Another technical discussion: Point defense vs. Railgun slugs

[GunnerJ]

Played my first game of GURPS tonight, and it was TS. It went very well, although I may eventually need help balancing things and I will need to acustom myself to the system more. This post describes an incident testing out the space combat rules involving a player who is a physics whiz. When I discussed point defense against railgun fire (not an idle discussion: the PCs' vessel has a railgun and they were firing it), he had some strong objections which we worked out after the game.

Deep Beyond lists stats and rules for railgun fire. The rules for point defense against railguns state that a success on a point defense roll with a laser will destroy a burst of ten slugs, and that even failure will destroy some.

The only viable point defense against a kinetic weapon is to a) vaporize it so it disperses, else you just have a hot and/or liquid mass moving at you as fast and with the same energy as before, or b) move it out of the way. Let's examine each in turn for a railgun. I will assume that a railgun fires tungsten slugs. Other givens:
-Speed of a slug in flight is 10 mps (DB, pg 152)
-Each slug is one-fifth of a cubic foot in volume, or 5663 ccs. This is derived from DB pg 152, which states that 26 bursts worth of railgun fire fit into 0.1 space, or 50 cubic feet. 26 bursts is 260 slugs, 50/260 = 0.2 cubic feet.
-Mass fo a slug is derived from the density of tungsten, 19 g/cc, to be 108 kg.

a) Vaporization.

Wikipedia lists the heat of vaporization of tungsten to be 806.7 kJ/mol. Tungsten's atomic mass is 184, so it has mass per mole of 184 g. This effectively works out to 806/184 = 4.4 kj/g. Since a slug masses 108,000 grams, it requires 475,200 kJ, or 4,752 MJ of energy to vaporize it. For ten slugs, that's 47,520 MJ. A vessel would need around 9,000 5-MJ lasers to vaporize a burst of railgun fire.

b) Moving it out of the way

Light has momentum, equal to its energy divided by the speed of light. For a 5 MJ heavy laser cannon, the momentum it can impart is 5 MJ / 300 M m/s = 0.02 kg m/s of momentum. Since force is equal to momentum over time, in a space combat turn of 100 seconds, a heavy laser exerts 0.02/100 = 0.0002 N of force. If a slug is 108 kgs, and inert, a heavy laser may be able accelerate it by 0.0002/108 = 1.85 * 10^-6 m/s^2. After 100 seconds, the inert slug will be travelling 0.000185 m/s. Ten slugs travelling 10 miles per second would doubtless be an even more formidable challenge.

I am posting this very late (or rather early), so my math may be off in some way. Assuming it is not, where, besides the desire effect a certain game world outcome (i.e., point defense making certain weapons obsolete) did the rules for point defense against railgun fire come from? Why wouldn't more spacebourne warcraft mount railguns instead of particle accelerators?

[Fnordianslip]

The only thing I can think of is this. You don't have to completely vaporize a slug to make it ineffective. The energy that goes into vaporizing even a bit of the slug has to go somewhere. Usually, that somewhere would be the rest of the slug. Also, I believe that during the course of partial vaporization, the forward facing bit of slug would actually act as a reaction mass slowing the slug down. All you would have to do is get it slow enough and/or burn off enough mass to make it useless. A slug at 10 miles/second is a deadly weapon, half a slug flying at an odd angle at 5 miles a second and a cloud of fast moving vapor expanding in all directions is probably less of a hassle. Though, that is, at best, a guess. Sigh, time to look back at the old physics book methinks.

[GunnerJ]

That is a possibility, but I unfortunately wouldn't be able to do any calculations on it; the OP demonstrates the extent of my ability to do physics. The kinetic energy imparted on a mass by partial vaporization... beyond my ken, at least at this hour.

[theltemes]

Originally Posted by GunnerJ

a) Vaporization.

Wikipedia lists the heat of vaporization of tungsten to be 806.7 kJ/mol. Tungsten's atomic mass is 184, so it has mass per mole of 184 g. This effectively works out to 806/184 = 4.4 kj/g. Since a slug masses 108,000 grams, it requires 475,200 kJ, or 4,752 MJ of energy to vaporize it. For ten slugs, that's 47,520 MJ. A vessel would need around 9,000 5-MJ lasers to vaporize a burst of railgun fire.

You need more energy than this. You need to add the latent heat of fusion (melting) to turn the slug from solid to liquid, and the energy required to raise the temperature from its initial temperature to the melting point as well as the energy to raise the temperature from the melting point to the boiling point.

Originally Posted by GunnerJ

b) Moving it out of the way

Light has momentum, equal to its energy divided by the speed of light. For a 5 MJ heavy laser cannon, the momentum it can impart is 5 MJ / 300 M m/s = 0.02 kg m/s of momentum. Since force is equal to momentum over time, in a space combat turn of 100 seconds, a heavy laser exerts 0.02/100 = 0.0002 N of force. If a slug is 108 kgs, and inert, a heavy laser may be able accelerate it by 0.0002/108 = 1.85 * 10^-6 m/s^2. After 100 seconds, the inert slug will be travelling 0.000185 m/s. Ten slugs travelling 10 miles per second would doubtless be an even more formidable challenge.?

One way around this is to use the lasers to vaporize part of the projectile (not directly on the facing side, which just slows it down, but on the side to deflect the projectile), using the ablated material to act as a rocket to push against the part that remains solid/liquid. For smaller craft, you probably only need to deflect the path of the projectile on the order of ~100m to make it miss entirely.

[GunnerJ]

One thing I neglected to account for is that while TS laser weaponry is rated for MJ, over the course of combat they're really effectively MW weapons, since they beam their listed energy every second for 100 seconds. So, the total energy deposited over 100 seconds by a 5 MJ laser would be 500 MJ, or 50 MJ per slug.

Still not enough to toally vaporize them, but having heard two people suggest that partial vaporization can move something off course, I'm inclined to believe it's plausible, especially with more energy at hand.

Now I'm just left wondering why, if laser damage represents a full 100 seconds of focus on a target, a point defender can damage multiple targets with only -1 damge per die as a penalty. Not related to this exactly, but it is another oddity of the TS system that seems to make point defense extrodinarily powerful. I'm inclined to make a point defender declare ahead how many targets he wishes to potentially defend against and with how many weapons, and then multiply damage by (weapons/targets) or something.

[GunnerJ]

There's actually another odditiy to the laser damage question. The space comabt rules list a light laser as doing 2d*5, or effectively 10d cDam, which is 1000d normal damage, over 100 seconds. In one second, then, it should do 10d damage. However, the weapon list gives a light laser's damage as 100d, or 1d cDam, in a single second. To do 10d cDam over 100 seconds, it would only need 10 seconds of focus. This seems to lead to two interpretations:

1) The weapon list is right, the space combat rules are wrong: a light laser does 1d cDam per second, and its final 2d*5 cDam for 100 seconds only represents 10 seconds of focus. A laser can do full damage in point defense on perhaps ten targets with a small damage penalty per target. Note that this also implies that a laser can attack 10 times in a single space combat turn and only suffer -10 damage per shot as a result (average damage on 2d*5 is 35, max is 60)

2) The space combat rules are right, the weapon list is wrong: A light laser does 2d*5 damage over 100 seconds of focus, and therefore should do 10d per second. A point defender cannot do full damage to multiple targets with only a pithy -1 per die; in fact, damage done should be halved for two targets, thirded for three, etc. Spacecraft-mounted lasers would be very, very bad at killing small targets like battlesuited people and vehicles in normal combat, since they "only" do 10d damage. Perhaps the damage done by man-portable kJ lasers should be reconsidered.

[GunnerJ]

Originally Posted by Agemegos

This isn't a point defence as such, but I notice that you are assuming a flight time of 100 seconds. Random evasion at 1/10 of a gee will produce a 3-mile uncertainty in your position after 100 seconds. If your ship; is less than three miles in radius, and if you can manage 1/10 of a gee, teh rail-gun is very unlikely to hit in the first place.

The rules address evading a railgun salvo, but you need to have taken a certain manuever on your last turn or something.

[Anthony]

I think one error here is that you assume that railgun ammo bays are solid ammo. Munitions packs, if my notes are correct, are 9.5 stons for 0.5 hullspaces. That works out to a mass of 6.6 kg per shot; including packaging, the actual weight of a shot of ammo is probably 3-4 kg.

[MrTim]

Originally Posted by GunnerJ

There's actually another odditiy to the laser damage question. The space comabt rules list a light laser as doing 2d*5, or effectively 10d cDam, which is 1000d normal damage, over 100 seconds. In one second, then, it should do 10d damage. However, the weapon list gives a light laser's damage as 100d, or 1d cDam, in a single second. To do 10d cDam over 100 seconds, it would only need 10 seconds of focus. This seems to lead to two interpretations:

A third interpretation is that the default assumption is that the laser will only be on target about a tenth of the time, even on a successful hit.

[GunnerJ]

Originally Posted by Anthony

I think one error here is that you assume that railgun ammo bays are solid ammo. Munitions packs, if my notes are correct, are 9.5 stons for 0.5 hullspaces. That works out to a mass of 6.6 kg per shot; including packaging, the actual weight of a shot of ammo is probably 3-4 kg.

I didn't think of railgun ammo as a munitions pack... I'll look at slugs-by-mass. 26 bursts worth of slugs weight 0.28 tons, or 254 kilograms. If we assume that these are pure slugs with no casing, it's about 254/260 = slightly under one kilogram per slug. They are tiny... Wow. I think you've solved it.

My friend mentioned that even if the laser vaporizes part of a slug, it can't get any more energy to move the slug away than that which was already in the laser. Combined with the fact that a 10 MJ laser is, really, a 10 MW laser beaming energy over 100 seconds, and that I underestimated the mass of a slug a factor of 100, this makes my initial estimates of point defense feasability off by about four orders of magnitude.

Originally Posted by MrTim

A third interpretation is that the default assumption is that the laser will only be on target about a tenth of the time, even on a successful hit.

Well, this seems like the first possibility:

Originally Posted by Me

1) The weapon list is right, the space combat rules are wrong: a light laser does 1d cDam per second, and its final 2d*5 cDam for 100 seconds only represents 10 seconds of focus.

Although I guess what you're saying is that the laser is only firing 10% of the time. I don't believe this is so. Consider the Laser Table on TS 181. It lists a 2.5 MJ laser either as requiring 5 MW of power or as draining 500 MJ from a capacitor for a whole combat turn. If the laser is only firing 10% of the time, this is about 5% efficiency. If it's firing for the whole 100 seconds, it's 50% efficiency. Thus, how the laser acts over a whole combat turn is linked to how efficient it is. I'm inclined to belive that TS laser weapons are more than 5% efficient (not in the least because there's no accounting for what happens to all that waste heat!).

If, however, you really mean that the laser is firing all the time but only on target for 10 seconds, then it's just the same as my first possibility, and has the same implications. If "full damage" only represents 10 seconds of focus, it's theoretically possible for a very skilled gunner to keep it on more than that, so it should be possible for a laser to fire ten times and hit ten times, albeit with some sort of penalty.