Damage Part 1 - Kinetic Energy, Something Else?

The question of doing damage to an enemy unit is a complicated one. Different weapons cause different injuries, there can be cuts from an edged weapon, stab wounds, blunt force trauma from objects like hammers or stones. Different types of armour offer different protection - chain mail for instance is very effective against cuts, but not really against blunt force. Almost by necessity, there will be gross simplifications in the model.

The simulation basically classifies damage by the effect it has on the ongoing battle:

lightly wounded soldiers will be able to fight on, albeit perhaps with reduced efficiency
heavily wounded soldiers will survive, but no longer contribute to the battle
and some wounds simply kill the soldiers

From an other perspective, damage is simply the application of kinetic energy to a spot - the more energy is available and the smaller the surface to which the energy is applied, the more likely it is that severe damage is done. An arrow hitting a soldier into the unprotected chest is likely fatal as its energy is released in a small spot, and so it penetrates deeply into the body. The whole point about plate armour is that it distributes the energy across a much larger area - the soldier with a breastplate still feels the impact as the kinetic energy dissipates, but because it is distributed across his whole chest he doesn't die. The picture changes again when more kinetic energy is applied - the bullet fired by a musket can defeat the steel plate and again cause a fatal injury.

So we might reasonably guess the relative amount of damage done by a weapon by comparing their kinetic energy and impact area - the more energy and the smaller the area, the more damaging the weapon (again, this is a general pattern, not a hard and fast rule).

Projectile weapons

Assessing kinetic energy for projectile weapons is much easier than of close combat weapons, because the situation of close combat is generally messy, weapons can't be used with optimal technique etc. For projectiles, there is always a moment when the projectile is undisturbed in the air and kinetic energy assumes a certain value.

Various sources and own estimates based on weight and documented range provide the following energies for various weapons:

170 lb English longbow	130 J
60 lb longbow	60 J
primitive bow and arrow	30 J
heavy crossbow	130 J
windlass pulled arbalest	550 J
light spear / javelin	160 J
heavy spear / pilum	105 J
slingshot	50 J
atlatl dart	50 J
Roman scorpio bolt	130 J
matchlock arquebus	650 J
matchlock musket	1900 J

Most weapons listed here have a small impact area, the slingshot is the main exception. So this table would readily allow us to assess that English longbowmen did a lot more damage than slingers, but were quickly eclipsed by musketeers whose weapons provided serious armour-penetrating capacity.

A separate discussion is how this translates into range - not all projectiles have the same drag coefficient. A famous example is the arbalest bolt, which has to be much more sturdy than the longbow arrow to survive the shock of firing - but that results in a much higher drag as well, so the full energy release happens only at point-blank range and the arrow gets superior quickly. However, we will defer this discussion to a later point.

Close combat weapons

The energy release of a properly done sword thrust is with 140 J about on par with that of a longbow. That is natural in that it seems to be what the human body can provide without technical help - in the table above, of the nun-gunpowder weapon only the arbalest reaches higher, and that is cranked with mechanical aid.

Howver, conditions at a battle line presumably rarely are optimal for using close-combat weapons - so more often than not the actual value would have been smaller. Also, the impact area of the weapon is often the edge, i.e. somewhat larger than the tip of an arrow. We may thus surmise that all things considered, a 170 lb longbow arrow does usually more damage than a sword for one impact, i.e. 50 archers shooting at point-blank range are more dangerous than 50 swordsmen stabbing in close combat.

Other, lighter weapons such as short swords can easily cause less damage, but it seems difficult to see how a close-combat weapon without technical help might have caused more damage, regardless of its nature. Such help might e.g. be the speed of a cavalry charge that provides additional energy for a lance when it impacts. We can estimate that a 3 kg war lance used from full canter has a kinetic energy of 220 J - significantly more than

It follows that assessing the relative danger of close-combat weapons is somewhat more guesswork unfortunately.

sword thrust	140 J
3 kg cavalry lance at charge speed	220 J
4 kg cavalry lance at charge speed	290 J

Damage in the simulation

While kinetic energy and impact area provide at least some way to establish a relative order of different weapons, it is rather unclear how to map this into wounded and dead per unit time. So admittedly this is much guesswork (some things we do know, for instance that English archers could reduce cavalry to a chaotic mess really quickly, so these data points are used), but otherwise the table is based on intuition.

For that reason, the simulation allows to adjust the overall level of damage that is done, and if finer control is desired, the ratio of damage and armour of different units can also be adjusted.

To assign damage values to units, the following guidelines have been used for close combat (note that this isn't strictly ordered according to kinetic energy but also based on impact area and energy dissipation):

bare hands	0
rocks, sticks,...	1
dagger, quarterstaff or similar	2
short sword or light fighting gear	3
sword, heavy infantry fighting gear	4
two-handed sword, waraxe	5
lance used in charge	6-7

For ranged combat the values are as follows:

stone from sling	1
30 lb bow	2
70 lb bow, light crossbow	3
120 lb bow, heavy crossbow, javelin	4
170 lb bow, scorpio torsion catapult	5
arbalest	7

Continue with Damage Part 2- Scaling.

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