Realistic damage formula for rpg

[Nicolas Jager]

I'm developing a computer game for which I hope to have the combat mechanics as realistic as possible--or at least based on real physics. While developing my formula for attack damage, I was considering using KE = (1/2) * m * (v^2) for thust attacks and KE = (1/2) * I * (w^2) for swings as a factor in determining attack damage.

 

However, I am unsure about the relationship between KE and damage, partly because I am unsure of how to define damage in physics. What function would best describe the relationship between the KE of an object and the damage said object inflicts upon a target? What other factors would this entail (ex. hardness, toughness, area of impact, ect.)?

[mytechuniverse]

Are you accounting for explosive/concussive force? I realize kinetic energy is one component, but a lot of damage is done in the explosives as well. I'm really not an expert; I was just throwing that out there.

[Nicolas Jager]

I'm asking about melee weapons.

[Schrödinger's hat]

It's hugely complicated.

KE isn't the only factor, I absorb more energy in a few minutes by standing in heavy wind, than would be contained in a bullet.

We have pressure, time sustained, location and angle of hit, probably a whole host of things I can't even think of.

The energy you can put into striking something is not completely determined by what is in the motion of the weapon. Follow through is very important, too.

The line between an ineffective attack and a fatal one could be a matter of a few millimeters, or someone not expecting/knowing how to roll with the blow.

You are probably better off using informed heuristics than anything you can glean from a physics textbook.

Not only that, but a skilled fighter will constantly be looking for weak points, while attempting to get blows to land on his strong points. He wont just swing wildly at whatever is nearest.

Go talk to your local medieval re-enactors, maybe a doctor.

[ydoaPs]

You need to at least take impulse into account. I=Fxt=p₂-p₁

 

The time in which the momentum change occurs determines the force applied. Force and pressure are both important in determining the amount of damage done.

[J.C.MacSwell]

There also is some threshold before any damage occurs and this would depend upon the weapon and any protection/armour where it makes contact. There is a reason some weapons are sharp and others blunt.

[baxtrom]

What function would best describe the relationship between the KE of an object and the damage said object inflicts upon a target? What other factors would this entail (ex. hardness, toughness, area of impact, ect.)?

 

Correct me if I'm wrong, but in gun ballistics there is a strong correlation between KE and damage. However, as already pointed out it's a complicated question. I don't know your exact application but if considering kinetic projectiles vs humans there are a number of parameters that could be of interest, i.e. volume of cavity produced by projectile, shock from rate of change of momentum, depth of penetration et c. I believe there were some rather nasty tests on goats trying to establish "empirical data" (Strasbourg tests) for incapacitation times.

 

In armor ballistics the penetration is the most important and simple models include - I believe - kinetic energy divided by projectile cross sectional area.

Edited May 26, 2011 by baxtrom

[InigoMontoya]

In armor ballistics the penetration is the most important and simple models include - I believe - kinetic energy divided by projectile cross sectional area.

Once upon a time I used to design armor for a living.

 

Can't say too much more but I'll say this....

 

Sectional density is important, obviously, but we found momentum to be a more reliable measure of penetrating ability than energy (all else being equal, obviously).

Edited May 27, 2011 by InigoMontoya

[ydoaPs]

There also is some threshold before any damage occurs and this would depend upon the weapon and any protection/armour where it makes contact. There is a reason some weapons are sharp and others blunt.

If accuracy is wanted, the biology of the target should be taken into account as well. Take humans for example: a punch to the throat may kill a man, but an identical punch to the arm might just annoy him.

[Nicolas Jager]

Thank you all for your responses so far. I realize what I'm asking you is complicated, and I appreciate the time you've taken to provide further insight into the situation. While some, I've thought about but forgot to mention, others are ones I haven't considered. If an exact function for damage isn't readily obtainable, even an approximation would suffice. I apologize in advance for this rather long post.

 

I see answers encompassing swing method (positioning, angle, follow-through), defense (armor, density), weapon type, and accuracy.

 

I feel there's a need to elaborate further on my situation, so that we can keep the discussion specific and not overextend ourselves. The game will be essentially a mix between rougelikes such as nethack, and the turn based battling system found in games like KQ and games made with RPG Maker XP. Players will have attributes such as strength, dexterity, constitution, intelligence, and wisdom, as well as skills.

 

In an effort to simplify attack calculations, I've divided attacks into various parts:

• accuracy -- Chance to hit, and if hit, chance to land a critical hit. This will be positively affected by increase in dexterity, and/or decrease in effective weight which describes how heavy the item feels based on player strength (inversely related to strength; ex a 16kg club may have an effective weight of 16kg for someone with 10 str, but would have effective weight of 8kg for someone w/ 20 str.).
• attack bonuses / penalties -- modifiers to attack damage based on weapon type (flail, blunt, cutting, piercing, stabbing, swinging) and enemy's armor type (platemail, ringmail, shield, ect). (Certain weapon types are more or less effective against certain armor types. Ring mail may protect against blades, but won't be very effective vs. clubs.)
• unmodified damage -- Damage an attack would cause prior to being submitted to attack bonuses/penalties and prior to accounting for defense's damage reduction. This is the portion I'm seeking help for. The KE formula will likely play a role here as will other factors. Strength, dexterity, arm mass and length, weapon mass and distance from pivoting point (shoulder) of weapon's center of balance, weapon velocity (for thrust) and angular velocity (for swing), and moment of Inertia (for swing) will play a positive roll in calculating this value. Attack area (the larger the area, the more the attack is distributed, and less damage is inflicted), impact time (time it takes weapon to stop moving when swinging/thrusting. The shorter the time in which the momentum changes to 0, the greater the counter-force that the target must exert to stop the weapon, and so, the greater the damage.)
• Defense / Damage Reduction -- The amount and/or factor by which the unmodified damage is reduced due to the target's armor/defense rating. I'll be using a simple formula for this. Different equipment will provide a AC value. A damage percentage reduction formula will be devised with lower and upper limits of 0 and 1 respectively. Ex. DMG_REDUCT = ((AC / AC + 40)). finalAttack = (unmodified damage * (bonuses/penalties multipliers) - AC*(DMG_REDUCT) ) * (1 - DMG_REDUCT). So, if the unmodified damage is 60 and the AC is 10, the final damage would be (50 - 10 * (10/50) ) * (1 - (10/50)) = 48 * .8 = 38.4
• Dodge/Evade -- chance to evade an attack. This will largely be determined by quickness (a factor derived from dexterity).

Because I'm choosing to deal with defense separately, it might be acceptable to consider the target to be unarmored. It could be considered to be the flesh of some animal (pig, cow, seal, ect) (though I realize the presence of bones may complicate this, consider just boneless flesh.) Or perhaps even imagine the target to be a large block of material (ex. clay) of some density p. (let me know what other factors may be needed here)

 

Though damage might not be properly defined, consider it to increase as the square of the penetration distance through a material increase. Ex. if damage is 8 for an attack that causes a gash 1 cm wide, 4 cm long, and 2 cm deep, it will be 32 for a gash 1cm wide, 4cm long and 4 cm deep.... so as the penetration distance doubles, the damage quadruples.

 

Anyhow, my question regarding attack damage formula can be regarded as what formula (or approximation) would represent the penetration of a melee weapon through a block of material of uniform consistency? I'm thinking KE, momentum, time it takes for momentum to go from impact momentum to 0, impact area, impact force may be things to look at when considering this.

[baxtrom]

Anyhow, my question regarding attack damage formula can be regarded as what formula (or approximation) would represent the penetration of a melee weapon through a block of material of uniform consistency? I'm thinking KE, momentum, time it takes for momentum to go from impact momentum to 0, impact area, impact force may be things to look at when considering this.

 

When I was young man I did a test using an air pistol (125 m/s) and a hunter's air rifle (>250 m/s). Same pellets, 4.5 mm. When shooting at normal incidence on a block of clay, the interesting effect was that the penetration depth was close to identical. However, the rifle pellet created a large conical "wound channel" in the clay with the pellet at the top of the cone. The volume of the cavity created by the rifle pellet was probably ~5 times that of the pistol pellet (perhaps close to the ratio of KEs).

 

If you look mathematically at penetration, I think you'll find that if the material is viscous and the force decelerating the projectile is close to proportional to its velocity (as perhaps expected from a fluid), the penetration depth will be proportional to the momentum [math]m v[/math] of the projectile. If the decelerating force is constant (independent of velocity), the depth will be proportional to the kinetic energy [math]0.5 m v^2[/math]. A constant force is perhaps a simple representation of a solid material.

 

Perhaps you could do a threshold model implementing both KE and momentum in some smart way? For example a geometric average that will only cause damage above some limit value. It's your universe, you do the rules

Edited May 27, 2011 by baxtrom