Kinetic Energy vs Momentum

Posted on February 7, 2011 by anteolsson

I have spent hours days and weeks on reading about what physical laws that determines the penetration of an arrow. The more extensive essay on the subject concluded that only Momentum was the important factor when determining if an arrow will penetrate what it hits or not. Then other smaller essays conclude that only Kinetic Energy determines the success of arrow penetration. Obviously we are missing something here.

I then thought about it and quite simply understood that penetration is two-fold. First at the very moment the arrow-head connects with the surface of the target. The most important physical relationship here, as in all other similar cases, is the pressure. pressure is the relationship between applied force and the contact area of the applied force. The area is derived from the arrow-head’s sharpness (the sharper the smaller area is in contact) . The force can be verified either from the momentum or from the kinetic energy, it matters little for the resulting force will be the same. Then it is the ratio of the target’s Hardness and the arrow head’s hardness that determine how much pressure is needed.

Now, once the arrow has penetrated some other phenomena appears. As the arrow head now is not only in contact with the target with its tip, it is also in direct contact with the sides of the arrow. Imagine you pushing a finger between two other fingers. It is the sides of the finger that is in contact with the fingers, not the tip. When this happens Friction will happen and act as an opposing force. From this I conducted an experiment.

I took a shelf and a book, leaning the shelf in an angle and putting the book to let it slide down. I measured the distance the book travelled and I measured the time it took for the book to travel the noted distance. I then increased the leaning angle of the shelf and found, naturally, that the book travelled the same distance much faster.

From this I could then calculate the ratio between the speed och the book and how long it would travel in the same time. This gave me the exact relationship of Distance is equivalent to Velocity to the power of 2. In other words. If you increase the velocity of the arrow to twice its speed, it will take it 4 times longer to be stopped through friction compared to the lower speed.

This inevitably means that Kinetic Energy decides how much an arrow will penetrate. However, the mass of the Arrow still has a very important role in this and I have yet to figure out how important it is and the relationship it has to the penetration.

If you are interested in the experimental data and the calculations, please let me know.

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Bow and Arrow Damage and Attack Rating

Posted on December 31, 2010 by anteolsson

I have sort of finished how Damage and Attack rating is calculated for a Bow and Arrow. I have not yet translated it to text so instead I have at this point published a HTML version and an excel file for anyones viewing pleasure.

HTML

XLS

I hope it can be interesting, for the moment at least.

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IDEA: Custom Special Traits, addition

Posted on December 22, 2010 by anteolsson

Before or after you read the previous post about Special Traits from Heritage or Experience, it might be interesting to know what further ideas I have for this. The thought is that when creating a new character there are many different Special Traits to choose from. If you feel creative enough and/or don’t like the once I come up with, then you should be able to make up your own Special Traits. You will then add a description, fit it into a category and add positive and negative effects. These effects are just a matter of numerical positives and negatives with a sum of 0(zero).

If possible, these new Special traits should then be added to a database for future use by oneself or others.

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IDEA: Special Traits from heritage or experience

Posted on December 22, 2010 by anteolsson

I have a wish to implement Special Traits from Heritage or Experience. I guess most of us are mostly familiar with this concept through brirth signs. This is what I mean but not what I call it. In any case, I would like to share some ideas and would like to have some critique on them. Here goes the first one:

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Category: Birth Blessings and Curses
Name: Brittle agonising voice of the dying witch

Description:
When your mother gave birth to you, a slow and painfully agonising death fell upon her. She was a powerful witch who in an attempt to recieve some final additional powers sold her soul for the great gift of bearing a child. A child that would withhold supreme primal powers. But with the great power a curse was also layed upon you.

You have been cursed with an annoying and painful voice that cuts like a rusted nife into the ears of the listeners. You have problems maintaining people you talk to and most often they find an excuse to leave you.

Effects:
Negative Effects – Minus 10 to all socialisation skills that involves talking.
Positive Effects – Your primal powers are increased equal to your Instinct and your Divided Attention is increased by 1.
Positive Effects – You get a bonus to Intimidation checks.

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What is this for? It is an attempt to go outside the pure numerical statistics, to give the character an additional touch of uniqueness. It is also in order to make it possible when creating a character to get a big benefit but at the same time a big disadvantage. This would lend to a more diverse gameplay where you are more or less forced to act and react on the consequences of your choices you took when creating your character.

This is only an idea, not an implementation, critique and questions are welcome from all angles.

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Energies and damage after impact

Posted on December 1, 2010 by anteolsson

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 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.

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A Moral System

Posted on November 1, 2010 by anteolsson

The backbone of role playing – the moral system. Most moral system, be it fictional or real, are usually built on the premise that there Is good and evil . The premise is not necessarily wrong it is just that it comes from our own history, a history that we have never been able to change or affect in any effective way.

The moral in Good vs Evil comes from our religions and mostly from Christianity with Jesus Christ having the highest virtue of good. Jesus seemed like a nice guy but for me he is not particularly interesting, neither is the whole “philosophy” of chrstianity. It is therefore my intention to go away from that point of origin when creating a moral system and instead of basing it on religion it will take a stand in philosophy.

What is more, apart from good vs evil, is that moral systems usually are based on What we do as defining the moral good. The proverb “What we do is what defines us” is commonly accepted. However, it is not necessarily true and neither is it for certain that it explains the whole of an individual or a group. You can instead turn the proverb around and say “Who we are defines what we do”. It is with these thoughts in mind that the following Moral System is shaped.

Two Axises
What defines our moral world view and our moral actions is broadly defined by two different axises. The first axis goes from Autonomy to Allonomy. Where an autonomous person relies on his own convictions and beliefs and is quick to question where he does not understand, for it is the highest degree of autonomy when he acts on a law the he has created for himself and that must come from an understanding of the law, be it conscious or not. Allonomous, then, describes the opposite, where a person is dependant on external influence and rules and laws created by others. A soldier in a troop would best be allonomous in order to be of most benefit for the troop as they are all dependant on the sargent’s orders. To some extent, the allonomous is more of a tool/vehicle for moral actions rather than the moral actor. It is easy for this person to avoid any moral responsibility, however the person has to deal with his own conscience which is where the subjective moral consequences take place.

The second axis goes from Judgemental to Non-judgemental. To judge another person, whether it is upon his actions or his character, one has to realise that you are referencing to something, often to a moral system. But where does that moral system come from? Is it subjective or objective? Can one be sure that the moral system you judge from is the same moral system that the one you judge is in? All in all, the one who judge another’s actions is equally immoral for you are acting against a particular moral system, namely the system of the one you are judging.

So, whether you are judgemental or not towards others describes how and why you act, be it moral or immoral.

The system might look something like this:

Autonymous/Non-Judgemental    Autonymous/Neutral    Autonymous/Judgemental

Neutral/Non-Judgemental        Neutral/Neutral        Neutral/Judgemental

Allonymous/Non-Judgemental    Allonymous/Neutral    Allonymous/Judgemental

Where Neutral and Neutral meets I would like to add that you have the choice of being true neutral, Variable or Amoral. Where true neutral always takes no stand in a conflict, the Variable takes the side which seems best for the moment and the Amoral is indifferent to which side he is on.

All questions are welcome!

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Sword damage from a circular swing

Posted on October 19, 2010 by anteolsson

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.

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TRAITS – Part I – Patience and Timing

Posted on October 6, 2010 by anteolsson

Patience
Patience is an important trait in many aspects of a character. Waiting for the right moment can be critical when determining the success of an outcome such as waiting for the fish to be hooked properly or for avoiding the blows from incoming attacks until the attacker shows where its weakness lie so that a strike can damage the attacker many times more severly than if the strike had occurred earlier.

A characters patience is by and large dependant on experience but also on how well you the person is able to control his or her emotions. Patience is then dependant on a characters Emotion. The higher the Patience the longer a character is able to wait.

Timing
Patience is good as long as you do not wait too long. A character therefore is in need of knowing When the right time has arrived. Timing is unarguably important here. More arguable, howeever, is what Timing really is and what other properties of a persona that governs the knowledge of Timing.

Most of us would describe Timing as a feeling rather than an exact science. Timing is therefore dependant on a characters Intuition and Emotion. The higher the Intuition the higher the chance of the persons Timing to be equal to the time that the execution has the most effectiveness. The higher the Emotion the higher the chance for the character to actually react when the correct Timing is due. To clarify the difference between Intuition and Emotion in connection to Timing I here draw an example too further illustrate:

An attacker weilding a shield and a sword strikes at you. You manage do dodge his first attack but instead of striking back you wait until the attacker strikes again. Here you make a Timing/Intuition Check (1d10 + Timing + Intuition) to first see if this is the right time to strike. If successful you know if you need to wait or if this is the right time to strike back or not. In this case your Intuition Check is successful and you know you need to wait, because the attacker has not shown you any weak spots yet. The attacker makes his second attack and you dodge this attack too. Again you make a Timing/Intuition Check and it is successful again. You notice that the attacker has lowered his shield enough for you to swing your sword over it and hit his throat, which is not protected. But at this point you only have a split second to decide if this is the time to strike or not. Therefore you need to make a Timing/Emotion Check to see if you strike back or not. In this case your Emotion Check is successful and immediately you swing your sword towards the attacker. As always when you swing your sword, the attack’s success is dependant on your Skill with that sword and the state of which your body is in.

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How you learn and develop your skills

Posted on October 6, 2010 by anteolsson

The learning of Skills is divided into three steps. Each step is dependant on one of the three information processing Mental Faculties> Instinct, Intuition and Intelligence.

First Step – Trained
The first step in learning a skill is to get a feeling for what the skill is about and how it works. It can be done through either immitation by looking at someone else or through experimentation and beginners practice. The faculty that descibes your innate ability for learning through immitation is Intuition and Intelligence and the faculty that descibes your innate ability for learning through experimentation is Intuition.

Second Step – Professional
As soon as you get familiar with a skill or a tool you need to get beyond your innate abilites to experiment and immitate. You need to start in deapth exploring and study the skill as if it were subject to speculation. Through this study and in deapth exploration together with practical training you are able to raise your skill level even higher. The faculty that descibes your innate ability for learning of in deapth exploration and study is Intelligence.

Thrid Step – ?
Once you have reached the higher proficiencies of a skill you might be considered a master by many but in truth there are always more to learn. At some point during your skill progression you face that it becomes difficult to learn much more through immitation, experimentation, exploration and study. When you are at this stage your body and mind is trying to become One with the skill or the tool and your instincts start to take over the learning ability. From being a conscious process of getting better at the skill, the skill starts to meld with your most primal states of body and mind and your execution of the skill is almost instant and automatic, where little actual thinking is in the works while the skill is being operated. The faculty that descibes your innate ability to learn and act through instant and automatic operation of the skill is Instinct.

The Steps
From Skill levels 1 through to 3 the first step applies. From Skill levels 4 through to 6 the Second step appies. From skill levels 7 through to 10 the third step applies. Every value below 1 (from 0 down to -10) you are considered Untrained

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A glimpse of the character sheet

Posted on October 1, 2010 by anteolsson

Character Sheet a glimpse

Introduction

The character sheet above is an early map of what is included and how a character is described. It is not finished but might give a good idea of what it will end up as. All the Skills, Traits, Talents and Allignment is missing and will be added as the progress goes forward.

The fundamental rules and principles

In the image above, an attribute is everything listed under Primal Powers, Faculties and Derivates (for a lack of a better word).
Each attribute has a value ranging from -10 to 10, where -10 represents the lowest effectiveness possible and where 0 represents the human average.

When an attribute reaches the values of 1, 3, 6 and 10 a new special ability will be learned connected to the attribute.

To further explain this here are some examples:

If you increase your Strength to a Value of 1 you will learn a new ability such as: 1 extra Damage Dice, +2 on all Push Checks, +2 on all Lift Checks and so on. The next time you will learn a new ability connected to your Strength you will learn an additional ability.

If you instead increase you Memory to a value of 1 you learn an ability that has to do with your Memory such as, Recall Memory Powers, +2 to memories triggered by Smell/Sound/Visuals etc,

The above is true for All attributes on your character sheet and so a first level character can know many different abilities depending on what values are allocated to the different attributes.

I hope this can imbue some excitement and maybe raise some thoughts of what this will end up as.
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