## Space Combat Iteration 2: Overview

Since we are modelling space combat closer to 3rd edition’s space combat, we can also look into adapting 3rd edition’s scaling to our problem.

### HP

Third edition’s spacecraft HP system assumes that HP generally scales with area, i.e. $\text{mass}^{2/3}$, contrary to fourth edition’s \text{mass}^{1/3}\$. If we take a 1000t craft (SM+8) as an example, and restricting ourselves to only cylinder-shaped ones with a width/length factor of 1:5, it will have a total surface area of about 15k sqft, and therefore about 225HP for a medium frame. Calling it 250HP and scaling by area, we get the progression seen in the table below. While the smallest spacecraft have the same HP, more massive spacecraft profit: At SM+8, HP is increased by almost 50%, and at SM+10 it’s more than doubled. This does fit nicely with our plan to avoid easy destruction of big craft.

SM Mass (t) HP (4th) HP (New)
SM+5 30 20 20
SM+6 100 30 35
SM+7 300 50 60
SM+8 1 000 70 60
SM+9 3 000 100 200
SM+10 10 000 150 350
SM+11 30 000 200 600
SM+12 100 000 300 1 000
SM+13 300 000 500 2 000
SM+14 1 000 000 700 3 500
SM+15 3 000 000 1 000 6 000

Additionally, THS has a frame part, where you can assign mass to a frame (either light, medium, heavy, or extra heavy) in return for different HP multiplicators, where each successive level doubles HP. Deleting the light frame from our system, we can instead introduce the Structural Reinforcement system. Each such system installed increases HP by the base HP (i.e. one installed doubles HP, with a maximum of three installed quadrupling HP). They have one particularity: A maximum of one system per spacecraft section (front, centre, rear).

### Armour

Armour is more difficult to manage. By THS rules, effective cDR is dependent on the mass allocated to armour, divided by the total area times the material weight chosen:

To adapt this to Spaceship’s rules, we’ll consider front, back, and centre separately, though front and back are identical.

Coming back to our example of a thousand-ton five-to-one cylinder, we get a front/back area of 0.3k sqft (kilo-squarefeet. I want my GURPS in proper metric :-( )), and a side area of 6.6k sqft. For our most basic armour (steel), this gives us 6cDR per armour system for front and rear, and 0.3cDR per armour system in the centre. Better armour increases that; diamondoid would give you 75cDR for front/back, and 4cDR in the centre hull. For an SM+5 design, this should be 1.2cDR for the front and 0.06cDR for the centre hull for steel armour.

However, the numbers above are ugly as they force us to deal with fractional cDR, and that the sides of a spacecraft can never be effectively armoured. Let’s therefore increase armour values everywhere, finding a nice ratio for front/centre hull (like 5). Call it 5cDR for an SM+5 steel front hull, and 1cDR for an SM+5 centre steel hull. This increases maximum steel armour from 6 to 30cDR in the front hull for a 20HP craft, or decreases - using Spaceship’s scaling - from 450 to 300cDR for diamondoid armour. It therefore brings all of the armours more in line with each other. The result can be seen in the following, gigantic Table, which shows cDR for the central hull (front and rear is 5x that number):

SM Steel Light Alloy Metallic Laminate Advanced ML Nanocomposite Diamondoid
SM+5 1 2 1d 2d 3d 5d
SM+6 2 1d 2d 3d 5d 7d
SM+7 1d 2d 3d 5d 7d 10d
SM+8 2d 3d 5d 7d 10d 15d
SM+9 3d 5d 7d 10d 15d 20d
SM+10 5d 7d 10d 15d 20d 30d
SM+11 7d 10d 15d 20d 30d 50d
SM+12 10d 15d 20d 30d 50d 70d
SM+13 15d 20d 30d 50d 70d 100d
SM+14 20d 30d 50d 70d 100d 150d
SM+15 30d 50d 70d 100d 150d 200d

### Damage

THS offers a total of five different weapons and damage options: Lasers, kinetic kill ammunition (KKMP), bomb-pumped lasers (XLMP), railguns, and particle beams. Additionally, there’s collisions, whether accidentally or by ramming.

#### Lasers

Lasers are offered in two sizes: The 2.5MJ Light Laser (5 tons, 2dx5), and the 10MJ Heavy Laser (~20 tons, 2dx10). This gives us scaling - quadrupling energy output (equivalent to quadrupling mass) doubles damage. The Light Laser is the major battery of an SM+6 craft; adapting the HP formula above (since the scaling works out similarly), we can call it 3dx5; the rest follows from that and is summarized in the table below. Interestingly, this also gives us how many shots an average, unarmoured, spacecraft can absorb from a major battery its own size (which stays constant for all sizes): Less than one.

The 6,000 mile range given in THS is shorter than the one given in Spaceships; we’ll instead give it a half-damage range of 2,000km and follow the progression from Spaceships. Damage is one-half out to double that distance, then quartered to quadruple that distance, i.e. the weapon does 3dx5 up to 2,000km, 3dx2 out to 4000km, and 3d damage out to its full range of 8000km.

Major Battery Railgun Damage Laser/Particle Beam 1/2d range Laser 1/2d range Particle Beam
SM+5 3d 3dx3 2000km 1000km
SM+6 3dx2 3dx5 2000km 1000km
SM+7 3dx3 3dx6 2000km 1000km
SM+8 3dx6 3dx10 5000km 2000km
SM+9 3dx10 3dx20 5000km 2000km
SM+10 3dx20 3dx35 5000km 2000km
SM+11 3dx35 3dx60 10000km 5000km
SM+12 3dx60 3dx100 10000km 5000km
SM+13 3dx100 3dx200 10000km 5000km
SM+14 3dx200 3dx350 20000km 10000km
SM+15 3dx350 3dx600 20000km 10000km

Note that the particle beam has armour division of (5).

Lasers do not have any roll-to-hit; they just hit. Right now, that’s a remainder from 3e’s rules (THS:197), which just had you roll to determine damage with a failure meaning half damage.

#### KKMP

KKMPs are the bread and butter of THS’s combat: A munitions pack containing thousands of tungsten pellets. They are launched via coilgun; a 333mm one is given a mass of 0.16 tons (empty) - far below Spaceship’s resolution. Spaceships instead has a 32cm gun at 5,000 tons (!). However, those are high-velocity guns, which launch projectiles at five km/s, while THS’ coilguns fire at about 750m/s. Instead, we’ll call the coilgun “Free Equipment” - every spacecraft can deploy KKMPs without any issue.

The KKMP itself does 1dxRV per hit, where RV is 2 + 2 per mps of velocity difference. Let’s call it 2d per km/s relative velocity difference.

Chance-to-hit is dependent on the speed with which the cloud of tungsten pellets expands. Essentially, a spacecraft can avoid every single pellet if it has enough time and acceleration to do so. We’ll first check the assumptions given above: An SM+8 spacecraft takes nine hits. Its front area is roughly 100$m^2$; we’ll call it a density of one pellet per 10$m^2$. This is also roughly the front area of an SM+5 craft. Side area is 5x that, so 5x as many hits. You can see the result in the table below; you can also check the Speed/Range Table: double SM, read the corresponding linear measurement in yards, and divide it by 100. As an example, SM+8 means you look at the +16 entry; that’s 1000, so you get 10 hits. Alternatively, subtract 6 from the SM, then double the result. As an example, SM+8 means you get 2, which is doubled to 4; looking at that entry in the range table nets you, again, 10 hits.

SM Base KKMP Hits
SM+5 1
SM+6 2
SM+7 5
SM+8 10
SM+9 20
SM+10 50
SM+11 100
SM+12 200
SM+13 500
SM+14 1000
SM+15 2000

Now we have to determine the spread of the pellets. We know that they do 2d base damage, compared to the railguns below at at 3dx5 base damage. This gives us a mass difference of a bit less than 50; with the 16cm railgun being about 33kg, we’ll call each pellet one kilo. Knowing this, we can also get the number of pellets in one KKMP; it’s one ton per shot for a KKMP, meaning we have a nice 1000 pellets per deployment. At the assumed density of one per 10$m^2$, we therefore have a “disc” of pellets with a diameter of 80 metres. That disk moves perpendicular to the target while expanding.

This also gives us the numbers on how to avoid them. If we assume an acceleration of 1G, four seconds are sufficient to clear the disk. Quadrupling acceleration halves time to get clear. This gives us an unavoidable range of 4*RV/a. At a closing speed of ten km/s, that’s only 40 kilometres. That range can be increased; each quadrupling of KKMP mass doubles the effective range. It is also increased by SM; every four seconds, decrease number of hits by two steps. I.e. a SM+10 craft will be hit by an average of 50 pellets after four seconds, 10 pellets after eight seconds, 2 pellets after twelve seconds, and by none after sixteen seconds, or 160 kilometres at 10km/s relative velocity.

#### XLMP

XLMPs are also deployable by every craft. They do 4dx5(2) damage. This is for “several” packages in one one-ton XLMP. Assuming damage scales same as the others, each quadrupling in mass increases damage by a factor of 2, i.e. a 64-ton XLMP would do 4dx40(2) damage. Half-damage range is 500 kilometres, maximum range 2,000. This is for a one-ton XLMP; larger ones should have a higher range.

#### Railguns

A 155mm railgun, from Deep Beyond, masses 22 tons and launches projectiles at 15km/s. The text claims that this velocity “is higher than the standard coilgun”. This is correct, insofar as claiming that a tank cannon launches projectiles with more velocity than a human thrower. In Spaceships, that would be a major battery for less than SM+8. It does 6dx(5+RV) damage, which is multiplied by ten if penetrating armour.

We’ll call an SM+8 major-battery railgun 3dx6xRV damage, where RV is again the relative velocity in km/s. You can see the values for different major batteries in one of the tables above. Note that, while railguns’ damage might seem small, it is usually multiplied by at least 15 - more if approaching.

Unavoidable range (the range in which a manoeuvring target cannot sufficiently change its position to avoid the shot) is far larger than the low-velocity coilguns; the relevant parameter is now time to clear one vehicle length.

This can be computed by looking into the “linear” column of the SSR table. To get seconds to clear at 0.5G, subtract five from SM, and divide the result by 2. Look this up in the SSR table. For example, an SM+9 craft can avoid any (unguided) shot after five seconds. If we increase acceleration, divide this number by the square root of the acceleration factor. 2G, for example, is 4x meaning it only takes 2.5s. The 0.5G version gives a railgun a range of 75 kilometres from rest. At ten kilometres relative velocity, it’s 125 kilometres. All in all, kinetic weapons are quite short-ranged.

But we’re not restricted to unguided projectiles! Replacing the rear third of the railgun projectile with many solid-fuel short-term boosters (ISP of about 0.15km/s each, so 0.9km/s total) and one of the core locations with a “control room”, it can now match a total of 0.9km/s acceleration of the target. For the Oberth example (1.5G), that’s 60 seconds (ignoring the time-to-clear from above). That’s an unavoidable range of 900 kilometres from rest, and 1500 kilometres from ten km/s relative velocity.

Against the previous example of 0.5G, that’s 180 seconds, for 2,700km range from rest - quite an improvement!

#### Particle Beams

Particle beams, unfortunately, do not actually have any damage statistics in Transhuman Space. We’ll therefore assign them the same damage as a laser, but give it a shorter range, mirroring Spaceships here. Also following Spaceships (that’s the Accelerator Tube Limits from SS7), particle beams cannot be mounted below SM+8 as a major battery (SM+7 spinal, SM+9 medium, SM+10 secondary, SM+11 tertiary).

#### Ramming

Last but not least, ramming. Ramming is very easy to scale: It does 3dx the lower HP of the craft involved in the ramming, times the relative velocity.

For context, this means an AKV moving at 1km/s should be able to destroy most SM+10 craft by ramming. That does make sense.