## Energies and damage after impact

To calculate the energies that the two objects, Sword and Target, have after the impact we first need to know the properties of the the objects involved in the collision.
In the data below I have assumed that the target wears an armour made of iron with a thickness of 5 mm. The scales for Sharpness and Hardness goes from 0 to 10. Cut Pressure Limit and Toughness Is a realistic value of how much pressure and energy it takes to cut and to break.

Weapon

Sharpness 1

Hardness 7

Toughness 25000

Weight 10

Armour

Hardness 10

Weight 100 Kg

Thickness 5 mm

Toughness 250000 kJ

Cut Limit 250000 MPa

Step 1 – Resolving the Kinetic Energy of the Sword after impact

Sword Velocity = ([Sword Effective Mass – Target Mass] / [Sword Effective Mass + Target Mass]) * Sword Effective Velocity

Sword Kinetic Energy = 0.5 * Sword Mass * Sword Velocity^2

The above is calculated according to the momentum laws of an elastic collision. Now, the collission between a sword and a target in armor is not entirely elastic. This can be solved by estimating how much of the energy that is dispatched as other types of energy: Sound, heat for example. Then we can just reduce the energies by a percentage.

Step 2 – Resolving the Kinetic Energy of the Target after impact

Target Velocity = ([2 * Sword Effective Mass] / [Sword Effective Mass + Target Mass]) * Sword Effective Velocity

Target Kinetic Energy = 0.5 * Target Mass * Target Velocity^2

Step 3Resolving if the the sword is able to cut through the target material.

Cut Factor = [Sword Hardness / Target Hardness] * Sword Sharpness

Cut Pressure = Sword Kinetic Energy Before Impact * Cut Factor

Cut Deapth = Cut Pressure / Cut Limit

The cut factor is a relation between the hardnesses of the two materials that are involved in the impact. The softer the target is, the harder the sword is and the sharper the sword is, the easier it is to cut through.  Therefore, the Cut Factor then is multiplied with the incoming kinetic energy of the sword. If this energy exceedes the Cut Limit of the material it will cut through. I have decided that it will cut through 1 mm per every multiple of the Cut limit. This might be wrong, but at the moment it feels like a feasible guess. This has to do with that as long as the sword is cutting through the material it is also at the same time losing momentum, and so loses kinetic energy.

Step 4 – Resolving if the Sword or Target Breaks

Sword Break Factor = Sword Kinetic Energy Before Impact / Sword Toughness

Target Break Factor = Sword Kinetic Energy Before Impact / Target Toughness

If the Sword Break Factor is above 1 then the sword breaks. If the Target Break Factor is above 1 then the target breaks. How severely it breaks is then of course defined by how much more than 1 the factors are.

This is all for the moment. It has to be determined of course what “damage” is. I think it is important to first define “what” it is you damage. If you do not reach cutting energies or breakable energies, the armour will of course absorb most of the energies and the target will instead perhaps stumble or even fall.
If the sword is reaching cutting energies then it will easily cut off a human arm for example, but there needs to be data for that to. There is more to think of when determining damage but that will be at a later stage.

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### 4 Responses to Energies and damage after impact

1. Jensan says:

Are the Sword Break Factor and the Target Break Factor tests done simultaneously? So that a sword may “break” a target while breaking itself?

2. anteolsson says:

Good that you brought that up. At the impact there needs to be some checks. The first check to make is a Hardness Check. I the target hardness is 3 levels above the Word hardness, there will be no possibility for a cut, even if the Cut Factor is over 1.

Once that is determined we need to see what types o materials that are involved. If the armor is made of leather then it cannot break, you can only cut and scratch it. Unless the leather armor is frozen first, o course. So we need to know that the toughness factor is below 10. In other word> If (toughness >=10) then target.breakable = false;

So if both the sword and the target has a toughness below 10 then both objects can break at the same time. Imagine them being made of glass!

Titanium has a hardness of 7 and I dont think it is realistic that a human can break it with only human strength. So maybe the check above also needs to be: If (hardness >=7) then target.breakable = false;

What do you think?

3. Jensan says:

It’s a lot of variables now, so it’s hard to say!
Maybe you should flesh out and describe what hardness represents a bit more, since it’s only an arbitrary number at this point. For instance: you say titanium has a hardness of 7, and therefore should be unbreakable. Maybe you should instead set certain properties along the hardness-scale (I just made these up as an example):

Hardness 1: Bendable
Hardness 7: Unbreakable
Hardness 10: Unmeltable

Another thing to consider: is the hardness scale linear or not? Is the step between hardness 5 and 6 equally in “distance” as between hardness 8 and 9? Compare with the decibel unit, for instance.

4. anteolsson says:

Hardness and Toughness in materials are already defined but I can try to explain more clearly what they mean. Hardness is the resistance to scratches and dents while Toughness is its resistance to breaking from momentum, or high energy impulses. Ie, how much energy the material can absorb before breaking.

The scales go from 1 to 10. Diamond is the hardest, 10. Materials such as plaster, talc and leather is 1. The toughness scale is the same, 1 to 10. Diamond is very tough and crystalised sugar is very brittle. Glass is very hard but not so Tough. You can break glass more easily than scratching or cutting it.

Wheather a material is bendable or not has to do more with its elasticity than hardness and toughness. Meltable is also another property that is not necessarily related to the above properties. I will add the formulaes for Heat Energy later. If you want to throw a fireball or you have a flaming sword, the damage you do is depending on the Heat Energy rather than the Kinetic Energy.

In the calculations the hardness and toughness scales are liniear.

I realise that the formulaes and statistics needs to be organised and explained individually so the definitions are clear. It will come sa smaning om