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I put armour on 4 times as thick, I've still roughly built 2 ships that can take a hell of a lot more of a beating than yours. 2 ships that don't need ANY support after being launched, you still have to build supply ships and bases.
First:
You are equating mass with volume. This is not correct. It is posible to make a ship that is a high volume, but low mass.
Armour has a lot of mass. So doubling your armour will increase the amount of mass you can set asside for missiles.
Armour is dense. So increasing the mass of armour would not increase the mass like increasing the missiles (or anything else) would.
A launch tube for instance is hollow and so would take up more volum for mass than armour would.
The factories work with mass, not volume. It is easier and takes less resources to create a cube 1m x 1m x 1m and have it hollow as compared to a 1m x 1m x 1m cube and have it solid.
Volume can not be equated as mass in these caclulations.
Increaseing your armour (high density) will reduce the volume of missiles (medium density) available to you by more than the extra volume of armour gained. You have not considdered this in your caclulations.
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250,000,000 for engines, fuel.
50,000,000 for a deployable refinery/factory system.
100,000,000 for pellets in my railguns. All guns firing, will take 3 hours. This gives me 1.0 × 10^14 pellets by the way.
100,000,000 for long range boosters that would have a number of Sabot attached to the front and fired at extreme range (Filling the role of your striker, in a rather small package, for cheap) gives me 500,000 long range boosters. They might not be fast, but they're hard to see and will pack a punch.
150,000,000 taking up space for structure.
50,000,000 for large warheads: The kind uses to blow holes in moons you're trying to set up a base on, packaged onto the same engine sabot with its own final stage booster. That gives me 1,250,000 of them, and I can get them all off in 4 seconds firing from all sides. These are more likely to be loaded on long range boosters however.
300,000,000 for smaller warheads packed in sabot, gives me 7,500,000 of them. In total I can unload them in 24 seconds.
You have neglected the volume of the weapons thenselves and the storage compartments and transport systems (to the fireing chamber) for them. You have given the ammo volume, but this is only part of the volume needed.
Another mistake is that I have a much higher surface area for weapons. So your rate of fire for missiles can be easily matched by my Drones. It won't matter how many missiles you have if I can have enough ammo (and point defence ammo is far smaller than missiles) and a high enough rate of fire to exceed your missile's rate of fire.
As I said a few posts ago. It is not how many warheads you have, but the ratio of the rate of fire for missiles and point defences.
if you can fire 10,000 point defense shells each second but I can fire 10,001 missiles each second, you will eventually be hit and destroyed.
If you waste all you point defence fire at my Drones, then you arn't fireing at the missiles that are aproaching your ship. You might destroy my point defence Drones, by that would have just allowed my missiles to get close enough to your ship.
Also their is the "Kill rate". You might be able to fire 102400 each side, but if you can only get 1 kill for every 1,000 pelets shot, then 103 missiles (in the same time period) will be able to breach your defenses regardless of how much ammo you have in reserve.
This is the critical number, not the volume or ammo reserves. Ammo reserves only come into play if the conflict is long lasting. Even then, a lot of the balance is detemined by the rate of fire.
If you have 10^14 pelets ammo reserve, and have a kill rate of 1:1,000 pelets, then 10^11 missiles will breach your defences regardless of the time taken to fire those missiles.
Kill rate to Rate of fire is important. You have not factored this into your calculatins.
I don't need to match your warhead storage capacity. All I need to do is exceed your ability to shoot them down.
Lets do this calculation:
If your Gunship is 1km each side that gives an area of 1,000,000m^2
If each Missile port takes up 2m^2 then you can have a maximum of 500,000 missile ports on a side.
But this leaves no room for point defence.
Lets add this in. Assuming that missiles and point defence takes up 3m^2 then we have 333,333 missile ports per side 166,666,000 point defense turrets.
PD turrets can only attack in the direction the attack is comming. So we only need to considder 1 side for PD. However misisles are guided and can change their vector so all sides can fire at a single target.
This gives 166,666,000 PD and 3,000,000 missile launchers for your GunShip.
Now for my Strikers and Point Defense Drones.
My Strikers are 1/16th the size of your GunShip and my PD Drones are 1/32nd the size (actually the sizes of them wwould be adjusted to give the best Rate of fire to storage capacity against your ship designs as that is what they are designed for so the 1/6th and 1/32nd ratios might be different if they would give a better rating against your ships).
At 1/16th the size my Strikers are 62.5m long each side giving an area of 3,906.25m^2.
This gives me 7,812 missile tubes each side and a total of 46,875 missile tubes total. Therefore I need 3,556 Strikers to overwhealm you PD. Volum to Volume I can produce 4096 Strikers to your 1 Ginship. So it is posible for me to overwhelam your PD and get hits on your ship.
But I haven't figgured in any PD for me yet.
At 1/32nd the size each PD Drone of mine will be 31.25m long on each side or 976.56m^2. Due to the smaller size, it becomes feasable for me to mount weapons on one side of this PD Drone and direct the muzzle as if it came for anotyher side. So to simplify, we can assume that I can get the equivalent of 3 sides pointing in 1 direction.
which give me an area of 2,929.68m^2 for mounting PD weapons. At 1cm each that givbe each PD Drone a capacity of 292,968 PD cannons each ship.
You can fire 3,000,000 missiles which means that 11 PD Drones can shoot down all your Missiles. Only 11! I can have a 100 or even a 1000 of these and still have enough to overwhealm your Gunships PD with Strikers. And this is equal volume.
For the volue of your GunShip I can produce 32,768 PD Drones. Even with 4,000 Strikers, I can have more than enough PD Drones to handle any missile strikes you send agains tme. I only need 11 to shoot down your missiles.
Sure you have more ammo in reserve, but I can destroy you before you can fire all your weapons.
For Missiles to be effective against a ship, the missile must be able to close the distance with the target in less time than it take the target to move out of the missile's manouvreing cone. A ship with more acceleration means this cone is smaller. For large ships (like your GunShip) this cone is huge. That measn that to engage my ships you have to be very close to them. For me to engage your ship, I can be further away. But we will be at a range much less than 1 light second.
If missiles taravel at 100km/s (max speed if all fue is burnt) and the engagement is at 1000km then one only need 10 seconds of fireing to reach the target. If you have 24 seconds of ammo, then 14 seconds are wasted. If it takes 3 hours, then there is a lot of waste (single engagement only).
This is why I said that your ships are designed for long term engagements, you have the advantage of endurance. But I have the advnatage of Rate of Fire.
The Motherships would exist in this situation just to provide my fleet with some endurance. If this is in the form of resupply or by auxillery ordinance, it doen't matter.
Rate of Fire will beat Endurance in a straight up fight any time.
If you are able to engage my ships over a much longer period of time, you will win. Over a short period of time, I win.
Also let us now factor in my Motherships.
Let us say that my Motherships are only 1/4 the size of your Gunships. That means that volume for volume I can have 64 Motherships.
Each mothership is indipendant with the same kinds of factory that you have in your GunShips. Also these Motherships don't need misisles so I can concentrate their weapons on point defence.
At 1/4 the length of your GunShip, this give me a length of 250m or 62,500m^2. At 1cm each PD turret, that give me a maximum of 6,250,000 turrets each side. But you can only fire a maximum of 3,000,000 from your entire ship. You can't touch my Mothership with any of your missiles. And I have lots of surface are to spare. And this is just 1 of them! I have 64 of them for every 1 of your Gunships.
With this kind of PD I might just send it in to combat with your GunShip along with my Strikers and PD Drones as a convenient Supply platform or if you attacked with a second flanking ship, I could just engage it and hold it off untill my Assult force has dealt with your other GunShip. Even if I loose one of my Motherships, I still have 63 more that can hold off your GunShip.
Who needs weighty armour when I can have this kind of PD protection? I just need to have enough armour to protect against micrometeors and shrapnel form the distant explosions.
I have chosen to ignore the amount of ammo available as PD ammo will always out number Missiles. It makes it next to usless to compare them. It is the rates of fire that is important for a single engagemnt.
So for each area that you can hold with your Gunships, I can hold off 64 of them. Each one of my Mother ships can be used to make the Strikers and PD Drones as these are much smaller than it. You have stated that You can make Missiles as large as my Strikers, so why can't I make an entire Striker and my PD Drones are smaller still so these too should be posible.
If we have the rule that we can't build a ship as big as the factory ship with the factory ship, then I can restock my fleet quite easily.