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[Pirate Bob]

Here is an update of the force where deflection drops from 100% to ~20% at large [IMPACT_FRACTURE] as a function of [IMPACT_STRAIN_AT_YIELD]. 

Spoiler (click to show/hide)

The new point is at [IMPACT_STRAIN_AT_YIELD]=3760, force=18, and goes below the minimum cutoff expected based on  momentum=IMPACT_YIELD/50000.  With this point, it is also clear that the curve does deviate significantly from cutoff momentum=50000/[IMPACT_STRAIN_AT_YIELD], especially at large [IMPACT_STRAIN_AT_YIELD], but the deviation is small enough that I can't really characterize it well.

My results from doubling the Contact Area for bolts from 2 to 4 show no changes at all:

Spoiler (click to show/hide)

The plots of the forces for 10% and 100% deflection as a function of [IMPACT_FRACTURE] are identical to those with contact area 2, and I could see no significant deviations in the raw data either.  I think Urist Da Vinci said he saw some difference from changing Contact Area, but I'm not sure what and I'm too tired to look it up now.

[Urist Da Vinci]

I found something interesting when looking at penetration, so I'll take a step back to recap:

I came up with the "uniarmor" concept several pages ago in this thread when testing the "ricochet" deflection of bolts off armor. The creature size or body part size didn't matter to that deflection type, but the LAYER_SIZE of the armor did matter. The "uniarmor" set covers a dwarf in a uniform layer of [LAYER_SIZE:20] plate armor. This was supposed to remove "where did the bolt hit?" from future research. It does in fact work for the "ricochet" deflection type.

Code: [Select]

[ITEM_WEAPON:ITEM_WEAPON_SPEAR_VARIABLE]
[NAME:variable spear:variable spear]
[SIZE:300]
[SKILL:SPEAR]
[TWO_HANDED:37500]
[MINIMUM_SIZE:32500]
[CAN_STONE]
[MATERIAL_SIZE:3]
The format is ATTACK:EDGE/BLUNT:contact area:penetration size:verb2nd:verb3rd:noun:velocity multiplier
[ATTACK:EDGE:2:1:1:1:NO_SUB:1250]
[ATTACK:EDGE:2:10:10:10:NO_SUB:1250]
[ATTACK:EDGE:2:100:100:100:NO_SUB:1250]
[ATTACK:EDGE:2:1000:1000:1000:NO_SUB:1250]
[ATTACK:EDGE:2:10000:10000:10000:NO_SUB:1250]
[ATTACK:EDGE:2:100000:100000:100000:NO_SUB:1250]
This is a variable spear. It has a bolt-sized contact area and several levels of penetration. I used it, and several other versions that went like "21,22,23,24,25,26" etc. to measure the thickness, in "penetration units", of skin, fat, muscle, and armor. "Measure" means stab each body part with each penetration size repeatedly.

The dwarf upper body is, in "penetration units", about 3 skin, 38 fat, and 229 muscle, so you need a weapon of over 270 penetration to stab a dwarf in the heart (a weapon of less penetration will only tear muscle and bruise the heart!). These penetration amounts are proportional to the CUBE ROOT of (body_part_size/10). A dwarf's upper body is relsize 1000 whereas the head is relsize 300, so the dwarf's head only has 25 fat.

A kea has about 1 skin, 9 fat, and 48 muscle. A giant has about 20 skin, 204 fat, and 1051 muscle. A dwarf has thicker muscle than a human or a scaled-down giant, because of the natural dwarf strength bonus in their RAWS, and [THICKENS_ON_STRENGTH] in the tissue template. For humans and giants, the upper body skin:fat:muscle is in the ratios 1:10:50, even though the tissue token is [BP_LAYERS:BY_CATEGORY:BODY_UPPER:ARG3:50:ARG2:5:ARG1:1]. This is due to [THICKENS_ON_ENERGY_STORAGE] in the fat tissue doubling the tissue thickness for healthy fat levels. Presumably fat dwarves are thicker, and starving thin dwarves have almost no fat.

Now for armor:

See http://dwarffortresswiki.org/index.php/DF2012_Talk:Weight where I gave a method to calculate the weight of clothing or armor. Extensive testing has revealed that the thickness in "penetration units" of armor is given by:

[BODY_SIZE]*(percentage)*[COVERAGE]*[LAYER_SIZE]*(step factor)/100000

So Uniplate (for the upper body) is 60000*0.1836*100*20*1.25/100000 = 275 penetration units
Unihelm=66
Unigreaves=385
Unigauntlets=22
Uniboots=26

  See the problem yet?

Since the penetration size required to penetrate armor with an edged attack (otherwise the attack is converted to blunt) is linearly proportional to the creature size, a giant has 5.3x the tissue penetration req. of a dwarf, but giant-sized armor has 150x the penetration req. (about 41314 for giant-sized uniplate). Worse, the clothing worn by those "deity" guys you can meet in adventure mode is about 55000 penetration units thick. Vanilla bolts have penetration 2000, and pikes have 12000. Do the math.

So in order to put a real uniform layer of metal across a dwarf, you have to make each piece of armor equal in volume, which means equal weight if the armor is all made of the same material. This extra weight makes it hard to move in combat.

I'd call it a bug if you need to wear a 17 kg boot to get the same thickness of metal as a 17 kg breastplate, even though the breastplate covers a larger body part (the upper body) than the foot. The armor should probably scale the same way that the body tissues scale (cube root).

[Pirate Bob]

I found something interesting when looking at penetration, so I'll take a step back to recap:
I came up with the "uniarmor" concept several pages ago in this thread when testing the "ricochet" deflection of bolts off armor.
*SNIP*

This is a very nice result!  In addition to be useful on it's own merit, it also gave me some insights into how LAYER_SIZE, CONTACT_AREA, and PENETRATION_DEPTH could influence the other type of deflections.  I realized that maybe I didn't change CONTACT_AREA enough to matter last night (I increased from 2 to 4), as it might be subject to weird rounding for this mechanism as well.  I will try again with say a 100-fold increase in CONTACT_AREA tonight.

This also confirmed a feeling that I had a few days ago that we need to create a summary of our results.  If I can't keep track of them, I can't imagine people not directly working on this project can understand what we're doing at all any more.  I have created a google doc where I am beginning to compile our results.  I would definitely like to create a wiki page for this eventually, but

• I have little experience editing the wiki
• I don't know what to title the page (maybe "Ballistics" or "Dwarven Ballistics"?), or how to move the page if we change the title later
• what I have so far is very rough, and I don't want to confuse people with misinformation

If other people involved in this project would like to help with wikifying it, then maybe we could do that sooner than later.  Otherwise, if anyone else would like to work on the google doc I have just send me your email address and I'll give you access (or do people think it would be safe to just grant access to anyone with the link?  I fear trolling...)

Finally (speaking of trolling ) I don't think I like using "ricochet"  to describe the first kind of deflection.  Maybe I don't understand what "ricochet" means, but based on my understanding and reading of wikipedia, it occurs when the surface hit is hard enough to prevent penetration, and the projectile is strong enough to resist fragmentation.  The projectile deflection we observe doesn't depend on the impact parameters of the armor at all.  Instead it requires that the SHEAR_YIELD/FRACTURE are high enough to convert the edged damage to blunt damage.  If the damage is blunted, then the chance of deflection depends on the mass of only the chunk of armor under the contact area of the projectile.  To me, this indicates that a chunk of armor of this size is being pushed in, as if the whole piece of armor is moving as a rigid unit then deflection should depend on say the mass of the entire breastplate, not just a section of it the size of the bolt's contact area.  Then, deflection occurs if the bolt's IMPACT_YIELD is small compared to the mass of the armor chunk moved, indicating that the bolt is deformed or fragmented.  To me, this sounds more like frangibility than a ricochet.  However, even if the deformation of the bolt is plastic and could be called a ricochet, I think the other type of deflection, which depends on the impact parameters of the armor and bolt momentum, is almost definitely a ricochet.  Therefore, I don't think the term "ricochet" is a good choice to distinguish these two types of deflection. 

First of all, this is only a matter of terminology, and really doesn't matter that much.  The only reason I care at all is I am thinking ahead to writing a wiki page etc, and I also wonder if maybe I don't actually understand what's happening in this type of deflection.  Second, I am by no means an expert in ballistics, so if I am wrong, please tell me so (and ideally explain why).  Maybe we could instead call it "bolt deformation" or "fragmentation" or something like that?  It doesn't sound as cool as "ricochet" though. 

Maybe a discussion of terminology is also premature since we really don't understand the second kind of deflection at all yet.  In any case, I don't mean to offend, and by all means Urist keep calling it whatever you want.  I just want to make sure that I understand what's going on, and that when we communicate what's going on to others we are as clear as possible.

[HiEv]

This also confirmed a feeling that I had a few days ago that we need to create a summary of our results.  If I can't keep track of them, I can't imagine people not directly working on this project can understand what we're doing at all any more.  I have created a google doc where I am beginning to compile our results.  I would definitely like to create a wiki page for this eventually, but

• I have little experience editing the wiki
• I don't know what to title the page (maybe "Ballistics" or "Dwarven Ballistics"?), or how to move the page if we change the title later
• what I have so far is very rough, and I don't want to confuse people with misinformation

If other people involved in this project would like to help with wikifying it, then maybe we could do that sooner than later.  Otherwise, if anyone else would like to work on the google doc I have just send me your email address and I'll give you access (or do people think it would be safe to just grant access to anyone with the link?  I fear trolling...)

I agree this needs a summary and needs to be wikified, but it also sounds like you're still in the process of getting to the bottom of things.

Adding stuff to the wiki is pretty easy, I can help if you need it.  Considering that this information is also entangled with armor, perhaps "Ballistics and Armor Physics"?  (Open to better suggestions if anyone has one.)  Moving a page is easy, you just mouse-over the little down arrow next to "View History" and pick "Move", give the page a new title, and then it moves the page and its talk page and sets up a redirect from the old name for you.

Once the results are nailed down a bit better, just post a summary here, and I can wikify that for you if you want.  (I've been avidly following this thread, so no need to email/PM me.)

[Pirate Bob]

I agree this needs a summary and needs to be wikified, but it also sounds like you're still in the process of getting to the bottom of things.

Adding stuff to the wiki is pretty easy, I can help if you need it.  Considering that this information is also entangled with armor, perhaps "Ballistics and Armor Physics"?  (Open to better suggestions if anyone has one.)  Moving a page is easy, you just mouse-over the little down arrow next to "View History" and pick "Move", give the page a new title, and then it moves the page and its talk page and sets up a redirect from the old name for you.

Once the results are nailed down a bit better, just post a summary here, and I can wikify that for you if you want.  (I've been avidly following this thread, so no need to email/PM me.)

I very much appreciate your offer to help with the wiki!  I think the most efficient thing to do would be for me (or maybe Urist Da Vinci, if he wants to do it) to post results to the wiki, and then for you and others more familiar with the wiki's style and format to edit them.  I am OK with editing wiki pages, I'm just not confident that I can create a "proper" dwarf fortress wiki page.  I think we are getting very close, and perhaps a few things (like the way velocities are determined) could be posted soon.  I do like the name "Ballistics and Armor Physics", but it also made me wonder if these should be two separate things.  I suspect (although I have no evidence for this) that the Armor Physics side will be the same for melee combat as for projectiles, and that if we could figure out how velocities are determined for melee weapons we would find similar or identical results to projectiles of the same momenum, size, and contact area.  I think Zivilin may be investigating this, but I'm not sure.  I guess I should see what he's found before posting anything, as if they are, then maybe we should have a unified "Armor Physics" page, and just append the bit about determining projectile velocities to the page for bows and crossbows, or something similar.

As for the testing, I have a bunch more results for varying IMPACT_FRACTURE and IMPACT_YIELD, but I don't see a clear pattern coming out of them yet.  I will try to post plots etc this weekend (my wife is out of town, so I should have time).  I also confirmed that changing contact area follows the same "round to 100" pattern for elastic collisions as for ricochet/projectile deformation collisions.  Specifically, if I increase contact area to 9 (contact area * size 20 = 180), nothing happens, but if I increase to 10, I see a significant change.  Furthermore, it appears that increased contact area widens the distance between the 100%-20% dropoff and the 20%-0 dropoff, which opens the possibility of having multiple armors with 0<deflection<100% at the same bolt momentum (I also have new results showing this is impossible by just varying momentum keeping all other parameters at vanilla settings).  Unfortunately, at contact area = 10 I also saw at least one instance of a hand being severed, and I know that one of the reasons Toady modified projectiles previously was he didn't like them severing body parts, so I'm not sure if increasing contact area is a viable option for fixing projectiles.  Maybe going to 10 would be acceptable, but going higher would almost certainly not.  Intermediate values like 5 might also be interesting if standard plate armor has any regions which overlap to give a thickness of 40 or more, or something similar.

Fortunately, Urist's previous investigations have also shown that decreasing bolt SIZE has the same effect as increasing CONTACT_AREA on projectile deformation, so I am hoping the same will be true for elastic deflection.  I am running this now.

[Mr S]

I am following this so much.  I just gobble up every post, even if I'm not terribly good at statistical analysis myself.  I love the science involved.  (Next, we will mod Lignite bolts for !!Science!!  Or not.)

Perhaps the Wiki entry could be titled:
Ballistics Affects on Armor
Ballistics Protection of Armor

Of course, this is assuming that it stays seperte from the Melee vs. Armor discussion, or even the larger Material Properties information thread as a whole.

I would think that it would be very valuable to point out early on in the Wiki article, as in the introdution section, that this is still a W.I.P. and that information listed now could very well change in future versions.

[HiEv]

Other alternate wiki entry titles:
Damage Physics
Attack and Defense Equations
Material Science

You can mix and match the first words with the last word of those for other possible titles.

[Urist Da Vinci]

...
As for the testing, I have a bunch more results for varying IMPACT_FRACTURE and IMPACT_YIELD, but I don't see a clear pattern coming out of them yet.  I will try to post plots etc this weekend (my wife is out of town, so I should have time).  I also confirmed that changing contact area follows the same "round to 100" pattern for elastic collisions as for ricochet/projectile deformation collisions.  Specifically, if I increase contact area to 9 (contact area * size 20 = 180), nothing happens, but if I increase to 10, I see a significant change.  Furthermore, it appears that increased contact area widens the distance between the 100%-20% dropoff and the 20%-0 dropoff, which opens the possibility of having multiple armors with 0<deflection<100% at the same bolt momentum (I also have new results showing this is impossible by just varying momentum keeping all other parameters at vanilla settings).  Unfortunately, at contact area = 10 I also saw at least one instance of a hand being severed, and I know that one of the reasons Toady modified projectiles previously was he didn't like them severing body parts, so I'm not sure if increasing contact area is a viable option for fixing projectiles.  Maybe going to 10 would be acceptable, but going higher would almost certainly not.  Intermediate values like 5 might also be interesting if standard plate armor has any regions which overlap to give a thickness of 40 or more, or something similar.

Fortunately, Urist's previous investigations have also shown that decreasing bolt SIZE has the same effect as increasing CONTACT_AREA on projectile deformation, so I am hoping the same will be true for elastic deflection.  I am running this now.

1. That's cool that the contact area behaviour is consistent.

2. I have new research which I should finish up in a day or so which suggests that there is no 100%-20% dropoff, but rather that the 20% extends all the way to zero and is overlapped by a 100%-0% dropoff, if you get what I mean.

3. If you look back where I listed how to find body part contact areas and a few examples, you see that the average dwarf hand has a contact area of 18. AFAIK from looking at wound data, severing requires 100% penetration over 100% of the surface, so maybe the hand was hit twice?

[Pirate Bob]

2. I have new research which I should finish up in a day or so which suggests that there is no 100%-20% dropoff, but rather that the 20% extends all the way to zero and is overlapped by a 100%-0% dropoff, if you get what I mean.

3. If you look back where I listed how to find body part contact areas and a few examples, you see that the average dwarf hand has a contact area of 18. AFAIK from looking at wound data, severing requires 100% penetration over 100% of the surface, so maybe the hand was hit twice?

2. I do know what you mean, and I was aware of this, but I guess I did not express it clearly.  At least, I think I understand what you are saying.  The way I believe it works is that there is some cutoff momentum above which deflection cannot be higher than 20% (or maybe 18.5%, whatever).  There is also a smooth transition from 100% to zero which occurs independently.  If the 100% to zero transition occurs at lower momentum than the 20% cutoff, then you don't see any cutoff.  This is the case for IMPACT_FRACTURE equal to or only slightly larger than IMPACT_YIELD.  If the 20% cutoff occurs at lower momentum than the 100% to zero transition, then you see a sharp drop to 20%, followed by a smooth drop from 20% to zero at higher momentum.  If they occur at approximately the same momentum, then you can see a smooth drop to say 80% momentum, then a sharp drop to 20%, and then another smooth drop to zero.  Basically, to draw the deflection curve, you draw the smooth 100% to zero dropoff first, and then you set any values above the 20% cutoff to no more than 20%.  For example, compare these plots at varying IMPACT_STRAIN_AT_YIELD (which moves the 20% cutoff) for several values of IMPACT_FRACTURE:

Spoiler (click to show/hide)

Increasing IMPACT_STRAIN_AT_YIELD results in a lower cutoff to 20%, but the portions of the curves below 20% always remain the same, and line up with the higher portions of the curves when they are visible at lower IMPACT_STRAIN_AT_YIELD.

3.  The full log did contain

Code: [Select]

The flying {iron bolt} strikes Arena Dwarf 59 in the right hand, shattering the bone through the small steel right unigauntlet!
A ligament has been torn and a tendon has been torn!
...
The flying {iron bolt} strikes Arena Dwarf 59 in the right hand and the severed part sails off in an arc!
So it appears you are correct and multiple hits were required to remove the hand.  I actually think this is relatively realistic - if you get hit more than once in the hand by bolts there will be nothing left.  Especially if they are broadheads.  Regardless, I will go ahead with a large scale test of CONTACT_AREA:10.

Some more results - varying bolt size DOES NOT change the deflection vs. momentum curve at all.  At first I got excited and thought it did, but it appears that SIZE gets rounded to the nearest 10, with 10 being the minimum (similar to layer thickness * contact area rounding to 100).  Therefore, size 5, 10 and 15 give the same results vs. velocity, but when size is increased to 20 velocities are halved for the same deflection (as mass doubles).   

I very much hope to post detailed results of everything this weekend.  I told everyone that I had nothing to do this weekend, which resulted in everyone wanting me to do stuff...

[Urist Da Vinci]

OK, this is embarrassing. We didn't check which body parts were doing the deflecting in the 18-20% case. It was the lower body and toes, only. The reason why is that the lower body is covered by both the breastplate and the greaves. This is what happens when you layer up armor!

Iron bolts vs steel uniarmor set at velocity 55 results in 18% deflection.

To fix, edit the uniplate like so:

Code: [Select]

[ITEM_ARMOR:ITEM_ARMOR_UNIPLATE]
[NAME:uniplate:uniplates]
[ARMORLEVEL:3]
[UBSTEP:1]
[LBSTEP:2] lower body now protected once
[SHAPED]
[LAYER:ARMOR]
[COVERAGE:100]
[LAYER_SIZE:20]
[LAYER_PERMIT:50]
[MATERIAL_SIZE:9]
[HARD]
[METAL]
Now only use the modified uniplate, plus unihelm, unigauntlets, and uniboots. Discard the unigreaves. Dwarves now go pantless!

Testing this with iron bolts vs steel armor at velocity 55 results in 0% deflections.

Pirate Bob, could you please retest the following plot after making the edit?

...

...

Could you also edit your script to output the percent of hits that include the word "tearing", and the percent of hits that include the word "bruising". A bruising-tearing transition should become apparent when those results are plotted along with deflection like above.

[Pirate Bob]

...
Pirate Bob, could you please retest the following plot after making the edit?
...
Could you also edit your script to output the percent of hits that include the word "tearing", and the percent of hits that include the word "bruising". A bruising-tearing transition should become apparent when those results are plotted along with deflection like above.

I can definitely do that today/tonight.  Hopefully this will make things much simpler.  I should have checked that the uniarmor worked as advertized, but I don't totally understand how coverage works.  I think I will also run a test where I reduce all armor thickness to 1.  If we understand how armor thickness is used correctly, this should make no difference compared to 20 (as both 1 and 20 * CONTACT_AREA=2 will round up to 100). 

I already have my script find the percentages that result in bruising and tearing, but I am just not recording the result right now, so recording it should be no problem at all.  I'm not sure exactly what you had in mind, so I think I will record %chips, fractures, bruising, and tearing all seperately, as well as the % which ONLY have bruising (which I was calling non-serious hits before).  If there's anything else you would like me to record, let me know and I can try to add it.  I also keep all the raw gamelog.txt files from all of my runs, so we can always go back and re-analyze them (or even look at them by eye) if you think of something later.  I'd post them to DFFD, but I think I'm up to several GB of logs now.  If there are ever specific logs you would like to see, please let me know.

Edit:
I did a quick run and verified that you are correct - with uniform armor thickness there is only one cutoff:

Spoiler (click to show/hide)

I am now setting up to do a full run and output %tear, %bruises etc. 

[Pokon]

...This has more in-depth information about the science of the effectivness of crossbows against armored creatures than I pumped out on my finals last year.

I wish this forum had a +1 button.

[Urist Da Vinci]

Before seeing my latest research, take a look at these 2008 Toady quotes:

http://www.bay12forums.com/smf/index.php?topic=30026.msg996723#msg996723
http://www.bay12forums.com/smf/index.php?topic=21498.msg371081#msg371081
http://www.bay12forums.com/smf/index.php?topic=21498.msg369028#msg369028
http://www.bay12forums.com/smf/index.php?topic=21498.msg368028#msg368028

In particular:

So we'll also have armor acting like a pseudo tissue layer for purposes of transmitting bludgeoning damage and so forth? Additionally, if we're talking about a steel-skinned creature (Giant Magma Ants?) instead of a steel-armoured creature, is the force transfer handled differently?

Yeah, that's basically how it works.  The armor is all checked in order from outer to inner, then it gets at the tissue layers, altering the character of the attack as it goes.  There's a little left to do there, so it's not completely clear to me which way it'll go as far as how much force is transferred (or if it matters if it's skin or armor -- it doesn't currently, though yeah, there is a difference in real life).  It has to be enough that skin doesn't stop bones from being broken, but not so much that armor is useless against impacts, depending on the mats and nature of the armor/clothing.

So what I did is give dwarves steel skin:

Code: (tissue_template_default.txt) [Select]

[TISSUE_TEMPLATE:SKIN_TEMPLATE]
[TISSUE_NAME:skin:NP]
[SCARS]
TISSUE_MATERIAL:LOCAL_CREATURE_MAT:SKIN removed brackets
[TISSUE_MATERIAL:INORGANIC:STEEL]
[RELATIVE_THICKNESS:1]
Lower is faster.
HEALING_RATE:100 removed brackets don't want dents to vanish
[VASCULAR:1]
[PAIN_RECEPTORS:5]
[CONNECTS]
[TISSUE_SHAPE:LAYER]
and then I shot iron bolts at them at various velocities. This appears to provide the same level of protection as the updated steel uniarmor set. The advantage here is that I can use dfhack to get the wound data (strains and the percent fractured/penetrated) whenever the steel skin is damaged.

One result is that the strain never exceeds the strain at the time the tissue is fractured:

strain at fracture = IMPACT_STRAIN_AT_YIELD * IMPACT_FRACTURE / IMPACT_YIELD
i.e. 940 * 2520000 / 1505000 = 1573 (sometimes 1574)

Another result is that we can compare the combat text for steel skin and steel armor at various iron bolt velocities (these are NOT threshold velocities):

Code: [Select]

v  steel skin dwarf                  steel armor on normal dwarf

1  glance away                       deflected
25 bruised                           deflected
30 bruised/dented                    deflected
35 dented                            deflected
40 dented                            deflected
45 dented/fractured                  deflected
50 dented/fractured, bruise muscle   bruise muscle through the armor
55 fractured 20-60%, bruise muscle   bruise muscle through the armor
70 fractured 100%, tearing muscle    tearing the muscle through the armor

See the plot below of strains in the steel skin at various velocities. The horizontal axis is the sample size, scaled to a sample size of 100. We see that bruising occurred 25% of the time at velocity 30, and denting the other 75% of the time, regardless of the body part hit. We see that fractures (only about a 5% fracture) occurred 23% of the time at velocity 45, and that is also regardless of the body part struck.

Spoiler (click to show/hide)

I'm not sure what to make of the stepped strains yet. It isn't related to contact or body part size, because both small and large parts were at all steps.

Interpretation:

- Damage to tissue and to armor is tracked the same way, but armor doesn't report if it is dented/partially fractured.
- Armor effectively insta-heals after each hit, whereas tissue keeps and accumulates damage.
- If the bolt can cut the armor, then the bolt cuts into the tissue underneath.
- If the bolt can't cut the armor, but can fracture it 100%, then the bolt cuts into the tissue underneath.
- If the bolt can't cut or fracture the armor, then a strain-related mechanism (which can occur during denting or partial fracture) may allow blunt damage to pass to tissue underneath.
- For a given velocity, bolts impact with a range of possible strains which appear to follow a pattern. The strains are just the bullet hole in the wall, we need to learn about the bullet (the strain is an effect, not a cause).

[Pirate Bob]

So what I did is give dwarves steel skin:
...
strain at fracture = IMPACT_STRAIN_AT_YIELD * IMPACT_FRACTURE / IMPACT_YIELD
i.e. 940 * 2520000 / 1505000 = 1573 (sometimes 1574)

This is amazing!  Knowing the strains will definitely help with understanding what's going on. 

Is it really correct that the strain at fracture does not depend on the contact area or the layer thickness?  If so, then how are these things playing into armor protection, as they clearly do matter for armor?  Do layer thickness and contact area enter into determining the strain? 

On my side, because I've been busy, I was careless setting up my run, and accidentally left SHOOT_MAXVEL set to 48, so I don't have results for adamantine, but all other armors were fully penetrated by copper bolts before velocity 48, so it wasn't that bad.  It appears for contact area=2 and uniform layer thickness of 20 there is no regime where bruising occurs at all for iron, copper, and bronze armor against copper bolts, but for steel only bruising occurs for all forces up to 48. 

Spoiler (click to show/hide)

I will have to run again with steel and adamantine to see what happens at higher forces for these.  I will also run at larger contact area to see how that changes things. 

Also, I'm not sure I understand your strain equation.  If I use this, I get

armor	strain	force
steel	1574	42
iron	638	25
bronze	766	17
copper	550	20

The "force" is the middle of the drop in my plot of deflection vs. shoot force, and strain is from strain at fracture = IMPACT_STRAIN_AT_YIELD * IMPACT_FRACTURE / IMPACT_YIELD.  So looking at the strain, bronze should be better than iron, but based on deflection it appears to be worse than even copper.  This is for deflection of copper bolts, not for iron bolts vs bronze  (which we expect to be weird due to the shear yield/fracture mismatch).  Maybe I messed something up because I'm tired, and maybe there's more screwiness in my data that I realize, or maybe I just don't understand your equation...

[Urist Da Vinci]

So what I did is give dwarves steel skin:
...
strain at fracture = IMPACT_STRAIN_AT_YIELD * IMPACT_FRACTURE / IMPACT_YIELD
i.e. 940 * 2520000 / 1505000 = 1573 (sometimes 1574)

This is amazing!  Knowing the strains will definitely help with understanding what's going on. 

Is it really correct that the strain at fracture does not depend on the contact area or the layer thickness?  If so, then how are these things playing into armor protection, as they clearly do matter for armor?  Do layer thickness and contact area enter into determining the strain? 

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Also, I'm not sure I understand your strain equation.  If I use this, I get

armor	strain	force
steel	1574	42
iron	638	25
bronze	766	17
copper	550	20

The "force" is the middle of the drop in my plot of deflection vs. shoot force, and strain is from strain at fracture = IMPACT_STRAIN_AT_YIELD * IMPACT_FRACTURE / IMPACT_YIELD.  So looking at the strain, bronze should be better than iron, but based on deflection it appears to be worse than even copper.  This is for deflection of copper bolts, not for iron bolts vs bronze  (which we expect to be weird due to the shear yield/fracture mismatch).  Maybe I messed something up because I'm tired, and maybe there's more screwiness in my data that I realize, or maybe I just don't understand your equation...

The strain is initially capped at the point where the material fractured, but it appears to creep upwards if the wound is repeatedly hit. The forces or energies or momentums that cause the strains are affected by contact size and layer thickness, but because of the round-to-100 thing then you don't notice the changes on dwarf-scale creatures. The skin thickness (but not armor thickness) is proportional to the cube root of the body part size, so the thickest skin on a dwarf is only 2-3x thicker than the thinnest skin.

Test results for copper bolts vs bronze skin at velocity 16 indicate that the damage falls into two categories:
a) The skin (armor in your case) is partially fractured 40%, 60%, or 80%. The strain in the armor is 766. No damage of any kind to underlying tissue. Some parts have fracture 41% or strain 767, but they were struck twice, so multiple hits each add 1 or more on top of the previous wound.
b) The skin (armor in your case) is completely fractured (100%), and the underlying soft tender bits are all cut up.

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 It appears for contact area=2 and uniform layer thickness of 20 there is no regime where bruising occurs at all for iron, copper, and bronze armor against copper bolts, but for steel only bruising occurs for all forces up to 48. 
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Yes, so bronze is worse than copper because it isn't being judged on strain. Only steel is good enough to meet the strain-or-whatever-induced-bruising criteria. If bronze didn't fracture so easily, you might see bruising because of the larger strain than iron.

So for steel, having IMPACT_STRAIN_AT_YIELD 1880 results in bruising immediately after yield (yield=metal skin denting). Having ISAY 940 (the default) means that bruising occurs just prior to the default IMPACT_FRACTURE (2520000). Having ISAY 470 means that no bruising occurs at the default IMPACT_FRACTURE (similar to bronze or adamantine), so you need to have a higher IMPACT_FRACTURE relative to IMPACT_YIELD before the bruising starts.

Spoiler (click to show/hide)

So how high does bronze's IMPACT_FRACTURE need to be raised before bruising appears, when copper bolts are shot at it? Then we can come up with an algorithm to predict that criteria.