Monday, August 17, 2015

Kinetic Energy of Strikes vs. Armor

I want to capture some data here about kinetic energy (Mass * Velocity ^ 2) of various strikes as well as armors.  This is important data about wounding and penetration capability.



* For different irons/steels, you can multiply these energies by: 
Munition quality iron: 0.5 
Low-carbon steel: 0.75 
Medium-carbon steel (Milanese): 1.1 
Hardened steel: 1.5 


So...  How is all this useful?

It informs a discussion of damage and armor systems.  We know that strikes inflict between 20J (average person with a knife) and ~350J (professional baseball player with two handed grip, world record boxer) of kinetic energy.  Typical break points include:
  • Light Knife, Underhand:  20-50J
  • Punches and Overhanded Strikes by strong people:  100-121J
  • One handed Weapons:  On order of 40-130J
  • Two Handed Weapons:  On order of 100-305J
  • Light Bows:  50J
  • Long Bows:  100J
  • Heavy Long Bows:  140J
Armors likewise protect against varying penetrating blows:
  • Padded:  20-50J (stacks with other armors)
  • Leather:  30J
  • Chain Mail:  80J
  • 1mm Plate:  55J (reasonable typical for lightly armored areas)
  • 2mm Plate:  175J (minimum for breastplates, helms)
  • Signficant Flesh Penetration:  ~30J
Slashing blows are about half as effective when defeating armor.

Those numbers are all rather large, so let's divide them by a common denominator, say, 25J, to get something more usable.

Modified numbers for strikes:
  • Light Knife, Underhand:  1-2
  • Punches and Overhanded Strikes by strong people:  4-5 (each standard deviation is +/- 1)
  • One handed Weapons:  ~2-5
  • Two Handed Weapons:  ~4-12
  • Light Bows:  2
  • Long Bows:  4
  • Heavy Long Bows:  6
Modified numbers for armors:
  • Padded:  1-2 (stacks with other armors)
  • Leather:  1
  • Chain Mail:  3
  • 1mm Plate:  2 (reasonable typical for lightly armored areas)*
  • 2mm Plate:  7 (minimum for breastplates, helms)*
  • 3mm Plate:  12 (not unreasonable for breastplates)*
  • Significant Flesh Penetration:  1+
*Cut plate defenses by 1/2 for cheap pot metal.  Increase by +50% for high-grade metal.

Interestingly, those numbers look a lot like usable numbers for damage rolls in a gaming context, do they not?  As a caveat, most of those damage numbers are high-end maximums (if only one number is given).  Most are also for penetrating force.  A slashing blow can do a more damage, but is less effective against armor by about half.

Strength Modifiers:  From the data on olympic boxers, we also have the data that each standard deviation adds or subtracts +1 (25J).  Now, olympic boxers are already above the bell curve, likely at least two standard deviations, but it is a reasonable modifier.


So now we start to get to a usable system.

Weapon Damage (average adult male):
  • Punch, Unarmed:  1d3
  • Light Weapon (Dagger):  1d6-1
  • One Handed Weapon:  1d6
  • Two Handed Weapons:  2d6
  • Light Bow:  1d6-1
  • Long Bow:  1d6
  • Heavy War Bow:  1d6+3 or 2d6-1 (or just 2d6 for simplicity's sake)
Strength bonuses:  Each standard deviation +/- 1 to above figures.
0-1 (-3), 3-5 (-2), 6-8 (-1), 9-12 (0), 13-15 (+1), 16-18 (+2), 19-21 (+3)

*As an optional rule, two handed weapons deal 1d6 (perhaps 1d6+1) damage as well but all strength modifiers are doubled.

Slashing weapons and strikes:  Roll one extra damage die and retain best against unarmored targets; roll one extra die and retain the worst against targets in chain or plate mail.

Bludgeoning weapons and strikes:  Bludgeons always do "bruising" damage, not lethal damage, but ignore the "soak" of armor.


Armor mitigates incoming damage.  Characters select either to wear a helmet and either full or half armor.  Full armor protects the torso and extremities.  Half armor protects only the torso, like a breastplate or coat of mail.

Characters may layer lighter protection for extremities (such as greaves for legs and gauntlets for hands) as desired with half armor.  For example, you could choose a steel breastplate for the torso and leather gauntlets/leggings for the extremities.

Cloth padded armor may be layered with any other type for more protection.
  • Cloth:  Soak 1
  • Leather:  Soak 1
  • Light Plate:  Soak 2
  • Chain Mail:  Soak 3
  • Medium Plate:  Soak 7
  • Heavy Plate:  Soak 12
With this system there are several checks:
  • Attacker checks "to hit."  This is based on defender's agility.
  • If there is a hit, defender gets to "save" and see if their armor helped out.  Roll 1d6:
    • 1:  Head (Helm)
    • 2:  Arms (Gauntlets)
    • 3-5:  Torso (Armor)
    • 6:  Legs (Greaves/Chausses)
  • Attacker rolls damage.  Armor, if present in the targeted area, "soaks" incoming damage.
    • If the damage roll is less than the "soak," the defender takes a bruising hit.
    • If the damage roll is greater than the "soak," the defender takes a lethal wound.
    • Extra Damage:
      • Hits against the head and torso result in +1 Wound (i.e. two wounds).
      • If no armor is worn, a damage roll of >=5 also results in +1 Wound.
      • If armor is worn, a damage roll that exceeds the soak value of the armor by >=5 also results in +1 Wound.
  • Cover:  The "save" system above also factors cover into effect.  Decide what part of the body is protected by cover and negate hits to that area.  For example, a low stone wall covering half of a warrior's body would protect against any roll of 4-6.
Wounds & Damage:
  • Lethal vs. Bruising:
    • Most weapons deal lethal damage.  Bludgeons as well as unarmed strikes deal "bruising" damage; armor can also "soak" incoming damage, converting potentially lethal strikes into bruises.
    • Bruises recover rapidly.  Enough bruises stack up to lethal damage.
    • Lethal wounds recover slowly.
  •  Characters have the following hit points:
    • 6+/-CON Bruises
    • 4+/-CON Lethal Wounds
    • If a character can no longer take bruising hits, then all future "bruises" become lethal wounds.  This represents a badly battered character having ribs cracked, suffering concussion, and other serious and life-threatening wounds.
The wounds and damage system needs some work, but it could be ok.  As an alternative, you could simply use the damage and soak values as is, subtract the "soak" rating from the incoming damage, and use normal D&D hit points.


Justinian said...

Whoa doggie look at that javelin strike! 360J

Are javelins underrepresented in D&D? Should they be flying greatswords?

Vedron said...

An Olympic javelin is 2.6M long and weighs 28 OZ. Athletes get a running start and chuck them almost a hundred meters. Now, accuracy is not a huge factor in competition. E=MV^2 means the high speed attached to long throws generates a lot of energy -- at least up close. Energy will drop off rapidly at longer ranges.

The comparable weapon in ancient times would have been something like a Roman pilum. The pilum was over 2M long and weighed more than a modern javelin (5-10 lbs). The throws were shorter, typically within 10-25M, due to the greater weight. The heavier pilum would have retained energy better to get armor penetration in combat at the expense of range. In combat, there would also be more of a premium on accuracy than range (and thus energy). So the pilum type numbers would likely be lower than modern javelin throws.

But... yeah... They kind of are flying greatswords. We're talking about two meter long hefty projectiles being hurled from a running start, and in the case of pila, designed to pierce shields/armor.

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