GURPS Ultra-Tech: Square Root of Destruction

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 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 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).

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.