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[sayke]

so what all variables are known to affect penetration/deflection, and can we write a function modeling their interactions?

[Zivilin]

I have a possible research topic. Are bows as effective as crossbows?

The only difference in the raws between crossbow+bolt and bow+arrow are the names, skills used, and the launcher size. The launcher size and strength is generally believed to not affect the projectile performance, except rate-of-fire in the case of a very heavy launcher.

The difference, if any, would likely lie in some hardcoding difference between the skills. The elven civilization (not creature) gets [IMPROVED_BOWS]. I don't exactly know what that does. It adds decorations to bows.

I'll just add that I ran a few preliminary tests, and could find no evidence that bows differed from crossbows in any way (The statistical data for bows was significantly different from crossbow data)

I do believe this is the finest scientific paper ever written in this board. And by science i don't simply mean dorf science, i mean true, systematic analysis of the game mechanics.

I wish i had to the time and expertise to creat the Annals of Dwarven Research. This thread would certainly count as one of it's finest papers.

You are too kind. It's mainly generating tons of data and then organizing it. The only "creative" parts are designing as objective an experimental setup as possible and defining useful criteria. The rest is mechanical and dull. Of course, obtaining interesting results at the end of the process is very satisfying.

An Annals of Dwarven Research would be nice <wistfully>. As it is, I'll try incorporating whatever data fits into the wiki.

A bit more testing suggests that the bolt material's threshhold IMPACT_YIELD is 3.4x the number used for the armor material's density, though this relationship is only valid for vanilla bolts and changes in an unknown manner when a few other properties are varied.

I.e. Copper bolts at [IMPACT_YIELD:26500] deflect off steel armor. Copper bolts at [IMPACT_YIELD:27000] deal damage through steel armor. Steel density 7850 * 3.4 = 26690.

I.e. Vanilla aluminum bolts at [IMPACT_YIELD:70000] deflect off platinum armor. Aluminum bolts with [IMPACT_YIELD:74000] deal damage through platinum armor. 21400 * 3.4 = 72760.

I.e. Vanilla iron bolts at [IMPACT_YIELD:542500] deflect off slade armor. Iron bolts with [IMPACT_YIELD:690000] deal damage through slade armor. 200000 * 3.4 = 680000.

This tickled my curiosity so I tried out a few parameters:

I took copper26500 and copper27000 and tested it against steel armor. As expected, copper26500 deflected, copper27000 caused damage. Then I continued running copper26500 and copper27000 against steel while changing promising parameters:

• I halved the IMPACT_YIELD of steel. No effect was observed (copper26500 defleted, copper2700 didn't)
• I increased SOLID_DENSITY of all coppers to 12000. No effect was observed (copper26500 deflected, copper27000 didn't)
• I changed around both ATTACK:EDGE parameters of bolts in the item_ammo text file. No effect was observed (copper26500 deflected, copper27000 didn't)

Finally, I doubled bolt size from 150 to 300. Lo and behold, both copper26500 and copper27000 caused damage. Assuming the simplest relation possible, I repeated the test with copper13250 and copper13500 (IMPACT_YIELDs halved compared to previous), and sure enough copper13250 deflected, while copper13500 did not.

The current equation is therefore:

The threshhold of the ammo's IMPACT_YIELD is equal to 510*ARMOR_SOLID_DENSITY/AMMO_SIZE

can we get a minecart impact study started... surely has some parallels with your research. 1000 dwarfs on track and run carts over them... should have enough results after every cart and trap of each material has been ran.... sorry just jumped on here to see if toady had tossed up an update, and found a good read.

Glad You enjoyed it. Unfortunately, I cannot replicate this research for minecarts, because I do not know how to create tracks/minecarts in Arena mode. Walls, floors, fortifications and creatures is my limit, I'm afraid.

so what all variables are known to affect penetration/deflection, and can we write a function modeling their interactions?

We know some of the variables, but probably not all. We actually got the beginning of a function with the last few posts

[Urist Da Vinci]

...
The current equation is therefore:

The threshhold of the ammo's IMPACT_YIELD is equal to 510*ARMOR_SOLID_DENSITY/AMMO_SIZE
...
We know some of the variables, but probably not all. We actually got the beginning of a function with the last few posts

Now it gets even more interesting:

Arena Bird Droppings:

Create a dwarf on team #1 in the arena, wearing armor
Create an eagle on team #1 a few z-levels above the dwarf, where the eagle is created with 100 bowls (under tools) of various metals (try lead, aluminum, iron).
The eagle appears and won't attack the dwarf, but since it has no hands it drops 100 items on the dwarf from above.
You can't do this with arrows/bolts since the items [100] are treated as a single object.
Weapons strike with an attack, other objects just have blunt collisions.

Similar blunt deflection behaviour is observed with this testing, except that the falling item's density matters (in apparently linear relationship).

Why does the bolt material density not matter, but the density of a falling item does? My theory is that the bolts are launched from the crossbow at a constant impulse or a constant energy, so that the density is used twice and cancels out of the equation, leaving only bolt size. Not sure how to test this.

EDIT: removed unreproduceable science. wouldn't be good to be creating myths right now.

[Oaktree]

Is there a chance for a dwarf to dodge dropped objects?  Or do objects traveling through a tile due to being dropped or flung (e.g. off a mine cart) going to hit anything that is in a tile?  Or at least the first object encountered going down a list*.

* - I think someone indicated in one of the threads on dropping objects that with multiple objects "senior" dwarves get hit first.  Which implies the code is scanning the dwarf list from top to bottom and not randomly picking who gets hit.

[rhesusmacabre]

You can't do this with arrows/bolts since the items [100] are treated as a single object.

You can assign many single bolts individually though.

[Zivilin]

Is there a chance for a dwarf to dodge dropped objects?

I repeated Urist da Vinci's dwarf-eagle setup with ten of each, and gave the eagles around 30 separate bolts, as suggested by rhesusmacabre. The dwarves were all Grand Master Dodgers, and I didn't give them any armor (in case it somehow impedes speed/dodging - I haven't tested this yet).

All dwarves died, not one dodged. This would imply dropping items are indeed undodgeable. I suspect dodging is a... combat-specific action, and doesn't occur when the dwarf is not being targeted by an enemy.

...

Why does the bolt material density not matter, but the density of a falling item does? My theory is that the bolts are launched from the crossbow at a constant impulse or a constant energy, so that the density is used twice and cancels out of the equation, leaving only bolt size. Not sure how to test this.

EDIT: removed unreproduceable science. wouldn't be good to be creating myths right now.

I remembered the term "constant impulse" from Your earlier post concerning pre-minecart knockback research, where You found that crossbow knockback did not depend on bolt density. I hope I'm not doubling up on research already done, but I decided to see if this is the case in 34.11.

I improvised an experimental setup where I could estimate the distance a dwarf is propelled without skidding effects. I used the whole arena to make a cliff with isolated lanes:

Spoiler: Fig.1. Cliff-top (Arena level 4) (click to show/hide)

Spoiler: Fig.2. Cliff-bottom (Arena level -4) (click to show/hide)

I modded crossbows to SHOOT_FORCE = 100'000 and SHOOT_MAXVEL = 100'000, and I modded light silver and heavy silver to SOLID_DENSITY 2000 and 30'000, respectively. Referring to figure 1, The top 3 dwarves used light silver bolts, the middle 3 dwarves used regular silver bolts, and the bottom three dwarves used heavy silver bolts. All dwarves were Grand Master Marksdwarves/Archers.

The results are presented in Figure 3.

Spoiler: Fig.3. Cliff-bottom (Arena level -4): Post-experiment (click to show/hide)

The spots marked with red circles are the spots the dwarves were at the moment the battle report informed that they were "skidding" for the first time, which I assume is their first contact with the ground.

Light silver bolts propelled dwarves the least, dropping them close the foundation of the pillar.
Regular silver bolts propelled dwarves the furthest.
Heavy silver bolts propelled dwarves... a medium distance.

Members of a given bolt weight category fell in the exact same distance, and from what I could tell, stopped skidding in the exact same spot. I later repeated the experiment with only regular silver, and veeery caaaarefully studied two of the trajectories tick by tick, and they were identical, even for the skidding part (even the moments skids were reported were identical). So results should be easily reproduced, with little to no variation between individual runs.

I have not yet formulated satisfying conclusions from this, but bolt density/weight clearly effects crossbow knockback in 34.11.

[Urist Da Vinci]

...
I remembered the term "constant impulse" from Your earlier post concerning pre-minecart knockback research, where You found that crossbow knockback did not depend on bolt density. I hope I'm not doubling up on research already done, but I decided to see if this is the case in 34.11.

I improvised an experimental setup where I could estimate the distance a dwarf is propelled without skidding effects. I used the whole arena to make a cliff with isolated lanes:
...
Light silver bolts propelled dwarves the least, dropping them close the foundation of the pillar.
Regular silver bolts propelled dwarves the furthest.
Heavy silver bolts propelled dwarves a medium distance.

Members of a given bolt weight category fell in the exact same distance, and from what I could tell, stopped skidding in the exact same spot. I later repeated the experiment with only regular silver, and veeery caaaarefully studied two of the trajectories tick by tick, and they were identical, even for the skidding part (even the moments skids were reported were identical). So results should be easily reproduced, with little to no variation between individual runs.

I have not yet formulated satisfying conclusions from this, but bolt density/weight clearly effects crossbow knockback in 34.11.

Here's a thought experiment. Say you launch bolts with a constant impulse. The light bolts would go really fast, but there is a MAXVEL on the crossbow. Normal bolts travel slower, and heavy bolts travel really slow. The light bolts hit a dwarf with reduced momentum (because the cap stole their velocity!) whereas the normal and heavy bolts have the same momentum at impact. Using conservation of momentum you find the new velocity of the dwarf w/ embedded bolt. The heavier bolt adds to the mass of the combination, reducing the final velocity.

Using real world-mechanics:

Code: [Select]

Momentum (N-m)  Mass (kg) Velocity cap (m/s) Bolt velocity (m/s) Impact (N-m) 87kg dwarf V (m/s)
        100000         45             100000                2222       100000                758
        100000        4.5             100000               22222       100000               1093
        100000        1.6             100000               63694       100000               1129
        100000        0.3             100000              100000        30000                344

Your light bolts were 0.3 kg and propelled the dwarf 2-3 tiles (depends on rounding when he hits the ground).
Your normal bolts were 1.6 kg and propelled the dwarf 11 tiles.
Your heavy bolts were allegedly 4.5 kg, but I suspect you had an extra zero in there to get 45 kg, as the dwarf was propelled 8 tiles. Look at the final column in my table above, and divide the numbers by 100. The distance travelled horizontally depends only on initial velocity and the (identical) fall time. DF uses floating point calculations for parabolic paths and minecarts.

[Oaktree]

Is there a chance for a dwarf to dodge dropped objects?

I repeated Urist da Vinci's dwarf-eagle setup with ten of each, and gave the eagles around 30 separate bolts, as suggested by rhesusmacabre. The dwarves were all Grand Master Dodgers, and I didn't give them any armor (in case it somehow impedes speed/dodging - I haven't tested this yet).

All dwarves died, not one dodged. This would imply dropping items are indeed undodgeable. I suspect dodging is a... combat-specific action, and doesn't occur when the dwarf is not being targeted by an enemy.

That carries serious implications for dwarven defense systems incorporating falling or flung objects.  Master level goblin leaders who dodge and block weapon traps and bolts with ease are basically as vulnerable to these as a low-level recruit goblin.  I have some anecdotal evidence from seeing such a leader block or dodge crossbow bolts for a while and then get totally de-limbed by a mine cart railgun shot of serrated discs.

[Zivilin]

Your heavy bolts were allegedly 4.5 kg, but I suspect you had an extra zero in there to get 45 kg, as the dwarf was propelled 8 tiles. Look at the final column in my table above, and divide the numbers by 100. The distance travelled horizontally depends only on initial velocity and the (identical) fall time. DF uses floating point calculations for parabolic paths and minecarts.

This would be a very elegant explanation and I would like nothing more than for my hand to have slipped and inserted that additional zero. Unfortunately, I redid the test with careful attention to SOLID_DENSITY modding, and the results were the same as the first time. Regular silver bolts propelled dwarves 11 tiles before skidding (and then an additional 8 to full stop), whilst heavy silver bolts (a stack of 100 of which weighed in at 450 kg) propelled dwarves 8 tiles before skidding (and then an additional 5 to full stop).

I also used regular silver against dwarves clad in full heavy silver armor, for an additional 291 kg of weight. Equipped weight is apparently not included in knockback calculations, since propelled armored dwarves flew 11+8 tiles, same as their naked brethren.

I then tested out a few more metals to increase the amount of experimental data (All parameters the same as in previous post):

iron:       drop 8, skid 6
copper:   drop 9, skid 7
silver:     drop 11, skid 8
gold:      drop 10, skid 8
platinum: drop 7,  skid 5

I must say, I find these results more than a little surprising. Why would silver cause the greatest knockback is a mystery to me (for the moment). For a moment I suspected other parameters to be involved, so I modded candy to be as heavy as silver, and tested both for knockback. All candy parameters are pretty extreme when compared to regular metals, so I thought this would show different results if any of those parameters mattered. However, both test groups were propelled 11+8, so I assume SOLID_DENSITY is the only material-related parameter which matters.

That carries serious implications for dwarven defense systems incorporating falling or flung objects.  Master level goblin leaders who dodge and block weapon traps and bolts with ease are basically as vulnerable to these as a low-level recruit goblin.  I have some anecdotal evidence from seeing such a leader block or dodge crossbow bolts for a while and then get totally de-limbed by a mine cart railgun shot of serrated discs.

I'm seriously considering equipping my fortress with anvil traps

[rhesusmacabre]

Toady did state while minecarts were being implemented that they, at least, could be dodged:

If the carts aren't going super fast and the dwarf has a space, they'll almost always dodge aside, and even if there is no space, if the cart is going slow enough, they'll just stop it.

I've never actually seen it myself, but I mostly just use carts in 1-tile wide tunnels so maybe that's not surprising. Whether minecarts on tracks are treated as a special circumstance, or it also applies to other projectiles, isn't clear.

[Oaktree]

Toady did state while minecarts were being implemented that they, at least, could be dodged:

If the carts aren't going super fast and the dwarf has a space, they'll almost always dodge aside, and even if there is no space, if the cart is going slow enough, they'll just stop it.

I've never actually seen it myself, but I mostly just use carts in 1-tile wide tunnels so maybe that's not surprising. Whether minecarts on tracks are treated as a special circumstance, or it also applies to other projectiles, isn't clear.

Goblins are apparently not that good at it.  Look up the F.R.O.G.G.E.R. system - it's a defense set-up that allows intruding goblins to attempt to cross multiple tracks of high-speed mine carts.  Though I consider the implementation more of a curiousity given the amount of space it takes up.

[Urist Da Vinci]

...
I then tested out a few more metals to increase the amount of experimental data (All parameters the same as in previous post):

iron:       drop 8, skid 6
copper:   drop 9, skid 7
silver:     drop 11, skid 8
gold:      drop 10, skid 8
platinum: drop 7,  skid 5

I must say, I find these results more than a little surprising. Why would silver cause the greatest knockback is a mystery to me (for the moment). For a moment I suspected other parameters to be involved, so I modded candy to be as heavy as silver, and tested both for knockback. All candy parameters are pretty extreme when compared to regular metals, so I thought this would show different results if any of those parameters mattered. However, both test groups were propelled 11+8, so I assume SOLID_DENSITY is the only material-related parameter which matters.
...

I tested the same arena layout and crossbow properties as you, and the same 5 normal bolt materials, except using cats as the test subject. All cats were propelled 11+10, regardless of material. I tested this with an ultralight creature and uberpowerful crossbow, and it indeed appears to be a knockback cap on bolt hits. Any testing results that hit the cap are probably invalid as the actual value could have exceeded the cap.

...
Finally, I doubled bolt size from 150 to 300. Lo and behold, both copper26500 and copper27000 caused damage. Assuming the simplest relation possible, I repeated the test with copper13250 and copper13500 (IMPACT_YIELDs halved compared to previous), and sure enough copper13250 deflected, while copper13500 did not.

The current equation is therefore:

The threshhold of the ammo's IMPACT_YIELD is equal to 510*ARMOR_SOLID_DENSITY/AMMO_SIZE
...

I tested this with dropped bowls, dropped bolts, and varying sizes and contact areas. The equation appears to be something like (500 + C)*ARMOR_SOLID_DENSITY/AMMO_SIZE, where C is a function of the contact area. The contact area of objects appears to be a function of their size (AMMO_SIZE), except for ammo with a defined ATTACK contact area.

A size 100 aluminum bowl deflects off steel armored dwarf at ~40000
A size 1000 aluminum bowl deflects at ~10000
A size 10000 aluminum bowl deflects at ~6400

A size 1500 iron bolt deflects off steel armor at ~2670
A size 1500 iron bolt with 10x contact area deflects at ~9000

Also, for threshold IMPACT_YIELD greater than about 10000, the difference between deflect and blunt damage on armor is binary. For thresholds 0-10000, the difference is fuzzy and also appears to depend on body part size or number of armor layers (i.e. lower leg deflects because boots+greaves, but upper leg damaged because only greaves!).

This research has useful applications because wooden arrows (i.e. from elves) kill dwarves in candy, aluminum, wood, bone, and leather armor, but heaver junk metals like pewter (i.e. artifact) or copper armor will safely deflect the arrows. The armor density needs to be at least 3000.

Armor would need to have a density of 59000 or greater to deflect bone bolts, and as shown earlier in the thread bone bolts do blunt damage through all vanilla metal armors.

[HiEv]

Bottom line - plate armor does nothing against bolts, and chainmail provides modest protection against them.  This is quite the opposite of what I would have expected.

Just curious, but what exactly is it in the raws about chainmail that makes it protect against bolts and arrows (projectiles) vs. how plate armor is defined?  Is it the "STRUCTURAL_ELASTICITY_CHAIN_ALL" in mail shirts?  Or is it the "ARMORLEVEL:2" (chain) vs. "ARMORLEVEL:3" (plate)?

And how does that affect pants?  I noticed that testing seemed to only mention greaves ("ARMORLEVEL:3"), and not leggings ("ARMORLEVEL:1" + "METAL_ARMOR_LEVELS" = chain when made with metal; "STRUCTURAL_ELASTICITY_CHAIN_METAL").  So do greaves work while plate doesn't?  Or do leggings work better than greaves?

I'm asking because I was wondering about creating headgear, such as a mail coif, that helps protect against projectiles.  The basic helm has "ARMORLEVEL:1" and "METAL_ARMOR_LEVELS" which means that it's effectively of the "chain" armor level when made with metal, but it doesn't have "STRUCTURAL_ELASTICITY_CHAIN_METAL", and doesn't seem to protect against projectiles.  This seems to suggest that it's the "STRUCTURAL_ELASTICITY_CHAIN_METAL" that gives it the resistance to projectiles.  Is this correct?

TL;DR: Exactly what raw token(s) give(s) armor the ability to protect against projectiles?

[Zivilin]

TL;DR: Exactly what raw token(s) give(s) armor the ability to protect against projectiles?

I'm not 100% certain at the moment, but I will be when I finish my latest study.

My current working hypothesis is that it is indeed the [STRUCTURAL_ELASTICITY_CHAIN_ALL] tag that grants projectile protection. More specifically, I believe this tag grants the convert-EDGE-into-BLUNT-damage ability to the armor it is added to. As a result, bolts made of equal or "worse" materials than the chain mail bruise and fracture instead of tearing. This protects against 3 death conditions: Throat tear, Heart tear, and half of the Spinal tears. From what I've heard (but not tested), chain mail does not protect against blunt damage, so that same tag when added could possibly also have the effect of erasing any blunt damage protection that armor might have had. 

Another interesting consequence of Pirate Bobs results is that plate armor appears to be useless against piercing attacks (or at least "extreme" piercing attacks), even if the piercing weapon is made from a "worse" metal than the armor. I'll be testing this on spears to see if the vulnerability persists for non-crossbows. However, it is known that plate armor protects well against typical slashing attacks made by weapons of "worse" metals (e.g. copper axes deflect of of steel armor), so this is not a general vulnerability to EDGE attacks.

I'll be posting more data on these issues when I have the results.

Having headgear with chain-mail like properties is an interesting idea. Unfortunately, I half expect that it will simply cause the bolt the jam the skull through the brain instead of outright tearing it - after all, blunt attacks are known to be vastly more effective at dealing head-related deathblows. However, if it happens to convert a significant percentage of what-would-have-been-brain-or-spinal-tears into bruising and skull shattering, then I'd call that a success. Current percentages for practically all non-candy metal bolts hitting the head are 10% non-lethal damage, 30% spinal tears, 60% brain tears.

[sayke]

this is fantastic - i eagerly await the experimental results! =D