'Speed Bumps' as a Lethal Trap in Space Ship Combat

Question

Deceleration as a weapon

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In a very interesting question about the scale of distance useful for a space opera game, I was inspired to consider the use of deceleration as a weapon.

Considering humans have a certain threshold of G's of acceleration/deceleration, is it possible to use sudden deceleration as a lethal weapon/trap in space combat?

Specifically, we want to ambush a ship is traveling at fast speeds, higher than, say, the voyager 2, at 15.2 km/s. (Originally was asking about sub/near light speeds, but realize that even a droplet of water would pulverize the ship).

If one could predict the exact location an enemy ship will pass through, and some materials are left locally at rest (0 velocity) at that location as a blockade to ambush them, is this 'Space Speed Bump' capable of incapacitating the enemy crew through impact deceleration alone?

The best answer would ideally have some form of calculations or citations to back it up (rough calculations are fine).

_{Hull Materials}

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After using the equation for armor penetration with a ball of 3g of sand (with the same F-coefficient as an armor penetrating bullet) traveling at 15,000m/s, it was found that against a Chrome Nickle Steel Armor plate with a perpendicular (head on) impact, it would penetrate 87m of steel armor. This is far beyond the limits for modern armor on hulls.

As such, the question needs to involve some theoretical materials, either being equipped with about 0.15-1.5 meters thick of carbon-fiber strength or nanotube hull, which can be up to 600 times stronger than steel.

Or assuming that a ship can have at least 100 meters of self-healing, steel-strength plating.

Without at least this level of hull strength, any random collision with a 2-3mm large spec of dust will cause a hull breach and kill the entire crew.

_Assumptions

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• We do not care about the state of the ship after, just that what incapacitates the crew is the deceleration.
• The ship and blockade share the same reference frame, perhaps velocity with regards to the center of the universe, factoring in (space's expansion).
• In regards to @JustinThymeTheSecond's questions about relative velocities, assume the ship will collide into the blockade at 15,000m/s (1/20,000th the speed of light), as the blockade and ship share the same reference frame (whichever frame is picked).
• The ship does not detect the obstacle in time to greatly decelerate or change course
• The basic ratios (using a space shuttle as reference): a shape like a cylinder, with cone diameter of 6 meters at the front, and weight of 120,000 kg. Scale as needed.
• Assume the blockade material has a similar density to water
• The ship hull is at least as strong as 100m of composite steel, or 1.5m of nanotube armor
• The hull will protect the crew from dying to a hull breach by grains of cosmic dust while flying in normal operation.

On a tangent, would it be possible for the deceleration to not cause heavy damage to the ship and its cargo, while still being deadly to the crew? Would we need a special material or setup to best spread this impact throughout the entire surface of the spacecraft?

Answer 1

Way out in left field answer number two.

So far, most answers are looking at something that the ship 'runs in to'.

Instead, A sticky solution. How about magnets?

Every ship produces an EM field around it. This EM field is traveling at extremely high velocities. So, feed the area with a gadzillion ball bearings. When a ship with a high EM field passes through, eddy currents will be induced in these ball bearings. These eddy currents are proportional to the speed of motion of an inductor in a field - i.e. very strong at spaceship speeds.

These eddy currents will generate a very large magnetic field around the steel balls, which in turn will be attracted to the ship hull, or indeed the EM field around the ship itslef. (Lenz's law - an induced magnetic field will oppose the field that prodced it). The ship does not have to HIT the ball bearings, they will be attracted to the ship (accelerate on their own) and all of this energy will be subtracted from the ship's forward momentum. Like the electric brakes on an electric car - the motor is turned into a generator and the power returned to the battery).

There would be a sudden deceleration jolt in the target spaceship, from three factors. One is the ship actually hitting a stray ball bearing, but I am sure the ablative shield could withstand it. Second, the mass of the ball bearings attaching magnetically and probably non-destructively to the ship, increasig its mass, and thus lowering the speed. But third, the induced back-EMF field opposing the motion that created it in the first place. This force, given the speeds involved, would be the strongest force, and not dependent on the mass of the ball bearings.

Of course, the target ship could avoid this by shutting down all sources of EM radiation, but this would potentially shut down all navigation and sensors. Also, I suspect even a ship traveling through background radiation would produce some induced EM field around it. However, an alternative would be for the ball bearings to be somewhat intelligent. Upon sensing an approaching ship, they would generate their own EM field. They would not only be attracted to each other, but collectively to the approaching ship. The effect would be like encasing the approaching ship in a magnetic fishing net.

Apart from a defensive move of a ship laying in wait, it would produce an effective speed-limiting measure around a space station. Only vehicles approaching at a very low rate of speed relative to the station would not be 'braked' by the system - a true 'speed bump' the purpose of which is to slow down the driver.

Edit Example

Here is an example of how eletric induction brakes are used to stop, for instance, trains and roller coasters.

An eddy current brake, also known as an induction brake, electric brake or electric retarder, is a device used to slow or stop a moving object by dissipating its kinetic energy as heat. Unlike friction brakes, where the drag force that stops the moving object is provided by friction between two surfaces pressed together, the drag force in an eddy current brake is an electromagnetic force between a magnet and a nearby conductive object in relative motion, due to eddy currents induced in the conductor through electromagnetic induction.

EDIT Food for Thought on 'stickiness'

Water, or in fact, most liquids, can not exist in space. With the almost nil (atmospheric? non-atmospheric?) surrounding pressure, the molecules of almost any liquid in space will boil off almost immediately. But it boils off, not in individual molecules, rather in 'clumps' of molecules. When the clumps, or particles, get very small, they will now 'freeze' (turn into a solid) - they have lost so much energy in breaking the molecular bonds in 'reverse boiling' (boiling not because external additional energy is added, but boiling because the pressure is lowered so that the existing energy causes boiling) that they now solidify into a very fine mist of crystals.

However, the property of a liquid would be useful in this case - liquids are deformable (wet) and can wrap around an object when impacted. This is a 'sticky' property of liquids. They 'pour' over an object, covering it, without necessarily 'impacting' the object at high velocity (first contact would be an impact, but when the remaining liquid surrounds the object, no catastrophic impact). Nevertheless, it requires energy to do this - energy that is taken from the speed of the object.

So how to replace the molecular bond of a fluid with another 'fluid-type' but non-molecular bond? Yes, of course, electromagnetism. With no current flow, there is no magnetic attraction. All of the ball bearings remain 'at rest' with respect to each other in a disjointed cloud. (Eventually, of course, gravity would clump them together.) But as soon as eddy currents are induced in the ball bearings, the eddy currents produce a magnetic field, and the particles now attract each other. One will follow the other in a fluid motion. Even if they connect, they will still act like a 'fluid', due to their roundness. They can move over each other. Thus, they can surround another object without forcefully impacting it.

But here is the thing. Inducing a current in these ball bearings takes energy. The stronger the induced current, the more energy is 'expended'. This energy comes from the forward momentum of the inducing object. But the faster the ball bearings move in the field, the stronger the eddy currents. Here is a good primer on induced eddy currents and energy conversion. They are so powerful, as I have stated, eddy currents induced in the wheels of a train can bring the train to a stop.

To clarify why I think there would be an EM field around a space ship, they have been proposed as a 'shield' to protect the ship against cosmic radiation and such. EM fields could conceivably be standard fare for space ships in the future.

TL:DR

To clarify, the idea of using induced electromagnetic fields in ball bearings, is not to use the impact energy of a 'stationary' ball bearing on a moving space ship to destructively cause a loss in momentum of the ship, but to use the momentum of the spaceship to induce a magnetic field in a stationary ball bearing, causing the ball bearing to impactlessly accelerate to the speed of the space ship. It is this acceleration of the ball bearings that in part creates the drag on the ship, that results in slowing it down, not any destructive direct impact.

Another factor in the loss of forward momentum in the ship is the loss of energy as it is converted into heat in the ball bearings, from the induced (short circuit) current flow. The greater the induced current flow in the ball bearings, the more heat generated, the more energy taken from the ship's forward momentum.

The induced eddy currents in the ball bearings are created, in the first place, by the forward movement of the EM field around the ship, relative to the stationary ball bearings.

Answer 2

I'm fond of a scene from the movie The Hunt for Red October.

Can you launch an ICBM horizontally?

Sure! Why would you want to?

We learn from here that it's not just deceleration, but the time during which a body is exposed to the deceleration. So, we either need a lot of acceleration for a short period of time or a little bit of acceleration for a long period of time. So, assuming some averages and guessing a little bit, we need either 5G for 60 seconds or 50G for one second.

Reference scenario:

• Your ship and my ship are indestructible.

• According to Wikipedia a fully-loaded Nimitz-class air craft carrier has a mass of approximately 91.8 million kg. When you really think about what it would take to move a ship and cargo/weaponry through space, I think this is a great starting point. So, the mass of both ships (for convenient math) is 10⁸ kg.

• We're sub-light. Let's assume 0.1c or about 30,000,000 m/s. The target ship is gliding at that velocity. So, kinetic energy = $\frac{1}{2}mV^2$ or $45e^{21}$ joules.

• My ship is already nose to nose with your ship. And I turn on my engines to accelerate at 5G for 60 seconds. Everybody's dead, but let's ignore that for a moment.

$$F=mA$$

So I just applied 16 billion newtons of force for 60 seconds for 960 gigawatts of power. You need to create that much power in friction with, I'm assuming, some agent (like sand) that you're carrying with you. Here's your problems:

1. We started with an opposing mass equal to the oncoming mass. If you're going to use a disposable mass (i.e., you want to live through the encounter), then you need to either bring that much mass with you (that's your 10⁸ kg ship hauling a 10⁸ slug with it) or you need to be traveling in the opposite direction with a velocity higher than your opponent's (how much higher depends on how much mass you can haul with you). Since kinetic energy scales by the square of velocity, if you can move against your opponent at the same initial speed (a total of 2X delta-V) then you can haul 25% of the mass. But that means you're moving at 0.2c (in my example).

2. Remember our stipulation that the ships are indestructible? Author Larry Niven circumvented some unpleasant realities in his stories by declaring that General Products hulls were indestructible ("an artificially-generated giant molecule, with the inter-atomic bonds artificially strengthened", causing the hull to resist "any kind of impact, and heat in the hundreds of thousands of degrees." C.F. Flatlander). If that's OK with you, it's OK with me, but if your ships are destructible, then a 5G deceleration for 60 seconds would be devastating. Remember, the back end of the ship wants to decelerate more slowly than the front end. That's the reason cars that hit walls look like crushed beer cans.

3. Friction causes, among other things, heat. Some of the kinetic energy lost through deceleration will go to pushing away the mass that's in your way. But some of it will be converted to heat. A lot of heat.

Now, to be fair, fighter jets capable of 9G turns don't burn out like an old flash bulb — but they're not sustaining 9G for 60 seconds, either. Nevertheless, one would hope that issues #2 and #3 were part of the design process for the ship.

BTW, there isn't a lot of difference using the second deceleration speed (50G for 1 second). It's about the same amount of force. The biggest difference is how much you need to spread the mass out (along a path of 1.8 million km or 30,000 km).

So, the real problem is issue #1

Can you slow a ship down via friction such that only the crew dies? Yes. Is it practical? No.

• You need to haul either mass equal to the mass of the target ship, or be traveling substantially faster than the target ship. It's a trade-off.

• At low-A, you're forced to depend on your opponent's reaction time. In my example, 60 seconds is a long time and your opponent can "pull up" and exit the debris field. If you're bringing enough debris to keep that from happening, you're substantially increasing the amount of mass you're hauling.

• At high-A, you're forced to depend on really accurate timing to drop the load. You get one shot, then you're a month turning around (and have to go pick up another load of sand).

One more thing...

Before we leave, note that there's two ways to look at this. One is the pirate ambush where they happen to see the target ship and act to go get it. That's unlikely given the size of space and the speeds involved. The other is the planned attack where you know your enemy's path before the attack and can lay a trap.

Why am I mentioning this? Because the friction idea is a one-off solution. You get one chance. Then you're out of abrasive material (or you're hauling so much that you're a big, slow whale that's easy to out-accelerate or really easy to lob missiles at). There's also the question of just how far ahead (in time) you can detect an incoming vessel? Lots of ugly in that situation.

But as a planned attack where the target's path is known... then you have the time to spread out the abrasive — and the longer the field the better as it would be harder (lower mass-per-cubic-meter) to detect (theoretically, there's some arguments to be made here). This is the Titanic-hits-the-iceberg solution. And in this case, I think it's a cool story/world idea.

Answer 3

Throwing something in their way would create more of a problem owing to their hitting something at such high speeds than through deceleration, though the deceleration itself.

The use of water as such a danger has been exploited as a plot device by such writers as Larry Niven and David Brin. (Owing to its apparent innocuousness, and its ease of transport in dense form, and piping out when needed.)

To actually get only deceleration damage, you would have to put the danger out far enough that they can detect it, but only far enough that their options to avoid it are limited to hard deceleration.

Answer 4

TL;DR You need to bring a 17 km/s ship to a complete stop in 0.035 just under 35 seconds to kill the crew.

Most space ships are actually pretty fragile, and bumping into something could be very bad. A google search shows that the minimum thickness of the ISS, which although probably is not the best answer, is 4.8mm. Even if you had this deceleration technology, it would probably be much easier to poke it with a needle and let the air drain out, killing all the crew inside and leaving the cargo a little cold but mostly okay.

Anyway, severe deceleration COULD work, but it would have to be pretty fast deceleration. If your target ship is going too fast, it could end up destroyed and then your speed bump is pointless because you can't capture the cargo. You say you want it to incapacitate the enemy crew, which I interpret as 'dead, unconscious, or unfit for combat', but that's just me. One thing you might run into is that you need to stop them really quickly. Car crashes and drag races have severe deceleration, and most of the time the people are alive, and mostly in the case of drag races, people are up on their feet relatively quickly. But this is SPACE, there is no gravity, so even if their legs are broken, they can grab a rifle and hold onto a wall. To have an effective stop sign, you need them knocked out or dead, which will be hard to do without breaking the ship unless it is designed for getting punched around or your world just has really strong ships for no reason.

But let's say the ships is immune to breaking, then we need to stop it quickly. If we assume your craft is going the same speed as Voyager, then it's going 17 km/s, or just over 38,000 mph. This is way faster than a car could ever go, so you can't exactly test the point where you black out or die. The most gs anyone has taken before is about 42 gs, but your crew is probably trained for this so we can round up to 50 gs. So let's see how fast we have to stop to get to 50gs!

So let's work backwards from 50gs. I'll be using metric, so we multiply by 9.8 m/s to get 490 m/s as the deceleration we need to get. Now we need a start speed, end speed, and time it takes to slow down. As said before, I'll be using 17 km/s for initial speed, and for an end speed I'll use 0 km/s so we bring it to a complete stop. Time is the variable we'll be changing until we get the desired result. After I did some calculations, time ended up being about 0.035 just under 35 seconds to get 490 m/s deceleration. How you stop it is up to you, this is how long you have to stop it if you want the crew incapacitated.

I know this is kind of a half answer, but my knowledge as to HOW it would be stopped is none, and I just googled most of this stuff here. You should probably check this yourself in case I did something wrong, but I'm pretty sure this is right.

Answer 5

I'm going to point out — because no one else has mentioned it — that a conventional 'speed bump' doesn't decelerate a car at all. A speed bump introduces an extremely unpleasant vertical motion: one orthogonal to the direction of travel, but proportional to the speed of movement. Cars decelerate because drivers want to avoid that jolt, not because the speed bump does anything to slow the car itself. One can drive over a speed bump at 60mph if one wants, and it won't slow the car; it will just make the car buck like a bronco, and give the passengers a taste of free fall for a second or two before the front end crashes down.

With that in mind, it might be wiser to consider a precision orthogonal push — a kind of space PIT maneuver — designed either to send the craft into a spin (push aimed at the head or tail), or jolt it severely sideways (push aimed center-of-mass). This could be done with jets of water of gas, possibly with a magnetic field, but the point would be to force the pilot to decelerate as soon as he is aware of the 'bump' in order to keep control of the craft. I'm sure someone else can work out the maths; I'm not up to it today.

Answer 6

Yes, a Speed Cloud made of sand

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Disclaimer: Answering my own question for reference purposes, but accepted answer came up with a better setup. This answer relies on the spaceship having enough hull strength to survive hits from grains of sand.

If we assume that the sand won't pulverize the hull (as by ensuring they are in a cloud, rather than a condensed block), we still have the question of whether the actual deceleration can be done with a reasonable amount of sand. From some resources and inspirations from other answers we can do some calculations:

Assuming a very normal space shuttle, moving at about 15,000 m/s (1/20,000th the speed of light), weighing in at 120,000kg.

It hits a 4000kg block of material of similar density to water, say, sand, which is 40% denser spread into a cloud. The sand would be very easy to store, fitting into a condensed 1.4x1.4x1.4m cube when not in use.

We throw this into a conservation of momentum calculator:

The important point to look out for is the delta-v for the spaceship, sitting at 500m/s. From the resource provided by @JBH, 50gs in one second, or 4-6gs in more than a few seconds is enough to kill most people. For reference, car crashes take fractions of a millisecond for delta speed change for objects equal in weight, but even if we assume it takes a much, much longer length of 5 seconds, we arrive at 10gs of deceleration over 5 seconds, or 50gs over an entire second, enough to kill pretty much any human. (Thanks @NuclearWang for pointing out the previous mistake in calculating G's).

Essentially, a cloud the width and height of the space ship (6m), stretched over the length of 0 to 1 to 5 seconds of travel or less (~0-15km-75km) should be enough to incapacitate the crew.

If we assume a massive ship maintaining a slow 15,000m/s, it will take no more than 3400 cubic meters of material, being stored in a 14x14x14 meter cube. It can be seen than the amount of sand needed scales linearly, due to momentum transfer being the considered factor in delta-v.

Thus, a collision with a cloud made up of a mere few cubic meters worth of sand is enough to kill most spaceships' crew members with deceleration alone.

This means that by using a cloud of sand, or a 'speed cloud', we could avoid destroying the spacecraft as long as the sand is not in large clumps. By using a cloud, the deceleration will happen along the entire front surface of the spacecraft coming in. This would cause less damage to the spaceship itself, but still be enough to lethally injure the crew with the decelerating force alone.

Answer 7

I am going to go way off on a tanget in this answer.

It seems to me that what you are after is some form of 'friction in space'. That is, something that will slow down the ship without actually impacting with it. Like a boat going through water, where the water changes density (through, say, seaweed), or a car changing from the road to sand. Not a speed bump (that would take a sudden strong and very local change in gravity), but a sand trap.

But space has no friction.

Except that it does.

The Higgs Field is so new, that it has not yet infiltrated sci fi writing. We just don't know enough about it, so it isn't used, or even speculated on. We use every other field (EM, gravity, for instance) but not the Higgs Field. This field has been described as a sticky field that gives everything inertia, and is present everywhere in the entire universe. It also seems to be uniform in 'density' throughout the entire universe. Makes it hard to get going, hard to stop, but when it is going at a constant speed, it offers no resistance. Since there is essentially no such thing as something having 'absolutely no velocity', the Higgs Filed is actually influencing everything, inertia wise, except that it exhibits its effect only on changing velocity.

So here's the thing. What happens if either the Higgs Field, or the number of Higgs bosons, changes in density? It would be like trying to accelerate or decelerate an object. In fact, I posit it would cause acceleration or deceleration, if inertia changed. If somehow a weapon is designed that can modify the Higgs Field by, for instance, creating a blockage of a huge number of Higgs bosons, then anything entering this altered area would experience a dramatic change in 'inertial resistance'. It would be like a car changing from driving on a road to driving on sand. The spaceship would experience sudden deceleration, without actually hiting anything. As long as the ship could withstand the inertial change through inertial dampening, it would be relatively unscathed. However, if the g forces created by deceleration were great enough, the humans would suffer very substantial effects, due to changes in blood and bodily fluid flow, load on the heart, probaly suffer embolisms and blood clots from pressure changes, and probably even concussions.

This is not hard science, but it is certainly speculative science, within the realm of what is known about the Higgs Field, with a bit of handwaving.

Answer 8

I think you're overthinking this.

Lets take a simpler weapon: A spacegoing "mine"--it's a missile that doesn't try to go after it's target, just tries to get in the way. (Think of the goalie in soccer.) They're seeded around in space, if they sense (or are told about) an enemy ship that's going to pass close enough they get in front and stay there if it tries to maneuver.

All of the deceleration will be delivered at once, producing the maximum damage for the mass involved. Nothing gets wasted being too far to the side--any mine that's too far to the side remains a functional mine and can engage another ship or be picked up and moved at a later date. It will also punch through far more armor than any of the light things you are thinking of.

Assuming your ship (120,000kg @ 15,000m/s), a 100kg mine half a meter across I get a peak deceleration of 45 GN--for a tiny fraction of a second you're looking at 38,239g. If you're in a General Products hull you're very, very dead, with something more sane the ship is going to flex it's as if you fell 8 meters on Earth. Not a certain kill but the crew is definitely not functional at that point. You also have a boom equal to 2.5t of TNT (but far more destructive as the energy is entirely directed inwards.)

This will be a much more effective weapon than any small dispersed matter. Furthermore, dispersed matter is the equivalent of WWII torpedoes--defeated by zig-zagging.

Answer 9

Edit Frame Challenge:

In comments moved to chat, the OP insists that a "stationary" object is the answer to crippling a crew, but keep the ship intact. It is argued in the question that it's not astronomically impossible for some ship to wander into this trap without it being completely massive in size. It is also assumed that a 15k m/s hit isn't going to completely destroy a ship.

Space is so large that 2 ships being in the same solar system and notice each other is pretty low on the probability scale, unless it's a known inhabited system. Having a "sand trap" of any material or sized particle would have to be massively large. It would be so large that it wouldn't be economically feasible to make it happen. And if it was done in an inhabited system, whatever authorities that happen to be around would either try to warn ships away from it or try to clean it up.

As for the forces involved in a 15k m/s hit, a hit of 1 ton of material, even in 3g pellets, would have a 10^11 Joule force impact. That would completely shred nearly anything. A kiloton of TNT is 4.184×10^12 J, but most of that is dispersed away from the target. Think about that being a shaped charge where only 10% is against the hull of a ship. That's a massive amount of force for a ship to be built to handle. And 1 ton of material is a tiny fraction of the material needed to make a trap like this.

And because it's so large and has so much mass, any reasonable ship is going to have sensors to notify the crew to avoid that part of space.

Unfortunately, this "stationary speed bump" idea just doesn't hold water. There are just too many reasons why it won't work, and that doesn't even get into celestial mechanics or gravitational effects by nearby planets or other bodies. It also ignores the gravitational effects of itself, if it's supposed to be a distributed mass of small particles. And a liquid like water would either freeze or sublimate, so that changes how it impacts the ship, but not it's ability to be detected by ship sensors.

The OP should reconsider the question frame to be more feasible in terms of real physics and astronomical laws.

End Edit.

What you and most of the other Answers are thinking about are on the order of depth charges. These are thing that hit the target and either do direct damage or try to slow down the vessel. There's a couple of problems with that.

The first is that an exploding device would have to be fairly close to do damage when it detonates, as only the shrapnel and some gasses are expelled, which dissipate fairly quickly in a vacuum and don't propagate a blast wave. And even with a lot of shrapnel and a large explosion, it would have to be a significant percentage of the target vessels force to have any real effect to slow it down. Even a nuke might not have enough power to slow it down, unless you also want to rip apart the vessel.

The second problem is the difference in speed of the vessel and the material launched at it. In order to make much difference to the pursuing vessel, you have to eject the mass at a high speed, otherwise it's just floating between you and them in a relative lack of motion. There's no wind to slow it down for you, so you have to do it yourself. And that might include explosives, which could damage your own vessel. Just letting decompression happen likely won't be enough, nor will it likely keep things concentrated enough to mean much. And when you run out of material, explosives, or air, you don't have any defense left.

Part 2 of the second problem is that if you launch material at a following vessel is that you are also launching yourself forward at the same force. Since you are trying to force your pursuer to slow down drastically, you are also speeding up drastically. Sure, the mass of each vessel depends on how much each happens, but a large vessel probably doesn't have much to fear from a smaller vessel in interstellar distances.

Part 3 of the second problem is the fact that the following vessel isn't likely to be following directly behind, so the force of this mass hitting them will need to much higher, or it'll only cause them to be off course, rather than slow them down. Also, they will be able to dodge the mass, unless the mass is spread out, which means even more mass is needed to slow down the chasing vessel. This gets mass-expensive fast. And with the chaser being not behind you, you'll still need a computer to calculate trajectories to make every hit at least try to count.

Besides all that, the equation for kinetic energy is weighted for velocity to matter more than mass. KE = 1/2 mv^2 What this means is that if you double your mass, you double your force, but if you double your speed, you quadruple your force.

https://www.calculatorsoup.com/calculators/physics/kinetic.php

Let's do some math. Here's some simple examples:
M = 1, V = 1; F = 0.5
M = 2, V = 1; F = 1
M = 1, V = 2; F = 2
M = 2, V = 2; F = 4
M = 4, V = 2; F = 8
M = 4, V = 4; F = 32
M = 10, V = 10; F = 500
M = 20, V = 10; F = 1000
M = 10, V = 20; F = 2000
M = 20, V = 20; F = 4000

I showed this without units, since that doesn't really matter at this point. As long as you use the same units, the differences are still the same. (If you just can't get past the whole "unitless" comparison, the mass is kg, the velocity is m/s, and the KE is Joules.)

So what does this mean? Use high velocity, small mass rounds to try to slow down your adversary. Sometimes these are called railgun rounds, but these usually do more damage directly than actually slowing down someone. Also, you're still having to deal with Problem 2.2, which is Newton's Third Law of Motion.

https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion