Terminal ballistics and armour-shattering arrows

Would anyone happen to know the answers to the following questions, with regards to collisions between projectiles (ex: arrows) and armour (ex: plate cuirasses)? I have, at this point, been able to determine that heavier, slower projectiles do less damage, but have an "armour piercing" effect; while lighter, faster projectiles do more damage, but begin to do less damage against armour (what GURPS(tm) would give an armour multiplier). However, actual math is...scarce; and, in essence, I have discovered no more information than I could have found out by watching 2-3 target-shooting videos on Youtube(tm). And yet, I have spent quite a bit more time searching than 1.5 hours. In fact, the best math I have found is the derivation of the GURPS(tm) formulas for gun damage...Which is formulated for Imperial units, and is thus impenetrable (to me).

1) How does surface area affect force of impact?
2) Should I use Newtons, *Joules, or some other unit of measurement?
3) Is there a **good terminal ballistics website that goes over the math?
4) Is there any ***questions that either I should have asked, and/or would have been better asked than the one(s) that I did?

* Attempting to back-calculate from Joules results in the aforementioned armour-shattering arrows.
** Most of what I have found is either thesis on the ethics of hunting, or thesis on the results of hunting. Neither is all that relevant to determining the depth and quality of steel plate (or, indeed, d20 System(tm) Mithral(tm)) that a longbow arrow may penetrate). In addition, searching for terminal ballistics books on Amazon reveals prices in excess of one hundred and fifty dollars, which is more than I am prepared to spend on what is, ultimately, an intersection of hobby and curiosity.
*** Inquiries as to my sanity or the point of all this can be answered in the same spirit as a mountain-climber who has found an interesting-looking peak.

With humorous frustration, Random Bystander.

You're getting into some seriously heavy math that, sorry to say, is beyond anything that I have done in decades.I can, however, tell you that arrows aren't going to penetrate tempered plate armour. It doesn't matter if it's a hundred and fifty pound English longbow at 30 feet; it's not going through. Arrows killed people in heavy plate by finding the places where the armour wasn't. The joints, under the arms, through visor slits.... They could punch through chain by shearing rivets or snapping rings but tempered steel plate, a few millimetres thick, isn't giving way. "Proof testing" of such armour, after the advent of firearms, was performed by shooting it with lead ball from a musket.

[video=youtube;Ej3qjUzUzQg]https://www.youtube.com/watch?v=Ej3qjUzUzQg&spfreload=10[/video]

Ryujin said:

You're getting into some seriously heavy math that, sorry to say, is beyond anything that I have done in decades.I can, however, tell you that arrows aren't going to penetrate tempered plate armour. It doesn't matter if it's a hundred and fifty pound English longbow at 30 feet; it's not going through. Arrows killed people in heavy plate by finding the places where the armour wasn't. The joints, under the arms, through visor slits.... They could punch through chain by shearing rivets or snapping rings but tempered steel plate, a few millimetres thick, isn't giving way. "Proof testing" of such armour, after the advent of firearms, was performed by shooting it with lead ball from a musket.

[video=youtube;Ej3qjUzUzQg]https://www.youtube.com/watch?v=Ej3qjUzUzQg&spfreload=10[/video]

Click to expand...

Well...I did actually learn more than "the heavy projectile penetrates the armour"; I was speaking out of some frustration. I have learned quite a bit of heuristic information. Thank you for the video, though.

"Guns, Guns, Guns" (or 3G, for short), is a good reference:

http://paizo.com/products/btpy7nyo?3G3-Guns-Guns-Guns

I'll have to look tonight to see if it covers armor penetration (but I think it does).

A problem of the video which is linked, above, is that the arrow shaft broke, so much if not most of the energy of the arrow was lost. I would be interested to see a similar test with a metal shaft.

The material quality of the arrowhead matters, too. A poor quality arrowhead will shatter and be useless for penetrating armor.

Thx!
TomB

tomBitonti said:

"Guns, Guns, Guns" (or 3G, for short), is a good reference:

http://paizo.com/products/btpy7nyo?3G3-Guns-Guns-Guns

I'll have to look tonight to see if it covers armor penetration (but I think it does).

A problem of the video which is linked, above, is that the arrow shaft broke, so much if not most of the energy of the arrow was lost. I would be interested to see a similar test with a metal shaft.

The material quality of the arrowhead matters, too. A poor quality arrowhead will shatter and be useless for penetrating armor.

Thx!
TomB

Click to expand...

That does sound useful. If it covers armour penetration formula(s), it would also be exactly what I need.

I wasn't aware there were metal arrow shafts during the medieval ages - I cannot recall ever hearing about this. I am aware of carbon-fibre shafts, and like ideas, in modern times. Interesting! I imagine the arrow shaft would be hollow?

And certain arrow-heads were more effective against armour, from what I have been told.

Remember, games are supposed to be fun. At some point all your research & math will cancel that out.

ccs said:

Remember, games are supposed to be fun. At some point all your research & math will cancel that out.

Click to expand...

Some of us find math fun. There is some good history here to be discovered, too.

I'm pretty sure medieval arrows didn't have metal shafts, but cross bolts did (or may have). I'm thinking metal shafts would be too heavy. And not really strong enough using medieval technology. From the quoted text, below, modern shafts can use an aluminum core wrapped with carbon fiber, which sounds nice from the point of view of getting both good stiffness while keeping weight reasonable.

The point was that in the demonstration, the arrow shaft was shown having been split, which means the penetration was limited by the material qualities of the arrow.

From wikipedia:

https://en.wikipedia.org/wiki/Arrow said:

The shaft is the primary structural element of the arrow, to which the other components are attached. Traditional arrow shafts are made from lightweight wood, bamboo or reeds, while modern shafts may be made from aluminum, carbon fibre reinforced plastic, or a combination of materials. Such shafts are typically made from an aluminum core wrapped with a carbon fiber outer.

Click to expand...

From the 3G book, penetration has to do with energy focused on a small area. The example given is that you can't push your finger through wood, but you can easily push through a thumbtack. Hence bodkin type arrow heads for penetration, and broadhead for higher damage.

The wikipiedia article on Bodkin arrow points has a vague-ish discussion of armor penetration:

[Quote="https://en.wikipedia.org/wiki/Bodkin_point]
Armour penetration

It has been suggested that the bodkin came into its own as a means of penetrating armour, but research by the Royal Armouries[1] has found no hardened bodkin points, though only two bodkin points were actually tested, not a statistically relevant number. Bodkins did, however, have greater ability to pierce mail armour than broadheads, and historical accounts do speak of bodkin arrows shot from close range piercing plate armour[citation needed]. Broadheads were made from steel, sometimes with hardened edges, but were more often used against lightly armoured men or horses than against an armoured adversary.

In a modern test, a direct hit from a steel bodkin point penetrated mail armour, although at point blank range.[2] However, the test was conducted without a padded jack or gambeson, which was layered cloth armour worn over heavier armour for protection against projectiles, as it was known to stop even heavy arrows.[3]

Armour of the medieval era was not completely proof against arrows until the specialised armour of the Italian city-state mercenary companies.[4] Archery was thought not to be effective against plate armour in the Battle of Neville's Cross (1346), the siege of Bergerac (1345), and the Battle of Poitiers (1356); such armour became available to European knights of fairly modest means by the late 14th century, though never to all soldiers in any army.[5]

Some recent tests have demonstrated that needle bodkins could penetrate all but heavy steel plate armour; one test used padded "jack" armour, coat of plates, iron and steel mail and steel plate. A needle bodkin penetrated every type, but may not have been able to inflict a lethal injury behind plate. As with all other tests, accuracy of these tests is called into question as the arrowheads were all high carbon steel and hardened, and the historical accuracy of the armour tested is unknown. In one test of historical arrows from the London Museum, a "type 16" barbed arrowhead was indeed found to be steel;[6] the composition of the other types of arrowheads (including bodkins) was not tested."
[/quote]

From the 3G book, an average person can put about 150KJ into an arrow, while a legendary athlete could conceivably get that up to 1000KJ. Those energy values correspond to .22's to .45's.

Thx!
TomB

tomBitonti said:

"Guns, Guns, Guns" (or 3G, for short), is a good reference:

http://paizo.com/products/btpy7nyo?3G3-Guns-Guns-Guns

I'll have to look tonight to see if it covers armor penetration (but I think it does).

A problem of the video which is linked, above, is that the arrow shaft broke, so much if not most of the energy of the arrow was lost. I would be interested to see a similar test with a metal shaft.

The material quality of the arrowhead matters, too. A poor quality arrowhead will shatter and be useless for penetrating armor.

Thx!
TomB

Click to expand...

Remember that in m y linked video the shot is taken at effectively point blank. That's the most energy you're going to get into an arrow because it loses energy to drag the moment that it's launched. From what I recall the arrow in the video is a true representation of a Medieval war arrow; heavy shaft which is thicker in the middle than at the ends, so that it can withstand the power of the bow. Bodkin point. Even crossbow bolts on heavy crossbows would have been thick wood rather than metal.