This topic feels endless. I have been doing so much research that I can’t put exactly everything together yet. When searching the internet you can find but one single extensive essay on this topic; it is not even necessary to mention it.
All in all this topic and the skill of swinging swords is still more an art than it is a science, judging from what I have learned at least. As a student of engineering I have found this interesting and to many extants understandable but it has been, and still is, a challenge to convert the physics of it to a stat based character sheet.
At the end of this post you should be able to find an excel file which contains the formulaes and where you can test this therory of implementing damage done by a sword swing into a role playing game.
Below is the formulaes and the reasoning behind them for calculating the Kinetic Energy of an impact from a sword swing. Note that this only covers a sword swing and not a club swing or a spear thrust.
STEP 1 – Resolving the Impact point on the sword
Impact Point = (1d10 + Skill)/2 + 3
Depending on where you hit with your sword you will both have a different Velocity and a different relation to the swords Center Of Mass and its Pivot Point. Therefore we need to calculate this first, so we can later determine the Effective Mass and the Effective Velocity needed for determining the Kinetic Energy.
The 1d10 is for determining the circumstances when the swing is performed, such as sudden movements and balance. The Skill is for determining how much the Skill of the weilder is affecting the precision of where you hit with your sword. It is then offset with +3 to compensate for the COM (Center Of Mass) which usually is a third into the sword, counted from the handle.
STEP 2 – Effective Speed
Effective Speed = (Strength + Skill – Weight/2 + Shape/5 + 10) * ([Impact Point]/10 * Sword Length) /4
When calculating the Kinetic Energy of a moving object the Speed is what has the most impact.
The Strength and Skill will affect the speed with a ratio of 1 while the Weight (the mass of the weapon) affects the speed negatively at a ratio of 0.5. The Shape of the sword will also affect the speed but not to the same degree, only at a ratio of 0.2. The Speed is then offset by 10 to determine at what speed you will at least swing with. Even if you are very weak and have no Skill, swingin’ a sword shaped like a tree branch, you will still reach a certain speed with your swing.
This is then multiplied by the impact point in realtion to how long the sword is. The further out on the blade you hit the higher the angular velocity is, and the longer the sword is the higher velocities you can reach. However, when you hit that far out on the blade you will not put so much Mass/Weight behind the impact. This is further discussed below when calculating the Effective Mass.
Finally the whole formulae is divided by 4 to reach more realistic results.
STEP 3 – Effective Mass
Effective Weapon Mass = (Strength/4 + Weight*3 + Skill/4) * ((COM-Handle Position) / ([Impact Point] – COM)) +Weight*2
This is a long formulae! With Effective Mass, I mean that even if the weapon has a static mass it will “weigh” differntly depending on where you hit on the sword. This phenomenon is called Torque in physics.
The Weight of the sword is affecting the Effective Mass at a ratio of 3 while the Strength and Skill of the weilder is only at a ratio of 0.25. This is then multiplied with the Impact point in relation to the COM and where the Handle of the sword, or where you are actually holding the sword. This second part of the formulae is really just calculating a relation of how far the impact point is in relation to the COM divided by how far the handle is from the COM, on the other side of the COM. If the Impact Point is at an equal distance from the COM compared to the Handle’s distance from the COM, the relation will be 1.
We then add the weapons static weight in the end to get a more realistic Effective Weight in relation to the Effective Speed.
STEP 4 – Kinetic Energy
Kinetic Energy = ([Effective Weapon Mass] * [Effective Speed]^2) /2
This is straight forward. The only thing we need to know is the formulae for Kinetic Energy; which is: (m * v^2)/2.
We already have the Effective Mass and the Effective Speed/Velocity, so we just put it into the formulae and out comes a number.
We have now calculated how much Kinetic Energy the impact point has. This is just the beginning and in the next step we need to resolve How much of this Kinetic Energy that will be really transferred to the Target and How much of that transferred energy that is actually damaging. Obviously, if we hit a heavily armored target, most of the energy will be absorbed in the armour and no real damage will happen. The most important part in this step is the Weight of the target. You can imagine the difference in hitting a soda can compared to a refrigerator. Hitting the refrigerator will probably damage the hands holding the sword more than the refrigerator.
But I have not gotten that far yet and I will have to update with that later. But please try the excel sheet and see what happens when you change your Strength, Skill and so on. Values to use are from 1 to 10.
PS. WordPress does not allow me to upload excel files and I am behind a proxy so I cannot reach my ftp, so the excel file comes at a later time.