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Railgun recoil: Newton won’t be denied! Pt1

I talked in my last post about the creep of technobabble into TV and movie Sci-Fi, and why I wanted more believability in my written fiction.

Z0053043Back in the early 80s, I used to design ships as part of the game, Traveller. And then I designed how the elements of a multi-ship force would work together for the game expansion called Trillion Credit Squadron (anyone still play that?) Typical ship armaments included meson cannons, pulse lasers and railguns.

Science fiction is fast becoming science fact. It’s a cliché, I know, but it’s happening in my lifetime. One of those exotic theoretical space weapons, railguns, looks likely become the main medium-range ship weapon for the US Navy over the next 20 years. They are already planning how to retrofit existing ships with enough electrical power in readiness.

Armed with a whole load of real technical data on railguns, they were a pick for my weapons in the Human Legion universe. (A special thanks goes out to all those dads who filmed their children’s railgun science projects).

So, what is a railgun?

500px-Railgun-1.svgTo make one, you take two parallel rails made from an electrical conductor (such as copper) and wire them up to a direct current supply. Place another conductor to touch both rails. This armature, as it’s called, must be able to move along the rails. When you supply the electrical power, a magnetic field is induced in the rails which pushes the armature along until it falls off the end of the rails, which breaks the electrical circuit.

In a school science project, the rails might be strips of aluminum foil taped to a board and the armature a steel bar that gently rolls along the board.

Real ones look might use a conducting sabot for the armature. A sabot is a jacket that wraps around a shell or bullet, enabling it to be fired more effectively. Search the ground after one of the fight scenes in my Human Legion books and you will be wading through spent sabot casings.

ASIDE: Coilguns and gauss guns. I’m talking here about railguns, because that’s what I chose as the equivalent of a modern rifle in the Human Legion books. But in another series I write, the Four Horsemen Universe from Seventh Seal Press, I’ve also written about coilguns and MAC cannons (Magnetic Accelerator Cannons).

Magnetic accelerator rifles, Gauss guns, and coilguns are all names for the same thing: a weapon where a sequence of coils around a barrel are switched on and off in a precisely timed sequence, accelerating a projectile. The recoil properties are essentially the same as railguns.

Anyway, back to Traveller and railguns. When I was designing heavy cruisers after school back in the 80s I used to imagine that when a railgun fired you would hear a hum of power build up followed by a whoosh. No bang. I expected it was recoilless too. Maybe that was because there was no explosive charge. With no exploding gases required to push the projectile along a barrel, there would be no recoil pushing back on the gun breech. Right?

Turns out I was wrong on all counts. It seems obvious to me now, but I knew a lot less physics when I was 13, and my misconceptions have stuck with me,

If you watch videos of real railgun test firings [such as this US Navy video below] there is a big bang when it fires. Lots of sound and lots of light. That’s what happens when you suddenly discharge a huge amount of power in an enclosed space, but it is not a chemical explosion as with conventional munitions. You don’t have all those hot, expanding gases pushing back against the breech. So does a railgun have less recoil than a conventional gun?

The answer is that the projectile has exactly the same recoil. In a conventional modern day rifle, this is equivalent to the recoil from the bullet leaving the barrel, and it’s called primary recoil.

But that’s not the whole story, because in a conventional firearm, there’s also a secondary recoil, which overwhelmingly consists of the hot gasses from the propellant escaping from the end of the barrel. In a rifle, the secondary recoil is usually greater than the primary.

You only have to see the muzzle fireball in the video above to see that the railguns also have secondary recoil, even though there’s no chemical propellant. However, the hot gasses in the railgun are, I presume, largely a result of the projectile compressing the air in front of it as it passes along the barrel, like a space capsule on re-entry. It’s a side effect rather than a cause of the shot and so although I don’t have the numbers, I make an assumption that the secondary recoil of a railgun is smaller than the primary recoil, possibly much smaller.

And as commenter, Matt, rightly points out, if the railgun is a spaceborne weapon and the inside of the barrel is a vacuum, then there are no hot, compressed gasses to expel out the tube.(*1) Secondary recoil would be significantly reduced. You might have some secondary recoil from expelled armature sabot sleeves (but only if the armature isn’t integrated with the projectile).

So certainly you have  recoil with a rail gun, but if my assumption that the secondary recoil is much lower than primary recoil (relative to a conventional rifle) then the total recoil will be less than with conventional weapons for a projectile with the same mass and same muzzle velocity.

I emphasized that last point because the recoil of the weapon ultimately depends on choices made by its designer. In the Human Legion Universe, soldiers are usually heavily armored. To penetrate, you might fire heavier projectiles, or fire projectiles similar to modern bullets but at a higher velocity. Or you might prefer to take the railgun’s ‘saving’ in recoil and use it for a higher or more accurate fire rate with some kind of armored piercing shaped charge rounds.

One of the features of the SA-71 personal railgun often seen in the Human Legion books is that it uses a great number of fire mode options and a flexible variety of rounds in their cavernous ammo bulbs. It’s the primary weapon for all theaters of combat, including shipboard and deep space operations, and it needs to be effective against pretty much anything it can come up against.

Having said all that, it still feels intuitively odd that there’s not explosive propellant in a railgun and yet it still has significant recoil kicking back against the breech.

It’s all to do with the law of conservation of momentum. It’s the same law that makes rockets fly into space. Also… It’s a basic law of the universe that you can’t get around by waving a technobabble phrase.

So in going for believability, conservation of momentum is something I can’t ignore.

I’ll cover more about railgun recoil in part2.

Notes

*1 The issue of spaceborne railguns is an interesting one. Current railgun testing involves three most common designs for armature. The simplest is where the projectile is made from a conducting material and acts as its own armature. Others use plasma (ionized gas), which allows for a non-conducting projectile, or a hybrid which uses plasma but not exclusively. Using high pressure plasma inside a depressurized gun tube will present additional challenges. Perhaps spaceborne and land-based railguns would develop along different paths for this reason.

73 Comments

  1. […] Railgun recoil: Newton won’t be denied! Pt1 […]

  2. […] The problem with railguns in science fiction is that they are fast becoming science fact. So I thought I’d better get my facts right. I posted part 1 of my recoil and railguns series today. You can read it here. […]

  3. Jean Caroline says:

    Tim, very interesting indeed… thanks. Jean C.

    • Matt says:

      If a rail gun is fired in a vacuum, wouldn’t that stop the secondary recoil?

      • tctaylor says:

        Thanks, Matt. That’s a very good point. I added something to the post on this. Yes, you’re absolutely right that if the gun tube is fully depressurized, there are no gasses to compress and push out the muzzle. But it got me thinking about the armature because that could be a problem in a depressurized tube if the armature is a plasma. In the book series I was planning when I wrote this post, I used a conducting armature sabot that acted as a sleeve to a wide range of largely non-conducting projectiles. I digress, though. Whatever the armature design, secondary recoil will be much less in vacuum and probably negligible if not zero.

  4. Hyperbion says:

    I too am trying to write accurate and believable science fiction. The biggest problems for me to face are the enormous distances in space and the fact that AI are projected to get vastly more intelligent that humans in the future (and thus, remove any need for human protagonists).

    But I got a message from a reader today, saying that he enjoyed my little novel so far, but was annoyed that my starships’ railgun had recoil. “Real railguns,” he said, “do not.”

    I now know that I am right.

    • LOL! Glad to be of service. All you can do is grin and bear it as part of being a writer, and consider that at least you’re engaging your readers. That’s always better than not being read.

  5. robert barber says:

    Actually, any opposing momentum would be related to the mass and speed of the object propelled. An opposing thrust provided by say an ion engine would enable the. rail gun to stay in a predicted orbit. As the mass and speed of the projectile would be predetermined, very reliable and preset counter-thrust could be used for stabilization. In addition, the use of only fissile material projected at mach7 could possibly be enough to detonate it without a trigger.

    • Absolutely. I’m sure that keeping a stable firing platform in orbit for kinetic projectiles requires some kind of counter-thrust as you describe. The battlesuits in the Human Legion stories do this for handheld weapons, but we’ve not yet seen how orbital platforms do this. Thanks for commenting 🙂

    • SGT MIKE says:

      For us grunts, it is just about the weapon going BOOM when we point the bang stick in the right direction!! 😛

  6. I’m playing with my new Savage Worlds Rifts RPG books, and was mulling the question myself about railgun recoil. I googled it, expecting to find a bunch of nonsense Rifts fan forums, but thankfully found this page instead. I played a lot of Traveller back in the day, but never “Trillion Credit Squadron” 🙁

    I’ll have to look up “Human Legion,” too.

    • tctaylor says:

      Delighted to help, Patric. After writing that post a few years’ back, my check for any new tech I dream up is whether it obeys conservation of momentum. If I can convince myself that it does, then it’s fit to write. I’ve never played Savage Worlds, but I’ve heard good things. Looks at a cursory glance like it’s core is GURPS with cool dice. Is that fair?

  7. Bob says:

    Thanks for the info! I was curious because I used to play RIFTS, and the Glitter Boy armor had a shoulder mounted railgun and a stabilizer spike that would deploy form the heels into the ground automatically when it was fired to counter the recoil. I wasn’t sure if those were necessary but apparently they were!

    • tctaylor says:

      Stabilizer spike — sounds like a cool idea. I’ve just got back from a writers’ conference last weekend and the topic of railgun recoil came up at the bar. It seems everyone needs railguns 🙂

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  10. Gunner says:

    This is completely incorrect. Although yes a rail gun will have recoil of a force equal to that of what is applied to the projectile, the recoil would be very mild compared to a traditional gun simply because the majority of the recoil generated from a tradional gun is created from gasses escaping the barrel, not the opposing force of the projectile. Most of this takes place after the projectile has left the barrel. Recoil yes, same as regular gun no.

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  13. Master Zed says:

    The thing about rail guns vs conventional guns is not just newton’s second law (equal and opposite reactions) but also HOW that law is applied. While total force is conserved (ie, if the total kinetic energy of the projectile is X kJ, then the launch platform must also experience X kJ of force (so less massive projectile with greater velocity = more massive projectile with proportionally more velocity). However, the manner in which the projectile is accelerated (and therefore it’s reciprocal force) is vastly different, and so too then is the nature of the recoil. Where a conventional bullet is accelerated by a small explosion that delivers all it’s energy in a very short amount of time, the rail gun actually accelerates its projectile along the length of the barrel (or at least the part containing the rail, which I think is fair to assume is most of the barrel length at least). Further, the rail gun’s acceleration is constant along the length of the rail (the velocity is increasing, but the force is generally uniform). This may SEEM a trivial difference, but it isn’t since what we humans experience is more often PRESSURE than TOTAL ENERGY. For example, falling from 6 feet off the ground results in identical kinetic energy being generated at the point of impact. So why then does hitting concrete hurt more than hitting water? Simple, the water decelerates you slower and therefore causes a less “jarring” impact. Rail guns have a similar relationship to conventional chemical propellants. So yes, while delivering a given amount of impact energy at the destination requires a similar amount of energy to be absorbed by the launcher, it doesn’t require the same PRESSURE (or energy over time). And in the same way falling 6 feet into a pool is MUCH better than falling 6 feet onto concrete, I believe a properly designed rail gun would have similar benefits to its recoil.

    • Master Zed says:

      It’s not so much that it’s recoilless, as it is that the recoil is more even and constant and therefore presumably easier to control and manage.

      Also, *less massive projectile with greater velocity = more massive projectile with proportionally LESS velocity — sorry about that

    • tctaylor says:

      I think you’re right. A conventional rifle will get most of it’s kick from the secondary recoil impulse which starts hitting when the hot gas vents out the muzzle. I don’t have definitive timing figures for this other than what I’ve found searching around, which suggests that kicks in something like 1-2 milliseconds after the cartridge ignites. The railgun’s recoil may be more spread out (as you say, like pressing against a wall).

      When I wrote this post (five years ago now!) I kept it simple and have been adding to it over the years. One of the simplifications I’m coming to regret is to talk about momentum. In fact, I think the most important part of the experience of recoil is not so much momentum, but impulse (change of momentum over time). It’s many years since I was integrating all this stuff at school, and my maths is no longer is fully up to it, but I can see that a (relatively) long, steady push will have a lower peak recoil impulse than the sharp kick of the gas venting out the barrel. On the other hand, later on, you make the point that with bullets, it’s the kinetic energy that does that damage rather than the momentum (or impulse), and so if we can increase the velocity of the bullet (or dart in the case of my fictional railguns) then we can reduce the weight of the projectile, its recoil when fired, and fit more into our ammo bulb. It’s science fiction and we’re dealing with civilizations that have worked on these problems for hundreds of thousands of years. So let’s make the muzzle velocity ‘really’ fast.

      However, I think the two ideas are working against each other, particularly with the SA-71 railgun and similar hand-held ‘rifles’. A steady acceleration along the barrel without the explosive gases will mean lower recoil impulse relative to a conventional rifle. Conversely, the faster we’re accelerating the projectile, the shorter the time the projectile takes before exiting the barrel, which increases the recoil impulse.

      I guess there ain’t no such thing as a free lunch 🙂

      1. Weight of projectile. 2. Time taken to accelerate out the barrel. 3. Muzzle velocity. In a fictional setting, I can’t make up the laws of physics (although I cheat them, as you point out) but I can set all three of those variables as I choose. I’ve never put numbers together, but my design had them very light (at least for standard rounds), very short and very fast. Where does that leave the amount of recoil? When I wrote the first bit of Marine Cadet seven years ago, I said it was like blowing bubbles with the recoil dampener active, but when the dampener overloaded then it was a beast to fire. I think that all still sounds plausible, but now I understand it better. Thanks.

  14. Master Zed says:

    Sorry, but all the above was to say that firing a well timed continuous fire rail gun is more akin to pushing against a wall than the “kick” that chemical projectiles create. The force is even and constant, and once braced against would have little to no real effect on the one firing the weapon.

    Further, that reciprocal force is actually being applied to the coils themselves (they’re the drivers) which could be mounted in such a way that they gather and store that reciprocal force and utilize it (to make more electricity for instance – we’ve been turning kinetic energy into electricity for quite some time already…). So there is no law stating that the rail gun needs impart any of that energy to the platform holding/mounting that rail gun – it’s just that our current recoil absorption technology isn’t up to speed with our current ballistic technologies.

  15. Master Zed says:

    Another thought I just had (sorry for the multiple posts) is that there is no reason to assume rail gun projectiles would need anywhere near the kind of kinetic energy that chemical propelled projectiles would. Even modern bullets don’t deliver much of their kinetic energy (unless stopped by a Kevlar vest or the like) or do damage based on their mass and velocity (related to it, but only loosely). They mostly do damage by puncturing vital organs/structures in the body (which again is a function of pressure not total kinetic energy). The bullet’s mass (as I understand it) is largely to help it survive the firing charge and fly more accurately (because greater mass means more gyroscopic stability – so long range rifles use larger calibers). A rail gun then, which can accelerate a mass to much higher velocities with much greater control, and does so by applying an even force along the length of the bullet, may not need to generate as much kinetic force in the projectile to deliver accurate and lethal strikes downrange.

    • tctaylor says:

      Thanks for your insightful comments, Master Zed. I’ve just returned from vacation, so reading your thoughts feels like a little welcome home present to get me back into full science fiction mode. I’ll properly digest and respond during the week. Thank you. Tim.

  16. Master Zed says:

    Looking forward to your replies. A couple of follow up ideas that I’ve had while designing the rail guns for my setting:

    1) The rails could easily be hooked up to “spring loaded” flywheels (or their high tech equivalents) to turn the linear reciprocal force into rotational energy which could then be used (via computer control or EXTREMELY clever engineering) to actually gyroscopically stabilize the gun. Basically, the longer you fire the gun, the faster the flywheels would spin and the more stable the weapon would become – higher stability the longer you fire. Computer controlled actuators (or carefully engineered systems) would then orient the flywheel(s) to stabilize or even move the barrel via targeting software or the like. This might be more difficult to accomplish in the hand-held version, but would be EXTREMELY useful to ship based weapons. The recoil could be almost entirely absorbed in this manner, ultimately being converted to heat energy or electricity over time after the gun stops firing as friction slowly decelerated the flywheel. It could be used to generate electricity via reverse induction (simply hook a driveshaft into the flywheel and reverse the induction). The electricity could then be used to power the next projectile (there would likely be energy loss to heat from friction – but if carefully designed this could be very minimal) – making such a railgun capable of firing whole clips on something like a small battery that compensates for the energy lost to friction – this battery could easily be built into the clip, making each clip a completely self contained firing solution.

    2) Rifling (bullet spin) is used to stabilize bullets in modern guus and increase their long range accuracy. Railguns have a unique capacity for creating this rifling through a few factors.
    2a) Twisting rails – the rails accelerating the projectile could themselves be twisted along the length of the barrel – imparting rotational velocity as they impart acceleration. This would likely result in some very strange spirals as the twisting may need to become more pronounced near the end of the barrel where the projectile has the most velocity – the best way to do this would require some serious thinking and math to do theoretically, which I just didn’t have the energy to undertake, so I’ll leave it to you if you want to research the details.
    2b) Rotational accelerator in either the loading mechanism (put an already spinning bullet on the rails) or at the end of the barrel (the accelerated bullet will likely have enough charge for a coil arrangement at the end of the barrel to impart significant rotational velocity. Heck, you could even just use normal rifling after the acceleration rails, though this might slow the bullet and create unnecessary waste to friction – whether or not this matters depends on the design.
    2c) A railgun doesn’t necessarily need smooth bullet surfaces and could build stabilization channels directly into the projectile (ie, fire “drill bits”). This, I think, is the least optimal method as it requires an atmosphere to work (although, rifling is used to overcome atmospheric disturbances, so this may not be a problem – won’t spin in a vaccuum, but also won’t need to, so…). It also means less contact surface for the charge to pass between the rails (may mean less efficient acceleration of the bullet, but again, there are compensating factors that could render this point moot, so again it comes down to final design). The one MAIN advatage of this type of rifling is that it may be useful for penetrating armor/targets more efficiently (again though, this would depend heavily on the nature of the target and/or armor – so could be more or less significant depending on situation and setting).

    3) Kinetic Energy and Kelvar vests. As a means of demonstrating the fact that the kinetic force of the bullet isn’t the lethal consideration: a Kevlar vest stopping a bullet means that the target wearing the vest MUST experience the FULL kinetic energy of the bullet (because the vest stops, not deflects, the bullet). Yet this is the defense against bullets – basically, the existence of Kevlar as bullet defense proves that the kinetic energy of the bullet isn’t what makes it dangerous, as experiencing the full kinetic energy is preferable to allowing the bullet to pass through (and experiencing significantly less of that kinetic energy).

    • tctaylor says:

      That’s certainly some intriguing ideas you have there, Master Zed. I spin projectiles by spiraling the rails (or, rather, twisting them into a helix), though I feel there’s probably a much simpler way of applying spin in the absence of rifling. I don’t like the idea of a helix because it doesn’t feel like a robust design to me and the stresses the rails will be subjected to will be severe.

      So, the setting you’re designing for. I’m intrigued. Can you tell me what that is?

      • Master Zed says:

        My setting is still in the very early stages, but I’d be happy to share a link with you (given the usual presumptions of no distribution and non-disclosure for early written works). If you’re interested, shoot me an email at messej_rc_junk@yahoo.com and I’ll get you a link to the WIP doc.

  17. Master Zed says:

    Hmm, as I think more about the rail gun’s recoil the above recoil compensation may not be valid – if the rails are allowed to move (or experience any acceleration in the direction opposite the projectile – even if converted to rotational energy via flywheel absorption) then that actually might just reduce the forward velocity of the projectile. The magnetic field generates a specific amount of force and that force would then be distributed to the rail AND the projectile – meaning any acceleration of the rail takes away acceleration from the projectile, so the rails may need to be “braced” (have a normal force applied) to actually impart forward velocity to the projectile efficiently.

    The question then becomes could you generate this normal force by having flywheels already at speed, effectively bleeding off their rotational velocity to impart linear momentum to the projectile – would this be any more efficient than simply allowing the flywheels to impart their energy mechanically – like a baseball or tennis pitch machine.

    Grrr… Physics…. lol, I just don’t know…

    I am fairly confident that the acceleration is even and (more or less) constant so the pushing against a wall analogy should hold.
    And the points about needing far less mass/total kinetic energy should still be valid.
    But I’m not so sure any more about the rails being separated from the launcher – at the very least conservation of momentum means the system would need to somehow conserve it’s total momentum. In the case of a person on a planet, I guess this is accomplished by stealing/imparting momentum to the planet you’re standing on, but again, this would convert linear momentum to rotational momentum, so why not flywheels? Grr, I guess this is why physicist is an actual profession – lol.

  18. Master Zed says:

    Did some quick unit analysis to see if I could get a feel for this… Figured I’d share it here for those interested.

    Kinetic Energy = 1/2 m*v^2 which is kg m^2/s^2 in SI units. (https://www.chem.wisc.edu/deptfiles/genchem/netorial/modules/thermodynamics/energy/energy2.htm)

    The v^2 is extremely significant here, as it means that velocity is exponentially more important than mass, specifically, this means that if you double velocity, you can QUARTER mass to get the same final kinetic energy. I think this is where the rail gun makes the difference, so let’s continue…

    From (https://science.howstuffworks.com/rail-gun.htm) we can get some rough estimates for velocities of CURRENT chemical and rail technologies.
    Chemical Projectile v = 1200 m/s
    Rail Projectile = 16,000 m/s

    From here we can get a relative velocity of 16,000 / 1200 = 13 1/3 (there is no guarantee this ratio will hold in a futuristic setting, but it is safe to assume this is a fair indicator of the MINIMUM relative velocities possible in a future setting, and we’ll use a lower ratio of 10 going forward to simplify the math anyways).

    Let’s assume our rail projectile has 10 times the velocity of our chemical projectile (well within the 13.33 given above). This means that a rail projectile 1/100th the mass of a chemical projectile can deliver the same kinetic energy to its target (as shown below). (please note this is the mass of the actual projectile, NOT the ROUND that’s loaded into the chamber.)

    KE Chem = 1/2 M.bullet * 1^2 == 1/2* M.bullet/100 * 10^2 = KE Rail

    To simplify later math, let’s go ahead and assume we want equivalent KE (kg m^2/s^2) – this is actually false, since what we really want is equivalent pressure ( kg m/s^2 ) at the point of penetration (so after armor). But since our Rail Projectile is 1/100 the mass, it should be fair to assume it also has a smaller surface of contact, or if we assume the projectile is being stopped/deflected by armor, equivalent KE becomes a fair indicator of stopping power at least and would be roughly equivalent (or better) for the Rail Projectile.

    This means we now have relative mass and velocity for both projectiles assuming we want equivalent Kinetic Energies, as follows (as relative measures, units don’t matter):

    Mass of Chem Pojectile = 1, Velocity of Chem Projectile = 1
    Mass of Rail Projectile = 0.01, Velocity of Rail Projectile = 10

    Using the 0.01 Mass and 10 Velocity of the rail projectile gives some interesting ramifications in terms of conservation of momentum and and reciprocal force:

    Momentum is Mass * Velocity (Mass is kg in SI units, Velocity is m/s in SI units, so kg m/s in SI units).

    Therefore the momentum of our Chemical Projectile is 1 * 1 = 1
    And the momentum of out Rail Projectile is 0.01 * 10 = 0.1

    Therefore, in order to deliver equivalent Kinetic Energy, our Rail Projectile has 1/10 as much momentum to conserve and the “recoil” should therefore be 1/10 as much as well.

    We can generalize this as follows:
    Assuming we want equivalent Kinetic Energies in our projectiles ( KE.1 = KE.2 )
    And assuming we’ll accomplish this by lowering mass as velocity increases, then we get:
    KE.1 = KE.2 => 1/2 M1 * V1^2 = 1/2 M2 * V2^2 => M2 = M1 * V1^2 / V2^2

    Assuming M1 and V1 are our unit values (ie we’re interested in proportional effects only) gives M2 = 1 / V2 ^2 (this is exactly what we got earlier, 10 times the velocity = 1/100 the mass, but it matters in out next step)

    Assuming we use conservation of momentum to approximate “recoil” (it’s not the complete story, see pushing on a wall above, but it’s a good start), we can introduce a constant R (for recoil) to determine the relative recoil of two different weapons with equivalent Kinetic Energies but different projectile velocities as follows:

    R = Momentum2 / Momentum1 = ( M2 * V2 ) / ( M1 * V1 )
    Again allowing M1, V1 to be our unit values, and substituting our M2 = 1 / V2 ^2 from before for equivalent Kinetic Energies gives us a final generalized equation of:

    R = ( 1 / V2^2 * V2) / ( 1 * 1 ) = 1/v2, in other words, recoil is inversely proportional to projectile velocity if we’re maintaining Kinetic Energy.

    This may not sound like a HUGE deal, but if we allow future rail technologies to get to something more like 20 or 30 times the velocity, then this means recoil drops to 1/20 or 1/30 for equivalent Kinetic Energy. For a real world reference, consider the following:

    From (https://hypertextbook.com/facts/2000/ShantayArmstrong.shtml) I got “A rifle can shoot a 4.20 g bullet at a speed of 965 m/s.”
    From (https://en.wikipedia.org/wiki/BB_gun) I got that a BB gun has a projectile mass of 0.35g with an upward velocity of 180m/s

    We can do the same kind of math I did above, and the two Momentum calculations are:
    Momentum Rifle = 4.2 g * 965 m/s = 4053 g m/s
    Momentum BB = 0.35 g * 180 m/s = 63 g m/s

    Meaning a rifle recoil is about 64 times that of a BB gun (to give our proportional comparisons a real world feel).

    So, a theoretical futuristic rail gun firing projectiles weighing 4.2 / 64^2 g at a velocity of 965 * 64 m/s would recoil like the above BB gun, but hit its target like the above rifle round. This is an EXTREMELY light projectile (aprox 0.001g) traveling extremely fast (at 61,760 m/s aka Mach 180 aka 0.0002 C), but it demonstrates why and how rail guns could have significantly lower recoil with equivalent performance (and MUCH larger ammo supplies)

    Ok, that’s my math quota for the day… 🙂

    • Master Zed says:

      BTW: The above formulas are simplified formulas that work well enough (very closely approximate) at speeds significantly lower than the speed of light (less than 0.1C). I just mention this because this discussion IS in the context of a scifi setting, so I wanted to make sure someone didn’t try to use these conclusions with 0.5 C projectiles or something. Since the fastest projectile I modeled here (the theoretical velocity * 64 rifle) only hits 0.0002 C, these conclusions should be fine for the purpose they were intended.

      It’s worth noting that even lasers have “recoil” despite their zero mass because they have near relativistic velocities (sometimes refered to as relativistic mass – though even this is a somewhat misleading nomenclature).

  19. Master Zed says:

    Just in case it doesn’t show up for a while (the post says it is awaiting moderation), I did the math to relate kinetic energy to momentum. (Very) Long story short:

    If you want to maintain kinetic energy (KE = M * V^2) you can increase velocity and decrease mass by that increase squared (so 10 times the velocity means 1/100 the mass).

    But momentum is just Mass * Velocity (not squared), which means increasing velocity and keeping Kinetic Energy equal results in proportionally less Momentum to conserve (less recoil) by the same amount.

    For example – if you want to turn something with the kinetic energy of a modern rifle into a rail gun that launches the projectile at 10 times the velocity with 1/100 the mass (very doable from my research), then you end up with 1/10 the momentum to conserve (or 1/100 the recoil).

    • Master Zed says:

      *1/10 the recoil, not 1/100 the recoil as I mistyped at the end of my last post — you get 10 times the velocity and 1/100 the mass, for 1/10 the momentum = 1/10 the recoil

  20. Master Zed says:

    One final note: Newton’s laws apply to a closed system only, so the guns you described as bleeding heat of into a separate dimension would not necessarily apply Newtonian laws anyways…

    This is also why I say a person firing a gun on a planet is conserving momentum by accelerating the planet (quite imperceptibly given the mass ratios, but still if you’re going neutonian, this is technically how you account for it)… Assuming they are braced against the ground (or something that’s braced against the ground, like a wall/etc), then the recoil from a gun goes from gun to arm, arm to feet (via kinetic linking), feet to rotational energy in the planet (because you’re on the surface which is far from the center of mass – so torque). You can say the limb and/or person compresses – but since people don’t shrink from shooting guns we can assume that at some point that energy is transferred to the planet, etc.) But here’s the rub, in reality that recoil isn’t all kinetic energy – the muscles burn chemical energy which contribute forces, the direction of the force arriving on the planet will have a component that is perpendicular to the surface and a component that’s parallel – meaning some of the energy becomes rotational energy and some becomes translational, the ground will compress to some extent probably releasing that energy as heat, etc etc…

    • Master Zed says:

      Sorry, forgot to close the system here, as our bullet is traveling off and unaccounted for… You see, the trick is that at some point the bullet will LAND (hit the Earth, or something connected to the Earth) – returning that borrowed momentum to the Earth and resetting the rotational energy, etc. Actually, if it’s a completely closed system, then you’ll need to account for any air resistance, heat exchange, etc etc. or your system just isn’t closed, and Newton will be denied… Just saying 😉

  21. Master Zed says:

    Another related discussion that helped make this all much clearer. The above is the reason it doesn’t kill you when you fire a gun. If the reactions were truly equal and opposite then a bullet that could kill a target would kill the person pulling the trigger too. So while the gun experiences the same force as the bullet (conservation of momentum), because the gun has much more mass, it ends up with less velocity and therefore transfers less kinetic energy to the attacker. This is also why properly bracing the gun further reduces the damage, holding it snug to your body means that the gun cannot accelerate separately from your own mass and the force must now accelerate your whole mass further reducing the amount of kinetic energy the attacker must absorb – and ideally, being properly set on the ground means that the whole planet’s mass becomes a factor, further reducing the total kinetic energy of the attacker must endure.

    Here’s the reference discussion that does a pretty good job of discussing these factors: https://www.quora.com/What-is-the-difference-between-kinetic-energy-and-momentum

  22. Master Zed says:

    Ok, just saw your response, so I thought I’d get into some of the math formulas if you want to respect the physics.

    Mementum for a BB gun is 63 g m/s, and a BB gun uses expanding air to ire, which should have a similar kind of peek impulse, so I think if you aim for around this number we can assume a pretty easy to fire weapon. So M * V would need to equal something small, like 50 – 100 g m/s. You can go higher if you want to allow for elaborate recoil compensation (like motors or springs that absorb then transfer that energy to prevent it from reaching the occupant of the armor) but this is our first boundary formula. M * V < 100 g m/s (mass of projectile * muzzle velocity – this keeps the momentum to around the BB gun range, you can decide if you want to go higher or lower but this is a pretty negligible recoil imo).

    Our next major formulas are kinetic energy (how much energy the impact has) and the projectile's cross section (to determine pressure).
    KE = 1/2 M * V^2 (g m^2/s^2)

    Pressure = Force / Area (g / ms^2)

    Area is the Cross section of the bullet and is in m^2 and would be VERY small (smaller is better since pressure divides by area which means that as area decreases, presure increases and is partially why bullets hurt alot more than baseballs. This is a variable you have alot of control over as follows: First, mass translates to volume based on the density of the material used for the bullet – higher density materials gives less volume for the same mass – the molar mass of the material used in the projectile should give a fair idea of the total volume needed – but alloys, forging methods, material sciences, etc can vary this a fair amount – especially in a scifi setting. Second: the shape of the projectile – the modern bullet shape is superior to the old musket balls because of its shape. The tip has a much smaller cross section for the same mass because its a cylinder rather than a sphere and comes to a roughly parabolic point. So the materials and engineering techniques ultimately determine this value, softer materials (like lead) will flatten on impact and increase the area and decrease pressure – which is why spherical musket balls were ok – they flatten on impact anyways, so the shpe in the barrel and in flight was relatively insignificant. If you want to go super scifi have your railguns fire something like a carbon nanotube (which I do believe is conductive) with a cross section only a few atoms across (for carbon this is around 7e-10 m^2 – http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/atomsiz.html) meaning that it'll increase pressure by 10 orders of magnitude, which is HUGE and would allow it to basically penetrate anything – however, this may not always be the ideal – see more later for possible drawbacks.

    Force = (g m/s^2) and translates from our kinetic energy as one less meters in the numerator, so while you'd need complicated calculus, a diagram of the bullet path through various layers, and some serious materials research to get a completely accurate answer, we can use the distance over which the projectile transfers its energy as a fair average approximation which works well enough for a sort of average/general comparative purpose. So basically, F = KE / Distance traveled in the target (which I estimated to about 0.1m for a humanoid target's chest – but this would be HIGHLY variable depending on individual, where and how struck, where/if the bullet stops in the target, exact path throught that target, armor material thickness and shape, etc. but long story short – the less distance it travels the greater the force in a given moment and therefore pressure/penetrative power at any given point – but see below for some more important considerations)

    So, our Kinetic Energy transforms to a force (and therefore pressure) as it is travels through the target. Basically, when the bullet hits its target it starts decelerating, that deceleration uses up some available kinetic energy to move through the target and displace the material its traveling through (it'll also inevitably lose some to to heat, etc through friction, etc. – so this isn't 100% efficient, but again gives a general feel for relative effectiveness). Here are the primary scenarios. Momentary pressure, nature of the target, etc determines which of these cases occur and the details, but these give the general idea of the range of possibilities and can be used to approximaet the distribution of the energy in each case.

    1) (The optimal case for "squishy" targets) Bullet penetrates a bit more than half way through its target (this is the reason for hollow points which are designed to have a small cross section at the surface – where there are fewer vital tissues – and through the air to penetrate them easier and expend less kinetic energy in these less desirable areas, then mushroom as they travel through the body to increase surface area decrease pressure and deliver more kinetic energy/damage to surrounding more vital tissues. This means that the bullet comes to a stop (all kinetic energy delivered) in a vital location (maximized tissue disruption).

    2) The bullet goes clean through (in all honestly, this is BY FAR the most likely case for a rail gun projectile unless VERY heavy, probably reactive, armors are involved). Since the bullet is still moving on the other side of our target, we know that not all of our kinetic energy was delivered – but there IS a hole where the bullet went through the target, which is more or less bad depending on where this happens. In a battlefield where armor and cover are major considerations, this is kind of the ideal situation as the extra kinetic energy basically translates to penetration power (the ability to go through more armor/cover). However, the damage is now more or less independent of kinetic energy and becomes dependent on cross section and path traveled (it'll make a hole roughly the shape of the cross section of the bullet along the path the bullet travels through the target. If we're minimizing the cross section to maximize pressure and penetration, this now means potentially less damage to the target as the hole is smaller – hence the balancing act that must be done regarding bullet cross section – increase it and you increase the width of the wound track, but decrease penetration – and vice versa). Considering it's VERY likely our railgun will be a VERY high rate of fire weapon (might as well, low recoil and light ammo makes this kind of perfect), it's not too big a deal to allow cross section to decrease and make this our ideal scenario, since a whole bunch of small holes means a good chance you've opened some holes in a fairly vital location – where even small holes are fatal, and the increased penetration power means the bullets can travel further, lose less kinetic energy doing so, and penetrate alot more cover/armor.

    3) Bullet is "caught" (stopped completely) by armor (kevlar vest scenario). This has the effect of turning our kinetic energy back into momentum (recoil), but likely does so over a VERY short distance/time (kick instead of pushing a wall), so the impact will be more jarring to the target, who (hopefully) also won't be as well braced against the direction of the impact further knocking them off balance which is far more disruptive to target than attacker. All kinetic energy is absorbed (since the bullet stops) and is transferred to the target as heat and momentum (recoil) primarily (how this happens depends GREATLY on the material and type of armor). But long story short, our super light high velocity projectiles would lose their v^2 advantage and go back to straight m*v and it'd be like trying to knock someone over with BB's (non penetrating BBs) — so least ideal for our rail gun case. Even a very high rate of fire isn't going to make much difference, in fact, the "plink" of the projectile hitting the armor and startling the target to trigger uncontrolled reflexive actions (flinching from the sound/surprise of the strike) is likely to be more disruptive than the actual impact of the projectile.

    4) The bullet is DEFLECTED by the armor (it hits the armor, but then continues on, possibly in a different direction). This is the worst case, as it's basically the above scenario, but with only a fraction of the kinetic energy getting transferred – so yeah, basically nothing for our low mass rail projectiles. Since its most likely to happen at the edges of the armor, we do get some advantage from leverage (the surface of the body is a distance from the center of mass, so leverage) which will multiply the force and translate it as torque – but you're basically shooting a BB (smaller and faster, but same momentum) at a carnival target, so it's not going to make enough difference to matter in most cases.

    So basically, our two ideals are scenario 1 and 2.

    Against an unarmored target without cover, we'd want to use something like a bolo/dumbell shot which gives up velocity and kinetic energy and decreases range/accuracy a little (since drag will eat up more of it in transit), but greatly increases cross section and distance traveled inside squishy meat targets as the weights snag and rotate as they pass bones and different tissue densities – lengthening the wound track and increasing the chance of striking something vital.

    Against an armored target or one with cover, or if we're trying to deliver a more accurate strike at long range, we'd want a more aerodynamic low cross section high velocity penetrating round which might only make a small hole straight through its target, but which can do so with ore accuracy.

    Here then are our ideals, and if you allow for computer assisted aiming, our rail gun now becomes WAY superior to our chemical weapon. Since the computer targeting system can calculate distance to target, composition of target, orientation of target, take all of these into consideration and load the appropriate projectile and set the current in the rails to give the exact velocity needed to penetrate armor/cover and stop inside the target. Basically, the computer can make it scenario 1 in all situations (or at least maximize probability of scenario 1) since our rails are actually variable force generators (unlike a charge of black powder which is determined by the amount of powder in the shot) and a computer could control the current and do the calculations to turn current into damage to target between bullet fires and then easily maximize that equation – it could further use approximations to account for things like armor and cover penetration based on sensor data. Our low mass ammo comes in doubly handy here since the high rate of fire will allow the computer to "guess and check" it's approximations across a VERY large sample size, subtly adjusting the velocity of the projectiles to maximize damage based on the results from the previous shot(s). Basically, a very simple AI and moderately complex computer (even by today's standards – much less future standards) could make a rail gun CONSIDERABLY more dangerous than a chemical weapon. And should the AI/computer assistant fail, the weapon could always default to "full power" and still do some pretty good damage just by turning people into perforated pin cussions via high rate of fire.

    • Master Zed says:

      So let’s run some numbers… (I’ll keep them simple to make it easy to adjust them to fit your setting and vision)

      Let desired momentum (Recoil) be 100 g m/s (recoil of firing a BB gun).
      Let muzzle velocity be 100,000 m/s (approximately mach 300 (291.5) or 0.00033 C if I did my math right)
      Then our projectile’s mass is 100 g m/s divided by 100,000 m/s = 1/1000g = 1 milligram (that’s TINY – 1,000,000 projectiles in a 1 Kg drum…)
      Let’s use carbon to make our projectiles since it’s abundant and has some other nice features – specifically we’ll basically fire graphine jacketed diamonds… (two allotropes of carbon, one which conducts electricity very well for our railgun, and one which is extremely strong, for surviving acceleration and impact)

      Ramifications:
      Allowing for a 0.1 meter rail (about 4 inches) this means a bullet is out of the barrel in 0.1 m / 100,000 m/s = 1 microsecond (one millionth of a second). Allowing for a peak possible fire rate of (pinky finger to corner of mouth) one million projectiles per second (that’s 1 Kg of ammo per second – so probably not the fire rate that is typically used, but wanted to give you an idea of potential rate of fire… btw, since this is continuous fire, this would be the equivalent of holding up a 10,000 Kg mass for 1 second in terms of strength/recoil stress fractures and the like — so NOT firing that by hand… that 10,000 Kg mass for 1 second number comes from a really rough approximation for turning that momentum back into weight given a 10 m/s^2 acceleration from gravity – which is off a bit but close enough to 9.8 m/s^2 for super easy math estimation) this sustained fire is how our pushing on a wall analogy works – let me know if you’d like me to work up an exact load formula that you can just plug numbers into to figure out this “recoil weight” based on mass, velocity, and fire rate.

      Since I’ve decided the majority of our projectile is diamond, I’m going to use diamond’s density of 3.51 g/cm^3 to determine the volume of the projectile. Which gives our 0.001g projectile a volume of 0.00028 cm^3 = 2.8e-10 m^3. Assuming a sphere (which isn’t the optimal configuration, but at this scale might not make much difference), this gives our projectile a cross section of 5.2e-7 m^2 (this is kind of a worst case scenario for lazy manufacturing – a dart shape would be far more efficient but much harder to manufacture, and since we’re talking about potentially firing millions of these per second, and we might want to make it possible for soldiers to produce ammo in a field situation, this isn’t a bad compromise.) Actually, to simplify our math later, let’s squish it just a iittle to make it 2.5e-7 m^2 and say it’s more rice grain shaped…

      Now we can figure out the kinetic energy and pressure delivered to our target per projectile (and per second if we wish).
      KE = 1/2 m*v^2 = 0.5 * 0.1 * 0.001 * 100,000^2 = 500,000 g m^2/s^2 = 500 joules of energy per projectile
      500 Mj per second at max fire rate (which we don’t actually use) = 500 MW of energy

      Pressure = Force/Area = KE / penetration distance / cross section = (scenario 1, assuming 0.1m of travel) 500 kg m^2/s^2 / 0.1 m travel / 2.5e-7 m^2 = 2e10 kg / ms^2 = 20 million pascals (for reference… 70 kPa can sever limbs… https://en.wikipedia.org/wiki/Overpressure) — let’s go ahead and assume this means our projectiles will easily travel through basically anything (scenario 1) – i mean that’s still 2 MPa after even 1 meter of travel…

      So now the REAL question becomes, can we just plain cut a running man in half by firing a short burst in front of them?! And if so, how long a burst?
      Given a thickness of less than 0.5 meters let’s say, and our projectile’s diameter of roughly 0.001 m, we’d need 500 projectiles to completely sever the upper torso from the lower torso – we’d literally use a stream of diamonds to chop a man (or basically ANYTHING at those pressures 0.5 meters across) in half… At our 1million rounds per second this is a 5 millisecond burst and consuming 0.5g of ammo.

      (need a break, will do more later)

  23. Master Zed says:

    Quick plug for some wonderful references that I’ve basically been stupidly recreating here – le sigh… 🙂
    https://en.wikipedia.org/wiki/Physics_of_firearms
    https://www.futurelearn.com/courses/maths-linear-quadratic-relations/0/steps/12123
    https://webpath.med.utah.edu/TUTORIAL/GUNS/GUNBLST.html
    https://www.bevfitchett.us/gunshot-wounds/loss-of-kinetic-energy.html

    Had some inspiration… Instead of estimating all this stuff, let’s use the desired numbers to calculate the realities of the weapon, as follows:

    My Goal: create a projectile that will penetrate armor (and thus be almost guaranteed to penetrate a body completely), and figure out the weapon’s profile from there.

    This brought me to this page (https://physics.stackexchange.com/questions/16817/penetration-of-armor-plate), from which I pulled the formula for penetrating steel of a given thickness (we can now express any future armors or potential cover as “equivalent to T meters of steel plating” to eliminate the need to figure out high tech material sciences)

    The top answer gave us some important information:
    “toughness of steel” = 2000 MPa = 2e9 kg m^-1 s^-2

    Ok, now we can determine our necessary KE based on Cross Section (square meters) and Equivalent Thickness (meters) of Armor.

    KE needed to penetrate armor equivalent to T (thickness) meters of steel with A (area) square meters of cross section= 2000MPa * T meters * A meters^2 = 2e9 kg m^-1 s^-2 * T m * A m^2 = 2e9 T A kg m^2 s^-2 <– Hey, that's the same units as our 1/2 M V^2 formula (convenient…)

    Kinetic Energy for the bullet's mass and velocity = 1/2 M V^2 = 1/2 M V^2 kg m^2 s^-2

    Setting these two kinetic energies equal tells how much Mass (in kg) and Velocity (in meters per second) we'd need to penetrate the equivalent of T meters of Steel with a bullet cross section of A square meters. But this is the KE needed at the point of impact, so we'd also need some KE to get the projectile there, but this is likely to be as trivial as the KE needed to pierce the fleshy bits behind that futuristic armor at these scales, so we'll ignore it for now.

    2e9 T A kg m^2 s^-2 = 1/2 M V^2 = 1/2 M V^2 kg m^2 s^-2 (our units cancel right away, and we can move all our variables to one side, to get)
    4e9 = M V^2 / (T A), or expressed slightly differently to put target on one side and attacker on the other
    4e9 T = M V^2 / A

    Which tells us that the ratio of Mass times Velocity squared divided by Cross Section area must be equal to 4e9 times the (equivalent) Thickness of the armor. Huzzah!

    Next, we can relate the cross section to the mass using the diamond spheres from earlier.

    Mass = density (Den) * volume (Vol)
    volume (Vol) of a sphere = 4/3 pi r^3
    great cross section (A) of a sphere = pi r^2

    Vol = M / Den (for our diamond spheres, Den = 3.51 g/cm^3 = 3510 kg/m^3, so…)
    4/3 pi r^3 = M / 3510
    r = 0.040812 M^1/3
    Side Note: Diameter = 0.08164 M^1/3

    A = pi r^2
    A = pi * (0.040812 M^1/3)^2
    A = 0.0052346 M^2/3

    Plugging this area back into our target/attacker formula gives:
    4e9 T = M V^2 / A
    4e9 T = M V^2 / (0.0052346 M^2/3)
    2.1e7 T = M^1/3 V^2

    Now we can either chose T and V based on setting, determine mass, then calculate the corresponding momentum, fire rate, etc.

    Or we can start with the desired Recoil Load from above, determine velocity and rate of fire and mass, then plug M and V in above to get T – which determines how much armor these guns can penetrate… Hmm, I might see if I can figure out a way to relate these all in a single formula that's basically tell you the recoil load for a "toughness" of target armor. This would actually likely be the most useful in terms of computer controlled/assisted targetting, since the computer would vary the rail power as necessary to hit the target, and therrfore projectile velocity, and therefore recoil load… The safeties would most likely be based on projected recoil load, which would then designate targets as green or red based on whether or not they'd require more recoil load than is safe.

    But I think that's all I can do for now…

    • Master Zed says:

      (previous reply awaiting moderation, so be patient if this response doesn’t seem to make sense, since I’ll be referring to information presented in it)

      I’m going to try to calculate the armor penetration of a railgun that’s designed to be fired with minimal impact on the user – and then calculate the armor penetration capacity of such a weapon. Here are my assumptions

      1) I’m going to set the fire rate, velocity and mass of the gun to be roughly the equivalent to holding 1 kg above your head (this is similar to lifting – and holding for the duration of the weapon’s burst – a one liter bottle above your head). Using approximately 10 m/s^2 for acceleration of gravity, then gives us 10 kg m/s^2 as our target recoil (this is TINY – just lift a liter of soda above your head to see how little force this is to resist).

      2) I’m going to use a 0.1 gram (1e-4 kg) carbon (graphine jacketed diamond) spherical projectile – this is about 1% the weight of a chemical bullet from what I can gather. This gives…
      1 million projectiles per kg of carry weight.
      a projectile volume of 0.1 g / 3.51 g / cm^3 = 0.0285 cm^3 ( 2.85e-8 m^3 )
      a projectile diameter of 0.38 cm (0.0038 m) – less than half a modern bullet
      a projectile cross section area of 0.11 cm^2 ( 1.1e-5 m^2)

      From 1 & 2 we can now calculate maximum allowed acceleration: given 1e-4 kg per projectile, and our target recoil of 10 kg m/s^2, we get an acceleration of 10/1e-4 = 100,000 m/s^2.

      3) I’m going to assume a 0.2m (8 in) long rail. This is a bit longer than a long pistol barrel, but rail length makes a big difference on a railgun’s performance, and given the more narrow barrel, the linear nature of the acceleration which means we can comfortably move more of the rail behind the grip, and the removal of length needed for a modern pistol’s “chamber”/bullet length – after all our 0.1 g bullets are only .4 cm long and don’t need a casing or powder charge this is still around the size of a modern pistol. And if we move the power supply away from the hand (to a hip mounted power pack with a small cable for instance) or have advanced battery tech that makes the power supply tiny this will make it even less unwieldy.

      We can now calculate the final velocity of the bullet leaving the rail:
      given a constant acceleration and no (relative) initial velocity means the time to travel a given distance is t = (2d/a)^1/2 (from d=1/2at^2), for our rail length of 0.2m and our acceleration of 100,000m/s^2 we get t = 0.002 seconds. Plugging that into our velocity formula v = at gives us a final velocity of 200 m/s (this is actually about half as fast as a pistol round).

      increasing barrel length won’t be a big help, since v = (2da)^1/2 tells us that the velocity is increasing based on the sq. root of rail length and acceleration. ie if we quadruple barrel length or acceleration, we only double projectile velocity. And as we can see, there are no other variables acting on the formula, which means MUCH high accelerations and longer barrels are necessary… This might be part of the reason they’re being considered for ship mounted weapons… but let’s press on…

      As a side note, the t = 0.002 seconds means we can comfortably maintain a rate of fire of 500 projectiles per second. For reference, given our 0.38cm diameter, this means we can cut out a line 190 cm long/second though basically anything we can penetrate, which we’ll calculate now… (given an approximate hip width of about 38cm for an average human, allows us to cut a human in half with a burst lasting 0.2 seconds and consuming 38/0.38 = 100 rounds, or 10g of carbon)

      assuming this projectile was being fired at point blank range (so peak velocity), the projectile would hit with:
      KE = 1/2 m v^2 = 0.5 * 1e-4 kg * (200 m/s)^2 = 2 kg m/s^2 = 2 Joules of KE
      Going to the above formulas, we could penetrate
      T = M^1/3 V^2 / 2.1e7
      T = 1e-4^1/3 * 1e5^2 / 2.1e7 = 22.1 m of steel?!

      (Did I mess something up in all these calculations?! – if not, I think we have a killer weapon here o.0)

      • Master Zed says:

        *10,000 rounds per 1kg of ammo
        (each burst does use 10g of carbon though, so a 1kg clip would be enough to chop 100 man sized targets sporting the equivalent of 22m of steel – 11m on each side – in half)

        * I totally messed up that last penetration calculation, I used acceleration instead of velocity (whoopsie)
        The correct calculation is:
        T = 1e-4^1/3 * 200^2 / 2.1e7 = 8.8e-5 m of steel (0.088mm, or 88 micrometers)

        (This makes alot more sense)

        Also note that the more useful version of the thickness of steel formula when designing a gun in this direction is

        T = 4.8e-8 M^1/3 V^2

        Where T is thickness of steel penetrated (in meters), M is the mass of the DIAMOND projectile (in kg) and V is the velocity of the round at point of impact (in meters per second)
        As we can see, mass has very little impact (being to the 1/3 power) and velocity has a huge impact (being squared).
        Though the original shows us that we can see that a 1 kg mass requires a velocity of just (2.1e7)^1/2 = 4,582 m/s to penetrate 1 meter of steel
        A 0.1 kg mass requires roughly 1.5 times this velocity (6726 m/s), and a 1g (0.001 kg) mass requires only roughly 3 times this velocity (14,491 m/s).

        Additional thoughts:
        1) Railgun projectiles have very little mass/inertia/momentum (momentum is just 2 g m/s), therefore they may be easy to deflect – their extremely high pressure (from high velocity + small size) may offset this though as they rapidly dig into any surface making sloped deflection very difficult. For sloped armor to deflect our diamond spheres they’d need to be of equivalent “toughness” (ie diamond/carbon fiber themselves) and/or use clever engineering that allows the projectile to penetrate, then guides it along “channels” inside the armor (very difficult to do against near perpendicular strikes). Kevlar style woven armor would be pretty useless as the diamond projectile does not deform like a normal modern bullet (this is the same reason Kevlar doesn’t stop “armor piercing” rounds). These are purely case 2 projectiles (ideally they pierce clean through their target, delivering very little of kinetic energy to their target).

        The ideal defense would actually be some kind of reactive armor (armor that exploded when hit by the projectile) – since the projectile has very little mass/inertia/momentum, so an explosion with an equal amount of momentum in front of the projectile would literally stop the diamond round in it’s tracks. For reference here, the equivalent of just one gram of TNT can produce 4,184 joules (https://en.wikipedia.org/wiki/TNT_equivalent) of energy, so we’re talking microgram explosives here – A LOT of them, but still – even stopping the full 100 round man-splitting burst (200 joules) only requires less than 0.05g of TNT equivalent (alot less of something like modern C4 and even less of whatever futuristic explosive gets thought of). BTW: These reactive explosions would have the same (or potentially less if engineered correctly) recoil as if the armor stopped the projectile which is roughly the same as the recoil experienced by the shooter (ie, trivial). The problem here though is that this is an ablative defense (it’s used up each time it protects against a projectile), so the extremely high fire rates and ammo capacities of rail guns would make it fairly easy to win such a battle of attrition – so even this defense is more a waiting game.

        As one last point, assuming the graphite jacket is engineered to be just thick enough to “burn off” within a very short time after leaving the barrel, the projectile becomes non-conductive and non0ferrous, making sci-fi style magnetic or EM shielding mostly useless as well. Diamonds are also great heat conductors, which means any kind thermal shielding wouldn’t be too useful either.

        2) These 0.2 second bursts mean Computer Assistance would be extremely useful, but not strictly necessary. A simple gyroscopic, or even mechanical, setup could cause the barrel to rotate the ever so small amount needed between shots to create a 100 round “line” of projectiles each time the trigger is pulled.

        With really good computer assistance (and control gyroscopes, or even just barrel actuation – the recoil is certainly in a range where adjusting the angle of the barrel is perfectly fine), you could fire much shorter, much more precise bursts. For instance, a human heart is in the neighborhood of 8cm across (roughly 20 rounds, 2g of ammo, 0.04 second burst – 10 rounds, 1g of ammo, 0.02 second burst if you’re willing to just cut open one chamber, which is probably enough… Large intestines are about 8cm across as well as well, so a 10 round burst could literally open a hole in the target’s bowels.

        In fact, firing a 10 round (0.02s) back to back burst like this with just a basic mechanically controlled “line” would be roughly the equivalent of getting stabbed clean through by a diamond sword or spear with a stabbing profile roughly 4 cm by 0.4cm… So, if you cannot afford a diamond sword, then perhaps consider this railgun…

        3) This is an absurdly low recoil, think of holding a fresh 1 liter bottle of soda for just 0.2 seconds… even catching a falling soda bottle would present more force to your arm as the bottle would have some velocity. You won’t even need to brace against this weapon – and that’s with ZERO recoil compensation built into the weapon or its firing platform…

        The momentum of the whole 100 round burst is 10g * 200m/s = 2 kg m/s. Assuming a 60kg person firing a 100 round burst in space (so not a soldier in great shape, no weight for armor, spacesuit, or even the weapon or its ammo, etc), this burst will cause them to “fly backwards” at 2 kg m/s / 60 kg = 1/30 m/s (0.067 mph).

        So we can probably increase this significantly.

  24. Master Zed says:

    Ok, wet full nerd and made a gul durn spreadsheet to address these problems. You can view and comment on the spreadsheet here:
    (https://docs.google.com/spreadsheets/d/1vkuZRIaXr5upcPRPZDSIcV3qWnO0M1dQY1apLH2Uihk/edit?usp=sharing)

    Before I get into the conclusions from my spreadsheet, here are a few more useful links:

    https://en.wikipedia.org/wiki/Buckminsterfullerene
    http://learn.parallax.com/tutorials/robot/elev-8/understanding-physics-multirotor-flight/inertia-momentum-impulse-and-kinetic
    https://en.wikipedia.org/wiki/Terminal_ballistics
    http://www.swordforum.com/vb4/attachment.php?attachmentid=115115&d=1358186298

    I modeled 3 different rail gun ideas. All three use a 1 NANOGRAM graphine jacketed spherical diamond projectile (I figured using the same ammo for all of them would be conveient in the world, but this doesn’t have to be the case). You literally can’t easily handle an individual “bullet” without tweezers or the like – they are about 82 micrometers across – for reference, a human hair is about 25 micrometers across, so these are about 3 hairs wide… I’m also assuming mechanical or computer assisted “aiming” to create lines of projectiles that essentially do damage by cutting a gash in a target. These tiny projectiles do not do damage like a conventional gun, instead they fully pierce their target, but the high rate of fire of the railgun allows the attacker to chain them together to carve out a gash similar to getting stabbed by a knife (2cm long slice), sword (4 cm long slice), or fully chopped in half (0.5m long slice).

    1 kg of ammo gives each of the guns the following number of “attacks”:
    Knife: 4billion+
    Sword: 2billion+
    Cut in half: 160Million+

    One thing that I did not do, but which could allow much higher velocities is use some kind of “shock absorbers” to spread the recoil over longer periods of time. Since the cut a man in half burst is only 6/1000 seconds long, a basic spring type recoil compensator could distribute this force over even 0.1 seconds and significantly reduce the forces applied to the arm – or allow increases in the rail’s acceleration forces.

    The first is a “pistol” style railgun, with a short (0.3m) barrel that can be held in the hand and fired basically like a normal pistol. I limited the recoil force to the equivalent of holding yourself off the ground in a push-up position. This isn’t nothing, but you can easily do it for several minutes if needed, and it’s not going to cause any kind of “knock-back” or even aiming difficulties – you can hold the gun in place with arm muscle alone and you can move the gun while firing without any resistance.

    Can fire up to 1 million rounds per second
    Projectile Velocity: Mach 1,166
    Penetrates 0.76 meters of Steel (ie, can easily penetrate unarmored or lightly armored foes)

    The second is an arm mounted “rifle” with a 0.5m long barrel that sticks out past the elbow and past the fingertips. It would sit on the arm kind of like a stowed tonfa. It can be strapped to the arm, or held by a handle in the hand. Ideally this would be mounted in the arm of a piece of armor. It uses heat build up in the gun to vent hot air in opposition to the force of firing, offsetting some of the recoil and allowing the rails to apply more force without the user having to experience it. Basically, it is partially recoil compensated through what amounts to a rear facing rocket that keeps it in place and easy to manage. As a result though, the back of the barrel should always be kept from facing anything you care about, like your ribs….

    Can fire up to 1 million rounds per second
    Projectile Velocity: approx Mach 3,000
    Penetrates 4.78 meters of Steel (ie, can easily penetrate cover and well armored foes, can cut a car in half – easily)

    The third is an over the shoulder version that stows on the back similar to a medieval sword in a fantasy movie. The barrel pivots on a special shoulder mount that is worn and designed specifically for the weapon. It is technically possible to wield two such weapons, but why would you need to?! The barrel is pulled into position when needed, then allowed to settle against the back when not in use. It vents gasses out the back of the barrel (which is several inches from your head) to FULLY compensate for any recoil (like a modern recoiless rifle). It is aimed with computer controlled actuators at the shoulder mount if using computer assisted aiming, or via a handle at the front of the barrel if manual fire mode is preferred.

    Can fire up to 2 million rounds per second
    Projectile Velocity: 1% C (Mach 9,329)
    Penetrates 48.9 meters of Steel (ie, can easily penetrate pretty much anything, could be used to sever a building from its foundations, or cut a large suspension bridge in half… lengthwise!)

    See the linked spreadsheet for more data. (Finally found some gun designs that actually do the job 🙂 )

  25. Master Zed says:

    *The pistol sports a 0.2m long barrel

  26. Master Zed says:

    Updated the spreadsheet to do some rebalancing, and added a tab for Ship Based Railguns
    (https://docs.google.com/spreadsheets/d/1vkuZRIaXr5upcPRPZDSIcV3qWnO0M1dQY1apLH2Uihk/edit?usp=sharing)

    Some quick Stats on the Ship Based Railguns:
    All use diamond spheres as ammo, but each type of gun uses a different sized diamond (ammo is not standard across all guns like with the personal railguns)
    The smallest gun uses a 1 Femtogram sphere (aprox 50million carbon atoms). The medium gun uses a bullet 10 times that mass, and the spinal rail uses one 100 times that (0,1 picograms – or about 1/10 the mass of a single strand of hummingbird DNA – ie, VERY small). At these sizes, there may be an argument to be made for simply using a particle weapon…

    If you look at the spreadsheet, you can see that all three weapons fire their projectiles at 0.99C (99% the speed of light). I have adjusted for relativistic effects (ie, used Einstein’s equations to ensure the projectiles exit with enough kinetic energy to actually reach 0.99C even when accounting for their relativistic mass — I don’t believe I did the math wrong, but well – that’s some advanced math, so no promises 🙂 )

    You’ll also notice that all 3 weapons have a recoil force of 550N. This is about the force that a small woman standing on the surface of the Earth – it is TINY – so there is very little concern that the weapon will experience any sort of problem with continual fire. This is also the recoil “thrust” that will have to be compensated during the weapon’s fire, so 550N of extra thrust per railgun will balance the recoil.

    The longest burst duration is the Wild Burst for the Small Turret (which really isn’t intended for that weapon anyways – it’d be the kind of attack a single 5m drone would have to use against an aircraft carrier sized ship) @ 0.23 seconds long – which is (as the name of burst suggests) a “Wild Burst”. The shortest is the Large Turret 1m gash at 0.01seconds. So these bursts lengths are usable at 1ls ranges (targets can’t detect and “dodge” them, though they may be able to reduce damage from Wild Bursts slightly by moving the impact point slightly – wld bursts are meant to fire a line so long that they will cut an aircraft carrier in half, this also means that the attacker can instead cut a zigzagging swath across all of smaller ship’s trajectories, possibly making avoidance impossible… (This is like the shotgun approach I discussed in another post, where even 5% of a 100m line is enough to chop a 5m diameter probe in half, so a “grid” pattern of projectiles could potentially cover all potential locations of the distant craft and secure a definite kill…

    Ammo is not really a concern for these weapons, the largest guns can fire 400Million aircraft carrier destroying “wild bursts” on just 1kg of ammo.

    all 3 guns can pierce thousands of meter of steel, however, the low mass may mean they are easily deflected. Given their velocity and impact pressure, it is unlikely this could be used as an actual defense, but it may mean the ship is severely “swiss-cheesed” instead of actually cut in half. Such an occurrence would probably be worse for the ship in question though, as bulkheads and airlocks would probably save much of the ship and its passengers after being cut clean in half, but this is very unlikely in the swiss-cheese scenario as the incredible amount of kinetic energy and small cross section means the could bounce around for quite some time piercing vital components and people at random. Also note that their extreme penetration and low momentum means they will do very little to “move” the enemy target. These weapons COULD split an incoming target in half, but they’re not likely to stop those two halves from continuing on to smashing into you – unless the target was pressurized of course, in which case the ship’s depressurization may save you from a collision. (basically, I’m saying lasers would make better point defense weapons… 😉 )

  27. Master Zed says:

    Just realized I’m using the wrong formula for pressure. The amount of surface in contact with the steel (and therefore the area I should be using) is the leading HEMISPHERE, not the cross section. Therefore I should be using 1/2 the surface area of the sphere (1/2 * 4πr² = 4πr²). This doesn’t make an exponential difference or anything, but does reduce the thickness of armor penetrated by a factor of 2. But since most guns were built with excessive penetration, I think the general idea still works. I have updated the spreadsheet though.

    Also, I’ve been considering the rifling and helical rails. I think curling the rails might be a VERY bad idea, as the magnetic field exists on the entire length of the rail behind the projectile and is spherical… For two linear rails this isn’t as much an issue – the rails do repel each other, but that’s just a matter of having a material capable of holding the rails together (basically a structure and material capable of withstanding the sheering forces of the rails they contain, or the rails themselves, pushing outwards – a circular barrel could do this just fine). However if the rails are curved, then the spherical magnetic force doesn’t just push, it’ll also pull on the rails on the opposite side of the barrel a bit further behind the projectile), and the forces accelerating the projectile also diminish and cancel out at points and is no longer 90 degrees to the direction of motion (which is where you get the spin from, but now you’ve also got only one a fraction of the force providing forward acceleration… higher power could compensate – which is very scifi appropriate – increases in power strorage and production are one of the most fundamental indicators of advancing technology, all the way back to fire – but would it be efficient, or would a small rifled section near the end be better – or even just a rifled projectile in atmosphere be better suited to this.) Further, as I do these mock-ups, I find the smaller the projectile, the better – and at the sizes, velocities, and distances we’re already talking about – I’m not sure rifling would even matter…

    “Traditionally, rounds were given stability in flight from the rifling of the gun barrel, which imparts a spin to the round. Up to a certain limit, this is effective, but once the projectile’s length is more than six or seven times its diameter, rifling becomes less effective” (https://en.wikipedia.org/wiki/Armour-piercing_fin-stabilized_discarding_sabot) – since I’m using spheres, rifling may still be effective, but in reality, as a sphere “tumbling” doesn’t really matter – it’s still a sphere from every angle… Rifling would matter for a dart, but the point of a dart is to reduce the surface area at the point of impact (thus increasing pressure) to allow deeper penetration (this also helps bullets to “tumble” once inside their target which causes further damage) – but since our projectiles are so small, penetration is barely a concern, and since I’m using high rate of fire to “cut people” with multiple projectiles, the tumbling thing isn’t really of value either – so I’m abandoning significant rifling – (a small amount of rifling to gyroscopic stabilize the round may be useful to help it fly straight, but at the masses my projectiles have gotten down to, I’m realizing a small rifled section at the end of the barrel should do this just fine – it’ll turn a small fraction of the forward velocity into rotational velocity – the space based rails won’t bother)

    The idea of the railgun is that the entire length of BOTH wires behind the projectile are generating a force in the direction desired. however, if you curl the rails, then the force is no longer perpendicular to the direction of travel and no longer accumulates as effeciently. In fact the rails further back would actually be pushing the bullet into the side of the gun…

    To visualize this, let’s use the right hand rule (and since the other rail conveniently has the opposite charge, we can use the left hand to represent that rail – convenient). Take your right and left hands, hold them out in front of you at roughly the same height and make fists, then stick your thumbs out so that they point straight up away from you fist (like a double thumb’s up sign). Now, imagine that your fingers are wrapped around our “rails” (like you’re holding onto poles that run straight up, floor to ceiling). Your thumbs point in the direction the bullet is being “pushed”, since we’re doing a thumb’s up, we’ll assume we’re trying to fire the projectile towards the ceiling, and as you move your hands up the pole, the thumbs keep pointing in the right direction, and we’re fine. However, now imagine you’re holding onto a pair of spiraled poles and “grab” them with your hands. Your thumbs now point somewhere else (more towards the corners of the room). There is still an upward component (so we’re still going upwards) but the more you coil that rail, the more towards the walls and the less towards the ceiling you’re pointing – so the less upward (or forward) force you get. More importantly though, in the straight up and down case, our thumbs never pointed at any of the rest of the rail – whereas with the curved rails, your thumbs do point at the other rails – this might be a problem (I’m not sure of the forces that would be involved, but it should be considered at least).

    • Master Zed says:

      *1/2 * 4πr² = 2πr² which is double the area of the cross section πr² I was using, which means half the pressure, which means half as much steel penetrated)

  28. Master Zed says:

    Ok, went to make some “recoiless” personal rail guns and managed to accomplish it I think.

    According to (https://en.wikipedia.org/wiki/Recoil), “zero-recoil, [is when] the counter-recoil force matches the recoil force in magnitude and duration”. So I designed the guns so that the muscles of the arm (or shoulder in the case of the long barrel) can EASILY provide counter-recoil force well in excess of the recoil force for basically forever… For reference, I calculated that the force exerted by each arm when holding yourself up in the pushup position is about 200N (62 kg for avg adult weight * 9.8 m/s² for gravity * 2/3 for 2/3 of weight on arms, 1/3 on feet in this position * 1/2 for force exerted by each arm). The “Pistol” exerts 4 N of “recoil”, the “Underarm Rifle” 10N, and the “Shoulder Cannon” exerts 20N. And this is only while firing, with the longest “chop a man in half” burst lasting only 0.013 seconds (less than 2 hundredths of a second… or less than 1/10 the time it takes you to blink – ie, blink and 10 men have been chopped on half…) I feel this MORE than makes them effectively “recoiless”…

    I accomplished this by reducing the mass of the projectile and increasing the velocity to compensate. All versions still use the same projectile, which is now a 0.1 Nanogram spherical diamond. This is about 1/10 the weight of a single human cell, and a single round penetrates approx 4-100m of steel (depending on the weapon used), so very little kinetic energy is likely to transfer to the target – even when firing a long burst – but the projectile is basically guaranteed to penetrate almost anything. They also only have a diameter of 3.8 micrometers, so a burst of almost 132,000 rounds is needed to effectively cut a man in half; though, as noted earlier, this only takes the gun 0.013 seconds to accomplish as all guns were designed to have a rate of fire of up 10,000,000 rounds per second…

    The potential problems are:
    1) The projectiles have velocities of around 1.3-6.6% the speed of light; so the projectile may not survive atmospheric interaction; but they are very light and very small, made of diamond, spherical (one of the strongest structural configurations) and effectively in the air only a VERY short time (to get to the horizon 5km away at 1%c = about 1/600 second; and to get to space 100km away takes about 1/30 second), so this might not be a problem, since the projectile literally might not be in the atmosphere long enough to disintegrate… I might check the rate of heat gain and the melting point of diamond at some point and see if I can confirm this, but even a stream of molten diamond going even 1% the speed of light will probably still get the job done… Also, being so small might make the sonic boom insignificant enough to not be a problem, I might look into this later as well…
    2) The guns use a fair amount of power by modern standards at 8-200 MW while continuously firing (though they also only need to fire for a fraction of a second if not attacking multiple targets). For reference, a modern nuclear reactor outputs around 1,000-1,500 MW per actual generator/tower, but massively increased power storage and generation is a standard of any scifi. Put another way, a 1 second burst from the shoulder cannon would require the mutual annihilation of approximately 2.2 micrograms of matter/antimatter (1.1 micrograms each) – which I believe is the maximum power generation physically possible (E=mc²).

    The following stats include many corrections I made to the spreadsheet, including correcting for the surface area of the sphere instead of the cross section to determine penetration depth.

    (Link to the spreadsheet for those interested in further details: https://docs.google.com/spreadsheets/d/1vkuZRIaXr5upcPRPZDSIcV3qWnO0M1dQY1apLH2Uihk/edit?usp=sharing)

    ALL Weapons:
    Mass of projectile: 0.1 microgram (spherical diamond)
    Rate of Fire: up to 10million rounds per second
    Hours of continual Fire on 1kg of ammo: 278
    2cm Gash (equivalent to a piercing knife wound):
    Ammo Consumed: 52.8 micrograms
    Burst Duration: 0.53 milliseconds
    4cm Gash (equivalent to a piercing sword wound):
    Ammo Consumed: 105.6 micrograms
    Burst Duration: 1.06 milliseconds
    0.5m Gash (chop a man in half):
    Ammo Consumed: 1.32 milligrams
    Burst Duration: 13.25 milliseconds

    “Pistol” Version (Hand held, 0.2m barrel)
    “Recoil” Force: 4N (Approx 0.9 Lbs)
    Rail Length: 0.2m
    Kinetic Energy per projectile: 0.80J
    Muzzle Velocity: 1.3% C
    Thickness of steel penetrated: 4m (about a car length of solid steel)
    Continual Fire power Draw: 8 MW
    M/AM fuel consumption by burst:
    2cm: 47 femtograms
    4cm: 94 femtograms
    0.5m: 1175 femtograms

    Forearm Mounted “Rifle” Version (Mounted under the forearm, 0.5m barrel)
    “Recoil” Force: 10N (Approx 2.25 Lbs)
    Rail Length: 0.5m
    Kinetic Energy per projectile: 5.0J
    Muzzle Velocity: 3.3% C
    Thickness of steel penetrated: 50m (approx half a football field of steel)
    Continual Fire power Draw: 50 MW
    Hours of Continual Fire per 1 kg of ammo: 278
    M/AM fuel consumption by burst:
    2cm: 294 femtograms
    4cm: 588 femtograms
    0.5m: 7345 femtograms

    Shoulder Mounted “Cannon” Version (Mounted on the shoulder, stowed accross the back, 1.0m barrel)
    “Recoil” Force: 20N (Approx 4.5 Lbs, or a half gal of milk)
    Rail Length: 1.0m
    Kinetic Energy per projectile: 20.0J
    Muzzle Velocity: 6.6% C
    Thickness of steel penetrated: 100m (approx a football field of steel)
    Continual Fire power Draw: 200 MW
    M/AM fuel consumption by burst:
    2cm: 1175 femtograms
    4cm: 2100 femtograms
    0.5m: 29,375 femtograms

    • Master Zed says:

      Regarding the destruction of the projectile by atmospheric friction:
      From various research regarding the frictional heating of a projectile in air, I learned that the dominant type of heating depends on velocity high) and pressure (low through air for our fast moving tiny projectiles), with the final mode of heating being almost purely radiant heat at speeds around mach 25 and above (which our projectiles definitely qualify for). At our projectile pressures the air is actually “pierced” and air molecules cannot move out of the way or be compressed (like with our targets, very little kinetic energy is transferred to the air the projectile moves through – so very little energy can be converted to heat), and the molecules will actually break apart (so small scale fission if I’m reading this correctly), resulting in a “tunnel” of ionized elemental plasma and radiation (mostly light and EM, and extremely minor at our projectile’s size – though at 10million projectiles per second, sustained fire could possibly pose an actual radiation hazard if someone wants to do the math >.<). Heating then occurs as a result of radiant heat (IR radiation) from behind the projectile "catching up" with it. Since our projectile is traveling at greater than 1%C, has a VERY small surface to receive this radiant heat (the radiation radiates through 3d space spherically, meaning very little of it is headed in our projectile's direction) and since our diamond is both largely transparent to visible light and a great heat conductor alot of the incoming energy will actually pass through the diamond projectile without heating it (the energy will be absorbed and almost immediately re-released into the atmosphere as light and heat resulting in little if any increase in the projectile's temperature). Having said this, the best data I could find regarding these things are:

      The Stardust sample return probe['s] maximum deceleration has been reported as 34g [or 333 m/s²]. Maximum temperatures are estimated at around 3,200 Kelvin […] at the surface.
      (Source: https://space.stackexchange.com/questions/15038/what-are-the-top-temperatures-occurring-during-reentry)

      Melting (and burning) point of diamond are: 2973K (and 1073K).
      (Source: https://www.kjons.com/articles/melting-point-of-a-diamond – converted to Kelvin for comparisons)

      Best formula I could find (though I got too tired before I could completely unpack it) was given here: https://www.researchgate.net/post/How_do_I_calculate_the_temperature_rise_during_friction

      I'm assuming it's unlikely at these speeds and size that sufficient oxygen will reach the projectile to allow significant combustion (feel free to double check this), which means that the 3200K is barely above our diamond's melting temperature of 2973K. But as mentioned in the cited article, this would require tremendous pressure as well which I don't think can apply here since the air is not being compressed by our projectile. Further, since the reentry probe is designed to maximize drag and our projectiles are designed to minimize it, I think it's safe to assume they are not experiencing anywhere near 34g of deceleration from the atmosphere and are probably quite safe. I could not find a more definitive answer since this is an extremely complicated fluid dynamics problem that goes way beyond layman levels.

      As a side note: the barrel's cross-sectional opening of 45 picometers means that air cannot refill the tube in the time between shots (pi * 3.8e-6^2 m * 1atm = 4.6e-6 kg / s2. Which, when double integrated across 0 to 1e-7 seconds gives only 4.6e-6*1e-7^2 kg = 4.6 × 10-17 g of air for the next projectile to displace (probably less if we account for the vacuum created in front of the barrel). This means that subsequent shots are accelerated (and largely fly) through a vacuum. Further, at these velocities (anything about about mach 25+, so yeah even the pistol's mach 11,600 will cause this) he first round will decompose and ionize the air, creating far less resistance for further rounds traveling almost the same path (a deviation of only 0.5 /132,000 meters / round for the longest burst.) So even if the first few rounds of each burst do turn to liquid, gas, or even plasma creating a firing channel for the rest, then at a bit over 5,200 rounds rounds for even the smallest burst modeled, this is hardly a meaningful concern…

      As for the sonic boom, I found this paper if anyone wants to try to unpack that… (https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19920002547.pdf)

      • Master Zed says:

        Forgot the coefficient of integration (>.<) so: 1/2 * 4.6e-6*1e-7^2 kg = 2.3 × 10-17 g of air to displace (which, by the way, is 7 orders of magnitude less than the mass of the projectile itself)

        Also, regarding the sonic boom, a few moments of though tells me that the boom is created by air collapsing in on the channel left behind in the air. So that complicated formula may not be needed, instead, our long burst of projectiles can be said to "displace" a volume of 1 atm air much less than 1/2 (area of a triangle = 1/2 b h) * 0.5m (leg of triangle described at target) * 10,000 m (a generous distance for how far the sound will travel before being dissipated) * 3.8e-6 m (diameter of our projectile which again is an overestimate since spheres) = less than 0.01 m³ (10,000 cm³), which I think means the sonic boom would be on the order of popping a 10 liter bottle? And again, this is kind of a worst case scenario since the radiation and plasma left in the wake of our bullets may decrease the pressure of the surrounding air, further damping the sound…

        Also, this volume may also be used to determine the scale of the "light" generated (equivalent to muzzle flash) which is gonna be pretty small (somewhere on the order of a 10 liter neon light seen from 10km away?)

        These are VERY rough back of the envelope type approximations… so treat them with a fair bit of skepticism…

      • Master Zed says:

        Not fission. Fission is the breaking up of an ATOM, we’re splitting MOLECULES only (so breaking covalent/ionic bonds only, NOT internal atom bonds). My Bad! 🙂

        • Master Zed says:

          This is also why “elemental ionized” wake. molecules bind by sharing electrons, break that bond and the electron escapes (leaving both atoms short one or more electrons), holds on to one atom (leaving the other an ion), or if sharing multiple electrons, some combination of the two. These escaping electrons (and the gathering of free electrons or recombination of elements into molecules moments later) are likely the source of the radiation (as the are knocked off they gather energy, then as they recombine they release that extra energy as primarily EM radiation)… I think…..

    • Master Zed says:

      A side effect of the ionized channel created by the projectile (as discussed in my air resistance post which is awaiting moderation) is that the gun could be given a non-lethal “taser” option (at least in atmosphere) by firing a single projectile at the target (which at 1/10 the mass of a cell won’t do any meaningful damage) and then send an electric charge down the ionized channel left by the bullet (like the classic scifi electro-laser).

      I think I’ve found my railguns! Thanks soo much for having this forum tctaylor!

      (PS: The spreadsheet linked earlier now has a “recoiless” (0.55N, 0.99c, 6km of steel, extreme RoF, low power requirement @ 288MW) version of the space based weapon too)

    • Master Zed says:

      I just realized that the ionization of the air means that this weapon can also easily be given a non-lethal “taser” option (stun setting) by firing a single projectile (at 1/10 the mass of a cell, 1 round won’t cause any significant damage) then sending a charge down the ionized channel left in the air! (like classic scifi electro-lasers)

      Also, added a “recoiless” version to the space based railguns on the latest spreadsheet.

      1m rail, 0.55N, 0.99C, 5,800m of steel penetration, low power requirement @ 288 MW under continuous fire.

      The long duration of bursts are the only downside I see. With a 0.023 second 1m slice, a 0.23 second 2m slice and a 2.3 second 100m slice, at about 1 light second out, the long bust may give the target time to maneuver and reduce damage a fair bit (the initial impact would be undetected, but a decent computer could determine attack angle and direction of movement along the hull of the rounds and then try to maneuver to move that stream of projectiles towards less vital areas, through holes they’ve already made (ie turn a 100m gash into a 1m hole by lining up the existing hole with further projectiles), or if maneuverable enough just run that stream right off the side of the ship – and with a 1second delay for the attacker to see these maneuvers, they would be difficult or impossible to fully compensate for. Meaning a drone probably can’t actually take out an aircraft carrier with this at 1 light second out – though it might still do damage; and at something more like 0.1ls (or less, we’re talking a drone here) it very well could carve an aircraft carrier sized target in half in a matter of a few seconds (it’s certainly not gonna run out of ammo at 530,000 hrs of continuous fire per 1kg of ammo!)…

      • Master Zed says:

        Correction: 0.23 second 10m (not 2m) slice

        Also: Take THAT Newton! Denied! 😉

      • Master Zed says:

        PSS: This maneuvering to reduce damage and the extreme penetration would actually make for some VERY interesting space tactics, where it might not actually be best to present the smallest profile to the enemy, as while that reduces the chance of being hit, it also exposes the ship to the greatest amount of penetration (like the “raking” of old sailing ships and equally as devastating for the same reasons) – so ships may be designed to “roll” out of incoming attacks like this, rapidly turning a thinner/non-vital location into the stream instead of trying to actually “out maneuver” it. Even large craft can do this relatively easily since inertia isn’t a significant factor (rotating about the center of mass) and longer ships would have proportionally longer “levers” to produce torque with. In fact, the likely limiting factor is the stress this maneuver would put on the hull, which now being compromised might literally rip itself in half. Such battle tactics would make form some EXTREMELY interesting wreckage fields after a fight – with ships that look like ruptured tin cans and possibly significant survivors huddled in sealed corridors and rooms (the ruptured areas may not have survivors, but if the target is willing to sacrifice functional time for passenger survival – ie a civilian craft – it could literally tear itself to pieces to avoid incoming fire and significantly minimize loss of life.)

        This kind of defensive tactic might also influence ship design and give human gunners and pilots a purpose as aiming for center of mass may be more or less beneficial depending on existing damage, target configuration, etc. etc. and human gunners can “intuit” best locations to target and human pilots can try to “out guess” their opponents in a sort of super high stakes game of feints and bluffs.

      • Master Zed says:

        And here come the lasers on larger craft – since a maneuverable drone could devastate the larger less maneuverable ship by closing in and delivering highly accurate strikes, the battleship will need to rely on highly accurate laser blasts to keep them from getting too close and suffering critical damage. At which point it becomes a competition between the battleship and the drones to see if the drones can get one in close enough to deal a fatal blow before getting vaporized by the ship’s defensive lasers. Oh MAN I want to write these space battles – and more importantly – SEE them! 🙂 Ok, back to writing, I think I’ve gotten my inspiration!

      • Master Zed says:

        Oh MAN! Add reactive armor as the predominant defense (since that’s the only hard scifi defense I can think of against high penetration no warning projectiles) and you’ve got a BEAUTIFUL space battle with lines of little explosions (caused by the target itself to disrupt the projectile) drawn across rapidly maneuvering large ships while a swarm of super fast drones tries to make it past the laser defenses losing drone after drone to wlidly flailing laser beams. Wacth this whole thing from the “first person” perspective of one of the attack drones! It’s a dance! And it’s Beautiful! And I think its even 100% hard scifi! Eureka I’ve struck gold! Please let me know if anyone wants to send me some thank you donations (at the very least a copy of the book(s0/movies/etc you used any of this in 🙂

        • Master Zed says:

          This reactive armor also effectively gives ships “hit points” as each explosion that prevents a MUCH worse piercing strike also slightly weakens the ship’s hull. Eventually “bare spots” would start to form and weapons fire would start further compromising load bearing structures, further destabilizing the hull integrity. Each such internal strike would effectively lower the ship’s maximum maneuverability (as the piloting computers would likely monitor and calculate stress failure levels of the hull, and limit the acceleration to prevent the ship from destroying itself). This would be the death spiral of the target under fire. Constantly striving to find ways to divert attacks against remaining armor or non-critical structures. Each time the defender fails to do so and the attacker succeeds at striking a vulnerable spot it becomes a little easier to do it again as the ships movements slow and armor gaps become large and significant. It actually makes disabling ships and surrender a very real occurrence (at some point the defender would just know they can’t survive any more attacks and would surrender given the option.)

          This also significantly changes how attackers would fight. For instance, distant ships may use coordinated unfocused lasers at long range, knowing full well the attack won’t do any real damage, but hoping that the lasers might trigger the reactive armor, potentially making a vulnerable point for the fast attack craft about to make contact with the target.

          The reactive armor could also contain laser scattering particles (like say, small diamond spheres?) to make it about as effective a defense against laser attacks. Further, these small diamond spheres may create incidental AoE defenses against swarming drones (further forcing them to keep a bit of distance lest they kill themselves by being too close and getting hit my too many of the reactive projectiles – it’d be a shotgun like defense, where close in its deafly but far off the density of the strikes is too low to matter).

          All of these options lead to significant variety in strategy and tactics.
          For instance, a daring pilot might “play possum” or act otherwise crippled to lure an enemy in close by exposing a vulnerable point to make the attacker act in a predictable way. Then assume the attacker is going to fall for it and maneuver unexpectedly to create a clean miss and line up an attack. The defender wouldn’t know if their ruse worked for a second or more and would have to act on blind faith. So if the attacker guessed the maneuver, the defender might be facing a face full of extremely dangerous raking strikes instead of the less damaging strike they would’ve taken just playing it safe. The computer would be great at “playing it safe” thus minimizing the average incoming damage, but would also be predictable allowing the attacker to compensate and eventually increase the average incoming damage…

          Feints would work the same way they do in normal fights (especially against narrow AIs or less experienced enemies). Continuously evade or attack with the same pattern until you notice your opponent has grown accustomed to it or confident they’ve found your tell – then use the predictability you’ve trained in your opponent to expose them to a super powerful unexpected strike.

          Drone swarms are extremely dangerous attackers, but the launching ship (and its allies) can’t really use any of its weapons to attack as it doesn’t know where its drones necessarily are any more than it knows exactly where its target is. Plus, the close range of drones (and their limited mass which means limited reactive armor) are vulnerable to much greater rates of attrition, especially against support ships specifically designed to destroy drones/missiles with large arrays of short range lasers. These support ships would be very vulnerable to Battleships though (since they have little means to fight back against the battleship’s larger, longer range weaponry). Battleships are vulnerable to drone swarms though (since much of the surface is dedicated to large long range weaponry…) And now you have a wonderful dance of flotillas of ships constantly trying to outmaneuver their opponents and exploit vulnerabilities. Employing feints and risky double or nothing maneuvers instead of always playing it safe. Etc. Etc. Etc. Hurray, I made hard scifi space combat fun again. 😉

        • Master Zed says:

          Reactive armor also makes larger, slower, projectiles a real threat again, as their greater momentum (but slower kinetic energy) means they have a greater chance of not being deflected by the reactive explosions, or triggering bigger patches of armor to detonate less effectively making them more effective against armor but less effective against exposed hull (or non-reactive armor).

        • Master Zed says:

          Ack, just realized that if the projectile is going .99c, then the reactive armor would need to propagate at near light velocities as well, or the bullet’s just gonna outrun it… That’s no good 🙁

          • Master Zed says:

            Ok, reactive armor is back! The reaction will not stop the initial bullet (or probably even the first few) but as smaller than DNA sized pellets this would mean very little (basically the ship permits something like a nanometer “gash” worth of projectiles to penetrate)… But the reactive armor could still deflect many of the projectiles that follow the first few (preventing meaningful damage), thus effectively reducing the damage to near minimal amounts. In fact, the reactive armor would probably be engineered in such a way that it only triggered after a certain total pressure over time to prevent attackers from doing things like firing shotgun patterns of single projectiles all over (instead of in a line) to detonate all the armor at once.

            Add in a layer of hull under the armor that is filled with sealant that basically instantly plugs the small holes those first few projectiles create and you’ve got a good defense again. The fun/interesting thing here is that if these first few projectiles can damage something delicate enough, then the defending ship may experience short power interruptions or other fun little scifi ship under attack tropes. 🙂

            This also puts more power back in the drones get close strategy, as being closer allows for more accurate (due to shorter information delay) targeting of more sensitive locations that have higher densities of potentially fragile equipment with these initial penetrations.

          • Master Zed says:

            Reactive Armor, more thoughts:

            Since the reactive explosion needs to exert PRESSURE on the diamond projectile to stop it, the extremely small size of the projectile + its extreme speed will more or less ignore any reasonable (non-nuclear?) reactive armor (for the sane reasons the ground versions basically ignores atmospheric drag). The reactive explosion would need to exert approx 1.2e7 MPa of pressure (half that or less if we allow for a shaped charge), so our target pressure is approx 6e6 MPa = 6,000 GPa = 6 TPa. It’s more than the pressure at the center of Jupiter I don’t know if that’s possible without nuclear reactions. For scale, the pressure at the rocky core of Jupiter is estimated to be about 3-4.5 TPa (https://en.wikipedia.org/wiki/Jupiter).

            Tensile Strength of Diamond is not known, though at least 60GPa has been observed (with a theoretical 90-100GPa for 100-300 nanometer diameters like our projectile which is approx 82 nanometers) https://en.wikipedia.org/wiki/Material_properties_of_diamond
            Also modern TPa research is being performed using nanodiamonds (about the size of our space projectiles), so our scifi diamonds may be able to handle even these pressures… (https://www.cambridge.org/core/journals/mrs-bulletin/news/new-nanodiamonds-open-up-materials-studies-at-terapascal-pressures)

            In short, the more I think about it, the less I think reactive armor is a viable hard sci-fi defense, it’s very possible you’d need tiny nuclear detonations to even remotely affect these projectiles. Perhaps some kind of super fast setting epoxy/insta-weld would be the best defense. If properly designed, the vessel’s internal pressure vs vacuum may make such a fast acting epoxy/weld possible. Each incoming “gash” would compromise the structure slightly, and possibly cut people and/or vital electronics (assuming nanoscale electronics with that level of sensitivity). Since the epoxy (or whatever equivalent “magic weld”) is likely to be less strong/secure than the original structure, these epoxy seals would still create structural weakness that would reduce maneuverability as discussed elsewhere.

          • tctaylor says:

            Perhaps a solution for reactive armor is to have multiple layers, each progressively nudging the incoming projectile so it is deflected rather than stopped. Or, at lower speeds, have a development of contemporary reactive armor that zaps the projectile with a high energy discharge like electric armor, or burns it. Diamonds are really hard, but they burn relatively easily. But if the projectile’s coming at you at near light speed, I’m not sure how much of this will work. Looks like the attack versus defense balance would have swung decisively to the attack, but if we’re in a scenario where we’re advanced enough to be shooting projectiles at near lightspeed, I think the designers of defensive armor will have many more avenues of thought than today to develop countermeasures.

          • Master Zed says:

            I don’t think burning the diamond will work, since there’s no oxygen in space. You might be able to get it to burn on the other side (or in between other layers) of the armor (once it’s in atmosphere). But I genuinely doubt the .99c diamond would be in that space long enough to combust more than maybe the outer layer a bit, you’d almost need an Oxygen based plasma to pull that off – at which point we’re basically talking force fields. The kind of energy needed to maintain that plasma and the magnetic containment fields, plus the kinds of dangers just maintaining such a field would represent – probably safer to take your chances with the projectiles, they’re less dangerous. Also, remember that these are carbon spheres, so they have the minimized surface area per volume(/mass) and therefore would burn at the slowest rate possible (minimized area for oxygen to bind to).

            Then there’s the heat it’d be exposing the ship too – in space, where heat management is already a major combat concern… Unless some future tech just pumped heat from the ship into this plasma field or something… Still, to those .99c projectiles with the relativistic length reduction, that’d need to be either a VERY powerful field, or a VERY thick one or it basically becomes a game of statistics as a certain percentage of projectiles are stopped, the problem being that the numbers I ran put the projectiles literally right on top of each other, so if even half the projectiles get through the ship is still severely perforated, like a stamp, and will likely buckle the first time any kind of maneuver is attempted – including just slowing down a the ship’s ultimate destination. That might make a good “firm” scifi defense.

            I considered the deflection idea too, but the problem it that the pressure renders that almost impossible. Simply put, the projectile is just moving too fast and hitting with too much pressure. Basically, it’s the same issue with the .01 light speed ground railgun and the atmosphere. Any armor can be thought of as a really thick atmosphere, and the .99c projectile is going to treat it the same way, for the same reasons radiation is penetrating.

            The best thing I’ve been able to come up with is basically a futuristic carbon fiber kevlar equivalent that somehow catches the bullets, since they have very little momentum to impart (ie, are recoiless – on both sides) and rely on piercing to effectively deliver damage, they won’t do much to the target ship either. I just can’t imagine any kind of even remotely equivalent atomic configuration. Part of the reason I chose diamond is that it’s a macro-molecule (the projectile is a single molecule of carbon arranged in one of the most strong/stable configurations theoretically possible), and the surface of contact is soo small that the fibers would basically be diamond themselves, at which point the mass of the armor starts getting impossibly prohibitive and maneuverability becomes a superior defense, so drop armor all together…

            And basically any armor made of a material that is stronger than diamond would just result in the projectiles being made of that material as well and you’re right back to the same problems…

            The one thing I haven’t really been able to check (and that probably needs to be checked) is if the impact might trigger fusion/fission (like in a particle collider) – at which point the whole “cut em in half” becomes unnecessary and it’s just “hit em with enough projectiles that they all die of radiation – even the electronics/AIs…

            But yeah, if we’re going sci-fantasy, then a shield would stop these bullets easily. Since you probably have inertial dampers (and these projectiles have basically no inertia/momentum) and force fields (and these projectiles don’t have much force – you’d basically need the same force as the recoil force over the same distance as the rail length – which for the recoiless space cannon is basically nothing – which is why its recoiless). But once you get to sci fantasy levels, it’s all just about energy management. The attacker is trying to overwhelm the defender by pumping in more energy than the defender can pump away – and every time the attacker succeeds, the defender pretty much vaporizes… Unless you almost completely rewrite the laws of physics – which is a completely fair thing to do in scifantasy – I’m just saying that these kinds of discussions become pretty moot at that point.

  29. Master Zed says:

    A few last notes on some of the statistics presented:
    1) Remember that these recoil forces would need to be converted to pressure (kg / m²) based on the size of the contact point with the weapon (so the surface area of the back of the grip or the like) to really translate how it’d feel to fire, but I think a fair approximation of firing the shoulder cannon would feel a little like laying on the ground and putting a half gallon of milk on your shoulder… “maneuvering” the shoulder cannon would feel like laying on your back and “aiming” that half gallon at different spots on the ceiling (actually easier, since the milk is gonna have fluid inertia that’s a bit harder for our arms to compensate for and the shoulder gun has a 1m lever to utilize and likely gyroscopic compensators and and possibly an assistive motor on the shoulder mounting).
    2) The “power requirements” are based on the energy given to the projectile only (conservation of energy) and so do not account for energy lost to inefficiencies in accelerating that bullet, like heat, the energy spent by the rails pushing on each other, etc. But the “real” power will be some multiple of these numbers not likely to exceed triple (https://en.wikipedia.org/wiki/Physics_of_firearms lists about 32% of the energy generated in a chemical bullet translating to projectile motion, so I’ve got to assume our high tech rail gun is doing at least as good as that) and will of course, depend on the assumptions of your setting.
    3) These barrels are EXTREMELY small, but I’m assuming made way thicker than needed to allow for comfortable handling. I’m also assuming they are carbon based (ie diamonds with perhaps with graphine rails?), at least on the interior to allow them to comfortably handle the stresses of the acceleration. But remember, the “recoil forces” are also the forces experienced by the rails and are EXTREMELY small. Naval railguns have problems because they use substantially more massive projectiles (because modern material sciences).
    4) In researching railguns I found that it’s important to have the projectile already in motion when it reaches the rails (for multiple reasons), so I assume ammo is delivered to the rails via an air soft like air pressure. I do not account for this initial velocity (since it’d be incidental), but it does mean you could give the bullet a “spin” before it hits the rail if rifling is desired; though I don’t think it actually matters, since piercing air = no significant drag and 0 to space in 1/30 of a second and 0.1 microgram of mass means gyroscopic stabilization is also probably an insignificant factor…
    5) At these fire rates manually creating a 2cm, 4cm, or 0.5m “line” at the target’s position would mean that I assume a laser rangefinder, small computer (or even just circuit board) and either a gyroscopic or actuated system handles this for the user, who just uses some method to indicate the length of burst desired (either trigger pressure – practiced like playing a trombone) or individual selector (that could be implemented as anything form a neural link to eye tracking in a helmet’s reflection, to a couple of buttons). If fire assist software and aim assistance is available (like in an armored suit that can actuate the barrel even slightly) these bursts can become even more controlled and the user would basically point at the taret and the computer would crunch the numbers and likely fire a 4-8mm burst to sever a carotid artery… or a 2-6cm burst through the target’s heart cutting it in half… a 10-15cm burst could transect the neck, severing the head from the body… a 0.25 meter burst could also be used to “draw a circle” around the heart, completely carving it out of the target’s chest… And finally, the 0.5m burst would cut a man in half at the chest/torso… the actual kinetic energy in these projectiles is incidental…

    • tctaylor says:

      Many thanks, Master Zed. It’s going to take me a while to work my way through all this and digest it, but please know that your thoughts are greatly appreciated.
      Tim

  30. Master Zed says:

    An Interesting thread on laser recoil and why it’s so low.
    (https://www.physicsforums.com/threads/does-a-laser-have-a-recoil.379922/)

    This is the same thing that is happening with the rail guns. As the velocity increases and the mass decreases by the square of that increase, the weapons become less and less useful as “thrusters” (ie have less recoil). So this definitely seems to be a general property of physics. Recoil is more a matter of velocity of projectile than mass by an inverse law (assuming equivalent energies), And looking at the equations, we can see this derived.

    Kinetic Energy = mass * velocity^2
    Momentum = mass * velocity

    We can solve kinetic energy for mass (mass = KE/v^2) and plug it into our Momentum equation (Momentum = KE/v^2 * v = KE/v) and see that for any given Kinetic Energy (ie, approximate power/lethality), momentum is the inverse of the velocity. The recoil force (or impulse force; Newtons, or mass acceleration) is the momentum divided by the time spent accelerating (if the acceleration is constant, if it’s not constant you either need to be able to break it up into discrete intervals, or calculus if the change is continuous).

    TL;DR: any near light speed weapons with roughly equivalent power will have roughly the minimum possible recoil for that energy level (since c is the velocity limit), regardless of the technology or method used to get it to near light speeds. And for any equivalent energy level, the higher the velocity of the projectile, the lower the recoil. Therefore (generally speaking) the recoil of equivalently powerful chemical projectiles > rail projectiles > lasers.

  31. Master Zed says:

    For those interested in a more perfect understanding of railgun physics, I found the following:

    http://web.mit.edu/mouser/www/railgun/physics.html

    My spreadsheet does not include the realities of railguns specifically, instead it is a generic system of physical conservation laws and forces. As such, it does not consider real world problems like the realities of engineering the capacitor, or providing unreasonably high voltages, etc. Instead these are whisked away as the magic of scifi (ie, the fiction is that the setting has sufficiently powerful and well designed power supplies to pull off whatever is needed within a volume that could reasonably fit in the hand/by portable.)

    It is worth noting that the Force applied to the projectile changes as a function of time and the current in the loop also changes as a function of time. I assume that the current is controlled to give constant acceleration with respect to time. However, it seems plausible to me that the realities of the light speed limit and the near light speed velocities of our extremely fast space based projectiles may make this physically impossible, but such reality checking is beyond the scope of my experience. (Ie, there may be a maximum rail length at which point the time it takes the current to reach the projectile to further accelerate it is greater than the time it takes the projectile to move forward – at which point the rail is no longer completing a circuit and no further acceleration would be possible. This would mean that any rail beyond this point is useless and we effectively have a maximum rail length. In reality I think it’s more likely that the field will simply drop off asymptotically towards this limit, making remaining rail contribute exponentially less forward force until it became impractical to use further rail to accelerate the projectile, which has the same effective result of a maximum practical length – but determining this would require considerable further research and some serious mathematics, so my spreadsheet does not take this into consideration…)

    Another realistic concern would be that at the sizes necessary to gt near light speed projectiles, especially given the vacuum conditions, that the current will simply jump the rails before the projectile, effectively removing it from the circuit and ending further acceleration. But again, this is beyond my scope.

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