To start with, the metallurgy was wrong and they never used an accurate reconstruction of a subarmalis. If you can't reproduce the conditions of the original situation then the results will have limited value. If the test doesn't conform to known facts then the test needs to be revised, you don't rewrite the known facts.The test shows that authentic lorica segmentata can't resist projectiles of 113 joules <---- That contradicts the "fact that the armour was fit for a purpose", how? Did the Romans record that Lorica Segmentata was designed to resist projectiles of 113 joules? And why the sudden dismissive attitude to field testing? You were demanding testing for Chinese crossbows replicas, yet they were built for a specific purpose too, and have been used for near 2000 years, which is way longer than 300 years.
The metallurgy of the tested armor was steel, whereas Roman iron armor was equivalent to mild steel (David Sim) in quality once we take into account their practice of differential hardening. How is the metallurgy wrong? If anything the tested armor could have had better metallurgy, as Alan Wilkins showed that harder plates resists penetration better. He also showed how plate hardness impacts its protectiveness and how armor thickness impacts its protectiveness. In short, making the armor twice as thick as the typical authentic ones would more than make up for a moderate disadvantage in metallurgy, and chances are the authentic ones didn't even have an advantage in metallurgy over the armor which was tested. More like the other way around, if anything. Please quote the sources to back up your statement. We don't know if the subarmalis was meant to provide additional protection, but either way the coin falls, you have to take into account that those wearing mail would have a subarmalis too.To start with the metallurgy was wrong and they never used an accurate reconstruction of a subarmalis. If you can't reproduce the conditions of the original situation then the results will have limited value.
You were arguing about comparative degrees of weapon resistance. And now you say that it's irrelevant. I'm not talking about the rest of your list, I'm talking about armor weight in relation to weapon resistance.I already gave you a long list of how mail was better than segmentata. Comparative degrees of weapon resistance was irrelevant. IMO the reason they stopped using segmentata can be found in the Diocletian reforms.
The energy of 113 joules was calculated from mass and velocity. Unless if the mass was incredibly abnormal, I assure you that the momentum wouldn't be that great either.I'm slightly concerned that people are treating the energy of a missile as the sole characteristic of how good it is at penetrating armor. I can think of a few others that are as/perhaps more relevant: impulse, force and pressure exerted. Something which is sharper has the same energy as something smooth, but obviously is going to penetrate a lot better. Two missiles can have exactly the same energy, but completely different momentum and exert completely different forces (it all depends on the mass). So saying "this armor can resist 110J, but breaks at 120J" is really bad physics. I would fail you in a high school physics exam if you wrote something like that. I don't mean to say that this is exactly what people in this thread are saying, but it is getting close to it.
Lastly, armor breaking or being penetrated might be *good* for the user. To break armor takes energy and momentum, absorbing it, therefore meaning that there is less of it to injure the wearer. This is exactly the reasoning behind crumple zones in cars. If the armour doesn't break however, then all that momentum and energy still has to go somewhere, generally the user. The best armour can do in that case is to spread it out over as large an area as possible so that the pressure is not high enough anywhere to injure the wearer.
tl:dr - There's more to armor than the energy at which it breaks (which isn't even something that can be defined)
The energy of 113 joules was calculated from mass and velocity. Unless if the mass was incredibly abnormal, I assure you that the momentum wouldn't be that great either.
You say you can think up of a few other variables that are perhaps "more relevant: impulse, force and pressure exerted".
Well, force = mass*acceleration. In this case it's irrelevant because for every ballista/bow/crossbow, the second the projectile leaves the string, it begins to decelerate, NOT accelerate. So it's irrelevant.
Pressure exerted is just force per unit area, so again irrelevant given the statement above.
Sometimes people instead (including me) define force as energy, but if we use that definition the 113 joules I mentioned IS THE FORCE.
In this case the pressure would still be irrelevant unless we are hitting the armor with some type of irregularly shaped blunted arrowhead, but this is not the case. The arrowhead was an "unhardened bodkin point". And looking at the picture provided, it's not a thin needle bodkin either.
Impetus is the force that causes a body to move. In this scenario it is far less important than joules and momentum, because these latter two show the property of the arrow when it already left the string. And when the arrow hit the armor, it already left the string, having already flown 50 meters away from where it was shot.
Currently most people either use force (joules) or momentum to determine the hitting power of a projectile. Based on your statement I think you need to do more study on the matter before you start tossing out variables.
Now I'm actually being generous by saying the replica armor was shot with 113 joules. In actuality the cherioballista could shoot a 102 gram bolt 47 m/s, resulting in 113 joules of energy or a momentum of 4.8. However, the bolt that was used to hit the replica segmentata was 70 grams, so the velocity/momentum would most likely be smaller than 113 joules and 4.8 respectively.
In comparison a 150 lb longbow could shoot at similar or greater joules, and if using an 87 gram arrow it would achieve similar momentum.
Also we are not talking about being hit with a hammer. We are talking about an arrow hitting you. If you would rather your armor "break" then that's on you, I wouldn't advise wearing armor which could get ruptured in that type of situation. Better a bruise than a getting your stomach organ punctured.
Sometimes people use them interchangeably, I already gave you the official definition as well.This is absolutely embarrassing, force and energy are simply not the same thing.
This was what I said: Sometimes people instead (including me) define force as energy, but if we use that definition the 113 joules I mentioned IS THE FORCE.You can't use them interchangeably; it's not that it's inaccurate to do so, it's just plain wrong.
If you are using force = mass * acceleration, then please let me know how an arrow can accelerate AFTER it left the string. Did the arrow have a rocket attached to it? Seriously, using the definition of force = mass * acceleration, then force is hardly the optimal way to calculate penetration power of an arrow.Then you claim that the force or pressure of a projectile hitting you is 0. That is absurd and risible, how would you ever feel it if there was no force? I'm sorry to use such strong words here, but this is the physics equivalent of someone saying the Pyramids where not build by the Egyptians, or by ancient aliens, but my Uncle Bob when he was on holiday there in 1987. And I don't have an uncle Bob. I'm not expecting everyone here to have a great understanding of mechanics, but I feel obliged to call out suffers of Dunning-Kruger when I see it.
I already gave you the energy and momentum of the cherioballista shooting at 113 joules with a momentum of 4.8. That's using a 102 gram projectile, the actual tested projectile uses a 70 gram bolt which would have decreased joules and momentum <---- These numbers were calculated using the same equations you just provided. Your "examples" are not so relevant in comparison.Okay, basic physics lesson.
Energy: E = 1/2 m v^2
Momentum: P = m v
Say I have an arrow with 100 J of energy and a mass of 100g. That means it has a momentum of 4.4 kgm/s. Now consider a javelin also with 100 J but with a mass of 2kb. That has a momentum of 20 kgm/s. That's five times as much! Also you seem to be using the initial k.e. in the discussion here, which is bizarre, the impact energy is clearly what is relevant to the armor!
Deceleration in itself won't hurt you, it just means the projectile is slowing down. What matters is not whether the arrow is accelerating or decelerating, what matters is the velocity of the arrow when it hits you.As for acceleration:
I wasn't talking about the acceleration of the projectile in flight, that doesn't matter apart from how it impacts the velocity when it hits you. But then the arrow/javelin decelerates very quickly when it hits something. It's this acceleration that creates the force that hurts you. The less time (T) or distance (D) it decelerates in, the higher the force. Specifically, F = P / T or F = E / D. I'm assuming everything is linear because this is not the place to teach calculus. I'm also assuming that things are hitting the armor square on, because otherwise there is only some deflection. Either way, neither P nor E are 0, and neither T nor D are infinite, therefore there most definitely is a force. Obviously, otherwise the missile would go right through you as if you weren't there.
The arrowhead isn't a needle bodkin. In fact I already said it seemed pretty typical for an arrowhead, so it's irrelevant.As for pressure, that is indeed force over area. So the smaller the area, the greater the pressure. A sharper weapon has a smaller contact area, and therefore increases the pressure it inflicts.
The tested armor was hit by an unhardened bodkin, a fairly normal arrowhead. It was not hit by a squash ball, so your example is irrelevant.Now what is it that causes armour to break? You cannot say that if it's hit by something over a certain energy or momentum that it will cause the armour to break. A squash ball hit by a good player can reach 125J. I put it to you that that is unlikely to break armor (otherwise how do the rackets survive?) A soccer ball passed will easily have a momentum of 5 kgm/s. That is more momentum than your arrow, but I think we both know that it won't break plate.
The bolt hit a dummy legionary with at least some padding. Ergo there was give.I suspect that pressure is the most important thing to break armor, but even that is probably an over simplification (my guess would be that the derivative of pressure in the radial direction is what causes the stress that will break plate, but that's just a hunch). In any case, pressure depends not just on the momentum/energy of the projectile, but also on the size of its point (which itself changes during the impact, making things harder still) and how quickly it comes to a stop. If the armour is mounted rigidly, then the halting distance is the thickness of the metal. If the armor, however, is mounted on something with give (like padding behind it) than that distance is much much larger. It goes from mm to cm. Wearing padding behind armor isn't there to save you in case the armor punctures, it's there to give the armor distance to move so it doesn't get punctured. Now when the armor breaks it also absorbs energy/momentum, so there is less force exerted on/energy transferred to the wearer still.
We are not talking about swords, or a "squash ball", or being in a car accident, or whatever other analogies you can think of. We are talking about being hit by an arrow, in this case an unhardened bodkin. The fact is, a 70 gram unhardened bodkin arrow travelling with less than 113 joules of energy and momentum of less than 4.8 managed to pierce the first 1.25mm layer of lorica segmentata and severly dented the second layer. This is thicker than most authentic lorica segmentata. Putting in analogies to "squash balls" and "swords" are irrelevant distractions, because we know the type of projectile which hit the armor and it's definitly not a squash ball.And don't even get started on what happens if it isn't a free moving projectile but say, a sword connected to it's user. Whats the relevant mass/speed/distance/time to use there? It's a fantastically complicated dynamical problem, there won't be a simple solution of the type "if quantity X is over value Y, then Z will break". That's not how the physics works at all.
When I say that the armor will be penetrated by an arrow of 120 J, I obviously mean arrows with typical arrowheads like that of the unhardened bodkin used in the test, not "squash balls", "swords", or "car accidents". The tested armor did have padding.Now we're talking about bolts vs arrows vs javelins, so there won't be as much difference between them as between arrows and footballs. But still enough so that it is wrong to say "This armor will break when hit by a projectile over 120 J". Secondly, what's behind the armor - how its mounted - for the test will have huge implications on whether it breaks or not. Imagine how fragile chainmail would be if it was pulled taught on a wooden board when hit by an arrow? I suspect that adding padding will help plate far more than chainmail, because plate is by default in its 'tense' state and needs something to give it leeway, while chainmail in it' normal free hanging form has some leeway already.