Space tactics (playing with physics)

[ArmillarySphere]

I've been following the Outsider webcomic for a while, and they've just gotten around to the major battle of the first chapter. Since the scenario interests me, I thought it might be interesting to play around with some physics.

Premise:
Side A (attackers) have managed to surprise side B (defenders) by hiding in the accretion disk of a star system. They've just come in visual range, and it's now time to select tactics.
Side A favours shorter-range weapons and have a substantial numerical advantage.
Side B favours longer-range weapons and have an acceleration advantage.

Numbers are fairly sketchy - let's call initial range 0.5 million km, side A capable of 20 G, and side B around 30 G. Effective weapon range varies from 100,000 km for side A to 200,000 km for side B. The exact numbers are just to get a feel for the situation.

Questions:
1. Side A wishes to get into close range as quickly as possible and stay there for as long as possible. What is the range of initial speeds that are best to accomplish this?

2. Side B wishes to keep the range open. Given an initial attacker speed, what direction should they dodge in? How long will they be in range for side B?

I have some solutions, but will make a separate post about those.

Some definitions to keep things on the same page. Sorry about the greek letters, but I'd like to avoid confusing angles with the other things:
s0 - initial distance between the fleets
v0 - initial approach speed between the fleets. Can be chosen by B as they please.
g - A's thrust rating
h - B's thrust rating
θ - the angle of A's thrust relative to the initial velocity vector.
φ - the angle of B's thrust " " "

With these definitions, the full equations are:
Δx = s0 - v0t + (h cos φ - g cos θ)t²/2
Δy = (h sin φ - g sin θ)t²/2
s² = Δx² + Δy²

vx = v0 + (h cos φ - g cos θ)t
vy = (h sin φ - g sin θ)t

 

[ArmillarySphere]

1. There's a minimum approach speed for fleet A if B chooses to accelerate straight away from them. (φ = θ = 0). With this configuration, there's going to be a point where B has equalized velocity and starts to pull away, at t = v0/a. At that time, the distance between the fleets must be at or below the weapons range, sw.
sw >= min(s) = s0 - v0² / 2(h-g)
v0 >= √[2 (s0 - sw) (h-g)]

Ideally, side A will come to a relative halt exactly when they come up even with B.
In this scenario, v0² = 2 s0 (h-g)
The time within weapons range is simply t = √[8 sw / (h-g)]

With the example numbers:
v0 >= 280 km/s to just get to weapons range
v0 = 320 km/s to rendezvous
t = 2800 s within weapons range

2. If B instead chooses to bore straight for the attackers, the scene changes. The effective net acceleration switches sign, and B will never come to a complete stop relative to A - their initial speed is now working against them.
By setting s = sw and getting the difference between the two roots, we get:

dt1 = 1/(h-g) * ( √[v0² + 2 (h-g) (s0 + sw)] - √[v0² + 2 (h-g) (s0 - sw)] )

With the numbers chosen, and v0 = 320 km/s, t = 450 s.
If v0 = 280 km/s , t = 470 s.

The theme continues, so that as the initial speed rises, the engagement time decreases. Funnily enough, it seems that the best move is to approach the enemy head-on, keeping the window small and taking your lumps. Once side B is out of effective range, they can reverse accel and approach at their leisure.

I haven't fully explored the option of side B taking off "sideways" to keep the range open - I don't think they will achieve enough range to make it matter. A full optimization of this problem is probably going to be pretty tricky, mathematically.

Well, that's all I had. Any other thoughs?

 

[Myriad]

Imagine (in a frame in which fleet A is stationary) fleet B at a distance of 110,000 km and moving perpendicular to the line between the fleets at a speed of about 3.3 km/sec.

From this state fleet B can use 10G (which is h - g) of its thrust to maintain an orbit around fleet A at 110,000 km range, while using the rest of its thrust (g) to match any acceleration A uses to attempt to escape. B wins.

So, fleet B's initial strategy should be to get into this condition as soon as possible. So neither closing directly nor fleeing directly is a good idea. If we start out with A and B moving toward each other from a good distance, B would thrust at an angle so as to reduce the relative velocity along the connecting line between the fleets, while opening up range laterally.

(This doesn't apply if the fleets start out at close enough range to give A an unavoidable first close range pass, but in that case B would have to do whatever needed to minimize the in-range time of that first pass, and then if it survives, use its superior thrust to get into a suitable winning orbit on the second.)

In general, we can simplify all scenarios in which each fleet is regarded as a single unit to fleet A being stationary and immobile, and fleet B having all the initial velocity and (h - g) of thrust. This makes it clear that unless fleet B's initial relative velocity carries it unavoidably into fleet A's range, fleet B will be able to close into an orbit around fleet A and destroy it at will. Fleet A is a sitting duck.

Of course, fleet A, knowing all this, will counter by dispersing their formation. So it's unlikely that either fleet would continue a direct head-on (or tail-on) course once they realize it's happening.

Respectfully,
Myriad

 

[rocketdodger]

I find space military tactics fascinating, especially when it gets into sci-fi territory.

Two novels jump to mind (pun intended) that explore the issue.

In "A Fire Upon the Deep" there are fleets of ships that make FTL jumps a few times a second, needing to power their capacitors (or something) in between each jump. So no ship ever stays in real space for very long, only a few hundred ms at most. The strategy the author arrived upon is for the two opposing fleets to try to sort of "match" each other's jumps and arrive in a volume of space a split second sooner than the enemy, laying mines where they predict the enemy will exit FTL and fall into real space. Since the number of mines a ship can carry is finite -- so you can't just spam every place you want to mine -- it becomes quite interesting.

In "DownBelow Station" ships don't fight from FTL but rather near-relatavistic sublight speeds. The interesting thing about this is that if you are a ship monitoring a section of space with radar, you have to account for the time it takes the signal to go out and back since the enemy ship will have moved significantly by the time you get data on it's last location. Ships also have a finite number of FTL probes that can be sent out, execute a FTL jump to a location, and then report back via FTL communication channels -- but again there is only a limited number of them. Added to that, the ships have to worry about their inertia and direction changes, etc, so "attack passes" and bringing weapons to bear on the enemy direction are important just like in real life sea and air warfare. In fact the battle sequence in this novel is incredible, I highly recommend it to anyone interested in naval warfare since it offers a very convincing glimpse into the future. It reads like the battle of midway in space, with commanders on each side getting out of date and incomplete information that they then need to make critical decisions with and act upon. Very compelling.

 

[ArmillarySphere]

You have an evil mind... I like it!

With this in mind, making sure you have enough speed advantage to force an engagement becomes vital, or the attack run is suicide.

A can't disperse to avoid B's cunning tactics either. Imagine that A have dispersed to a sphere of some radius. B can simply surround the sphere at the appropriate range and circle the formation, picking off the outermost ships first. Spread the formation wide enough, and we're back to the original scenario with single ships instead.

Using lateral thrust seems to involve solving a quartic (4) equation, which I'm not sure I'm up to doing. There's a definite problem here, as the numbers I put in would allow side B to escape without entering the engagement window at all unless the approach speed is high enough. (time to zero dx t0 = s0/v0, distance at zero dx = (g-h) t0²/2 gives a minimum speed of 350 km/s, with a definite preference of having even higher approach velocities.

The weapon ranges I stated are effective ranges, by the way. The maximum range is large enough that both sides can take potshots from much further out, so they aren't quite as helpless as it might seem. The disadvantage of firing outside that range is that hits are less likely, and do less damage.

(In the actual scenario, side A outnumber the others by 3-1 odds, so the tactical situation is less clear-cut. Plus, they have missiles)

 

[ArmillarySphere]

I'm not the only one then Both the books you mention are on my shelf.

I've been using fairly pedestrian Newtonian physics so far, but it applies equally well to any reasonably hard-SF scenario. From shuttles to the Honorverse, so to speak.

 

[Cuddles]

Just remember - the enemy's gate is down.

Effective weapon range varies from 100,000 km for side A to 200,000 km for side B.

What does this mean exactly? The weapons are only effective at around those ranges, are effective at any range up to those ranges, or that's the maximum range and there's also a minimum range? It seems that could make quite a big difference to the outcome.

Edit: Also, are there any issues regarding ammunition, fuel, acceptable casualties, and so on? As it stands, it seems that as long as A is not wiped out at the start, they're guaranteed to win eventually. Even with just one ship left, they could just sit out of range and take out all of B given enough time. In order to work out how to get the best outcome, we need to know what kind of outcome each side actually wants in the first place. Is B happy with a suicide run that takes out even a few ships? Will everyone's ammunition run out making tactics that reduce losses but prolong the engagement a bad option?

 

[Andy_Ross]

If you have a range advantage then stay out of range of the enemy.
Look at a historic perspective. Spanish Ships of the Armada had a numeric and size advantage over the English Fleet but the English ships had an advantage of range and speed so they stayed upwind andfired on the Spanish ships from fairly safe position. In WW1 and WW2 Battleships would try to avoid fighting at extreme range as incoming shells would be plunging down onto the decks which were comparatively weakly armoured. It was an advantage to get in closer and take any fire on the main armoured belt.

 

[Myriad]

If you have a range advantage then stay out of range of the enemy.
Look at a historic perspective. Spanish Ships of the Armada had a numeric and size advantage over the English Fleet but the English ships had an advantage of range and speed so they stayed upwind andfired on the Spanish ships from fairly safe position.

Actually the English ships didn't have the effective range they thought they had. They hadn't yet realized that how far a cannon could shoot a ball on land had little to do with how far away a shot from a rolling ship could hit anything. So both sides banged away rather ineffectually at long range until out of ammunition after which (to make a long story short) a storm wrecked the Spanish fleet.

I disagree that a dispersed formation is guaranteed to be an ineffective tactic for fleet A. It prevents fleet B ships from getting into a worst-case range (well within their effective range but just outside of A's) of most of fleet A's ships at any given time, because the A ships can cover one another using their superior numbers and power. As for B staying outside of A's entire formation and attacking only the outermost ships at longer range -- that works if B has unlimited time. But the scenario is that B is the defender, so presumably they're defending something and their time runs out (with a win for A) when a significant portion of A's force gets there.

The Battle of Lexington and Concord is an interesting comparison, if we make A the British column. B had the speed (due largely to not having to bring their wounded with them due to being in friendly territory), and while the maximum effective range was comparable or a slight advantage on B's side, A had a very large advantage (bayonets and cannon) at close range. The numerical advantage shifted back and forth along the road. A close look at when each force chose to disperse and when to concentrate, with what results, is interesting. (One must of course look at real accounts of the actual battle, not the elementary-school-history-class fiction of the British column brainlessly marching in a line the whole time while allowing Americans to fire at them from a few yards away.) That battle is generally regarded as a success for the Americans but casualties were comparable on both sides, and if the objective had been to prevent the British column from reaching Boston, it would have been considered a failure.

Respectfully,
Myriad

 

[ArmillarySphere]

Interesting - I didn't think of bringing land battles into this as a comparison.

My intent with the OP was to explore the implications of Newtonian physics when it comes to maneuvers in space. The differing weapons ranges are mostly there to indicate that one side wants to get up close and personal, while the other would stay further out by preference. The exact numbers are less interesting, but serve to get a feel for the magnitude of the various solutions.

So far, the most effective tactics for the defender seems to be to move off the initial approach line. Whether this means 90 degrees angle or something else would probably be a matter of solving that dratted quartic equation. I may do that if I have the time, but the solution isn't going to be for the timid.

 

[eriqk]

Some time ago, I spent several evenings reading this. Lots of ideas on space warfare: weapons, tactics, etc.

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

ETA: Reading the above has the definite downside of never being able to watch sci-fi the same way again. The outsider is a case in point: While nice I found myself quietly griping about the layout of the ships, wondering if by "fuel" the author might have meant "propellant" and pedantic things like that.

 

[MG1962]

Aside from the range. The firing rate of the weapons is important. It is the reason a destroyer can survive an encounter with a battleship. It relies on the slow rate of fire of the battleship, while trying to do as much disruptive damage with its higher rate of fire

 

[Andy_Ross]

A Destroyer wouldn't do much damage with it's guns against a Battleship and a single hit on a Destroyer from a Battleship would sink it. Battleships had a secondary armament in addition to the mains. For example the USN 'Iowa' class of second generation Battleships had 9 × 16 inch and 20 × 5 inch guns. A US Destroyer was armed with 8 to 10 x 5 inch guns That's enough to overwhelm any Destroyer that tried to get close enough to engage with its guns. Destroyers would attack with torpedos, not guns. If a Battleship was caught without a Destroyer escort to intercede it would turn away from a well pressed Destroyer attack from the fear of torpedos, not the guns.

Look at actions in the Med, there were several occasions when both the Royal Navy and the Regia Marina failed to press home attacks after Destroyers joined in.

Typical textbook tactics were for the Destroyers to turn away under smoke and then run back into the smoke and fire a torpedos. It was a very brave commander who would push his Capital ships into smoke.

 

[MG1962]

A Destroyer wouldn't do much damage with it's guns against a Battleship and a single hit on a Destroyer from a Battleship would sink it. Battleships had a secondary armament in addition to the mains. For example the USN 'Iowa' class of second generation Battleships had 9 × 16 inch and 20 × 5 inch guns. A US Destroyer was armed with 8 to 10 x 5 inch guns That's enough to overwhelm any Destroyer that tried to get close enough to engage with its guns. Destroyers would attack with torpedos, not guns. If a Battleship was caught without a Destroyer escort to intercede it would turn away from a well pressed Destroyer attack from the fear of torpedos, not the guns..

What was the range of Allied torpedos in WW2?

What was the range of 16 inch guns?

Fortunately the commanders involved in the battle of Samar were unaware they had no chance

 

[Andy_Ross]

They knew they had no chance but would attack anyway. That's why I refered to the actions in the Med. In the RN Derstroyers would alway press home an attack, Losses of destroyers was high.. In the Norwegian Campaign HMS Glowworm Rammed the Hipper before it was sunk. Well handled Destroyers would see off a Battleship. Even of they didn't fire torpedos the Battleships wouldn't risk it. Battleships wouldn't risk attacking into a Destroyer smokescreen, they expected torpedos.

This is getting well of the subject of hte OP though.