Thursday, March 6, 2014

Firearms in Fantasy Campaigns III - Damage

Continuing my look at firearms technology and how to mesh it with a fantasy campaign, I've spent some time researching the technology by by era.  As previously stated, firearms need to be categorized by range, rate of fire and damage.  The first two concepts are reasonably straight forward and documentation for them can be found in many locations online.  The third concept, damage, or more precisely it's target - hit points, has been a source of contention within the hobby for years.  D&D has always embraced the ever increasing hit point side, while RuneQuest and Warhammer allowed characters only minor increases to the amount of damage they could absorb at a time over their dangerous careers.

The second point of view, where characters' hit points are treated as a physical characteristic which remains near constant, is actually easier to model with firearms.  One bullet, like one arrow can kill a man and often will.  What I would like to come up with is a model which can handle either end of the system.   One other consideration in rule tinkering is playability.  The fewer number of rolls needed to resolve a situation, the better.

Facts and Figures

A weapon is any object that is used to apply physical force a creature with the intent of damaging or subduing it.  With that definition, it becomes apparent that damage is related to physical force, so the first step is to measure the physical force each type of weapon produces.  Physical force is equivalent to Kinetic Enegery KE and can be calculated in foot pounds by the formula (Velocity in feet/sec) squared * (Projectile weight in grains) divided by 450,240.


Weapon TypeProjectile Weight
 (grains)
Muzzle Velocity
 (ft/sec)
KE
Arrow (Clothyard shaft)65621064
Handgonne - short11560192
Handgonne - medium11552771
Handgonne - long1151527630
Wheellock Pistol494305102
Matchlock Musket494457229
Flintock Pistol
(Thompson Pistol)
178607146
Flintlock Musket
(Brown Bess)
545900980
1851 Colt 'Navy' Revolver80840125
Prussian Dryese Needle Gun47830599
Colt .45 M1911A1230850369
M1 Garand17426402693
Browning M2 Machinegun
(One round, included for OMG!)
700291013,166

At first glance the above chart tells the whole story about why guns replaced bows and arrows - but it's deceiving.  I included the information on the longbow as a baseline for missile weapons, the limited force it applies (enough to hunt big game with) is outweighed by it's superior range and rate of fire for centuries.

You can see that if we scale damage linearly, we end up with a WWII M1 Garand doing 42 times the damage that a longbow is capable of.  That certainly takes care of hit point inflation, one shot one kill on many dragons and small gods.  But that's too powerful, many, but not all shots by a modern weapon will kill or at least functionally incapacitate the victim, but by no means all, so I have to scale it differently.  I decided to do damage brackets, using increasing multiples of 64 ft/lbs, so 64 ft/lbs and down would be one die of damage,64-196 ft/lbs would do two die of damage, etc.  I wasn't satisfied with the vanilla damages over ever increasing ranges, so I divided each range in thirds, thinking that I could use different die sizes (4,6 and 8) with the same multiplier.  But that doesn't work because 3d8 is more damage than 4d4.  That's when I had an 'aha!' moment, the die sizes can differ, producing a smoothly scaling damage model.  I also centered the first range bracket on 64 (Representing a standard arrow) and used the lower range for smaller than usual damage amounts.

RangeKEBase DamageDamage Range
(Min-Avg-Max)
0-96: 1 die damage0-1611-1-1
17-321d21-1.5-2
33-541d41-2.5-4
55-761d61-3.5-6
77-961d81-4.5-8
97-224: 2 dice damage97-1391d6+1d42-6-10
55-762d61-7-12
77-961d6+1d81-8-14
225-416: 3 dice damage225-2882d6+1d43-9.5-16
289-3523d63-10.5-18
353-4162d6+1d83-11.5-20
417-672: 4 dice damage417-5023d6+1d44-13-22
503-5884d64-14-24
589-6723d6+1d84-15-26
673-992: 5 dice damage673-7794d6+1d45-16.5-28
780-8865d65-17.5-30
887-9924d6+1dd85-18.5-32
993-1376: 6 dice damage993-11205d6+1d46-20-34
1121-12486d66-21-36
1249-13765d6+1d86-22-38
1377-1824: 7 dice damage1377-15266d6+1d47-23.5-40
1527-16767d67-24.5-42
1677-18246d6+1d87-25.5-44
1825-2336: 8 dice damage1825-19957d6+1d48-27-46
1996-21668d68-28-48
2167-23367d6+1d88-30-50
2337-2912: 9 dice damage2337-25288d6+1d49-31.5-52
2529-27209d69-32.5-54
2721-29128dd6+1d89-33.5-56
2913-3552: 10 dice damage2913-31269d6+1d410-35-58
3127-334010d610-36-60
3341-35529d6+1d810-37-62
One of he last questions on damage is the Critical Hit multiplier, in researching this I discovered that 1e did not have Critical Hits (funny I thought it did, maybe we house ruled them). For d20 systems a standard arrow does *3 on critical hits and the highest multiplier for any weapon is *4.  Of course, at 4*damage an M1 Garand will do an average of 130 points on a critical hit.  So I'm going to rule pistols and Handgonne's use a *3 multiplier, rifles and other long guns use a *4 multiplier on Criticals.

Knockdown - getting hit by a bullet involves the transfer of a lot of energy into a bag of flesh, often that will be enough to knock the victim off of their feet.  For Pathfinder, if the damage from a single round exceeds the victims CMD, they are knocked down.  For 3.x they will make a Fortitude save DC = damage to remain standing.  For 1e Save vs Paralyzation or be knocked down.

Massive Damage for all systems, I'll use a variation of the d20 Massive Damage rule.  If the damage exceeds 50 points (and you're still alive) Fortitude save DC (15+ damage/10) or die.

2 comments:

  1. Wow, your charts are impressive. I too have been considering firearms in D&D. Though I do think you are overthinking damage a bit here. After a certain point, bullets with a greater KE just go through a bag of flesh at a greater speed and slightly bigger hole, and can go through things like plaster walls and have enough KE left over to enter a bag of flesh. (I read somewhere that an M16 can go through up to 6 suburban houses before the bullet stops.) So basically after a certain point additional KE will not do additional damage.

    Also from taking a few physics courses with gun force problems on the tests, knockback from being hit by a bullet is mostly a Hollywood thing. It is also partially psychological, because in the case of the Zulu wars, the Zulus had not encountered firearms before, so when hit by a bullet instead of falling down or back, they would just keep on fighting until they died because they had no expectation of what getting shot meant. But for cinematic effect knockback should probably be included.

    An M1 Garand does a minimum of 9 hp. That means that for a 0 level human there is no such thing as a grazing shot or a flesh wound if hit, it's instant death or total miss. That doesn't seem to be very good simulation of reality.

    Though I have put much though into this, I have not come up with much better than what you have done. I originally though of doing damage as a scaled percentile of total hp. Which may work if the target's defense went up with it's skill level, but it doesn't in D&D. I ended up going with a concaconating roll. Roll one die and if you get the max number for the die, roll again and add the new roll to it. Repeat until you no longer get max, or you reach a limit that you may have set for that particular firearm. It's not perfect, smaller dies have a greater chance of getting the max number, the damage range skips numbers, but it does better model that getting hit by a bullet can do as little as a 1 hp graze up to craploads of damage that would make a high level character flinch when a gun goes off.

    Thoughts on the matter?

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  2. I'm glad you like the work and you've raised a couple of interesting points. I hadn't thought through the knock down effect enough. I didn't take into account that with modern projectiles not all of the KE is transferred to the target. I can see three options - scrap it, make it apply only to weapons with heavy projectiles and lower velocities -such as muskets or change it from a physical effect to a save or lose a turn while you check to see if any important bits are missing effect. I can also see keeping it as it is for the Hollywood reason you mentioned - people have the idea that it happens and describing the effect as the player shoots the bad guy causing him to fly off the wall adds color.
    IRT the minimum damage of modern weapons - (a) red shirts die, (b) guns are designed to kill and (c) a grazing shot really is a miss, isn't it ? None of which really address the point that not all of the KE is transferred to the target. I should revisit the table and change the rate at which it scales at higher energy levels.
    If you want to model grazing shots, how about any attack roll between AC and AC+2 is a grazing shot doing 1d3 damage? Another option would be throw out the critical multiplier for firearms, do full damage only a natural 20, everything else is a graze.

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