Wednesday, March 18, 2015

Battletech Heap: Laser Equations

Whenever I was doing the FATE inspired by Battletech stuff, I wanted to do some adaptations of some old custom mechs. Because I've changed computers a half-dozen times since I last did any Battletech stuff, it was hard to track down a lot of my records. I had some old Xanga accounts that I kept a lot of it on and I had to download and dig up some of those accounts. For some of the information. And now I have heaps--heaps!--of old Battletech designs and house rules that I'd like to have in an accessible, long-lived here.

If you're the 99% of people reading who don't like Battletech, I'll be explaining stuff a bit, but I won't bullshit you; Wednesdays may not be be a good return on investment for your time so much in the near future. Sorry.

For those of you who are--for you, skiltao, you've probably seen all of this stuff before. Hell, some of this stuff may have been superseded by actual equipment. Whether it's nostalgia or novelty, I hope you enjoy it.

Standard Laser Equations
There are many way to classify Battletech weapons. "Introductory Tech" (sometimes referred to as "Level 1 Tech") is the simplest classification. They're the simplest weapons from which to make a battlemech. There are three types of stanadard laser; large, medium, and small. It's that simple.

Those lasers jump from 3 to 5 to 8 damage with a wide variety of ranges, heats, and tonnages in there. What if we reverse engineer the formulas to derive the other sizes of lasers that are still as simple as the standard lasers?

Equations Deriving Range from Damage

ShortRange = SQR(8 * Damage - 15) - 2

MediumRange = ShortRange * 2

LongRange = ShortRange * 3

Equation Deriving Heat from Damage

Heat = (2 * Damage^2 - Damage) / 15

Equation Deriving Tonnage from Damage

Tons = (13 * Damage^2 - 89 * Damage + 180) / 60

Equation Deriving Critical Slot Size from Tonnage

Crits = (2 * Tons^2 - 3 * Tons + 37) / 36

Plug everything in, then round. For Crits, heat, and range, round as per normal to nearest integer. For Tonnage:

Round: N.01 to N.24 to N         [2.22 becomes 2.0]
Round: N.25 to N.74 to N.5       [7.66 becomes 7.5]
Round: N.74 to N.99 to N + 1     [14.8 becomes 15.0]

I totaled up the lasers of classes 4, 6, 7, and 9-12. Results shown below.

Name        Dmg   Heat SR    MR     LR   Tons  Crits  Canon(Y/N)
Small Laser  3     1    1     2      3    0.5    1      Y
Quad Laser   4     2    2     4      6    0.5    1      N
Medium Laser 5     3    3     6      9    1      1      Y
Laser 6      6     4    4     7     11    2      1      N
Laser 7      7     6    4     9     13    3      1      N
Large Laser  8     8    5    10     15    5      2      Y
NonLaser     9    10    6    11     17    7      3      N
DecaLaser   10    13    6    12     18   10      6      N
11 Laser    11    15    7    13     20   13      9      N
12 Laser    12    18    7    14     21   16.5   15      N

The Quad Laser makes the Small Laser obsolete, so it's pretty much out.

The rest have a place except for the DecaLaser. It's a weak PPC. Dropping 3 hexes of minimum range isn't worth three extra tons, crits, and heat. It's worthless.

The 12-Laser is useful only because it's a headcapper with the range of an LRM. It's the decision of the player as to whether or not 18 heat and 16.5 tons and more crits than an AC/20 with four tons of ammo is worth it. That's five tons of IS TC.

There's nothing in the 1-2 damage range because the way I worked the ranges (calculating short range from damage) meant that you couldn't have less than 1 hex (which the Small [3] Laser has). If I changed the equations to yield long range instead, I could have 1/2/- and 1/- lasers. However, they can't weigh less and have less heat than a Small Laser, so either the entire idea is a malfeasance (which many will say it already is) or that I'd have to "bank" these picolasers and nanolasers so that each weapon actually represented smaller clusters of the weapon grouped to yield significant tonnage, heat, and crits (which will be fractional before rounding).

IIRC, I assumed that the original numbers for the small, medium, and large lasers were the center of their values. That is, I assumed that a Large Laser's damage value was 8.0 and not 7.5 or 8.49. Further work could be done to waggle those values and create a different set of stats, which might invalidate the Quad Laser (unlikely. Fear the Quad Laser) or maybe nudge the pico-, nano-, and deca- lasers into usefulness.

Also, how are these font changes working? Shifting from Verdana to Courier and back seems like it would be jarring, but not as jarring as a whole post written in Courier.

On the topic of Battletech, if you're not a Battletech person, I am planning on contextualizing these a bit. If a more thorough explanation or an outright overview would work better for you, let me know and I'll see if I can work up a primer.

Also, as I look through the old blogs I realize I used to complain about personal stuff a lot and don't anymore and that's really worrying.


SkilTao said...

"Hell, some of this stuff may have been superseded by actual equipment."
Yep. If I remember right, your "finned heatsinks" inspired the discussion which resulted in Partial Wings.

Switching fonts is helpful, since it helps call out the switch from old material to your current reflections on the old material.

With only 4 data points, I'm sure there's a number of different systems that could replicate the standard laser stats. My dream (which I am not atually pursuing just now) is still to reverse-engineer the Fusion Engine Table, but this time with an (Engine Rating)^(3/2) term, and with separate significant and positive terms for each of the reactor, engine/transmission/myomers, and radiation shielding so they can be accounted independently of each other.

MOST of the people I know who used to complain about personal stuff online ALSO stopped after a number of years. Not sure why that'd be worrying, unless you've got a time machine and get stuck with your past self as a co-worker.

VanVelding said...

Ugh. I could never get stuck with myself as a co-worker; I don't work anywhere that long.

Man, the engine formula. That's the holy grail. Can you make a thing that reverse-engineers formulas and then takes out engine weights that break the curve the hardest?

I mean, the stated weights aren't holy; they're not based on an original formula or extensive playtesting (as far as I know). Some of them need to be knocked around to create a sensible formula.

And I'll be honest; the finned heat sink thing sounds vaguely familiar, but I don't remember any of it. It doesn't come up a lot, but I have a really bad memory.

SkilTao said...

The finned heat sink thread is from Dec '05; I couldn't have named it if I didn't have a copy saved.

I strongly suspect the engine weights *were* originally derived via an equation; at the very least, they follow a reasonably simple curve pretty closely, which Rick Raisely reverse-engineered many years ago:

If I want my new equation then yeah, I think I'll pretty much *have* to write a program to find it for me; and with XL (and XXL) engines becoming ever more normal, weights probably ought to be rebalanced anyways.