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[WindComeCalling]

Edit: Skip to the Edit at the bottom, this isn't quite right.


Take a look at the formula for the momentum of a weapon attack: https://dwarffortresswiki.org/index.php/DF2014:Material_science#Attack_Momentum.

Do some algebra by multiplying both the numerator and denominator by the weapon density, then rearranging the terms a bit. You'll get something like

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(Size*Str*Vel/10^6) * w_density/(w_density+[i_size/w_size])
We can relabel [i_size/w_size] as something like 'size_ratio' and then rewrite the momentum formula as a proportionality relationship:

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Weapon momentum proportional to (w_density/[w_density+size_ratio]).
Let's call that 'w_density/(w_density+size_ratio)' the 'Momentum Scaling Factor'.

One last trick: let's look at orders of magnitude here. There are 2 native blunt weapons in the game, the Mace of size 800 and the War Hammer of size 400. Their size_ratios relative to a standard 60 000 size dwarf is 75 or 150. Meanwhile, the w_density of iron is 7850 kg/m^3, or about 100 times as much as the size_ratio of a mace. The Momentum Scaling Factor is now about 100/101, or about 0.99. Even if you multiplied the density of the weapon by a factor of 10, the Momentum Scaling Factor would only grow to 1000/1001, or 0.999, or about 0.9% more. That's barely anything.

In case you don't believe me, here's a table with materials, their densities, and their resulting Momentum Scaling Factors:

Material	Density (kg/m3)	Momentum Scaling Factor
Iron/Steel	7850	0.99054
Bronze	8250	0.99099
Copper	8930	0.99167
Silver	10 490	0.99290
Gold	19 320	0.99613
Platinum	21 400	0.99651

      [/s]     
The largest possible improvement here is going from Iron to Platinum for your mace, which multiplies its momentum per swing by a factor of 0.99651/0.99054 = 1.006. In other words, more than doubling the density of your weapon only added 0.6% to its momentum.

For further confirmation, look closely at the table “Momenta for dwarves of strength 1250 hacking (velocity 1.25) with battle axes (size 800)” at https://dwarffortresswiki.org/index.php/DF2014:Material_science#Attack_Momentum. Notice how little difference there is between the momenta of the iron and silver battleaxes. Literally any other factor will swamp the effects of this difference, it practically speaking has no effect on anything. All it can do is slow you down and tire you out, which is why dwarves armed with slade warhammers actually did worse in testing than dwarves armed with steel warhammers. Density doesn’t do anything beyond that, practically speaking.

TL;DR: Density has no effect on weapons.

(There's one exception to this: Weapon Traps. The momentum of a weapon swung in a weapon trap is always directly proportional to its weight, so it's always proportional to its density. That means that you should build the blunt weapons in your weapon traps out of the densest material possible.

It might even be worth selecting a denser but weaker material for your edged trap weapons as well, to do more damage overall - platinum has almost the same Shear Fracture as bronze, while being significantly denser, so overall a platinum Giant Axe will strike with about 2.15 times as much force as a bronze one.)

(Originally written up at: https://www.reddit.com/r/dwarffortress/comments/o7llyz/density_has_no_effect_on_blunt_weapons/. Posted here due to readers saying it'd be worth doing.)

Edit: Ah, I just realized that the formula I'm using here is off by a factor of 10 somewhere. More specifically, in the transition between step 2 and step 3 of the formulas shown at https://dwarffortresswiki.org/index.php/DF2014:Material_science#Attack_Momentum, a factor of 10 is lost: it should be

Code: [Select]

1 + (10*i_Size)/(w_density*w_size)in the denominator.

In other words, the Momentum Scaling Factor should be

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(w_density/[w_density+{10*size_ratio}])
The table of Momentum Scaling Factors (for a mace wielded by an average size dwarf) redone:

Material	Density (kg/m3)	Momentum Scaling Factor
Iron/Steel	7850	0.8396
Bronze	8250	0.8462
Copper	8930	0.8562
Silver	10 490	0.8749
Gold	19 320	0.9280
Platinum	21 400	0.9345

           
The largest possible improvement here is going from Iron to Platinum, which multiplies its momentum per swing by a factor of 0.9345/0.8396 = 1.131. The change of material added 13.1% to the power of your attacks, or about as much as two more skill levels (+100% at Grandmaster/14 skill levels, so +14% at 2 skill levels). While the effect is small and easily swamped by training and numbers, it's real. So small that there's no real difference between a copper weapon and a silver one (only 2.2% more momentum), but still there all the same.

TL;DR: Density has a small effect on weapons.

Further trick: if you take step 1 of the momentum formula shown at https://dwarffortresswiki.org/index.php/DF2014:Material_science#Attack_Momentum and rewrite it a bit, you get

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(Size*Strength*Velocity)/(10^6+[10*i_size/W])
Separate out that 10^6 and you get

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(Size*Strength*Velocity/10^6)/(1+[{i_size/10^5}/W])
Note that Size is 60 000 for a dwarf and Strength can be expressed as a multiple of the average dwarf's Strength value of 1250. In other words you can rewrite the Size*Strength value to be 60 000 * 1250 * Strength Ratio, where the Strength Ratio is how strong a dwarf is relative to other dwarfs. (A dwarf with a 5000 in strength has a Strength Ratio of 4, for example). Note that this turns into 75 million * Strength Ratio, with the million then being canceled out by the 10^6 in the denominator. In other words, momentum per swing simplifies to

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75*Strength Ratio*Velocity/(1+[{i_size/10^5}/W])
To further simplify things, let's note that the average size of a dwarf is 60 000 and i_size can be expressed as a size relative to that average dwarf: i_size = 60 000 * Relative Size. So i_size/10^5 becomes 60 000/100 000 * Relative Size, a.k.a 0.6*Relative Size. Plug that in and we get:

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75*Strength Ratio*Velocity/(1+[{0.6*Relative Size}/W])
Let's call

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(1+[{0.6*Relative Size}/W] the 'New Momentum Scaling Factor'. It is 1 for a weapon that has infinite weight and 0 for a weapon that has zero weight; in other words, all weapons approach but never reach a New Momentum Scaling Factor of 1 as you increase their weight. In other words, for an average dwarf, the momentum per attack is just:

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75*New Momentum Scaling Factor = 75*(1/[1+0.6/W])
Here's a table to illustrate the concept:

Weapon Weight (kg)	Base Momentum	New Momentum Scaling Factor	Final Momentum
0.6	75	1/2	37.5
6	75	1/1.1	68.2
60	75	1/1.01	74.3
Infinity	75	1/1	75

So when your dwarves make an attack, their momentum is just

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75*Strength Ratio*Velocity*New Momentum Scaling Factor
With this formula, it's very simple to calculate the momentum of an attack. Someone should probably add this to the DF Wiki, and/or fix the missing factor of 10 in the momentum formula it shows.

[Ulfarr]

Weapon's material density isn't restricted to just momentum generation but also affects how said momentum is transfered when the game checks whether a blow is deflected by armor etc. (for reference)

My understanding of all this info is that:

1) the denser metals also happen to be bad for edged weapons so you are better off making blunt ones with them (and save any iron/steel for armor and edged weapons)

2) outside of fringe cases (ie adamantine warhammer) user's strength is the major factor in the effectiveness of blunt weapons

[WindComeCalling]

Weapon's material density isn't restricted to just momentum generation but also affects how said momentum is transfered when the game checks whether a blow is deflected by armor etc. (for reference)

Oh, that armor deflection check only cares about the density of the armor, not the density of the weapon. The weapon can be made of cork for all it cares about at that specific step, the important thing is the weapon's Impact Yield versus Armor's density (when it comes to material choices on both sides). Candy bashing weapons have no problems at this step because their Impact Yield is good and their density is irrelevant.

[Alastar]

Just going by the available info, nothing matters.

Momentum difference should be minor for mainstream weapon materials as OP stated. The impact yield vs armor density check is non-factor against most armor materials. The (2IF-IY) check should only matter when weapons with a large contact area hits a small target of a very specific size; mostly relevant for edged hits that fail to penetrate, where this should be dominated by edged performance in most cases.

Testing doesn't really show any clear superiority of the mainstream materials, but the performance of adamantine with blunt weapons and bolts implies there are other considerations.

[Ulfarr]

Oh, that armor deflection check only cares about the density of the armor, not the density of the weapon. The weapon can be made of cork for all it cares about at that specific step, the important thing is the weapon's Impact Yield versus Armor's density (when it comes to material choices on both sides). Candy bashing weapons have no problems at this step because their Impact Yield is good and their density is irrelevant.

Yeah but it has an affect on layer penetration which is the next step in the calculations and it is affected by a weapon's density. Now for vanilla DF that is probably neglible in most cases as well, so I'm just saying it does have some effect.

Should we factor in wooden weapons/shileds? I mean they are technically in vanilla DF but I doubt any player uses them with how easy it is to get access to metals.

[WindComeCalling]

Yeah but it has an affect on layer penetration which is the next step in the calculations and it is affected by a weapon's density...

That's the thing though: weapon density has no effect beyond determining the momentum of each swing. If you Control + F for 'density' through https://dwarffortresswiki.org/index.php/DF2014:Material_science, the only references to weapon density in the formulas are for determining momentum. For everything past that, like determining deflection, only armor density matters - 2 identical Impact Yield swings from 2 different density warhammers will look the exact same at the deflection step. Weapon density only affects the momentum of swings, and unless you're using adamantine it barely has any effect.

[ldog]

Being as I recently found a way to churn out non-artifact platinum war hammers, maces and crossbows so far I find them underwhelming, but we've seen limited use so far.
I've got a low strength low skill hammerdwarf and I've watched her beat on unconscious giant olms and the like with a mastercrafter platinum war hammer until she is unconscious as well. The stronger (I forget offhand, but decent starting) and more skilled (5) commander does much better of course. The macers seem better, but being that is the heaviest weapon I only assign the strongest dorfs .

At higher skill and strength they might be better, but I think all the extra weight kills their usefulness before then. I'm not sure the extra weight on the crossbow is worth it either (this is considering the xbow as a melee weapon, which it frequently is used as). So for fortress mode it probably isn't worth beelining to the "superior" materials.

[Stimraug]

Sorry for the necro, I read this but am not sure whether it makes the old "silver warhammers are better than steel ones" -wisdom false? Could someone clarify, thank you.

[Flying Dice]

Sorry for the necro, I read this but am not sure whether it makes the old "silver warhammers are better than steel ones" -wisdom false? Could someone clarify, thank you.

Even if you assume that OP was entirely correct, and assume that no other factors are at play which were not accounted for, silver is still better for blunt weapons than iron/bronze/steel both in terms of performance and in terms of providing a way to arm dwarfs effectively while conserving steel. It's just not a "OMG it's twice as lethal" difference.

[Stimraug]

Still not fixed (the factor of 10 error).. I looked for the error at 3:30 am for several moments x_x, someone fix please thank you

Also, thank you for the reply

EDIT: the part where "let's call (1+[{0.6*Relative Size}/W] the 'New Momentum Scaling Factor'. It is 1 for a weapon that has infinite weight and 0 for a weapon that has zero weight"
seems to be missing a "1 / " before the entire equation.

EDIT2: Just before you reach your conclusion, you're also missing the strength and vel modifiers from one equation

EDIT3: using your formula and the one referenced, i.e these:
M = 75 * StrRatio * Vel * ( 1 / ( 1 + ( 0.6 * SizeRatio ) / ( w_size * w_density ) ) )
and
M = Skill * Size * Str * Vel / ( 10^6 * ( 1 + i_Size / ( w_size * w_density ) ) )

I get 149.99 and 149.34 respectively for a maul of 1300 size and 10490 silver density. I'm too tired to find the error source now, could someone help locate its origin, thank you. (rounding error?)

[Putnam]

Silver is better than steel for warhammers. The small area means the material properties matter very little. I haven't found the formulas just yet, but there does seem to be something that causes more damage in bending etc. for higher density, which likely has a large effect.

[Stimraug]

Thank you Putnam. I'm balancing a small mod's weapons I'm making by using the formula discussed by OP, do you think it is close enough to be useful? Thanks again.

[Alastar]

Density just affects momentum, and this scales very degressively. Small advantage for silver (or platinum if you make that happen), so small it's hard to verify in-game.

There's a pass/fail check that involves the weapon's impact yield, armour density, and contact area. Hammers and maces will pass this against any common armour material even when they're made of copper (lowest impact yield of the regular weapon materials). Impact Yield might matter occasionally for flails or nonpenetrating hits of edged weapons, when a weapon with a large contact area hits a small body part.

[Stimraug]

Another thing that frustrates me, please someone enlighten me, is how the edged penetration check works on the page:

M >= (aSY/wSY + (A+1)*aSF/wSF) * (10 + 2*a_quality) / (Sha * w_quality)

this equation.. basically says, if we assume same material for armor and weapon with standard quality, that momentum must be higher than 12 * contact area to penetrate? Where is the sense in that??

Standard quality Steel short sword vs. standard copper armor: ( 70 000 / 430 000 + ( A + 1 ) * 220 000 / 720 000 ) * ( 10 + 2 * 1 ) / ( 1 * 1 )

If we assume about 90 momentum for the steel short sword from an average dwarf, then for steel to penetrate copper armor, the copper armor's A, the contact area should be at most something like 25!
Something's either terribly wrong with my thinking or the formula for edge penetration. Please help.

[Putnam]

It can still penetrate after, it'll just penetrate as blunt, which is likely to be successful.