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Distance in space battles is a crucial variable that affects the tactics and outcomes. With the following tech what is a reasonable distance for battles to be engaged:

Engines:
Fusion drives with max safe acceleration at 156 m/s2
Maneuver drives with max acceleration at 20 m/s2

Weapons:
Railguns with velocity of about 5000 m/s every 5 minutes or 7500 m/s every 4 minutes for the bigger ones.
Missiles with about 650 m/s2 acceleration and a 10 kilometer sphere kill zone.
PDCs not really a good weapon but like small Gauss guns firing 1000's of rounds at 2000 m/s

Fire control and sensors:
Able to track and lock most ships and missiles using radar and lasers. Jamming and chaff for countermeasures. Missiles are self homing with radar and heat tracking.

Numbers: About 20-3 ships per side. Most will be corvette/destroyers with a small railgun and 30 missiles. About 4 of the ships will be cruiser with 2 medium railguns and 50 missiles. On or two will be battle ships with 2 heavy railguns and a hundred plus missiles. The PDCs are not really offensive weapons.

So with these parameters what are a realistic distances for space battles?

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    $\begingroup$ Can you clarify your units? You use mp/s for velocity and acceleration, which should be meters/seconds and meters/(seconds^2). $\endgroup$ – abestrange Jan 13 at 18:32
  • $\begingroup$ Ships can accelerate at 15G? But maneuver at only 2G? $\endgroup$ – Zeiss Ikon Jan 13 at 18:37
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    $\begingroup$ @ZeissIkon think of the space shuttle, which has its main engines on the tail but which also has an OMS system (otherwise it would be hell to rendezvous and dock in space). $\endgroup$ – The Square-Cube Law Jan 13 at 18:40
  • $\begingroup$ Are the missiles going fast enough?? I was not sure so I did about 50Gs. $\endgroup$ – 11Bravo Jan 13 at 18:42
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    $\begingroup$ Can you give us information of size and ammo capacity of your ships? In addition the number of ships you expect to be in a battle group would be helpful. $\endgroup$ – worldsmithhelper Jan 13 at 18:50
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You have to wrap your mind around the fact that space warfare is 6 dimensional. X, Y, Z positions and Vx, Vy, Vz velocities. The set of possible future positions of a spacecraft is an opening exponential horn. (Actually, something more complex than a horn.)

You want to set up a spreadsheet with the speed, distance and acceleration equations.

You need to decide how long the powered flight envelope is for your missiles. In Weber's Honorverse books, missiles at the start have an acceleration of about 8,000g and a burn out time of about 3 minutes. This gives them a range measured in millions of km. Later in the series missiles improve. In general the armaments race makes an interesting thread that runs through the series.

Weber doesn't use the free flight option much. But consider a weapon that was smart enough to be left behind, or to circle around the target. Or consider a missile that could be retrieved if it missed the target.

You need to decide how smart the missiles are. Do they have frequency shift radar so that jamming is harder? Tagged pulses so that each missile knows it's own radar return signals. A somewhat lighter version that comes in ahead of the pack as electronic jammers for the slower main bombardment. Do they have bomb pumped x-ray lasers to increase their kill radius.

Much depends on the electronic counter measures. E.g. When a rail gun throws a slug, is it coated with a radar absorbing coat? How far can the enemy detect the magnetic pulse from firing? How far can they detect the shell? Do rail guns throw explosive shells? What is their radius of effect? Same as missiles?

Missiles are easier to detect due to exhaust plume. Seeing one gives you an aiming point for tracking radar. But consider a missile that is restartable. It accelerates for 20 s, at 650m/s so it's now going at 13 km/s At this stage it throws an asymmetrical cloud of objects that have the same radar cross section. Suppose they are thrown sideways at 1 km/s. Now your target ship has to figure out which one is real. While the target's tracking computer is having fits, 2o seconds later the cluster of decoys is 40 km wide. In that same 20 seconds your missile has traveled another 260 km. Now only 2 seconds from the target, the missile restarts its engines and makes the final dash.

So missiles have a target envelope measured in hundreds of km given 20-30 seconds burn time.

The Vulcan Phalanx on the aircraft carriers throws shells at an incredible rate, and fire director radar tracks the outbound shells to refine the solution. It fires 90 rounds per second at velocity of 1.1 km/s so for a target 2 km away there are about 160 rounds in flight. It uses a 20 mm shell. This, I think, is the role of your rail gun. It targets incoming missiles and attempts to destroy them at a distance of about 20 km. If it could fire at, say 5 rounds per second using amount the same size shell that WWII anti-aircraft artilery used, but vary the muzzle velocity slightly so that a 4 second burst arrived on target at the same time. In addition the final aim would be modified so that the coverage included the space where the incoming missile could evade to, they would explode at the same time, creating a wall of shrapnel.

https://en.wikipedia.org/wiki/Phalanx_CIWS

Rail guns don't matter until you are very close. If the kill radius of the warhead is 10 km you don't want it blowing up any nearer than 20 km to yourself. So if you had an optimum engagement envelope for RG of 40 km that means that it has 8 seconds travel time. Target ship has to change it's path by 10 km in 8 seconds. That would require an 8 second 12G burn at right angles to the present course. Pushing it.

But if the cycle time of an RG is 5 minutes, then it becomes a game of tracking when the opponent last fired. 300 seconds at 5g (50m/sec2) is 1.5 kps. In that time 1/2 at2 = 25 * 90,000 = 2400 km. Lots of time to get close enough

I don't think rail guns matter initially.

Are rail guns on turrets, like a modern battleship, or are they essentially fixed, like the bowchaser on a 1800's frigate.

Railguns may be better used as an anti-missile defence.

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Here's a quick break down with your values listed, without going into any deeper speculation or theory.

Assume two ships are pointed at each other and about to fire. How close can they be and still dodge an incoming shot?

If we assume the ships are cylinders with a 10 meters radius and are stationary with respect to one another, we can use the Distance equation of Distance = 1/2 * Acceleration * Time^2 + VelocityInitial * Time. The ship need to be able to move 10 meters in any direction to dodge a shot, and can maneuver with 20m/s^2 of acceleration.

So that solves to Time = sqrt(2 * Distance/Acceleration + 0) = sqrt(2 * 10/20) = sqrt( 1) = 1 second.

You have 1 second to dodge an incoming shot with your maneuver thrusters.

That means that if the enemy is about to launch a projectile with 7,500 m/s velocity, you can be ~7,500 meters away and still have time to dodge. If you need an additional second to detect the round, plan and plot evasive maneuvers, and get moving, then you can engage at around ~15 kilometers.

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    $\begingroup$ +1. Would you mind if we formatted your answer to have math symbols in the equations (i.e. the square root)? $\endgroup$ – The Square-Cube Law Jan 13 at 18:53
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    $\begingroup$ "That means that if the enemy is about to launch a projectile with 7,500 m/s velocities, you can be ~7,500 meters away and still have time to dodge." But only if your ship is capable of shifting its trajectory and predicted position by at least one width, length, or height of its hull (whichever is smaller and matches the direction you're shifting) in less than a second, though $\endgroup$ – Darth Biomech Jan 13 at 18:59
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    $\begingroup$ Since in battle the spaceships will presumably do randomized bursts to create an unpredictable path, dodging would almost be automatic. $\endgroup$ – D.J. Klomp Jan 13 at 19:17
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    $\begingroup$ @11Bravo with your parameters, sure. Realistic space mounted rail guns will most certainly be able to go faster than 5km/s, as our current research railguns can achieve ~3km/s. The faster the projectile, the larger the engagement distance. $\endgroup$ – abestrange Jan 13 at 19:45
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    $\begingroup$ Broadsides allow for more guns to engage the enemy. In the case of a bobbing ship and inaccurate weapons, the probability of hitting the target as well as the potential damage increased with the number of guns firing in each volley. In space, the shape of the ship can be very functional, with no consideration for fluid dynamics. There's no reason an array of very long rail guns can't be mounted front, side or rear, whether parallel or orthogonal to the rest of the ship. $\endgroup$ – jwdonahue Jan 18 at 1:22
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Won't Know Until You Fly Them

As has been previously mentioned, a ship of an arbitrary size (10 meter radius and cylindrical) would be able to dodge your weapons at about 7,500 meters provided it had 1 second of warning. But there are some problems with this (excellent) "perfect secnario" mathing out of your question.

1: It isn't a perfect universe. These things look simple, but as Clausewitz said, "In war simple things are hard" (Drink!) Are your ships flown by humans? Their reaction times might not be quick enough to dodge, and it only takes one mistake to have a Very Bad Day. Computers? Their sensors can be fooled by offensive jamming/decoys. Maybe you have algorithmic "jinking" programmed in. But then of course the enemy would try to figure out our patterns, and with computers there's always a pattern. To mitigate that maybe your "ideal" engagement range isn't as close as you would think. After all, if you can hit your enemy 99% of the time at 7,500 meters, your enemy can hit YOU 99% of the time at that range as well! For example, before WWI the Big Gun ships (meaning armored cruisers and larger) had trained to fight engagements at about 2/3 of their top speed (because top speed involved occasional explosions in engine rooms if you were unlucky and people thought captains wouldn't risk the extra speed with the chance of becoming dead in the water in a fight) and at rangers of about 10,000 yards, despite the guns themselves having much longer ranges. Well the war broke out and what do you know! Captains and Admirals went as fast as they could, and stayed at the maximum range of their weapons (up to 20,000 yards in some instances, 2x further than theorized!) because they didn't want to take losses! There are also some great instances where one squadron would keep the range at THEIR maximum (say, 16,000 yards) because even though they were more accurate at shorter range the enemy's guns only reached out to 14,000 yards, so why get shot back? Given two equally-equipped fleets, the engagement range is likely to be as-far-away-as-possible, with the more inexperienced fleet either trying to get in close (an aggressive commander, trying to get where he can shoot back even if takes more losses) or stay far away (a cautious commander, trying to minimize his own damage and hope to get lucky hits on the foe).

2: Armor. Sure you might be hit by a railgun or missile from a destroyer, but does your Battleship actually care about that? If it does, why have a battleship at all? The speed vs armor equations on all your vessels will dictate different preferred engagement ranges. If they can shrug off multiple missile hits, they won't mind getting into ranges where they'll get hit but can deliver devastating strikes themselves. If they can't survive even a single hit, they'll keep as far away as possible to maximize their own survival.

3: Armaments. Does your battleship carry bigger missiles than your destroyers? Or just more? Does it have enough launchers to overwhelm point defense of smaller ships at range, thereby preferring a "stand off" attack compared to the smaller ships who MUST launch closer to get their warheads through enemy countermeasures? Or just more missiles, allowing it to sustain engagements for a longer period? Does one fleet have different doctrinal approaches? For example, if one fleet decides that economy of force is paramount it might order destroyers to make individual close-in runs, relying on their greater maneuverability to make 1 shot/1 kill attacks while avoiding enemy fire. Whereas another fleet similarly equipped might decide that a ship's main job is to not blow up, and have their destroyers attack at maximum range, launching coordinated strikes which cost a lot of missiles for the same amount of hits as a more daring close-in attack.

4: Countermeasures. How good are they really? Does 1 chaff launch guarantee all missiles within X seconds of impact miss? Or does it always spoof one missile into missing but is overwhelmed by multiple launches? Do ships carry more chaff than they do missiles? Is it only 50% effective? 20%? 90? All that will dictate engagement ranges as well. If I know I have 60 loads of chaff and they will 99% stop 1 missile per launch, I feel pretty good getting close to a 30-missile destroyer to make sure my own missiles work. Or maybe forgo missiles entirely with my big immune-to-destroyer-railguns battleship and blow that destroyer away with myrailguns. Chaff only 20% effective? That's a hope, not a strategy, and I maintain a long range and launch chaff as an addition to dodging, not a replacement.

I'm not trying to rain on your parade by saying all this, I'm just pointing out that a realistic engagement range has a LOT more variables than just doing math on how quickly something can turn or accelerate.

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    $\begingroup$ Wow. For your first answer this is very in depth. I can not predict every variable so this answers is pretty good. $\endgroup$ – 11Bravo Jan 15 at 19:33
  • $\begingroup$ Welcome to the site, great first answer. (From review). $\endgroup$ – A Rogue Ant. Jan 15 at 19:38
  • $\begingroup$ I think your answer is better than mine. The arms race is going to be a critical feature of this. Counter measures. And counter-counter measures. EMP optimized nuclear bombs that fry the opposing electronics. EMP counter missles. Radar operating in diferent bands to avoid jamming. Laser range finding vs perfect black missles... $\endgroup$ – Sherwood Botsford Jan 25 at 18:50
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Really close.

You don't have offensive lasers. All your weapons are subluminal. You do have lasers and radar & presumably other EMR sensory techniquies. That means you can detect incoming projectiles at a distance and negate or deflect them with your own projectiles. You wont need to dodge. Those defenses are outgrowths of older defenses against meteroids and so they are mature and effective. It is hard to get past. The question is how fast you can detect incoming and fire a defensive railgun round.

The offensive solution is to get close enough that there is no time for detection / deflection of a projectile. At such distances, boarding operations also become realistic.

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  • $\begingroup$ Even closer. My counter defensive solution is to get so close that if you fire a missile you're in the blast radius yourself and we're effectively down to firing broadsides at point blank. You did set up your ship to fire broadsides didn't you? OP is asking for missile based combat, that means working out the equivalent of "Over the Horizon" distances. $\endgroup$ – Separatrix Jan 15 at 16:23
  • $\begingroup$ Only if you can see it. A shell coming in that is painted with radar absorbing paint might not be visible at all. Missiles can change direction up to the last minute. High speed auto cannons (90 rounds/second) have trouble with subsonic cruise missles that are detectable at a range of miles. $\endgroup$ – Sherwood Botsford Jan 25 at 18:53
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Missiles with a 10km zone kill capability are going to keep ranges out at at least the 10km (and probably a lot more since you want to be out of the damage range not just the killzone), until everyone's magazines run dry because you can't engage with them at ranges smaller than that 10kms without them killing the ships that launch them. If those missiles can effectively loiter, shut down and hang around the battlefield undetected until a good target becomes available, then closing combat range after they're all fired becomes suicidal unless and until you can positively account for all the self-guided munitions launched by the opposition, and maybe yours too depending how smart they are.

With the railguns being linear accelerators the most logical ship design is a long cylinder with a heavy armour belt forward ringed with maneuvering thrusters. Main engines aft with lateral fire missile batteries around them. Head-to-head even at very low ranges such ships may not get a hit but a LOT depends on sensory data and minimum tolerances.

For example is your sensory system good enough to tell you your opponent is charging the capacitors for their main guns or do you have good enough Van Eck phreaking to know where a shot is aimed and when it will be fired?

In terms of tolerances the minimum vector change you ship and it's weapons can traverse, because there will be one, massively effects weapon accuracy tolerances and also firing windows. You may think your weapons are on point when you're .01° off which isn't a lot when the muzzle is touching the target but it is over two and half metres at 1km.

A couple of ships with poor sensory systems and high minimum tolerances facing off nose to nose at 100m with 1° offset fire rounds with a 1m diameter more-or-less simultaneously, the two rounds glance off each other producing a cloud of plasma and shrapnel but neither scoring a direct hit on target, and that is without either ship trying to dodge.

So the answer is railgun engagement range will be as close as possible, with a lot of maneuvering going in to trying to gain high cross-section firing intercepts, crossing the T comes back into it's own for example. Railguns will only be used AFTER everyone has run out of missiles and the battle groups have either left their range from launch area or positively eliminated the threat. The optimal ranges for firing passing will depend on the exact cross-sectional size of vessels and the firing cones of the railguns being used.

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It is my belief that any space ships trying to battle one another are going to a close distance. Any further away than a single light second, you run into complications that make any form of combat impossible, especially with slower than light weaponry.

Let's say you fire a missile at an enemy ship, from ten light minutes away, that enemy ship sees that you fired a missile ten minutes ago and because that missile is way slower than light, the enemy ship still has plenty of time to coarse correct to dodge it. So unless you are within one light second, any fight will look like Neo dodging gunfire from the Matrix, especially if your fastest projectile can only go 0.000025 of light speed.

Railguns are pretty much the best long rang space weapon because of how fast they can go, the only way you can do better is with lasers. So the only way I can see long-range engagements would be like a sniper picking enemy ships off, and if you have stealth tech for your projectiles, that might work. But if your fastest projectile still takes over an hour to hit the target within one light second, your only hope is to get in close, empty the clip and run.

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  • $\begingroup$ There's a technical difference between missiles and rockets, and it seems you're thinking of the latter. Missiles aren't so easily just dodged, they follow you, to a limited extent, perhaps, but they follow. $\endgroup$ – Separatrix Jan 16 at 12:05
  • $\begingroup$ Depends on how smart the missile is. see Weber's Honorverse where he has plausible battles fought at ranges of 150 million km with missiles reaching velocities of c/2. You have to grant him his currently unavailable propulsion systems though. $\endgroup$ – Sherwood Botsford Jan 25 at 18:58
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There's nowhere near enough information here to answer the question. To address it we should look to videogames--specifically, the concept of damage per second, often called DPS. I have never played such a game where range is an appreciable factor, but in this scenario it is.

For each possible range (you'll have to pick some interval to calculate it at) put the fleets that distance apart. Figure each shot is one point of damage, multiplied by the chance that it actually is aimed well enough and multiplied by the chance the enemy fails to evade/intercept the shot. Do the same calculation for the enemy. Now compute the ratio of your damage to their damage--your ideal engagement range is the range where this ratio is highest.

Note that if you outrange the enemy this ratio is infinite at all ranges beyond their maximum range. (Yes, there can be maximum ranges on weapons. Consider the previously-mentioned Honorverse. Missile performance vastly exceeds ship performance, evasion is not possible and nobody meaningfully tries. However, once a missile's booster burns out it's ballistic--it has no performance at all. Move beyond it's standoff range and it's harmless, or simply orient your ship properly and it can't attack (Honorverse ships have completely invulnerable top and bottom shields.) Hence everyone wiggles around enough to keep the enemy from trying ballistic attacks.)

To make matters more complex you have to add velocity to the picture. Just because you're at your ideal range now doesn't mean you can stay at that range. (Once again, thinking of the Honorverse novels, there are multiple battles earlier in the series where one side comes barrelling in because they know they're inferior at missiles but superior at lasers--they'll take losses while closing but laser battles are decisive. Then later in the series there are a few fights where someone thinks they can do this and learns the hard way how utterly obsolete their ships are.)

Then to make matters even harder you might have a situation where having different ships at different ranges might be superior. This is only viable if intercepting inbounds is not a big part of the battle so the more forward ships don't need the defense cover of the ships that don't get as close.

Also, how much ammunition do you carry? Do you have to conserve ammunition during the battle, only firing high probability shots, or can you simply open fire as soon as you can get hits? The former case makes the damage calculations even harder.

Is ganging up a viable strategy? Those little, maneuverable ships are good at getting out the way of that 10km lethal range on the missiles--but what if you fire 6 of them, each set to pass 10km from the target, spaced every 60 degrees around it. Oops, now you have move nearly 20km to get out of the lethal range. If defense comes from interception how good are ships at intercepting inbounds aimed at another ship? (I'm thinking of playing Harpoon long ago--if you could punch out a fleet's airborne radar you could then pick off the outer ships layer by layer with very little defensive fire as each ship was now on it's own and got at best only one round of defensive fire.)

You're going to need a lot of computer power to simulate all these options and without that you don't have an answer.

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What you should consider is the amount of fuel a missile carries, and it's powered flight time. As many before have pointed out, an unpowered missile can be easily shot down by railgun fire. But with a 10 km kill radius, the missiles could explode outside PDC range and still be effective. Though they have to be able to maneuver to avoid being shot down, so they need to have fuel until they detonate. You could also use missles as counter missles. With a 10k kill radius, that would be quite effective. You could potentially accelerate missiles with electromagnetic launch tubes, so the firing is not as easy to detect and have them fly unpowered in a wide pattern, until they are closer to the enemy. Then they all ignite their drives simultaneously, striking from different angles, trying to overwhelm the enemies' missile defenses. You could even lay a spread of missiles as a minefield.

I imagine, a battle would be started at extreme range. Depending on your missile range, hundreds or even thousand of kilometers. Each side will fire missiles and counter missiles, as fast as possible, trying to overwhelm the other sides' missile defense. Then if they either run out of missiles, and still want to engage, or if the range drops below 10km, it will become a railgun slugfest.

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