Missile Equations: Finale, Pt I

Man, after a lot of work, I finally have my 'good enough' missile equations. Let's get to it.

Is It Good?

So I ran these equations for SRMs, LRMs, and MRMs. I had to do the rest as templates because the numbers were cray. I also had to base factors on two things: damage per shot and to-hit over 38 hexes.

Damage per shot lumped damage per missile and missiles per shot (tubes) into one big factor that ignored cluster size. Surely, SRMs would change significantly if they landed in clusters of 5. These equations mostly don't care about that. Somehow, I made equations that allow for Thunderbolt launchers to be added as a template.

To-hit over 38 hexes, TH38, looks at the maximum range of Extended LRMs and using that as a cap, incorporates cluster bonuses/maluses, to-hit bonuses/maluses, minimum ranges, and range brackets into one factor that can be worked with. All I cared about was that the TH38 for SRMs was less than that for MRMs, which was less than that for LRMs. It was, so I ran with it.

Doing the equations for the big three (short, medium, and long) were satisfactory, but not perfect. LRM 10's and MRM 20's lost a half-ton. LRM 20's lost a full ton and MRM 40 gained a ton.

MRM 30's gained a crit and MRM 20's gained two crits. It failed in that it is incorrect, but it makes sense. Why wouldn't an MRM 20 be as big as the LRM 20? 

"Making sense" isn't my metric; a trade-off of flexibility and fidelity are my goals. But making sense is a big plus in a system flexible enough to make valid, custom missile systems.

The LRM 20 and MRM 20 each generate one additional heat. I hoped to ensure that larger launchers were more heat efficient than their smaller counterparts--and I generally succeeded--but it's disappointing the LRM 20 backslid a bit there. The MRM 30 generates 1 less heat.

Missile efficiency is the same. There's 121 points of damage per ton of LRM ammo instead of 120. I'm sure that the benefits that confers on the LRM 11 won't be insurmountable. MRMs also picked up an additional point of damage per ton of ammunition. Not bad.

When these numbers were run and templates were applied to other systems, it also produced some inaccuracies. Of course, the Extended LRMS are all off because they were clearly designed while fucking high as hell. 

Seriously, a 6-ton, 1-crit ELRM 5? Fucking seriously? Larger racks should be more efficient than smaller racks and I just made an Azmad with three ELRM 5's, but damn, that's irrationally bad. So of course, ELRMs derived from a logical, consistent system are going to be non-canon.

Fuck Rocket Launchers.

Equations 

TH38 = 

    Cluster Hit % * 

    SUM (

        [LongRange-MediumRange] * Lookup[4+ToHitBonus, ToHit%Table],

        [MediumRange-ShortRange] * Lookup[2+ToHitBonus, ToHit%Table],

        [ShortRange-MinimumRange] * Lookup[0+ToHitBonus, ToHit%Table],

        Lookup[MininumRange,MinimumRangeTable]

    ) / 

    38

Given that:

Tonnage

Tonnage per (Damage/Shot) = -0.822+(20.3*TH38)-(120*TH38^2)+(253*TH38^3)

Multiply by maximum damage per shot, and you get the tonnage of the launcher.

Crits

Crits per (Damage/Shot) = 0.21-(0.0185*Damage/Shot)+(0.00249*(Damage/Shot)^2)-(0.0001*(Damage/Shot)^3)+(0.00000122*(Damage/Shot)^4)

Yes, it uses Damage/Shot as a factor and as a multiplier to get the final crits. What can I say? It works. It also means that missile range doesn't matter one whit in calculating crits. Yes ELRMs and NLRMs do have more crits, but they're templates, not calculated missiles.

Heat

Heat per (Damage/Shot) = 0.452-(0.0085*Damage/Shot)+(0.000125*(Damage/Shot)^2)

This one also uses Damage/Shot as a factor and multiplier, and this works for LRMs, SRMs, and MRMs.

Total Damage per Ton of Ammunition 

Damage/Ton = 526-(5669*TH38)+(22170*(TH38^2)-(28069*TH38^3)) * ClusterSize^0.5

I literally had to tweak this by hand to get it, but I got it. I really tweaked those cluster sizes to try and get it to work just right for everything, but to no avail. Eventually, 0.5 was just the simplest-fit number.

Templates

These are based on an in-character document I currently have drafted.

    Thunderbolt System - The equations above do not work for single-tube system, due to the Tamarian Dual-Loading System, a single-tube system is about the size of a two-tubed system. For dedicated single-tube systems, use the multipliers below.
    Tonnage: x1.77
    Heat: +1
    Ammunition Damage/Ton: Instead of applying the multiplier to the damage per ton coefficient, just use the base result of the Ammunition Damage/Ton equation and divide by damage per shot to determine shots per ton of ammunition.

    These systems will always have a minimum range of one and deal half damage within that range. They are also incapable of using alternative ammunition types not specifically made for single-tube systems.

    Enhanced LRMs - These equations allow a change in tonnage per tube for a reduction in minimum range. Like other non-LRM missiles made with these equations, it loses indirect fire abilities and the ability to use alternative ammunitions for a ‘mech that shares damage per missile and SR/MR/LR (including NARC and Arrow IV). To gain those abilities back, multiply the crits of the system by 1.9.

    Streak SRMs - Streak systems weigh 1.5x more than their conventional SRM counterparts.

    Extended LRMs - These equations produce very heavy racks with relatively few crits and relatively little heat. If a 17-ton system which deals 10 damage on a good day appeals to you, have at it. Like other non-LRM missiles made with these equations, it loses indirect fire abilities and the ability to use alternative ammunitions. To make a conventional Extended LRM system, apply the following tonnage multiplier (as always, before rounding). The conventional Extended LRM systems still cannot use alternative munition types and have the usual malus for firing within minimum range.
    Tonnage: x0.51
    Crits: x1.75
    Heat: x1.59
    Ammunition Damage/Ton: x0.65

Multi-Missile Launchers - Multi-Missile Launchers can deploy missiles for two types of non-Thunderbolt launchers.
    Tonnage: Tonnage per tube is based on the missile launcher with the larger tonnage per tube coefficient.
    Criticals: Crits per tube is based on the other missile launcher, which must have a larger criticals per tube coefficient.
    Heat: Heat is the average of both launchers for a rack of that size.
    Efficiency of ammunition: Is dependent on the ammunition type used.
If a multi-missile rack can fire munitions from a streak system, all of the munitions it can fire must be streak munitions.

Next week, I'll list some new missile systems and maybe expanded missile systems so you can see that LRM 11.