How to make classical firearms effective on space habitats despite the coriolis effect?

The direction of the force will always be perpendicular to velocity and pointing to the opposite side of the rotation direction. In plain terms, any object traveling in the rotation plane: up (toward the axis), down (from the axis), Westward (spinward) or Eastward (counter-spinward) will seem to be caught in unfelt tornado winds, one that its axis parallel to the ship or station rotation axis but reversed in direction. For upward movement the body will drift spinward, for downward movement a drift counter-spinward, for spinward it be downward and for counter-spinward it be upward. - Atomic Rockets

The Coriolis force is proportional to the rotation rate... The Coriolis force acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object's speed in the rotating frame (more precisely, to the component of its velocity that is perpendicular to the axis of rotation). - Wikipedia

The Coriolis effect is pretty bad for classical firearms on reasonably sized spin-gravity space-stations (20m to 50 km (maximum for steel-based construction) with rotation rates between 0.1 and 6 rpm(go to SpinCalc for details). You shoot your handgun at someone and if they are:

• Spinward the bullet will experience massive bullet drop and slam into the ground

• Anti-spinward the bullet will curve up and fly in a circle around the habitat until it hits something or someone or is slowed down by air resistance

• Up or down the bullet will fly spinward or anti-spinward respectively

• Parallel to the axis of spin fly just as it should on Earth

• A combination of the other options go wherever the combined vectors take it

From you the bullet will go anywhere, but where you intended it to go.

While I know that the precise details will depend on the parameters of the station in question, does this make firearms almost useless for firefights on stations?

I thought about a few solutions which might help, but none of them seem to be amazing.

• Use training (effort and requires adaption to every new habitat)

• Use a computer and augmented reality so people know where their bullets will go (woundable to electronic warfare)

• Use smart bullets (smart bullets might not be maneuverable enough and there comes the point where you are effectively using a gyrojet and not a slugthrower anymore)

• Use other weapons like gyrojets, flamethrowers, heat-rays, blazers, ray-beams, particle weapons, e.c.t (those are only slightly inferior to slugthrowers in most aspects in my setting)(This is not an undesired outcome, I just want to make sure that it is the most plausible solution and that slugthrowers really can't be fixed easily.)

• Comments are not for extended discussion; this conversation has been moved to chat. – Monty Wild Sep 16 '19 at 9:11
• Perhaps it would be best not to, particularly since there is vacuum outside the walls. – Adrian Midgley Sep 16 '19 at 10:56
• Just a sidenote: "Parallel to the axis of spin fly just as it should on Earth" - option is somewhat wrong. Bullet move straight, but shooter move in circle. It means that bullet would fly down (somewhat as on Earth, but it is not a parabola) and spinward (not like on Earth). – ksbes Sep 16 '19 at 11:48
• Would it be possible to use a bullet whose spin is carefully calculated to counter the coriolis effect (much like baseball pitches are given various trajectories based on the spin they're thrown with)? With a smart gun detecting current direction and automatically applying the appropriate spin it may be possible for the projectile to more-or-less move in a straight line after exiting the barrel. I believe current guns and bullets aim to minimize spin induced drift, but with engineering effort going towards maximizing it instead it may be workable, but I can't do the math for a proper answer. – Steven Jackson Sep 16 '19 at 18:32
• Coriolis effect is highly predictable, and long distance precision shooters on Earth already have to account for it. The effect would be larger on a space station, but the calculation wouldn't be any more difficult. – StackOverthrow Sep 16 '19 at 20:28

TL;DR: deflection due to coriolis force depends strongly on the angular velocity of the station. In slow rotating stations (eg. very large ones) coriolis effects on short range engagements will be negligible, but can be significant at longer ranges (eg. 100s of metres). In very fast rotating stations (eg. very small ones) the coriolis effects will be so big that you really shouldn't be shooting projectiles at all.

High velocity rounds will partially offset coriolis effects, the faster the better. A combination of training and specialist equipment is probably the way to go.

Neither the mass of the projectile nor the radius of the station affect the strength of the coriolis force, but they do affect the strength of the centrifugal force. I won't consider this here, but you should care about it.

Edit: sudden obvious realisation... the equivalent of "the high ground" in a rotating habitat is the ground spinwards of you. If you're shooting spinwards, coriolis forces will reduce your range as your bullets appear to be dragged downwards. The people you're shooting at on the other hand, will find their range increased, and may be able to "shoot round corners" (or at least, shoot "up" under an obscuring ceiling). Defensible areas in a rotating habitat will therefore be more strongly fortified to the spinward side. People trained to fight in a rotating habitat will preferentially advance in the antispin direction. Untrained people may not realise this, and problems will ensue (including blowiong themselves up with grenades because they couldn't throw as far as they thought).

Edit 2: the coriolis force doesn't just affect projectiles, but any moving object. This includes your arms, legs and head. Even if you do have lasers which will always shoot in a perfectly straight line, your ability to aim or track a target will be limited by your familiarity with and acclimatisation to the environment and your training. Even apparently simple operations like reloading a weapon could become challenging in a high-RPM environment, and using a laser will not prevent this. Have a read of Artificial gravity station station phsiological effects and design criteria, a NASA report from the early 70s.

Disclaimer: I Am Not A Mathmologist nor a Physician, so things like mechanics and vectors are a bit of a foreign language to me. Naturally, this answer requires both. E&OE.

I'm assuming you're in a rotating habitat with artificial gravity provided by centrifugal force. I'll assume the specific example of an O'Neill cylinder, so I'll use terms like "endcap", but this can be translated to any other rotating habitat, I believe.

I'm not going to consider centrifugal force here, as your question is explicitly about the coriolis force, but in a rotating habitat with substantial vertical distance changes (eg. walking up steps on the endcaps) the effects of centrifugal force will also do odd things to projectile trajectories. Don't forget this! I'm also not recomputing the effects of the coriolis force once deflection occurs. A projectile deflected down a little by coriolis effects will then be deflected antispinwards a little, and so on. Trajectories can form very strange shapes, though at high projectile speeds and low station velocities things don't get too crazy, so I'll just talk about the initial forces affecting the projectile. I think my approximation here is OK, though it won't hold for things like thrown grenades in smaller stations!

The strength of the coriolis force is defined as $$F^\prime = 2m\Omega \times v^\prime$$, where $$F^\prime$$ is the resultant force vector, $$m$$ is the mass of the moving object, $$\Omega$$ is the rotation vector of the station, and $$v^\prime$$ is its velocity vector relative to the rotation vector of the station.

Lets make a coordinate system with Z pointing radially inwards at the axis from the rim (ie. "up" in the artificial gravity field). $$\omega$$ is the angular velocity, and $$v$$ is the projectile velocity. If I shoot the projectile along the X axis, in the direction of rotation:

$$F^\prime = 2m\begin{bmatrix}0\\\omega\\0\end{bmatrix}\times\begin{bmatrix}v\\0\\0\end{bmatrix} = 2m\begin{bmatrix}0\\0\\-v\omega\end{bmatrix}$$

you get all the force in the -z direction, or your "massive bullet drop". How how massive is massive? Well, the downward acceleration experienced by the projectile will be $$a = -2v\omega$$, and the drop $$s$$ over time $$t$$ will therefore be $$s = \frac{1}{2}at^2 = -v\omega t^2$$. Doubling your velocity doubles the strength of the coriolis force, but quarters the time you experience it for so the drop will end up being half as much.

Lets start with the 50km radius station. To get a 1g apparent gravity, you need a spin rate of about 0.134rpm (or 0.014 radians per second). Lets shoot a projectile at 400m/s (a conventional 9mm pistol round might go this sort of speed). I'm gonna be super, super lazy and neglect bullet drag... lets assume some idiot has been firing projectiles in a space station, and punched a bunch of holes and let the air out. The acceleration due to the coriolis force experienced by the projectile will be...

$$a = -2v\omega = -2 * 400 m/s * 0.014 rad/s = -11.2 m/s^2$$

...about the equivalent of 1g, approximately. At a 400m range, which seems a little far to be shooting a 9mm bullet, you'll get an additional drop of about 5.6m. Shoot antispinwards, and you'll get a drop reduction of 5.6m. Shooting a round twice as fast will get you half the drop. A NATO 5.56mm supersonic rifle round travelling at 880m/s will get a drop of ~2.5m firing spinwards, etc. At a more cosy 20m range, your pistol round's deflection will be more like a couple of centimetres... enough to spoil your score in a shooting range, but not really enough to make you miss all by itself.

Take home message: for close engagements, no special equipment or training is needed, probably. For longer engagements, eg. the sort of ranges that typical modern-day military forces expect to fight at, problems will arise.

Now lets look at the other end of the spectrum, with a 20m radius centrifuge spinning at a dizzying 6.6rpm, or about 0.7 radians per second. The strength of the coriolis force is therefore 50 times greater. The distances involved are vastly smaller, of course... you're shooting 40m, tops. In that time, an object in the station will have rotated 0.07 radians, or 2.8m around the circumference (which is the maximum displacement if you're shooting someone diametrically across the centrifuge from you). It'll certainly feel like your bullets are bending in that situation!

Take home message: don't go into a centrifuge with a gun that fires bullets. Something bad will happen, to someone. Just thrown in some grenades first.

Edit: prompted by Harper's comment, lets have a look at 2001's Space Station V. It has a 150m radius and rotates at a little under 1rpm to give lunar-equivalent gravity. Its fast rotation rate leads to strong coriolis forces (about 3.7x stronger that the massive O'Neill for the 400m/s bullet) but under a 3m ceiling your longest line of sight is only going to be no more than 60m. This gives a maximum z-axis deflection of ±0.92m. This means that if you lie on the floor and look antispinwards and can see their toes, you can shoot them in the abdomen. This is also very approximately the spread of a long-barrelled shotgun with a full choke at the same range, so in this environment a shotgun might well be a sensible choice if you weren't expecting to face armoured opponents. It has a the nice knock-on benefit that unlike supersonic rifle rounds, you're much less likely to shoot a hole in the world and let all the air out.

You've thought of lots of neat ideas, but here's my take:

1. Use smart sighting devices. For closer-range engagements, for example, combine a laser sight with an inertial measurement unit and a laser rangefinder. The sight can detect the rotational parameters of the current environment and the direction in which you're pointing the gun, and then steer the laser to point where the bullets will actually land.

On a planet, or a really big habitat at close range, it'll work just like a regular laser sight. As the strength of the coriolis force increases, the laser will point in slightly (or extremely) different directions to the gun. The relationship between the two will be confusing for the untrained, who will wave the gun around frantically in the wrong direction in the heat of the moment and then get shot. They'll need lots of practise in varing environments to learn to use the sight properly.

2. Use guns which shoot high velocity rounds to mitigate the effects of the coriolis force. These are generally preferable in most circumstances, unless you wanted to be stealthy in which case supersonic weaponry is undesirable.

3. Use guns which shoot a lot of bullets in a short time, perhaps tracers, if you're feeling brave. You can walk your fire onto the target, given small aiming errors.

4. Use grenades, flashbangs and gas in confined spaces at high RPMs.

5. Use guided projectiles at long range.

6. Consider using shotguns against unarmoured targets in smaller stations, for both ease of hitting and environmental safety.

7. Deliberate use of low-velocity projectiles to shoot around corners and under obscuring ceilings in fast-spinning stations might be a good tactic, given some practise.

• @TheDyingOfLight I've been putting off doing stuff with the coriolis force for ages, because it had vectors in it, and they're a hassle. Turns out it isn't that bad after all! – Starfish Prime Sep 14 '19 at 21:31
• There's a fatal flaw here. You're imagining a shot at 400m range, but you will not be able to see your target because the ceiling will break line-of-sight. Assuming sensible ceiling height, the limit of long-range shots would seem proportional to the coriolis strength. So let's say a 10cm radius is "still a kill", would the range where your error is 10cm vary by station diameter, or would it be a constant? – Harper - Reinstate Monica Sep 15 '19 at 4:20
• @Harper why would the ceiling break the line of sight in a station with a 50km radius? Especially in an O'Neill cylinder (see paragraph 2, below the break) where there needn't be any ceiling at all. Also, why would you expect to do "long range" work in a building with a low ceiling? That just seems weird. Anyway: the strength of the coriolis force depends only on the angular velocity of the station and the relative velocity of the projectile, so it doesn't vary by station radius. – Starfish Prime Sep 15 '19 at 6:03
• @Harper $r = (s^2 + l^2) / 2s$ where $s$ is the ceiling height (say 3m) and $l$ is half the line-of-sight distance (say 200m, giving a total LOS of 400m), giving $r$ = 6668m. Any station with a radius larger than this will support 400m+ LOS under a 3m ceiling. Of course, if it has 1g artificial gravity, the bullet drop at 400m even with the supersonic bullet will exceed the ceiling height (>7.6m drop with 800m/s), so you can see people but not shoot them to spinwards, and shoot people you can't even see to antispinwards. – Starfish Prime Sep 15 '19 at 6:52
• As evidence of this engagement on 10's of meters that leads to "it doesn't matter so much" : donaldmsensing.blogspot.com/2003/06/… – Dast Sep 16 '19 at 10:53

Essentially the firearm has a smart sight unit attached. Like modern smart phones, it will need an built in accelerometer and a display (indeed, you could probably write an app for an Android or iPhone today), the accelerometer to determine the spin rate and angular velocity, the app calculating the offset and the display giving you the target information. In practice it may look like a modern "reflex" sight, the only difference is the red dot is not going to be aligned with the barrel. However like a reflex sight, the shooter uses both eyes open to rapidly acquire a target, and places the red dot on the target before squeezing the trigger.

Did you think I was joking?

Intelliscope

Given other features and the computing power embedded in smartphones, the ability to "zoom" in on distant targets, switch between day/night/thermal and incorporate other features like rangefinders, maps, "Blueforce" trackers and so on are almost a given. Creating tactical "mesh" networks so all elements are in communication with each other is also a feature military weapons (or weapons used by police, military and paramilitary forces) are likely to have.

Perhaps the biggest limitation will be the user interface; the soldier or police officer isn't going to have time to scroll through menus looking for the right app in the middle of a firefight.

• Just want to point out that zooming, night vision, thermal optics, and range finders, are all well outside the range of what a smartphone can do right now. At least when dealing with something at ranges a firearm can reach out to. My nitpicks are unrelated to the OP's question though. – RToyo Sep 16 '19 at 18:34

Schlock Mercenary has something about shooting in rotating frame references more than ten years ago.

https://www.schlockmercenary.com/2008-08-17

Schlock and his commanding officer were shot. Schlock then tried to shoot back and failed. Finally he said "I'm gonna have to walk my shots". In other words, he then included tracer rounds and watched where they landed and so adapted his shooting as needed, but still failed to hit the sniper and destroyed a lot of things in the process.

The sniper on the other hand had a special scope to compensate for the coriolis effect, such hat he was able to land direct hits without tracing.

https://www.schlockmercenary.com/2008-08-10

I thought about a few solutions which might help, but none of them seem to be amazing.

use training (effort and requires adaption to every new habitat)

1. Definitely use training. This is amazing. As things are on earth, you can be the lamest couch potato ever and use a gun to go out and kill loads of ninjas. Guns are so overpowered. In your world, guns are useful only to Gunslingers - persons who devote hours of practice to sensing and compensating for the varying trajectories one encounters in space. This would be way more fun than a bunch of doofuses with machine guns.

• The issue is that I could simply hand out directed energy weapons to the soldiers and they would be as effective as normal without extensive training to adjust for each station's specific spin rate and the velocity of the bullets. – TheDyingOfLight Sep 14 '19 at 19:07
• I wonder if instinctual training would be effective - after all, when you're on a spinning station it should be impossible to tell which direction you're going without firing off a practice round. – Dubukay Sep 14 '19 at 19:20
• @Dubukay Just drop something, like your pistol or a coin, and observe where the Coriolus effect takes it. This is how you determine which way is spinward. – TheDyingOfLight Sep 14 '19 at 19:33
• @TheDyingOfLight can I just point out that it is the "coriolis" effect? no "u". – Starfish Prime Sep 14 '19 at 19:48
• @TheDyingOfLight I'd add emitter efficiency, power limits and frequency ranges in there too. But none of those things are insurmountable. Just a Simple Matter Of Engineering, right? – Starfish Prime Sep 14 '19 at 21:32

You missed an option, design a gun that gives the bullet an equal and opposite force to the other direction so "dumb" bullets fly stright(ish).

I give you the Hop-up - used in airsoft to give a bit more range as it basically creates an "up" force to the pellet during it's flight it shouldn't be too much of an issue designing a spacegun to include a similar mechanism that will provide a round bullet (and yes it must be a round bullet) a counter force to the direction of rotation:

• The gun will need some electronic to detect the direction of rotation of the ship, and move the "hop-up" mechanism to the right position around the end of the barrel (think of it as a end of barrel attachment)
• The "hop-up" will need to be more robust to be able to handle the extra power given with a real firearm compared to an airsoft one but that's also possible to design
• The "hop-up" will also need to be longer due to the increased bullet speed but even at 5 times the length of a airsoft one it will still be within the length of a long barrel firearm
• bullets will need to be round but they can still come in self contained casing so no issues with semi\full auto
• Hop-ups are adjusable so you can use a simple lever to decide on how much the "spin" the bullet and thus match them to the speed of the space habitat, this will need to be done when zeroing in the gun much like when you zero in a gun sight.

Smart bullets or smart scopes

Already we have smart bullets that can adjust themselves in flight to hit a laser pointed target

We also have smart sniper scopes that adjust for distance, compensate automatically for wind as well as the Earth's rotation.

See smart scopes

We already have the tech today to do just this.

Counter Coriolis Effect With Spin Effects

The math is a bit beyond me (Nasa has a tool that may help you nail down more exact numbers at https://baseball.grc.nasa.gov/), but it seems plausible that projectiles with a high enough spin rate in an appropriate direction could mostly cancel out the coriolis effect, at least as long as you're firing in an environment with sufficient atmospheric drag.

Cons

1. Different spin needs to be applied based on the direction you're shooting (spinward, anti-spinward, etc.)
2. If the station were depressurized for any reason, you'd lose the spin effects you're accustomed to
3. The required properties of the projectile to enable sufficient spin effects may conflict with nice properties we currently expect projectiles to have (they may need to be spherical, or larger, or have a deliberately high drag coefficient by having a rough instead of smooth surface).

Dealing with #1 would be easiest with a smart gun which could detect the relevant parameters and apply the appropriate spin automatically, but in a lower tech setting could maybe be dealt with by carrying multiple sidearms (one designed for spinward shooting, one designed for antispinward shooting), corresponding the the directions you expect to be engaging in, and making manual adjustments from there.

Dealing with #2 might actually be an interesting plot point.

Dealing with #3 may cause bullets to be less precise, have less velocity, be louder, more mitigable by armor, or other undesirable effects.

Pros

Most natural solution for soldiers who are trained and operate in earth-like environments, where training for a specific station may not make much sense. Without some intuition for the Coriolis effect, even lasers that lead the target may be confusing in engagements with multiple combatants on each side. Losing track of which dot is yours and trying to figure out where you're aiming would waste time vs "point and shoot like you always have".

This solution could co-exist with other solutions: tasks forces that operate primarily on stations would probably have more specialized training and use another method of countering the Coriolis effect to avoid the drawbacks that come from adjusting projectile ballistics in order to increase spin effect. Combatants without the benefit of this training would be issued the (cheaper?) "spin-guns" to provided maximum effect with little investment.

• The "Bend it like Beckham" solution is impressive, very good first post here. +1 (From review) – A Rogue Ant. Sep 16 '19 at 19:52
• Nice idea, though I note it is the same as the "hop-up" device that was referred to (but not actually described) in Cypher's answer. – Starfish Prime Sep 16 '19 at 20:22
• I think Gyrojets would be pretty amazing at adjusting their spin comppred to slugthrowers. This is very good and interesting answer. +10 – TheDyingOfLight Sep 16 '19 at 21:21