Realistic DR for rigid armor

[Gustavus Adolphus]

First of all, sorry for my bad English, I speak a quite horrible EN language.

I've read the Alan Williams' book "The Knight And The Blast Furnace: A History of the Metallurgy of Armour in the Middle Ages & the Early Modern Period". The resistance of homogeneous rigid armor increases or decreases exponentially if thickness increases or decreases, following a 1.6 exponentiation. Alan Williams divided the iron-steel quality in four classes, comparing their quality values with industrial mild steel resistance (W = 1)

I: munition iron, average W = 0.5 (bad quality: TL2 lorica segmentata, cuirassier's armor)
II: low-carbon content steel, average W = 0.75 (average quality: TL3 typical medieval armor)
III: medium-carbon content steel, average W = 1.1 (good quality: 1450's TL4 milanese knight armor)
IV: hardened medium-carbon content steel, average W = 1.5 (excellent quality: 1550's TL4 maximilian knight armor)

In my personal Home Rules current set (only in Italian language for now, I'm sorry!) I've considered the typical TL3 rounded-surface knight armor (W=0.75, 2 mm thick) as DR 6 (w.o. padding). Fluted armors of same thickness have ca. 16.6% more DR. Flat-surface armors of same thickness have ca. 16.6% less DR

Example:
1) TL3 rounded-surface knight armor (W=0.75, 2 mm thick): DR 6
2) TL2 flat-surface armor (W=0.75, 2 mm thick): DR 5
3) TL4 fluted knight armor (W=0.75, 2 mm thick): DR 7

Here's the formula to calculate realistic armor DR (in relation of typical DR 6 TL3 knight armor, W=0.75, 2mm)

DR = 6 x (thickness in mm/2 mm)^1.6 x (W/0.75) x form-factor (1 for rounded armor, 0.833 for flat armor, 1.166 for fluted armor)

Example 1: DR of a 1560's TL4 heavy gonne-proofed breastplate (W = 1.1, 3 mm thick, fluted)

DR = 6 x (3 mm/2 mm)^1.6 x (1.1/0.75) x 1.166 = DR 19 (19.64 rounded down). The DR is really high, but an average musket do 4d+2 pi++ of damage (medium damage 16, maximum damage 26) and heavy muskets even do more damage.

Example 2: DR of a TL2 lorica segmentata (W = 0.5, 2 mm thick, flat)

DR = 6 x (2 mm/2 mm)^1.6 x (0.5/0.75) x 0.833 = DR 3 (3,332 rounded down).

In my personal HR, CF multiplier is proportional to thickness and exponential for quality (thick cheap-iron armor are much less expensive and much more bulky than thin high quality steel armor with same DR)

CF (thickness): x(thickness/2mm)
CF (steel quality): x(W/0.75)^2

[GodBeastX]

I didn't understand all the math in the post. I can say I ended using the blunt force rules for plate armor mention in Lowtech and that gives much better results.

[Polydamas]

Originally Posted by Gustavus Adolphus

First of all, sorry for my bad English, I speak a quite horrible EN language.

I've read the Alan Williams' book "The Knight And The Blast Furnace: A History of the Metallurgy of Armour in the Middle Ages & the Early Modern Period". The resistance of homogeneous rigid armor increases or decreases exponentially if thickness increases or decreases, following a 1.6 exponentiation. Alan Williams divided the iron-steel quality in four classes, comparing their quality values with industrial mild steel resistance (W = 1)

I: munition iron, average W = 0.5 (bad quality: TL2 lorica segmentata, cuirassier's armor)
II: low-carbon content steel, average W = 0.75 (average quality: TL3 typical medieval armor)
III: medium-carbon content steel, average W = 1.1 (good quality: 1450's TL4 milanese knight armor)
IV: hardened medium-carbon content steel, average W = 1.5 (excellent quality: 1550's TL4 maximilian knight armor)

In my personal Home Rules current set (only in Italian language for now, I'm sorry!) I've considered the typical TL3 rounded-surface knight armor (W=0.75, 2 mm thick) as DR 6 (w.o. padding). Fluted armors of same thickness have ca. 16.6% more DR. Flat-surface armors of same thickness have ca. 16.6% less DR

Ciao, Gustavo! You should know that damage is proportional to the square root of energy in GURPS, not to energy. Therefore twice the damage or DR represents four times the energy or resistance to energy, and the DR of solid plates is proportional to thickness.

[Gustavus Adolphus]

Well, I like math :D

Jokes apart, I find current low-tech DR armor rules unrealistics at all, especially in TL4 settings. With current GURPS Low-Tech rules, Reinassance plate armors sucks against firearms. Historically, plate armors and firearms shared four centuries toghether on battlegrounds.

@Polydamas: but this is also incoherent with stopping power and wounds. If one ST 10 ordinary man could do 60 to 130 Joule of force with a 1kg one-handed weapon (typical sw 1d+1; 2-7 damage, coherent because penetrating flesh requires a little extra amount of energy), one ST 12 man with a two-handed weapon could reach ca. 200 Joule of force (sw 1d+5, 6-11 damage). This is quite linear, not quadratic, I think.

PS: corrected 'cause my very bad English!

[Varyon]

Originally Posted by Gustavus Adolphus

Jokes apart, I find current low-tech DR armor rules unrealistics at all, especially in TL4 settings. With current GURPS Low-Tech rules, Reinassance plate armors sucks against firearms. Historically, plate armors and firearms shared four centuries toghether on battlegrounds.

TL4 firearms have extremely low firing rates and aren't very accurate, meaning you often only get off a shot or two before melee battle occurs - at which point plate armor is a life saver. I should also note that, even with LT's armor values, you can resist most firearms - a thick breastplate (DR 12) will protect from a caliver, and mere heavy plate (DR 9) is nearly proof against pistols. Muskets are pretty much out of the question, but those things are monsters - they require ST 12 (nearly half again the strength of a normal man) and a musket rest to properly wield them, and even then that anti-caliver breastplate from above can take them from "He's dead, Jim" (average 16 damage, for 32 injury) to potentially-survivable (average 4 damage, for 8 injury).

Originally Posted by Gustavus Adolphus

@Polydamas: but this is also incoherent with stopping power and wound. If one ST 10 ordinary man could do 60 to 130 Joule of force with a 1kg one-handed weapon (typical sw 1d+1; 2-7 damage, coherent because penetrating flesh requires a little extra amount of energy), one ST 12 man with a two-handed weapon could reach ca. 200 Joule of force (sw 1d+5, 6-11 damage). This is quite linear, not quadratic, I think.

The Basic Set ST-based damage progressions are rather unrealistic - note an ST 12 man with a sling deals damage comparable to most TL4 pistols. ST 15 should really do 1.5x as much damage as ST 10, not the slightly-better-than-double we see now.

[Gustavus Adolphus]

@Varyon: I consider "X-proofed" one armor that could fully resist to medium X-weapon damage and could save the combatant to Mortal and KO-limited damage (Equal or superior to combatant's ST). Maximum damage is a well-placed shot who fully hit the chest with the best angle of inclination.

Example: realistically, hussites hand-guns (gonnes) could reach little less than 1000 Joule of power. 500 J for an old firearm have enough stopping power to kill a man if the slug hits the torso.
1400's gothic armor is 2 mm thick, rounded, and it's made of quality II steel (W = 0.75). One round slug requires 700 J of force to penetrate the armor (penetration = cavity large than the projectile's diameter). 1400's milanese armor is 2 mm thick, rounded and it's made of quality III steel (W = 1.1). One round slug requires 1000 J of force to completely penetrate the armor.

WITH GURPS LOW-TECH RULES:
Gonne: 2d pi++ (medium 7 BD, maximum 12 BD)
vs. Gothic armor (iron medium plate armor with DR 6 plus 1 DR padding): 0-5 BD = 0-10 total damage (15 if the shot hits the vitals)
vs. Milanese armor (steel medium plate armor with DR 7 plus 1 DR padding): 0-4 BD = 0-8 total damage (12 if the shot hits the vitals)

WITH MY HOME RULES:
Hussite Gonne: 2d pi++ (medium 7 BD, maximum 12 BD)
vs. Gothic armor (plate armor, 2 mm, W = 0.75; DR 6 plus 1 DR padding): 0-5 BD = 0-10 total damage (15 if the shot hits the vitals)
vs. Milanese armor (plate armor, 2 mm, W = 1.1; DR 9 plus 1 DR padding): 0-2 BD = 0-4 total damage (6 if the shot hits the vitals).

With standard low-tech rules, even a milanese-armored knight is still vulnerable to hussite's gonne fire; with my HR, the slug begins the fracture of the Milanese armor, but didn't penetrate completely the armor and the risk to suffer of a major wound for a typical ST 11 knight is minimum (<0,5% if the slug hits the torso, a very lucky shot with a very inaccurate weapon).

Regard the quadratic DR, why two layers of DR 1 material have total DR of 2 and one layer of the same material has DR 2? Combining two 1-mm layers of the same metal is less effective than one single 2 mm layer, because one 2 mm layer is three times more resistant than a 1 mm layer.

[Anthony]

Originally Posted by Gustavus Adolphus

1400's milanese armor is 2 mm thick, rounded and have quality III (W = 1.1). One round slug requires 1000 J of force to completely penetrate the armor.

If you think it takes 1,000J to penetrate 2mm of TL 4, you've got a problem with your equations.

[Gustavus Adolphus]

@Anthony: Old rounded slugs require by far more power to penetrate the same thickness compared to modern conical slugs.

[Varyon]

Originally Posted by Gustavus Adolphus

Maximum damage is a well-placed shot who fully hit the chest with the best angle of inclination.

Maximum damage is a shot that hit a weak point in the armor, and for most TL 4 firearms is about as likely as a critical hit. When determining what armor is considered "proof" against, you should really use average damage, as this is what real-world tests typically check for. Thus, DR 7 is "proof" against almost any TL 4 pistol (the petronel being the only exception, but it's more like a carbine than a pistol), while DR 12 is "proof" against anything less than a musket. This is the way GURPS works, and firearm damage and DR are actually calculated based on this - a firearm that is known to penetrate half an inch of RHA steel (DR = 70/inch) would do 10d of penetration (which may be instead written as 5d(2) or similar, depending on bullet composition). Your system appears to rescale things such that an inch of RHA steel would be somewhere between 300 and 400 DR, which would necessitate changing firearm damage to be appropriate (an M82A1 would need to be around 60d instead of 12d for its armor piercing ammunition to have comparable penetration to now).

[DouglasCole]

Originally Posted by Gustavus Adolphus

@Varyon: I consider "X-proofed" one armor that could fully resist to medium X-weapon damage and could save the combatant to Mortal and KO-limited damage (Equal or superior to combatant's ST). Maximum damage is a well-placed shot who fully hit the chest with the best angle of inclination.

I'll tell you flat out that "proof against maximum damage" is the wrong standard to use and still be within GURPS. GURPS defines "proof" as "will resist average damage" and has for a long time.

You can do things however you want, of course, but to ensure clarity I suggest that you make it very clear that you're defining DR 6 as proof against 1d damage, rather than what GURPS assumed in 3e and 4e: DR 3.5 is proof vs 1d.

If you have an issue with the variability of rolled damage, look up Armor as Dice.