be calculated as

$v = at$

Based on your constraints of $d = 18 \ km$ and $v = 150 \ km/s$, I get an acceleration of about $600 \ km/s^2$ and a time of about a quarter of a second.

That means 60000 times the acceleration we experience on Earth. If you push 1 kg with that acceleration, the projectile will experience a force equivalent to the weight of 600 tons!

I have an hard time figuring out any precision mechanism that can withstand such forces without breaking apart. And after that smack, you want also to use the other two stages...

My advice would be: go simple. 1 rail gun on hormones is already enough for the suspension of disbelief. Don't challenge it further.

• I'd was going to write this but you got here first. There are a lot of molecules that couldn't handle the energy input from that primary acceleration without coming apart, especially ones designed to come apart like fuels, oxidisers, and explosives. – Ash May 23 '18 at 12:28
• Spot on, also worth considering that the sub critical mass in a nuke would likely be compressed to the point of super critical just as it launched, it wouldn't explode like a nuke would but it would throw huge amounts of radiation out into the ship as it passed down the "barrel" and deform the sphere stopping a decent chain reaction – Blade Wraith May 23 '18 at 14:46

The ever handy Atomic Rockets site provides the sorts of details and tables to do the calculations you want, but there are actually several simpler ways to think about these things (before pulling out napkins to do calculations)

First off, kinetic energy is a truly awesome thing in a space setting. The magic equation is Ke=1/2Mv^2. Since velocity in space is astonishingly high by the sorts of standards we are used to, the "v" suddenly becomes extremely important. At the very modest speeds of 7km/sec in earth orbit, flecks of paint which peeled off boosters or satellites suddenly become dangerous projectiles capable of damaging the heavily armoured windows of the old Space Shuttle and the ISS. Interplanetary velocity just goes up from there, the fastest any unpowered object can go and remain in the solar system is 72 km/sec. Punch that figure in your calculator and look at the number of Joules of energy in the result.....

In Science Fiction, there is a small convention of terming the energy of kinetic projectiles in space as "Ricks" of energy (after Rick Robinson), who pointed out that an object moving at a leisurely 3km/sec has the same kinetic energy as its mass in TNT. You could strike a spacecraft with the used kitty litter from the ship's cat's litterbox and have the same effect as using an explosive warhead.

As for actual rail/coilguns, here is a relevant section from Atomic Rockets:

As an example, suppose we have a synchronous coilgun, and that the coilgun can generate 1 tesla fields (a good number that will not saturate the ferromagnet). Our presumed ferromagnet is probably mostly iron, with about 8000 kg/m3. To reach 100 km/s, you will need 40 TJ per cubic meter of projectile. Since this is 100 million times the energy density of the field, you will need the projectile to sweep out 100 million times its volume in order to accelerate up to the desired speed. This means you need an accelerating track 100 million times the length of your projectile. If the projectile is the size of a dime, with 1mm thickness, you will need a 100 km long track. If 2.5% of the energy goes into the projectile as heat as a result of inefficiencies, you get 100 GJ of heat per cubic meter of projectile, or 12 MJ/kg. This is three times the specific energy liberated by detonating high explosives, so you can expect your projectile to explode like a bomb inside your coilgun barrel. Consequently, this appears to be an unworkable design.

So some adjustment is in order.....

The last thing to think about is your definitions. You state "Relativistic" projectile, but the generally accepted definition of RKKV's is a weapon moving at a large fraction of c. When you are slinging weapons around at that speed, you are presenting existential threats to not just spacecraft, but space stations, small moons and asteroids, many of which would likely be inhabited in such settings. A miss or deliberate strike at an Earth-like planet is likely to damage continents, or deliver the sort of energy that "dinosaur" killer asteroids do. Boldly announcing or using such weapons (regardless of how improbably long or powerful the launcher has to be) is likely to trigger an arms race, given that anyone capable of actually fielding such a weapon could simply end your entire civilization. Based on many of the factors already listed, it actually seems likely that if such things could exist, they would be more like shore batteries mounted on asteroids and moons to take out enemy spacecraft at long range, rather than spacecraft weapons themselves.