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.
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 3 – Resolving 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.