Space combat: how big is an inch, how long is a turn?

[bigdamnhero]

A spinoff from the "It's almost 5AM..." thread:

 

According to TE, the Empress-class Battleship has a maximum sublight speed (non-combat) of 504" per turn, which translates to a not-exactly-stellar 190mph. At that speed, it would take 52 days to travel from the Earth to the moon. In fact, since it's 250" long, it can only cover it's own length twice per turn.

 

Obviously, that doesn't compute. I know SH says "GMs may wish to establish that each hex on the map is larger than 2 meters," but there's nothing in TE or AW (that I can find) specifying what the "official" scale is for those settings. Is there any kind of "official" ruling? Whether there is or not, what do most folks use? Or do you even worry about it?

 

Related question: do you mostly use mapped or unmapped (intercept?) combat for space combat?

 

 

bigdamnhero

[Zeropoint]

Re: Space combat: how big is an inch, how long is a turn?

 

The solution I'm going to be using is to give all spacecraft infinite Non-Combat Multiplier on their main engines for free. Ships with more inches of flight will have better acceleration and be able to move faster while maintaining combat readiness, but any ship can accelerate as much as it wants to, given time.

 

I'm using a reactionless drive, so reaction mass consumption isn't an issue.

 

Also, I'm goint for a moderate space opera flavor, so scientific rigor isn't my top priority.

 

Zeropoint

[bigdamnhero]

Re: Space combat: how big is an inch, how long is a turn?

 

The solution I'm going to be using is to give all spacecraft infinite Non-Combat Multiplier on their main engines for free. Ships with more inches of flight will have better acceleration and be able to move faster while maintaining combat readiness' date=' but any ship can accelerate as much as it wants to, given time.[/quote']

That makes sense to me. But it's not quite the question I was asking. When ships get into combat, how far apart are they? Meters? Kilometers? Light-seconds? Do battles last seconds, minutes, or hours?

 

Also' date=' I'm goint for a moderate space opera flavor, so scientific rigor isn't my top priority.[/quote']

Understood - it's not mine either. But I like to have at least a general idea of how such things work. And the combat system had better make some kind of sense or my players will howl. Sooner or later, someone's going to ask "What scale are we using here?"

 

 

I tried running some different numbers, ignoring Flight speed and just looking at acceleration. If we take the SH guideline of 5" of flight equals 1G of acceleration, then the Empress-class (42" flight) can pull 8.4 Gs. After 1 hour of full accel, it would be up to 296 km/s, and would have travelled 533,000 km. Assuming 8.4 Gs accel for half the trip, then 8.4 Gs decel for the second half (starting and finishing at 0-velocity) the trip from Earth to the moon takes about 50 minutes; Earth to Mars would take 10 to 28 hours (depending on relative orbital position) and Earth to Pluto would take 4 or 5 days, with a max velocity (at midpoint) of 12% lightspeed. Not too shabby.

 

[Edit: Actually according to SH the 5” flight = 1 G rule is by segment, not by phase; 1 G is really 60” per turn. Using that calculation, the Empress IBV’s 42” of Flight and 3 SPD calculates out to just over 2 G, or 8 G at (x4) non-combat speed.]

 

 

bigdamnhero

"Bye bye, boys! Have fun storming the castle!"

[Cancer]

Re: Space combat: how big is an inch, how long is a turn?

 

Doing spaceship combat "right" is going to be a difficult thing. You not only have to define how the ships behave, you have to define how the weapons behave, and what defenses the ships have (other than avoidance).

 

Then you need to examine in terms of your game world where spaceship combat is likely to take place, and what that means with the interstellar drive handwave you are using.

 

For example: If combat can only happen at sub-light, but the technical circumstances and strategic situation means that combats will only happen in places where the ships can activate their interstellar drive at will, then combat will generally be bloodless, as any captain with any sense will realize he's about to be hit, and jump out before the warhead arrives, unless ship defenses are capable of handling approximately any attack.

 

Edit: gah, what a horrible word -- the "be" above -- to have left out.

 

Lasers/any "realistic" energy weapons always propagate at c, so you can't see them coming, but they also follow precisely-defined trajectories (literally, they follow exactly the line of sight). So anything that blocks light will block the laser (once, anyway).

 

It may be, given your assumptions about interstellar travel, that spaceship combat is more or less impossible except in strategically implausible situations. It's your job to work that out.

[Zeropoint]

Re: Space combat: how big is an inch, how long is a turn?

 

One thing that's always bugged me about cinematic space combat is that the ships are frequently fighting from a distance of two or three ship-lengths. That's just silly--early twenty-first century ship-to-ship weapons have ranges from several miles to several dozen miles, and cruise missiles can reach about a thousand miles.

 

I haven't thought it through completely yet, but I figure that point defense systems will have a range of several kilometers, magnetic acceleration guns an effective range of maybe fifty to a hundred kilometers, limited by the ability to predict target motion, and particle cannons, with relativistic beams, will be able to reach out and touch someone at hundreds or even thousands of kilometers.

 

Missiles and torpedoes will be much, much slower than particle beams, but their ability to guide themselves will potentially allow hits at longer ranges.

 

 

 

What space combat will look like is heavily dependent on the relationship between effective weapon range, detection range, and ship speed, as well as how many shots it takes to bring down a ship.

 

I realize that I don't really have a lot of helpful suggestions here, but this isn't something that can be reality checked. I suppose you'll have to decide what you want space combat to be, and design the technology to support that.

 

Zeropoint

[bigdamnhero]

Re: Space combat: how big is an inch, how long is a turn?

 

One thing that's always bugged me about cinematic space combat is that the ships are frequently fighting from a distance of two or three ship-lengths. That's just silly

Yup. In movies & TV it's a necessary evil because you have to fit both ships on the screen. But in RPGs it makes no sense.

 

I realize that I don't really have a lot of helpful suggestions here' date=' but this isn't something that can be reality checked. I suppose you'll have to decide what you want space combat to be, and design the technology to support that.[/quote']

Absolutely. I was just curious what other folks were doing.

 

 

bigdamnhero

“This is the kind of conversation that can only end in a gunshot.â€

[Jaxom]

Re: Space combat: how big is an inch, how long is a turn?

 

Simple answer to why you don't fire at long ranges.

 

In space there is no ability to predict where something will be a few seconds later unless you enforce some pretty strict limits on inertial motion. This goes back to the question I posted in the prior thread... Where can you provide thrust from? Do you have steering jets? Do you allow complete reversal of thrust from the main engines?

 

The simplest answer is to calculate flight time of the projectile, then calculate the acceleration potential of the target over that time and create a sphere of that size and say "the target could be anywhere in this sphere depending on his heading and acceleration".

 

If you're talking a ship that is 100 yds long and accelerates at 3Gs which is 60 kms (chosen to simplify the math) away and you fire a bullet at it at 3000 m/s (again, using typical muzzle velocity from a modern rifle). Then your projectile is travelling in a straight line for 20 seconds. Assuming that the target registers that you fired 10 seconds later and can then fire full thrust in any direction, it will travel 1/2*a*t^2 yds off of it's current path (i.e. where you aimed). At 3Gs that's 1/2 * 32 yds/s/s * 10s^2 = 1600 yds. In other words, your target can have travelled 16 times his own length in half the time it takes your projectile to get there.

 

Even if you up your projectile speed to incredible levels (say a rail gun provides 10,000 m/s velocity instead of 3000). You still get a travel-time to target of 6 seconds. How much of that are you going to allow your target to be thrusting to get off your line of fire? And can he use full thrust or not?

 

Heck, he doesn't even have to turn, all he has to do is turn his engines on or off at will and you cannot predict where he will be with the accuracy needed.

 

 

Laser weapons work better because they travel at c which means no time for the target to react and a direct hit on a target at up to 300,000 kilometers away in a second. Of course, pointing then becomes an issue. At 60 kilometers, a ship 100 meters in length presents a target of less than 1/10th of a degree which means that you need some pretty amazing targetting systems (not to find the line, but to swing a gun to that line and stop it exactly on that line). Put it this way, we can point telescopes with that kind of accuracy but it takes us a few minutes to line them up. Also, if you have any motion relative to one another, your target is only good for the fraction of a second that it takes you to move 100 meters relative to him, then your angle is wrong again.

 

 

There's a reason that early in the Russian space program they fired a rocket at the moon and were ecstatic that they actually hit it. And that is a target that you can pretty much predict won't change course.

[Jaxom]

Re: Space combat: how big is an inch, how long is a turn?

 

Oh, and I forgot to mention that your best reason for limiting the amount of thrust allowed is that the humans inside the tin can turn into paste at accelerations of about 8G. Either you're putting some kind of anti-inerta field around the ship or you are limiting your acceleration drastically. In addition, if you *are* using some kind of anti-inertial system and expect combat, you're carrying at least two spares because if for some reason you lose that anti-inertial system, the first time you change course you are back to the fine red paste lining the inside of your spaceship. (You can continue on course with no changes without problems, but see the prior post for why that might be a bad idea. You immediately become *very* targettable.)

[Zeropoint]

Re: Space combat: how big is an inch, how long is a turn?

 

For the record, a typical modern rifle muzzle velocity would be more like 3000 FEET per second.

 

Even so, it's quite obvious that projectile weapons, despite having an infinite range in space, will have a sharply limited effective range.

[Nyrath]

Re: Space combat: how big is an inch, how long is a turn?

 

The simplest answer is to calculate flight time of the projectile' date=' then calculate the acceleration potential of the target over that time and create a sphere of that size and say "the target could be anywhere in this sphere depending on his heading and acceleration".[/quote']

Absolutely!

 

The equation I found was:

H = C/(78.54 * A^2 * (D/150,000)^4)

where:

H = maximum percent chance to hit target given light-speed lag(0.0 - 1.0)

C = target ship's mean cross section (m^2, for a purely convex object this is 1/4 of the surface area)

A = target's acceleration (Gs)

D = range to target (km)

 

http://www.projectrho.com/rocket/rocket3x.html#laser'>http://www.projectrho.com/rocket/rocket3x.html#laser

 

The thing most people do not realize about missiles is that if a ship's propulsion system can be scaled down to missile size, the missile will have equal or greater endurance of the target ship. If the target ship can travel all over the solar system so can the missile. This is because the missile can devote a greater percentage of its total mass to fuel than can a manned spacecraft. Unlike a missile, the spacecraft needs to devote part of its mass percentage to life support, habitat modules, and all those other things needed to keep those weak human beings alive.

 

This means that you cannot out-run or wear out a missile. Unless you kill it with point defense, the missile will eventually catch up with you and blow up on your ship.

 

Notes on space war

http://www.projectrho.com/rocket/rocket3t.html

 

Detecting enemy ships

http://www.projectrho.com/rocket/rocket3w.html

 

Weapons

http://www.projectrho.com/rocket/rocket3x.html

 

Defenses

http://www.projectrho.com/rocket/rocket3y.html

 

Tactics

http://www.projectrho.com/rocket/rocket3z.html

[Outsider]

Re: Space combat: how big is an inch, how long is a turn?

 

A ship might have to cary life support, habitat and other things for the fragile human crew, but a missile generally carries some sort of warhead, so that might be a wash, capability wise. Missiles might also tend to carry a higher percentage of their mass as engine, in order to have superior accelleration so that they can quickly catch up to their intended target, and they might also carry a higher percentage of their mass as defensive systems so they dont get shot down on their way. And if ligfe support vs warhead is a wash, those last two advantages will come at the expense of fuel/energy reserves, reducing the range of the missile.

[Nyrath]

Re: Space combat: how big is an inch, how long is a turn?

 

Maybe, but it is easy to argue either way. Generally the only defensive system a missile carries is maneuverability. Unlike spacecraft, missiles do not have to return to base, so they have effectively four times the fuel capacity.

 

(Say the base is at point A, and the mission is at point B. A spacecraft need fuel to {1} accelerate to cruising speed to travel to point B, {2} decelerate to a stop at point B, {3} after the mission accelerate to cruising speed to return home to base at point A, {4} decelerate to a stop at point A. That's four fuel segments.

 

A missile with the same mass-ratio of fuel can use all the fuel to accelerate to cruising speed, reserving only enough to maneuver and hit the target. In other words, it can use all four fuel segments for stage {1} )

 

My point is that since one can argue either way, in lack of hard performance numbers it seems likely that some missiles will have inferior range to spacecraft, but some will have superior range.

[Outsider]

Re: Space combat: how big is an inch, how long is a turn?

 

True. Of course, guidance might be a problem if the missile is too far from the ship that launched it. A missile wont have much of a sensor rig of its own, being small and disposable. That may not be an issue, though, if the setting says that star drives (even when not in use) put out a big, hard to disguise signature that can be detected with a small apparatus.

 

As for the defensive systems carried by a missile, yes, their primary defence would be their manuverability and small size, but they could also carry jammers, decoys, or even a short duration force field to cover them just during their terminal approach.

[Ben Seeman]

Re: Space combat: how big is an inch, how long is a turn?

 

Space nukes (at least in TE) are built as vehicles with an onboard computer that includes tracking sensors and ECCM. This IMO creates a more realistic view of how missiles behave in "reality".

[bigdamnhero]

Re: Space combat: how big is an inch, how long is a turn?

 

The simplest answer is to calculate flight time of the projectile' date=' then calculate the acceleration potential of the target over that time and create a sphere of that size and say "the target could be anywhere in this sphere depending on his heading and acceleration".[/quote']

Another possibility might be to just saturate the sphere with enough projectiles that the question becomes not if but how many hits you get, and what part of the ship they damage. Not the most elegant solution, perhaps, but sometimes brute force does the job just fine.

 

 

bigdamnhero

“Damn you! I'm not an actor, I'm a movie star!â€

[Nyrath]

Re: Space combat: how big is an inch, how long is a turn?

 

Another possibility might be to just saturate the sphere with enough projectiles that the question becomes not if but how many hits you get' date=' and what part of the ship they damage. Not the most elegant solution, perhaps, but sometimes brute force does the job just fine.[/quote']

At least until you run out of projectiles...

[bigdamnhero]

Re: Space combat: how big is an inch, how long is a turn?

 

At least until you run out of projectiles...

I didn't say it was a perfect solution.

 

Still, with sufficient launch velocity and dense enough materials, you don't necessarily need a terribly big projectile. I would think a ship the size of a Star Destroyer could carry a lot of ball bearings.

 

 

bigdamnhero

“You can't expect to wield supreme executive power just because some watery tart threw a sword at you!â€

[Cancer]

Re: Space combat: how big is an inch, how long is a turn?

 

Another possibility might be to just saturate the sphere with enough projectiles that the question becomes not if but how many hits you get' date=' and what part of the ship they damage. Not the most elegant solution, perhaps, but sometimes brute force does the job just fine. [/quote']

 

Quite true, but questions about tactical options should come after you've settled questions about technology and the most likely strategic situations.

 

There's lots of instances of people choosing what they want spaceship combat to look like purely from their own preferences, ignoring the physics/technology/economics/strategy of the rest of their game world. In fact, approximately all space combat games that I know about are this way.

 

X-wings and TIE fighters are essentially WW2 airplane combat, even though that's absolutely absurd physically; it's just a cinematically cool flavor, that's all. I can imagine someone having a similar emotional attachment to, say, 18th-Century sea warfare, and then your space combats would look like yardarm-to-yardarm broadside exchanges between ships of the line, even though that may make absolutely no sense in terms of the rest of the game-world.

 

Probably one could rationalize a situation where space combat looked like the trenches of 1916, too, but I somehow doubt that gets many other people interested in the game.

[Jaxom]

Re: Space combat: how big is an inch, how long is a turn?

 

Cancer and I were talking about these threads last time we sat down to throw dice in anger (Tuesday night, it was) and there are some very important things to consider that are kinda being glossed over here...

 

He's already made reference to this elsewhere, but it bears repeating (over and over and over). The environment and physics that you have claimed for your universe will have incredible impact on the way combat occurs in your system. What mechanism for FTL do you use? Can it be used near a planet? In atmosphere? Does it require accelerating to some large normal velocity before turning it on?

 

Most ideas have already been covered in books so you can find something of interest out there somewhere I am sure. I've seen combat described as ships shifting in and out of real-space randomly and firing off patterns of proximity mines while in real space with the net result that there was almost no real-space movement and the area around the tactical goal was so littered with mines that it was unsafe to approach in real-space.

 

I've seen universes where space combat was non-sensical because FTL could occur from in-atmosphere (the hyperspace shift method).

 

I've seen universes where space combat was common because FTL was limited to specific paths way out beyond the Oort Cloud and therefore everything had to enter system (and approach tactical points) by sub-light drive which allowed tactical action.

 

 

So what does your physics say about how you can approach your tactical targets?

 

 

Now, what other tech might have bearing? Do capital ships have so much armor that only captial-class armaments can harm them? Then ignore fighters and bombers. Can a bomber carry a weapon capable of harming a capital ship? Does it have the range to fly safely? Do you want small craft to swoop and dive like planes or to behave like they are in zero-G?

 

All these questions need to come before you worry about how you want to handle combat. Anything else means that you risk your players asking why they are not handling a situation some other way and you risk being short-circuited before you get started.

[bigdamnhero]

Re: Space combat: how big is an inch, how long is a turn?

 

Quite true' date=' but questions about tactical options should come after you've settled questions about technology and the most likely strategic situations.[/quote']

You and Jaxom both make excellent points, and I agree with you about most portrayals of space combat being anachronistic (to put it charitably.)

 

However, it's also perfectly legitimate IMO to do it the other way around: decide what you want space combat to look like, then figure out a technology mix that supports it. I'm not a theoretical astrophysicist, nor do I play one on the Internet. I'm a story-teller. I figure out what kind of stories I (and my players) want to tell, and then speculate about what sort of technology, etc, will support those stories. If I want players voyaging to other worlds in a reasonable length of time, well then I'd better dream up some sort of FTL. If I want individual characters to be able to influence the outcome of events, then I'd better make sure technology doesn't totally overshadow their actions. Are either of these assumptions "realistic?" Does it matter, as long as they lead to an enjoyable game? (Given that most of this board is dedicated to discussing spandex-clad vigilantes throwing cars at one another, how much “realism†do we really need here? )

 

Similarly, if I decide I want space combat to be a part of the game, then I’d better make sure “my†technology supports this. If I don't want ships to be able to just FTL out to avoid action, then I might establish that FTL doesn't work within a star's gravity well. Or if I want to have space pirates preying on established shipping lanes, then I might decide that FTL only works between established points. If I want fighters, I’ll design my fictional-physics accordingly. If I don’t want fighters, I’ll design my fictional-physics accordingly.

 

Don’t get me wrong: I absolutely agree with you that technology and tactics are firmly intertwined, and that the one should influence the other. I’m not suggesting we throw physics out the window here. (As I’ve stated, I prefer vector-based movement to atmospheric movement.) And I'm certainly not trying to play "my future is more believable than your future." I was just wondering what other people have come up with, particularly in terms of scale, to make their space battles playable, plausible and fun. (Not necessarily in that order.)

 

I can imagine someone having a similar emotional attachment to' date=' say, 18th-Century sea warfare, and then your space combats would look like yardarm-to-yardarm broadside exchanges between ships of the line [/quote']

Actually, that's almost exactly what David Weber did with the Honor Harrington series. Not what you'd call Hard SF, to be sure, but it makes for a fun read. And the techno-babble is consistent enough to explain why it works the way it does.

 

 

bigdamnhero

"The use of unnecessary violence in the apprehension of the Blues Brothers...has been approved.â€

[LoresLost]

Re: Space combat: how big is an inch, how long is a turn?

 

The simplest answer is to calculate flight time of the projectile, then calculate the acceleration potential of the target over that time and create a sphere of that size and say "the target could be anywhere in this sphere depending on his heading and acceleration".

 

I looked at that and had to make a comment about this... assuming no miracle engineering such as inertialess drives, you can determine current direction, acceleration and speed with in milliseconds (real life device example - air combat radar) and your sphere quickly becomes a cone, and depending on your speed and acceleration that cone becomes very tight vector.

 

Targeting is then just a matter of trianglation on the most likey point of contact.

 

You would need to figure out in your Universe how in general FTL and normal space drives work if you want space combat. Inertia-less drives or more realistic fair for normal space.

[bigdamnhero]

Re: Space combat: how big is an inch, how long is a turn?

 

I looked at that and had to make a comment about this... assuming no miracle engineering such as inertialess drives' date=' you can determine current direction, acceleration and speed with in milliseconds (real life device example - air combat radar) and your sphere quickly becomes a cone, and depending on your speed and acceleration that cone becomes very tight vector. [/quote']

I assume he's talking about a sphere not from where the ship started it's move, but from where it would be in "x" seconds if it applied no thrust. In other words, he's not plotting the ship's movement -- which you're right, would look more cone-like -- but the sphere at the cone's end.

 

(Sorry if I put words in your mouth, Jaxom.)

 

 

bigdamnhero

"I understand the inventor of the bagpipes was inspired when he saw a man carrying an indignant, asthmatic pig under his arm. Unfortunately, the man-made sound never equalled the purity of the sound achieved by the pig."

-Alfred Hitchcock

[Beast]

Re: Space combat: how big is an inch, how long is a turn?

 

continous beam weapons

or a beam that lasts 2 to 4 seconsds(speeds 3-6)

with that length of time how much of an arc could you swing the weapon

 

modern jet fighters(F-14,15,16,18) all have a gun sight mode that projects a line that a 1 second burst will cover

If the target is touched by the line then some bullets will hit it( at 3000 rnd per min that is a burst of 50 rnds but it might only be hit by 5 rnds

your working on the assumtion that all the energy will hit the target and will be needed to damage it

where a beam weapon may be x100s as powerful but usually hits with only 1percent of the beam (effectively the same damage)

so you have the limitation of full phase to use a weapon

in 3 seconds(spd 4)you could have a beam weapon do a outward sprial(closing ot chasing target or a zig-zag w for a crossing target wWwWwW that creates line of death that the fighter's HUD creates

 

Simple answer to why you don't fire at long ranges.

 

In space there is no ability to predict where something will be a few seconds later unless you enforce some pretty strict limits on inertial motion. This goes back to the question I posted in the prior thread... Where can you provide thrust from? Do you have steering jets? Do you allow complete reversal of thrust from the main engines?

 

The simplest answer is to calculate flight time of the projectile, then calculate the acceleration potential of the target over that time and create a sphere of that size and say "the target could be anywhere in this sphere depending on his heading and acceleration".

 

If you're talking a ship that is 100 yds long and accelerates at 3Gs which is 60 kms (chosen to simplify the math) away and you fire a bullet at it at 3000 m/s (again, using typical muzzle velocity from a modern rifle). Then your projectile is travelling in a straight line for 20 seconds. Assuming that the target registers that you fired 10 seconds later and can then fire full thrust in any direction, it will travel 1/2*a*t^2 yds off of it's current path (i.e. where you aimed). At 3Gs that's 1/2 * 32 yds/s/s * 10s^2 = 1600 yds. In other words, your target can have travelled 16 times his own length in half the time it takes your projectile to get there.

 

Even if you up your projectile speed to incredible levels (say a rail gun provides 10,000 m/s velocity instead of 3000). You still get a travel-time to target of 6 seconds. How much of that are you going to allow your target to be thrusting to get off your line of fire? And can he use full thrust or not?

 

Heck, he doesn't even have to turn, all he has to do is turn his engines on or off at will and you cannot predict where he will be with the accuracy needed.

 

 

Laser weapons work better because they travel at c which means no time for the target to react and a direct hit on a target at up to 300,000 kilometers away in a second. Of course, pointing then becomes an issue. At 60 kilometers, a ship 100 meters in length presents a target of less than 1/10th of a degree which means that you need some pretty amazing targetting systems (not to find the line, but to swing a gun to that line and stop it exactly on that line). Put it this way, we can point telescopes with that kind of accuracy but it takes us a few minutes to line them up. Also, if you have any motion relative to one another, your target is only good for the fraction of a second that it takes you to move 100 meters relative to him, then your angle is wrong again.

 

 

There's a reason that early in the Russian space program they fired a rocket at the moon and were ecstatic that they actually hit it. And that is a target that you can pretty much predict won't change course.

[Zeropoint]

Re: Space combat: how big is an inch, how long is a turn?

 

Thermonuclear beehive rounds are where it's at. Take a small fusion device, stack a block of polyethlene on top of it, and then a bunch of ball bearings on top of that. The nuke vaporizes the plastic, which propels the ball bearings at breat speeds in a cone of swiss-cheesy devastation.

 

Use whatever propulsion and guidance systems seem appropriate.

[Jaxom]

Re: Space combat: how big is an inch, how long is a turn?

 

I assume he's talking about a sphere not from where the ship started it's move, but from where it would be in "x" seconds if it applied no thrust. In other words, he's not plotting the ship's movement -- which you're right, would look more cone-like -- but the sphere at the cone's end.

 

(Sorry if I put words in your mouth, Jaxom.)

 

Nope, you got it dead on. More specifically, the cone shape only applies to the space that the ship will pass through in the time the projectile takes to get there, which is meaningless since you only care when the projectile is actually there. Hence, you can start with a specific point (known ship location when you fire) and, to the accuracy of your ability to measure, a stright line which predicts it motion until impact if the target doesn't accelerate. Then you factor in the target's ability to accelerate and you get uncertainty about the projected impact point. If the target can accelerate at full thrust in any direction (which is true in space or most small objects) then you have a spherical region of uncertainty.

 

You can, of course, play games to change the actual shape with more precise math... If the target can only accelerate along a specific axis (i.e. only has jets at the rear) and you know the facing of the target when you fire, then the region of uncertainty gets smaller toward the (current) back of the ship since it can't immediately thrust in that direction. You can further limit the uncertainty if the ship cannot change facing very quickly (which is probably true of a capital ship). All these limits serve to make the area of uncertainty more and more ellipsoidal. For smaller ships, though, the time to turn is going to become negligible. There are examples today of things which orient in fractions of a second using gyroscopes. Take a large enough (or dense enough) flywheel and you can orient using that for ships up to fighter sizes without much work. This will become more and more the case as the ship moves away from the traditional cylindrical model (in other words, a TIE fighter would be able to change facing faster than an X-wing because of the moment of inertia).