GURPS Ultra-Tech: Square Root of Destruction

[Mailanka]

Pyramid #34: Alternate GURPS includes a fantastic article on converting GURPS Spaceships into a sort of GURPS Vehicles replacement. Additionally, he added a new set of charts for converting Spaceship's energy weapons from the "cube root based" numbers of standard GURPS with "square root based" numbers, thus increasing the damage of high powered weapons and more closely matching the progression of projectile weapons.

I thought it would be nice to do the same with GURPS Ultra-Tech, but I quickly ran into the problem. Exactly where are the cube roots in GURPS, so we can extract them and replace them with square-root based damage numbers? It doesn't seem to be the value of the energy in joules, nor can you derive it directly from the damage itself because the numbers in the Pyramid article do a funny thing: Below a certain threshold, they actually get smaller than the cube-root numbers, which suggests we're looking at the fractions of some value (the cube root of a fraction is larger than the square root of a fraction). After some experimenting, I found that the mass of the weapon seemed to be most important factor: (60 x weapon mass in tons)^(1/3) = dDam 1 in dice (to derive dDam2, double the equivalent value of dDam1). For example, a 10MJ weapons system is a single system on a +5 ship (making it about 1.5 tons), we'd expect a standard dDam1 value of 4 dice (8 dice with dDam2), and that's just what we see. If we replace the cube root function with a square root function, we expect to have a dDam1 value of 9.5, and we see we have 9d+2 (and 20 dice with dDam2). If you go below 100 KJ (that is, below 0.015 tons), you'd expect to find your square-lasers become weaker than your cube lasers, and they do just that.

The numbers aren't perfect, but if you account for rounding, they do match up pretty nicely to the actual numbers in the table, nicely enough for our purposes.

However, we already have both charts. We don't need the math behind it for spaceships. No, we need to know the math for the beam weapons in Ultratech, so we can make our Laser Rifles more competitive with Storm Carbines, right? However, these weapons are more complex. We have a difference between the mass of the weapon (the stock, the barrel, the grip) and the power cell (the only source of energy), the number of shots that the weapon can fire, the RoF and so on. So I pulled open the book, a spreadsheet and my trusty calculator and started to see if I could find a relationship between any of these and the damage value.

To my surprise, the only thing that seemed to matter across the board was the weight of the weapon (not, as I expected, the cell. I mean, you'd think the stock has nothing to do with how much damage a laser rifle can kick out, but apparently the stats in Ultra Tech assume a minimum amount of gun necessary to fire the shot), the TL of the weapon, and the nature of the beam being fired. It seems to work thus:

Take the cube root of the weight of the weapon in pounds, and multiply this by a value based on the TL and the type of beam fired (We'll call this the "Beam Factor").

The Laser Beam Factor:
-TL 9 Lasers: 1.5
-TL10+ Lasers (of any kind): 3

The Blaster Beam Factor: 3

The Pulsar Beam Factor: 6

the Plasma Beam Factor:
-TL 9 Flamers: 3
-TL 10 Plasma: 5
-TL 11 Plasma/Fusion: 7

The Graviton Beam Factor: 1.5

The Force Beam Factor: 4

The Disintegrator Factor: 60

The Ghost Particle Factor: 6

This will derive the value of every ultra-tech beam weapon (accounting for some rounding) for every weapon but the following:
-Several Rainbow Weapons (the Rainbow Dinosaur Laser seems to be in error, but the Rainbow Strike Laser won't work with this formula)
-The Graser Rifle (probably an error and meant to be 6)
-Most "Particle" Cannons, including the Blaster Cannon, the Pulsar Cannon, the Plasma Cannon and the Fusion Cannon
-Force Cannons
-The small-scale disintegrators, which have no logic that I can fathom (perhaps they're made up numbers to suit genre, rather than based on any consistent formula).
-The Semi-Portable Flamer

I think it's highly likely that at least some of the numbers that don't fit are either erroneous or arbitrarily changed to match some sci-fi trope, but I expect the majority of my mismatches are the result of me not actually having the numbers right in front of me. There's probably some subtle factor that I'm missing, one that doesn't show up at low levels but becomes more important with larger weapons, especially with particle/anti-particle/plasma cannons, explaining the discrepancies. Also, there's some judicious rounding going on, and some numbers fit better than others, which also suggests to me that I'm missing some factors... but the above seems to work 90% of the time, which means that it's probably close enough for our purposes until GURPS Vehicles comes out.

So, if you want to bring the Square Root of Destruction into the hands of your players, you need only take the square root of the mass of a weapon, and then multiply it by the Beam Factor above to derive the new and improved damage. Expect pistols to remain about where they are, rifles to see a small improvement, and semi-portables and heavy weapons to see a huge increase.

[Refplace]

That's cool.
On your concern about weapon weight rather then just the energy cell.
I recall it being mentioned that the stocks likely contain some of the electronics and are more a part of the weapon then just handling like in modern firearms.
And it seems reasonable that different beam emitters will have an effect more then just the energy supplied so I am quite comfortable with and prefer the entire weapon weight being factored in rather then just the cell.

[Anthony]

Originally Posted by Mailanka

I thought it would be nice to do the same with GURPS Ultra-Tech, but I quickly ran into the problem. Exactly where are the cube roots in GURPS, so we can extract them and replace them with square-root based damage numbers?

Just take the 3/2 power of damage, though that will produce balance issues because things aren't tuned for that; 3/2 power of weapon mass will do a better job balance-wise but may have bizarre effects. On the other hand, converting to square roots doesn't solve anything anyway, GURPS Vehicles scaling was always messed up anyway.

[Mailanka]

Originally Posted by Refplace

That's cool.
On your concern about weapon weight rather then just the energy cell.
I recall it being mentioned that the stocks likely contain some of the electronics and are more a part of the weapon then just handling like in modern firearms.
And it seems reasonable that different beam emitters will have an effect more then just the energy supplied so I am quite comfortable with and prefer the entire weapon weight being factored in rather then just the cell.

It just surprised me. I imagine it reflects the fact that more... laser-stuff around the cell leads to a greater efficiency of applying the energy down field. And naturally the weight of the cell are factored into the weight calculations.

I've read that GURPS Ultra-tech was originally designed as a "gadget-building toolkit," and that this mission statement changed later into the gear-catalog we have today, but you can still see elements of that toolkit there. The weapons, after tearing them apart and putting them back together, seem to represent the bare minimum weight necessary to construct a proper weapon (that is, the cell, the focusing-doohickeys, the power-relays, the whatchamajiggers) with things like stock, ironsights, the grip and the trigger representing negligible amounts*, and if you, say, went though HT and started adding stocks and ruggedizing the components so they weighed more, obviously the weapon wouldn't suddenly deal more damage.

*(In fact, you'll find my numbers tend to trend "too high" on the pistols, not by much but enough that you have to round down to get the proper numbers. I imagine there are actual numbers regarding how much handling mechanisms like the grip and trigger actually weigh, and these are less negligible for a pistol than for, say, a semi-portable fusion gun)

Originally Posted by Anthony

Just take the 3/2 power of damage, though that will produce balance issues because things aren't tuned for that; 3/2 power of weapon mass will do a better job balance-wise but may have bizarre effects. On the other hand, converting to square roots doesn't solve anything anyway, GURPS Vehicles scaling was always messed up anyway.

I'll be honest, I did this little experiment more out of a desire to understand the formulas for building my own guns than anything else. I'm one of those jerks that totally wanted GURPS Vehicles yesterday, and I've just consigned myself to tearing apart what they keep spitting out, putting it back together, and trying to figure out how things work. Somethings are becoming more clear to me and I'm becoming better than I thought I'd be without any actual formulas in front of me.

As to whether or not squares are better, or your method is better: squares won't do squat for pistols, I've found, they don't do much for rifles, semi-portables notice a big jump in power, and beam cannons put projectile cannons to shame. Simply multiplying beam damage by 3/2 would boost pistol damage, and wouldn't overpower cannons quite so much, so it might actually be better balanced than squaring our cubes.

[Anthony]

Originally Posted by Mailanka

Simply multiplying beam damage by 3/2 would boost pistol damage, and wouldn't overpower cannons quite so much, so it might actually be better balanced than squaring our cubes.

3/2 power does not mean multiply by 3/2. It means multiply damage by the square root of damage. A 2d attack would become 3d-1, a 4d attack would become 8d, an 8d attack would become 22d+2, a 16d attack would become 64d.

[Mailanka]

Originally Posted by Anthony

3/2 power does not mean multiply by 3/2. It means multiply damage by the square root of damage. A 2d attack would become 3d-1, a 4d attack would become 8d, an 8d attack would become 22d+2, a 16d attack would become 64d.

I've never heard of this particular solution. Why would you use it? Where did it come from? Is it from a GURPS book, or did you come up with it on your own?

[Anthony]

Originally Posted by Mailanka

I've never heard of this particular solution. Why would you use it?

If you have an equation in the form D1 = k * E^1/3 and you wish to transform it into an equation of the form D2 = j * E^1/2, you do so through the transformation D2 = j * (D1/k)^3/2, or D2 = (j/k^3/2) * D1^3/2. I don't happen to know the value for (j/k^3/2), so I set it to 1; alter to taste. This is first year algebra.

[Humabout]

Originally Posted by Anthony

If you have an equation in the form D1 = k * E^1/3 and you wish to transform it into an equation of the form D2 = j * E^1/2, you do so through the transformation D2 = j * (D1/k)^3/2, or D2 = (j/k^3/2) * D1^3/2. I don't happen to know the value for (j/k^3/2), so I set it to 1; alter to taste. This is first year algebra.

More simply put, when dealing with fractional exponents, you first raise the number to the power of the numerator and raise the result to the denominator-th root. For example, x^(y/x) = z-th root of (x^y).

All of that aside, the sort of thing Mailanka is talking about has bugged me for ages. I need some sort of formula for creating my own guns. The ones from 3e don't do the trick, but I'll bet the new ones are based on them in some fashion. Considering the regularity of the beam weapon damage tables, I'd bet the accuracy, range and weight are functions of beam type and beam damage, shots, and RoF. Bulk is a function of configuration and beam type, and ST is a function of weight, straight up (IIRC, just finding the minimum BL to lift the weapon usually works for non-pistols, and adding 2 to that gives a pretty accurate result for pistol configurations). I also have something for slug-throwers based on minimum BL and impulse, but I'd have to look it up.

Any chance you could post what you have so far, Mailanka? Perhaps if we get everyone working on it, we'll all get closer to the answer.

[Mailanka]

Originally Posted by Humabout

Any chance you could post what you have so far, Mailanka? Perhaps if we get everyone working on it, we'll all get closer to the answer.

My original post is all I got. It may seem simple, but it involved a day of putting things out on a spreadsheet, creating models and seeing how well they matched up to the actual stats, and the above was the best model I got. You do get a lot of mileage from making spreadsheets out of the weapon-stats and then sorting based on certain things to start to see the patterns that form, and then cross-referencing things with what you find in Spaceships, which seems to be a simplification of what we'll actually find in Vehicles.

I suspect range is also a factor of power, and the number of shots you get is a function of what cell you use (that is, a particular weapon weight requires a certain amount of energy to power it, and the more cells you stack on, the more shots you get. That also explains why superscience cells result in x5 shots, but no additional damage).

[Langy]

TL10+ laser weapon damage in Ultra-Tech and Spaceships is approximately 10 times the cube root of the weapon's weight in pounds, then rounded to the nearest 'decent' number.

Note that the weapon weight is the weight without including any power cells.

Weapon cost is purely a function of weapon weight and laser type.

Normal Laser: $1000*Weapon Weight
Rainbow Laser: $1000*Weapon Weigh
X-Ray Laser: $2000*Weapon Weight
Gamma-Ray Laser: $3000*Weapon Weight

A few weapons don't cost this exact amount, but I think that's probably errata (and reported it as such a long, long time ago, though I don't know if it ever was accepted).

A laser pistol has Acc 6, laser rifles Acc 12, and heavy laser weapons Acc 18.

Bulk depends upon the weapon's form-factor:

Holdout Pistol: -1
Pistol: -2
Carbine: -3
Rifle: -4
Heavy Rifle: -5

This is a very rough estimate, though. Basically just eyeball what you think the Bulk should be. If it's especially short for its weight, it's +1 Bulk, if it's especially longer for its weight, it's -1 Bulk, etc.

ROF of laser weapons is completely arbitrary. It has no effect on weapon price, weight, damage, or anything else. Same with number of shots.

1/2d Range for normal lasers is approximately 100 yards*(Dice of Damage). Some weapons have ranges 100 yards higher or lower than this value. Max range is 3*(1/2d Range). Range for rainbow lasers is randomly between 2 and 3 times that for normal lasers.