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[thompson]

I have to say it's quite unusual for me to back GC up, but I'm part of an iron age reenactment group, specifically covering the 1st century Roman invasion of Britain, and we do have access to a ballista, albeit a small one. I'm not so sure about later cultures, but afaik ancient Roman ballistae were made largely of wood, iron was only really used as structural reinforcement, not as a material for the limbs. I have seen crossbows with metallic limbs, not entirely sure exactly what period they were from, but it was definitely post western Rome. You were right about the sinew string though, it was more like rope than string but still.

The ideas on the evolution of warfare on the other hand are definitely off the mark, yew and crossbows seem to have been confused with gunpowder and firearms. We have checked, you need more than a yew longbow or an early medieval crossbow to get through lorica segmentata. We did manage to get a pilum through it but I can't guarantee that'd work on a fresh new set, our test lorica was old and rusty. Still enough to repel arrows and bolts though.

Also, even disregarding eastern Asia because eurocentrism, the crossbow is older than people think.

I must have confused Roman ballista with later crossbow designs by somehow combining features of both. It's kind of beside the point though. GC is asking whether elastic properties are scalable, and I'm saying they are, subject to constraints that I have defined mathematically. You'd need to run the numbers to see how big you can go, but switching from wood to non-brittle* metals gives you a lot more room there. Unless you're looking at a celestial-scale giant scalability isn't a deal breaker.

*Or very ductile metals like copper that will simply bend permanently.

[Atarlost]

For most of history people did not have access to materials *both* strong and elastic enough to make large bows out of.  This is why warfare ends up being dominated by heavily armoured spearmen and swordsmen, even when you might logically assume that holding back and shooting is a better tactic.  The bows then were too small to reliably penetrate armour, this problem was only solved in medieval times by changing the mechanics (crossbows) or by using better materials (yew longbows). 

At this point people started to deploy archers/crossbowmen in lines to face the enemy head-on when previously archers had only been deployed as skirmishers supplementary to the main battle.

Are you trying to claim that longbows were impossible prior to the medieval period?  The oldest known bows are longbows.  Elm flatbows from Danish bogs (the Holmegaard bows) used the same natural heartwood/sapwood compositing as Welsh longbows and fall into the same size range.  Once yew began to grow in northern Europe we start seeing yew bows, so the neolithic people were clearly not too stupid to recognize a good bow wood.  Horn/wood/sinew composite bows have superior strength to any self bow and begin appearing in the third millenium BC. 

The Greeks and Romans just sucked at archery.  Everyone else in antiquity made heavy use of it. 

[GoblinCookie]

You might be confusing cast iron (which is not elastic) with wrought iron (which is). If you really want to be pedantic you could say both are elastic to a limit (which is actually in the raws for df materials). Beyond this limit you either have plastic deformation (wrought iron) or brittle fracture (cast iron). The reason people didn't make bows from wrought iron is that elastic potential energy scales with elongation (draw length) squared, while the restoring force scales with elongation. So, a greater draw length in a material with a relatively weak restoring force such as yew wins out over a very strong material like wrought iron that no one could pull back more than a few inches.

The equations I showed above deal with the scalability issue of elastic properties by enforcing a maximum allowable shear stress. It would also allow fantasy materials that have excellent properties for bows, and allow different types of wood to perform differently in-game using values already defined in the raws.

As a final note, you can confirm that many iron-based materials are indeed elastic by compressing a spring. When you release it it will return to its original shape. On the other hand, if you compress it too far for too long plastic deformation will set in and it will not return exactly as it was but may remain permanently shorter. The idea with bows is similar except you're inducing shear stress instead of compressive stress.

It does not matter if some kinds of iron are more elastic than others, as all kinds of iron are insufficiently elastic to make a decent bow out of.  Most kinds of wood are too inelastic to make a bow of sufficient power to deal with a heavily armored opponent. 

Are you trying to claim that longbows were impossible prior to the medieval period?  The oldest known bows are longbows.  Elm flatbows from Danish bogs (the Holmegaard bows) used the same natural heartwood/sapwood compositing as Welsh longbows and fall into the same size range.  Once yew began to grow in northern Europe we start seeing yew bows, so the neolithic people were clearly not too stupid to recognize a good bow wood.  Horn/wood/sinew composite bows have superior strength to any self bow and begin appearing in the third millenium BC. 

The Greeks and Romans just sucked at archery.  Everyone else in antiquity made heavy use of it.

If the human race forgot how to make longbows, would that matter?  If you do not have yew, you cannot make longbows; if you have yew you can make longbows; it does not require an advanced scientific mind.  Conceptually it is not a great leap to make a larger bow, the problem is the materials and the working of them.  The general point I was making is that the size of bows cannot be increased indefinitely for as long as you can find someone strong enough to use them; the nature of the materials restricts the maximum size and power of any bow.  If cave men had longbows, that proves nothing other than that they had access to the materials to make them; the technically interesting development is the crossbow.  What is certain is that longbow technology was forgotten at some point during the ancient world and then was reintroduced at some point in the middle ages.

If the Greeks and Romans sucked at archery, that was because they did not have longbows or crossbows; which meant however good at archery they might have become there was no reliable way to penetrate the armour worn by heavy infantry or cavalry which meant that archers were not an efficient means to win wars.  Successful military forces made use primarily of heavy infantry and cavalry because nobody could simply line up their archers and slaughter them at range before said melee troops reached them.  The reinvention of the longbow changed the rules altogether, so we start to see things like the Battle of Agincourt where despite being outnumbered English archers managed to dispatch an army of French heavy cavalry. 

Nothing like ever happened or could have happened in the ancient world.  Archers were used for skirmishing or to man fortifications but they were never fielded in such a bold manner, the only circumstances where archers could have prevailed against heavy cavalry is with a heavy numerical advantage.  I suspect that this is actually the reason why the Greeks were able to prevail over the Persians, their armies made heavy use of bows because prior to the invention of heavy armour bows (not longbows) had been an effective weapon.  In effect one Greek was worth more than one Persian because it took now more than one archer to take down an infantryman, so despite being outnumbered the Greeks were able to win in a kind of Anti-Agincourt. 

[Ninjabread]

It does not matter if some kinds of iron are more elastic than others, as all kinds of iron are insufficiently elastic to make a decent bow out of.

Spoiler (click to show/hide)

Most kinds of wood are too inelastic to make a bow of sufficient power to deal with a heavily armored opponent. 

If you're talking about an opponent in plate armour then there is no wood, nor any bow design, that allows you to actually pierce the armour. Until the advent of gunpowder, most ranged weapons weren't intended to pierce armour, rather they were supposed to hit people in the places where there were gaps.

If you do not have yew, you cannot make longbows; if you have yew you can make longbows; it does not require an advanced scientific mind.

No, yew makes the best longbows but you can make a longbow out of a great many different woods, I think my longbow is ash. The longbow is to do with the design, not the material.

What is certain is that longbow technology was forgotten at some point during the ancient world and then was reintroduced at some point in the middle ages.

Again, no. The longbow is literally just what the name suggests: a long bow, typically around the same height as the user. You don't need any extra technology, if you can make a bow you can make a longbow, you just need a bit more wood. It was actually during the bronze age that bowyers began to prefer yew as a longbow material, you know, ancient Greece time. It's also believed that the Germanic tribes in the black forest that gave Rome such a hard time were using longbows or something very similar, perhaps the flatbows that Atarlost mentioned?

If the Greeks and Romans sucked at archery, that was because they did not have longbows or crossbows

Did you even read my last post?

The reinvention of the longbow changed the rules altogether, so we start to see things like the Battle of Agincourt where despite being outnumbered English archers managed to dispatch an army of French heavy cavalry. 

The field of battle was arguably the most significant factor in deciding the outcome. The recently ploughed land hemmed in by dense woodland favoured the English, both because of its narrowness, and because of the thick mud through which the French knights had to walk...

... As the battle was fought on a recently ploughed field, and there had recently been heavy rain leaving it very muddy, it proved very tiring to walk through in full plate armour. The French monk of St. Denis describes the French troops as "marching through the middle of the mud where they sank up to their knees. So they were already overcome with fatigue even before they advanced against the enemy". The deep, soft mud particularly favoured the English force because, once knocked to the ground, the heavily armoured French knights had a hard time getting back up to fight in the mêlée. Barker states that some knights, encumbered by their armour, actually drowned in their helmets.

Sounds like Agincourt was won through exceptional tactics and no small measure of luck to me.

Nothing like ever happened or could have happened in the ancient world.  Archers were used for skirmishing or to man fortifications but they were never fielded in such a bold manner, the only circumstances where archers could have prevailed against heavy cavalry is with a heavy numerical advantage.

How do you know that nothing like that happened back then? Do you expect any literate ancient society to admit to such a humiliating defeat? The majority of the Roman records on their conquests are essentially just propaganda which is why, for example, the death toll on auxillia was not recorded.

Also, the archers were fielded in a bold manner? Look at the map of the battle in the article you linked. They were literally hiding in the bushes, and it says in the article that they were also protected from cavalry with pointed wooden stakes that had been driven into the ground. Sounds like fortifications to me.

I suspect that this is actually the reason why the Greeks were able to prevail over the Persians, their armies made heavy use of bows because prior to the invention of heavy armour bows (not longbows) had been an effective weapon.  In effect one Greek was worth more than one Persian because it took now more than one archer to take down an infantryman, so despite being outnumbered the Greeks were able to win in a kind of Anti-Agincourt. 

Persians technically won the battle at Thermopylae, they just took such heavy casualties that they had to abandon their campaign, it's called a Pyrrhic victory. Fun fact about that, the last of the remaining Greeks at Thermopylae were surrounded on a hill and bombarded with arrows until there were none left alive.

The general consensus is also that good training and tactical use of terrain (again) were both just as important as the quality equipment that the Greeks had. If either of those things weren't in Greek favour, they likely would've been significantly easier to deal with.

[scourge728]

PTW

[Flying Teasets]

QUX

[Atarlost]

If the human race forgot how to make longbows, would that matter?  If you do not have yew, you cannot make longbows; if you have yew you can make longbows; it does not require an advanced scientific mind. 

But it does require gross ignorance of the subject matter.  The oldest known longbows are made of elm and date to before the climate warmed enough for yew to grow in the region where they were found.  Composite bows can be made with even poor bow woods because the wood serves mostly as a spacer between the sinew that bears the tension and the horn that bears the compression.  Composite bows are usually not long, but because their strength is vastly superior to any wood they can achieve the same draw lengths in a shorter bow more suited to use on horseback.  The composite bow tradition is continuous in the near east from the late bronze age until they were displaced by gunpowder. 

You obviously have an internet connection.  Try doing some research.  Start with Carrhae. 

[thompson]

You comment is rather ironic, as "stronger short bows" was part of the argument GC made in favour of bows being useful even for short civs. We've now come full circle. GC has a habit of trying to perform point-by-point rebuttals, but they rarely go well as it just fragments whatever argument he is trying to make and the point gets completely lost (usually over an argument about some secondary issue). My only real comment is that material properties should be used to determine bow effectiveness, and that there is no need to impose an upper limit on size arbitrarily as material properties will do that for you.

I've given some more thought into bow dynamics. My earlier approximation was a little crude so I've been thinking about improvements. I'll probably fork it into a separate suggestion once I'm done as it goes beyond the original scope of this one significantly.

[GoblinCookie]

If you're talking about an opponent in plate armour then there is no wood, nor any bow design, that allows you to actually pierce the armour. Until the advent of gunpowder, most ranged weapons weren't intended to pierce armour, rather they were supposed to hit people in the places where there were gaps.

Not so.  Until the reinvention of the longbow and invention of the crossbow what you describe was the indeed the case.  The fact this was the case prevented the use of archers as 'line' troops (troops that directly confront the enemy) for everyone pretty much between the times when the Persian Empire rose to power and the Middle Ages.  Hitting the gaps in armour at range is not easy without supernatural accuracy, while this prevented

It was for this reason that the crossbow was controversial, in fact the Pope tried to ban them at one point precisely because it could go through the armour worn by knights *and* be used by pretty much anyone. 

No, yew makes the best longbows but you can make a longbow out of a great many different woods, I think my longbow is ash. The longbow is to do with the design, not the material.

I am getting the impression you are arguing for the sake of it here.  I claimed that it was not possible to make functional longbows out of most wood but it is possible to make smaller bows out of most wood.  I never claimed that there were no other woods that could make longbows in the world. 

The longbow has to be good enough to offset it's inherent disadvantages (slow rate of fire, high level of training required), it may be that some with woods while you can make longbows out of them do so with sufficient drawbacks as to make them infeasible for military use.   

Again, no. The longbow is literally just what the name suggests: a long bow, typically around the same height as the user. You don't need any extra technology, if you can make a bow you can make a longbow, you just need a bit more wood. It was actually during the bronze age that bowyers began to prefer yew as a longbow material, you know, ancient Greece time. It's also believed that the Germanic tribes in the black forest that gave Rome such a hard time were using longbows or something very similar, perhaps the flatbows that Atarlost mentioned?

They did not prefer yew as a longbow material, because they did not have longbows.  Nobody did, including the German tribes.  If the German tribes used bows it was in the skirmish/supporting capacity for the regular infantry, or else the histories of Romans fighting the Germans would consist of them being turned into pincushions in a serious of Agincourt style defeats rather than being hacked apart with axes, which is what actually tended to happen. 

Did you even read my last post?

They had a prototype.  They had prototypes for lots of things, including computers but they certainly did not use crossbows on a large scale or else we would have heard of it big-time.  At one point they (Archimedes) invented a machine to use the suns rays to burn ships, but that was never used on wide scale either.  At some point in the middle ages quite likely someone took those prototypes and actually put them into widespread manufacture; why it was not done earlier is mysterious but probably has to do with the shortage of the needed parts. 

No Greek or Roman army ever fielded crossbows to anyone's knowledge. 

The field of battle was arguably the most significant factor in deciding the outcome. The recently ploughed land hemmed in by dense woodland favoured the English, both because of its narrowness, and because of the thick mud through which the French knights had to walk...

... As the battle was fought on a recently ploughed field, and there had recently been heavy rain leaving it very muddy, it proved very tiring to walk through in full plate armour. The French monk of St. Denis describes the French troops as "marching through the middle of the mud where they sank up to their knees. So they were already overcome with fatigue even before they advanced against the enemy". The deep, soft mud particularly favoured the English force because, once knocked to the ground, the heavily armoured French knights had a hard time getting back up to fight in the mêlée. Barker states that some knights, encumbered by their armour, actually drowned in their helmets.

Sounds like Agincourt was won through exceptional tactics and no small measure of luck to me.

Luck and tactics will only get you so far when you are archers outnumbered by cavalry.  That is very much rock-paper-scissors in favour of cavalry but that the archers were able to stand their ground and win shows that something has fundamentally changed in warfare.  If they had been fighting heavy infantry of the roman/greek style, their victory would be a shoo-in under pretty much all circumstances, because cavalry are faster than infantry which makes them ideal for killing archers in a straight contest but still they lost.

In the ancient worlds archers were used to man fortifications or to support non-archer troops by adding a few extra casualties. 

How do you know that nothing like that happened back then? Do you expect any literate ancient society to admit to such a humiliating defeat? The majority of the Roman records on their conquests are essentially just propaganda which is why, for example, the death toll on auxillia was not recorded.

Also, the archers were fielded in a bold manner? Look at the map of the battle in the article you linked. They were literally hiding in the bushes, and it says in the article that they were also protected from cavalry with pointed wooden stakes that had been driven into the ground. Sounds like fortifications to me.

If mountains are molehills then pointed stakes thrown hastily into the ground count as fortifications.  By fortifications I mean actual permanent walls and by skirmishing I mean ambushes/hit and run tactics not just using cover in a battlefield to confuse an enemy.  The Romans still had an effective counter to fortified archers in the Tortoise Formation which basically is why the Roman Empire existed on the scale it did, since nobody they were fighting had archers capable of reliably penetrating the shields of the Romans even when firing down from a fortress wall which basically means that they are hitting with the greatest amount of force it is possible for them to do so.

Basically you are using the conspiracy theorists favorite argument, the ancient world people's wars were really dominated by archers but the Romans and Greeks who 'sucked at archery' (your words and true, except for the Cretans) are still the one's writing the history.  The reason they are writing the history is because they won and they won because archers in general sucked at that point in history so that being no good at it was no impediment to conquering the known world. 

Persians technically won the battle at Thermopylae, they just took such heavy casualties that they had to abandon their campaign, it's called a Pyrrhic victory. Fun fact about that, the last of the remaining Greeks at Thermopylae were surrounded on a hill and bombarded with arrows until there were none left alive.

The general consensus is also that good training and tactical use of terrain (again) were both just as important as the quality equipment that the Greeks had. If either of those things weren't in Greek favour, they likely would've been significantly easier to deal with.

Why did they take heavy casualties when they had such a numerical advantage, if their arrows work effectively while not just sit and turn the Spartans into pincushions from afar and win the battle with no casualties since the Spartans had at Thermopylae no archers of their own as far as I know of.  The reason is that the combination of their fortifications and the armour of the spartans meant that their archers were useless and they were forced to engage them in melee.

The Persians outright lost the battle of Marathon to the Athenians+Allies in the previous Persian-Greeks and the Spartans did not even turn up on time there.  The wars against the Persians were not decided by a single battle which the Greeks technically lost. 

But it does require gross ignorance of the subject matter.  The oldest known longbows are made of elm and date to before the climate warmed enough for yew to grow in the region where they were found.  Composite bows can be made with even poor bow woods because the wood serves mostly as a spacer between the sinew that bears the tension and the horn that bears the compression.  Composite bows are usually not long, but because their strength is vastly superior to any wood they can achieve the same draw lengths in a shorter bow more suited to use on horseback.  The composite bow tradition is continuous in the near east from the late bronze age until they were displaced by gunpowder. 

You obviously have an internet connection.  Try doing some research.  Start with Carrhae. 

Carrhae was won by a cavalry charge that was so effective because the Romans had adopted their uber-anti archer formation.  The Romans were generally of an opinion that they could simply wait until the archers ran out of arrows (the Romans are not idiots, they know that archers are of limited effectiveness).  It is a good example of effectively using archers in a supporting capacity for regular cavalry, it is not an example of an Agicourt style victory. 

It requires ignorance of a facts irrelevant to the subject matter, I was not talking about neolithic warfare if indeed there even was such a thing and world peace was not the rule back then.  You informed me that they had yew longbows back then, which I did not know but does not prove that the ancients had longbows unless we believe that technology never moves backwards.  The story is then, they forgot how to make longbows which is hard to fathom unless you remember that the ancient world civilizations are *not* a simple descendant of neolithic societies.

The reason is that the original societies that had the longbows were replaced by the societies of the Indo-Europeans.

You comment is rather ironic, as "stronger short bows" was part of the argument GC made in favour of bows being useful even for short civs. We've now come full circle. GC has a habit of trying to perform point-by-point rebuttals, but they rarely go well as it just fragments whatever argument he is trying to make and the point gets completely lost (usually over an argument about some secondary issue). My only real comment is that material properties should be used to determine bow effectiveness, and that there is no need to impose an upper limit on size arbitrarily as material properties will do that for you.

I've given some more thought into bow dynamics. My earlier approximation was a little crude so I've been thinking about improvements. I'll probably fork it into a separate suggestion once I'm done as it goes beyond the original scope of this one significantly.

The issue here is that we are talking about a computer game.  The limitations on bow size imposed by the materials does not automatically exist simply because we model the properties of the materials, it has to be specifically programmed in. 

[Ninjabread]

Not so.  Until the reinvention of the longbow and invention of the crossbow what you describe was the indeed the case.  The fact this was the case prevented the use of archers as 'line' troops (troops that directly confront the enemy) for everyone pretty much between the times when the Persian Empire rose to power and the Middle Ages.  Hitting the gaps in armour at range is not easy without supernatural accuracy, while this prevented

Archers didn't aim for gaps in the armour, they didn't even aim at specific people, they were fielded in such large numbers that accuracy was irrelevant, just bombard the general area that the opponent is in and someone will hit something.

If longbows and crossbows worked the way you think they do, nobody would use anything but longbows because your archers would win battles before they even started, since longbows loosed arrows at a rate of 10-12 per minute at a range of 165-228m, let's round that to 200 for simplicity in calculations, and let's say 50% of the arrows miss because your archers are new, so 5 hits a minute minimum. Presuming their opponents were sprinting at them at ~16mph, which is pretty fast even if you aren't wearing armour, each archer would still take out 2 infantrymen before anyone reached them. That's better than early firearms.

It was for this reason that the crossbow was controversial, in fact the Pope tried to ban them at one point precisely because it could go through the armour worn by knights *and* be used by pretty much anyone. 

If they could pierce the armour of knights, why would the knights even bother wearing armour?

They were controversial because it takes a few weeks at most to become passable with a crossbow, such that the king of England could be, and was, killed by a child with a crossbow.

I am getting the impression you are arguing for the sake of it here.  I claimed that it was not possible to make functional longbows out of most wood but it is possible to make smaller bows out of most wood.  I never claimed that there were no other woods that could make longbows in the world. 

The longbow has to be good enough to offset it's inherent disadvantages (slow rate of fire, high level of training required), it may be that some with woods while you can make longbows out of them do so with sufficient drawbacks as to make them infeasible for military use.

First off, you said

If you do not have yew, you cannot make longbows; if you have yew you can make longbows; it does not require an advanced scientific mind.

Secondly, you're still wrong, yew just makes the best longbows, other woods are still usable for war in longbow form, they will just be outperformed by yew.

Finally, longbows weren't slow, that's the whole point behind certain countries not adopting the crossbow, and all bows require a high level of training, no matter how big it is.

They did not prefer yew as a longbow material, because they did not have longbows.  Nobody did, including the German tribes.  If the German tribes used bows it was in the skirmish/supporting capacity for the regular infantry, or else the histories of Romans fighting the Germans would consist of them being turned into pincushions in a serious of Agincourt style defeats rather than being hacked apart with axes, which is what actually tended to happen. 

Longbows for hunting and warfare have been made from many different woods by many cultures; in Europe they date from the Paleolithic, and since the Bronze Age were made mainly from yew, or from wych elm if yew was unavailable.

They had a prototype.  They had prototypes for lots of things, including computers but they certainly did not use crossbows on a large scale or else we would have heard of it big-time.  At one point they (Archimedes) invented a machine to use the suns rays to burn ships, but that was never used on wide scale either.  At some point in the middle ages quite likely someone took those prototypes and actually put them into widespread manufacture; why it was not done earlier is mysterious but probably has to do with the shortage of the needed parts. 

No Greek or Roman army ever fielded crossbows to anyone's knowledge. 

If the very design of a crossbow made heavy infantry as worthless as you seem to think it does, the Greeks would have fielded them by the hundreds, if not thousands, against each other and against Rome, but they didn't, because you're wrong.

Luck and tactics will only get you so far when you are archers outnumbered by cavalry.  That is very much rock-paper-scissors in favour of cavalry but that the archers were able to stand their ground and win shows that something has fundamentally changed in warfare.  If they had been fighting heavy infantry of the roman/greek style, their victory would be a shoo-in under pretty much all circumstances, because cavalry are faster than infantry which makes them ideal for killing archers in a straight contest but still they lost.

In the ancient worlds archers were used to man fortifications or to support non-archer troops by adding a few extra casualties. 

War is not rock-paper-scissors. The luck was the terrain and the poor organisation and forethought of the French, which further improved the terrain advantage. The tactics was their use of small fortifications and terrain to nullify the cavalry charge against the archers, said archers severely wounding and killing the poorly armoured horses by bombarding the muddy field, made even harder to traverse by the cavalry churning it up during their retreat. Any infantry charges would not only exhaust themselves just trying to get to their opponents, and would take constant attritional casualties from the bombardment. All of this info is in the wiki article you linked. Read your own sources my dude, luck and tactics go a long way.

If mountains are molehills then pointed stakes thrown hastily into the ground count as fortifications.  By fortifications I mean actual permanent walls and by skirmishing I mean ambushes/hit and run tactics not just using cover in a battlefield to confuse an enemy.  The Romans still had an effective counter to fortified archers in the Tortoise Formation which basically is why the Roman Empire existed on the scale it did, since nobody they were fighting had archers capable of reliably penetrating the shields of the Romans even when firing down from a fortress wall which basically means that they are hitting with the greatest amount of force it is possible for them to do so.

Stakes in the ground are manmade changes to the terrain intended for defensive purposes, and thus are fortifications.

But let's give you the benefit of the doubt and go by your descriptions of fortifications and skirmishing. You're still wrong. I'm not an expert on the Greeks, so I'll use what I know best: Rome. Romans might have been crap archers but Romans weren't the only people in the Roman army; the majority of their forces were made up of auxilia, plenty of whom were good at archery. Rome didn't like skirmishes, their strength comes from their organisation and cooperation en masse, so they vastly preferred large battles in open plains. They used auxilia archers in these battles. They also had archers in their hilariously sub-par navy, so unless a boat counts as walls you're wrong there too.

I have to give credit where credit's due, at least you're aware that the testudo was for use in sieges, my reenactment group tends to have to do a demonstration as to why it doesn't work so well elsewhere.

Basically you are using the conspiracy theorists favorite argument, the ancient world people's wars were really dominated by archers but the Romans and Greeks who 'sucked at archery' (your words and true, except for the Cretans) are still the one's writing the history.  The reason they are writing the history is because they won and they won because archers in general sucked at that point in history so that being no good at it was no impediment to conquering the known world. 

Except we have physical evidence that shows that things didn't happen the way that the Romans said it did. Old battlefields that don't line up with the Roman narrative, battles they were clearly involved in that go unmentioned, and other battles that they did mention but we have no evidence of. We know for a fact that they lied to their people, I'm simply asking the question of how you would know they didn't leave out any humiliating defeats involving many archers.

I also never claimed ancient warfare was dominated by archers either, I just said that an Agincourt-esque defeat of Roman forces wasn't completely impossible.

(Oh and, not my words, Atarlost's words, I'm well aware of Crete, Cretan archer auxilia played a notable role in the invasion of Gaul iirc)

Why did they take heavy casualties when they had such a numerical advantage, if their arrows work effectively while not just sit and turn the Spartans into pincushions from afar and win the battle with no casualties since the Spartans had at Thermopylae no archers of their own as far as I know of.  The reason is that the combination of their fortifications and the armour of the spartans meant that their archers were useless and they were forced to engage them in melee.

The Persians outright lost the battle of Marathon to the Athenians+Allies in the previous Persian-Greeks and the Spartans did not even turn up on time there.  The wars against the Persians were not decided by a single battle which the Greeks technically lost. 

I already said why they took such heavy casualties: Greeks had superior equipment sure, but also training, and a big terrain advantage. They didn't just sit back and fill them with arrows for three reasons: 1) fresh troops with shields take minimal casualties from arrow volleys, if any at all, because as long as you hold it in the right place you don't get hit, but if they're tired they might struggle to hold it steady, 2) the arrows were tipped with bronze, which is expensive, and 3) they underestimated the Greeks. When the first volley failed, they just sent infantry in expecting to win with ease. Three days of poor decision making later and they decided to do exactly what you suggested, and it worked.

I didn't mention Marathon because the Athenians there weren't wearing bronze chestplates, but rather some sort of linen gambeson, therefore they aren't really relevant to a discussion on heavily armoured troops.

[GoblinCookie]

Archers didn't aim for gaps in the armour, they didn't even aim at specific people, they were fielded in such large numbers that accuracy was irrelevant, just bombard the general area that the opponent is in and someone will hit something.

If longbows and crossbows worked the way you think they do, nobody would use anything but longbows because your archers would win battles before they even started, since longbows loosed arrows at a rate of 10-12 per minute at a range of 165-228m, let's round that to 200 for simplicity in calculations, and let's say 50% of the arrows miss because your archers are new, so 5 hits a minute minimum. Presuming their opponents were sprinting at them at ~16mph, which is pretty fast even if you aren't wearing armour, each archer would still take out 2 infantrymen before anyone reached them. That's better than early firearms.

The accuracy rate is a lot worse than 50%.  Then we have to account for cover, element of surprise, bad weather or nightime reducing accuracy further and the limited supply of ammunition. 

But yes, you are describing the situation that the introduction of crossbows and longbows in the middle ages created, it became possible to destroy foes at a range as they approached you over an open field.  Prior to this you could reliably march heavy infantry across said field while taking only light casualties because the arrows were not powerful enough to penetrate the armour they were wearing and had to rely on luck hits. 

If they could pierce the armour of knights, why would the knights even bother wearing armour?

They were controversial because it takes a few weeks at most to become passable with a crossbow, such that the king of England could be, and was, killed by a child with a crossbow.

Because knights are on horseback and the armour penetration is not perfect.  The knights can reach the archers fairly fast and cut them down in melee.  The main issue here is not knights but heavy infantry like greek hoplites, phalangites and roman legionaries, *they* suddenly became completely useless because they would be shot to pieces by archers or crossbowmen. 

Secondly, you're still wrong, yew just makes the best longbows, other woods are still usable for war in longbow form, they will just be outperformed by yew.

Finally, longbows weren't slow, that's the whole point behind certain countries not adopting the crossbow, and all bows require a high level of training, no matter how big it is.

The longbows have to be good enough to offset the disadvantages they have. 

Longbows are slow in relation to smaller bows because it takes longer to draw back the bowstring and the archers tire faster.  That means that your longbows have to be good enough at rate of fire, ease of use and armour penetration to justify the drawbacks to using them.

If your longbows do not have enough power to get through the armour your opponent is wearing and you need to rely on lucky shots; your aim is to loose so many shots that one of them is bound to hit an unarmoured point.  The same principle applies even more with crossbows. 

Longbows for hunting and warfare have been made from many different woods by many cultures; in Europe they date from the Paleolithic, and since the Bronze Age were made mainly from yew, or from wych elm if yew was unavailable.

Wikipedia is wrong here.  They had longbows in the paleolithic and then forgot how to make them, there is no since in the equation. 

If they had longbows in the bronze age, nobody would ever used any other weapon back then at all (I'll get to why that is later).  They did not have longbows in the iron age either and the Roman Empire would not have existed had they had them.
 

If the very design of a crossbow made heavy infantry as worthless as you seem to think it does, the Greeks would have fielded them by the hundreds, if not thousands, against each other and against Rome, but they didn't, because you're wrong.

No because the prototype crossbows were not good enough to penetrate armour yet.  The Greeks never adopted them en-masse because they did not have the rate of fire to replace bows nor the armour penetration to make their slower rate of fire worthwhile. 

War is not rock-paper-scissors. The luck was the terrain and the poor organisation and forethought of the French, which further improved the terrain advantage. The tactics was their use of small fortifications and terrain to nullify the cavalry charge against the archers, said archers severely wounding and killing the poorly armoured horses by bombarding the muddy field, made even harder to traverse by the cavalry churning it up during their retreat. Any infantry charges would not only exhaust themselves just trying to get to their opponents, and would take constant attritional casualties from the bombardment. All of this info is in the wiki article you linked. Read your own sources my dude, luck and tactics go a long way.

Yes war *is* very much rock-paper-scissors.  The reason they lost is that the muddy terrain prevented them from moving at their full speed, so in effect they were rendered in a similar position to heavy infantry, especially once their horses are slain.  So Agincourt really demonstrates the uselessness of heavy infantry once longbows are in use, heavy cavalry remains useful at that point because their speed counteracts the effectiveness of the archers somewhat.  It is only when gunpowder is invented that heavy cavalry also becomes useless since guns armour penetration is even greater than longbows/crossbows.

Stakes in the ground are manmade changes to the terrain intended for defensive purposes, and thus are fortifications.

But let's give you the benefit of the doubt and go by your descriptions of fortifications and skirmishing. You're still wrong. I'm not an expert on the Greeks, so I'll use what I know best: Rome. Romans might have been crap archers but Romans weren't the only people in the Roman army; the majority of their forces were made up of auxilia, plenty of whom were good at archery. Rome didn't like skirmishes, their strength comes from their organisation and cooperation en masse, so they vastly preferred large battles in open plains. They used auxilia archers in these battles. They also had archers in their hilariously sub-par navy, so unless a boat counts as walls you're wrong there too.

I have to give credit where credit's due, at least you're aware that the testudo was for use in sieges, my reenactment group tends to have to do a demonstration as to why it doesn't work so well elsewhere.

If the Romans enemies had longbows, their preference for fighting large battles in the plains would have been their end.  The whole reason the Romans prevailed with the tactics they did was because none of their enemies had longbows or crossbows. 

As I said, mountains and molehills but you clearly did not get what I was saying, ships are fortified enough to count as fortifications but a line of stakes in the ground is not.  The testudo was used whenever the Romans came under missile fire in open ground, which tended to be fortresses because that was the only open ground context in which archers were generally effective against heavy infantry.  The effectiveness of this formation is entirely based upon the lack of armour penetration of the contemporary missile weapons causing them to be completely dependant upon lucky shots, which the testudo formation denies them.   

Except we have physical evidence that shows that things didn't happen the way that the Romans said it did. Old battlefields that don't line up with the Roman narrative, battles they were clearly involved in that go unmentioned, and other battles that they did mention but we have no evidence of. We know for a fact that they lied to their people, I'm simply asking the question of how you would know they didn't leave out any humiliating defeats involving many archers.

I also never claimed ancient warfare was dominated by archers either, I just said that an Agincourt-esque defeat of Roman forces wasn't completely impossible.

(Oh and, not my words, Atarlost's words, I'm well aware of Crete, Cretan archer auxilia played a notable role in the invasion of Gaul iirc)

That X lies therefore what I say is true is the Conspiracy Theorist's Fallacy.  You have just doubled down on it there; that we know the Romans lies and cover stuff up, does not mean that what they are covering up is the evidence you are correct. 

The Romans did use archers and yes they were auxilia.  Crete was also where the best archers came from, but ask yourself the question?  Why is it the Roman Empire and not the Cretan Empire? 

I already said why they took such heavy casualties: Greeks had superior equipment sure, but also training, and a big terrain advantage. They didn't just sit back and fill them with arrows for three reasons: 1) fresh troops with shields take minimal casualties from arrow volleys, if any at all, because as long as you hold it in the right place you don't get hit, but if they're tired they might struggle to hold it steady, 2) the arrows were tipped with bronze, which is expensive, and 3) they underestimated the Greeks. When the first volley failed, they just sent infantry in expecting to win with ease. Three days of poor decision making later and they decided to do exactly what you suggested, and it worked.

I didn't mention Marathon because the Athenians there weren't wearing bronze chestplates, but rather some sort of linen gambeson, therefore they aren't really relevant to a discussion on heavily armoured troops.

They wore a mixture of linen and metal, they had a metal helmet, a metal breastplate and a linen skirt under the breastplate to protect their legs.  Oh and they also wore metal greaves on their legs under their skirt, the linen vs bronze distinction you are using does not exist in Ancient Greek infantry, they always wore a mixture of cloth and metal. 

Bronze!!!  This is the Iron Age silly, the bronze age ended centuries before this point so all the armour, shields, weapons and arrows are now made of steel.  Here is why that matters, heavy infantry rule the Iron Age but not the Bronze Age because of basic physics; the metals involved have got stronger but the men wielding the metals have not. 

When we take two substances of the same strength and hit one substance (the armour) with a second substance (the weapon) all the damage done to the first substance is the extra force added to the equation by the person or missile thrower.  While hitting bronze armour with a bronze weapon does not involve more force than with steel weapons+armour in absolute terms, in relative terms the difference in the extra power on the side of the weapons vs the armour is greater with bronze than with steel so the armour takes more damage.

That is why I said that if Bronze Age people had longbows, nobody would ever have used any other weapon.  Bronze arrows against bronze armour is much more effective than steel arrows against steel armour.  It is for that reason that heavy infantry becomes dominant in the Iron Age.  In the Bronze Age masses of archers are used as front line troops and chariots are used to counter them, chariots are of a dubious effectiveness compared to cavalry in an actual charge but their dominance is because they provide cover against missile fire; even if you kill the horses with arrows the chariot itself provides cover for advancing infantry. 

The Persian armies unlike the Greeks were mostly archers, the Spartans at Thermopylae were not fighting heavy infantry like themselves; they were fighting hastily converted archers while is why they did so well.  The Persians archers were useless, so they were forced to use them in melee but the Persians did not realise the uselessness of archers because their tradition of warfare did not take into account that the physics of warfare had changed by the transition from bronze to steel.  They thought (like you) that archers were still effective at the front line and like you they were wrong. 

[Ninjabread]

The accuracy rate is a lot worse than 50%.  Then we have to account for cover, element of surprise, bad weather or nightime reducing accuracy further and the limited supply of ammunition. 

But yes, you are describing the situation that the introduction of crossbows and longbows in the middle ages created, it became possible to destroy foes at a range as they approached you over an open field.  Prior to this you could reliably march heavy infantry across said field while taking only light casualties because the arrows were not powerful enough to penetrate the armour they were wearing and had to rely on luck hits. 

We also have to account for troop formation density, and the fact that in your mind longbows are basically railguns so a hit to the armour still counts.

And no, this was not the situation created by crossbows and longbows in the middle ages, infantry still existed and made up the bulk of most armies, even during battles on open fields.

Infantry were recruited and trained in a wide variety of manners in different regions of Europe all through the Middle Ages, and probably always formed the most numerous part of a medieval field army

I figured I should source my arguments, since if you try to do the same you might realise how wrong you are.

Because knights are on horseback and the armour penetration is not perfect.  The knights can reach the archers fairly fast and cut them down in melee.  The main issue here is not knights but heavy infantry like greek hoplites, phalangites and roman legionaries, *they* suddenly became completely useless because they would be shot to pieces by archers or crossbowmen. 

Good part about sourcing your arguments is that you can find out when you're wrong; the pope did outlaw crossbows (or rather the use of them against christians) because of ease of use and armour penetration, you were right about that. However if you look up the dates, that law was made in 1139, and the first proper plate armour since the fall of western Rome was made in 1420 (presumably this is why DF plate armour seems very hoplite-y). The armour penetration was likely in reference to maille armour, which, when unriveted was totally penetratable by more or less anything stabby, and when riveted was still suceptible to quite a few ranged weapons.

When the mail was not riveted, a thrust from most sharp weapons could penetrate it. However, when mail was riveted, only a strong well-placed thrust from certain spears, or thin or dedicated mail-piercing swords like the estoc could penetrate, and a pollaxe or halberd blow could break through the armour. Strong projectile weapons such as stronger self bows, recurve bows, and crossbows could also penetrate riveted mail.

As for your actual argument in this post, it entirely relies on your railgun long/crossbows being real, since I completely agree that horses charging at you will reach you fast. I'll just leave this here.

The longbows have to be good enough to offset the disadvantages they have. 

Longbows are slow in relation to smaller bows because it takes longer to draw back the bowstring and the archers tire faster.  That means that your longbows have to be good enough at rate of fire, ease of use and armour penetration to justify the drawbacks to using them.

If your longbows do not have enough power to get through the armour your opponent is wearing and you need to rely on lucky shots; your aim is to loose so many shots that one of them is bound to hit an unarmoured point.  The same principle applies even more with crossbows. 

If you're strong enough to use a longbow properly they take the same amount of time as any other bow, the motion is the same, the distance you pull the string back is the same, it just takes more power. They did tire out faster than people using lower poundage bows, obviously, and would have paced themselves so they didn't exhaust themselves before they exhausted their arrow supply, but it was a negligable difference, especially when compared to the massive range advantage they had compared to the lower poundage bows.

With a firing rate of three – five volleys per minute they were however no match for the English and Welsh longbow men who could fire ten – twelve arrows in the same amount of time

That was English & Welsh longbowmen vs Genoese crossbowmen at the Battle of Crécy. 5-6 seconds to pluck an arrow out of the ground, load it, draw, and loose as a volley with all the other archers, is not slow by any means. I can't find a figure for other bows, but they'd have to be pretty damn fast to have their speed be a big advantage over the longbow

As for the armour piercing comment, I refer back to the link in the previous section.

Wikipedia is wrong here.  They had longbows in the paleolithic and then forgot how to make them, there is no since in the equation. 

If they had longbows in the bronze age, nobody would ever used any other weapon back then at all (I'll get to why that is later).  They did not have longbows in the iron age either and the Roman Empire would not have existed had they had them.

I provided a source. If you think my source is wrong, provide me with a more reliable and up-to-date one, rather than simply making the baseless claim that my source is wrong.

No because the prototype crossbows were not good enough to penetrate armour yet.  The Greeks never adopted them en-masse because they did not have the rate of fire to replace bows nor the armour penetration to make their slower rate of fire worthwhile. 

Or maybe it's because Greek armies had lots of training, enough for the crossbow's advantage of being easy to use to be irrelevant, because plate armour actually works.

Here's a video of faulty replica plate armour still working against functioning replicas of crossbows from the century after the armour was used. Makes some dents and small holes, but never actually hits the "body" underneath until the plate is removed. Also note that the crossbows have those metallic limbs that you claimed wouldn't work.

Yes war *is* very much rock-paper-scissors.  The reason they lost is that the muddy terrain prevented them from moving at their full speed, so in effect they were rendered in a similar position to heavy infantry, especially once their horses are slain.  So Agincourt really demonstrates the uselessness of heavy infantry once longbows are in use, heavy cavalry remains useful at that point because their speed counteracts the effectiveness of the archers somewhat.  It is only when gunpowder is invented that heavy cavalry also becomes useless since guns armour penetration is even greater than longbows/crossbows.

In rock-paper-scissors, there is no situation in which scissors turn into rock, so already you've gone against your own analogy, but there's also some other questions it raises, like what happens when your cavalry has bows? If infantry is rock and cavalry is scissors, why were cavalry charges into infantry formations so common? Where does siege equipment fit in? Since numbers afford an advantage in warfare, how many pairs of scissors does it take to cut a rock?

If the Romans enemies had longbows, their preference for fighting large battles in the plains would have been their end.  The whole reason the Romans prevailed with the tactics they did was because none of their enemies had longbows or crossbows. 

As I said, mountains and molehills but you clearly did not get what I was saying, ships are fortified enough to count as fortifications but a line of stakes in the ground is not.  The testudo was used whenever the Romans came under missile fire in open ground, which tended to be fortresses because that was the only open ground context in which archers were generally effective against heavy infantry.  The effectiveness of this formation is entirely based upon the lack of armour penetration of the contemporary missile weapons causing them to be completely dependant upon lucky shots, which the testudo formation denies them.   

noun

• the act of fortifying or strengthening.
• something that fortifies or protects.
• the art or science of constructing defensive military works.
• Often fortifications. military works constructed for the purpose of strengthening a position; a fort

Stakes driven into the ground to protect against cavalry charges, under these definitions, are indeed fortifications as they are constructed for the purpose of strengthening a position. Small fortifications when compared to most others, but fortifications none the less. Boats on the other hand are not built for defence. Some boats do have fortifications on them, but Rome used polyremes, rather than defensive fortifications, they had offensive rams that were used to puncture the other ship's hull and sink it.

the trireme was essentially a ship built for ramming

Also why are you bringing up the testudo again? I agreed with you, it's used for sieges, because shields are quite good at stopping arrows, but the troop is left very open to flanking due to poor visibility, and has little to no oppourtunity for retaliation to melee attack without breaking formation.

That X lies therefore what I say is true is the Conspiracy Theorist's Fallacy.  You have just doubled down on it there; that we know the Romans lies and cover stuff up, does not mean that what they are covering up is the evidence you are correct.

I wasn't the one making claims though. You said that there was a thing that definitely never happened, I asked how you knew that, explaining that absence from Roman records isn't a reliable way to draw that conclusion, then you called me a conspiracy theorist. The burden of evidence lies firmly upon you.

The Romans did use archers and yes they were auxilia.  Crete was also where the best archers came from, but ask yourself the question?  Why is it the Roman Empire and not the Cretan Empire? 

Because war is not rock-paper-scissors, good archers don't always beat heavy infantry.

They wore a mixture of linen and metal, they had a metal helmet, a metal breastplate and a linen skirt under the breastplate to protect their legs.  Oh and they also wore metal greaves on their legs under their skirt, the linen vs bronze distinction you are using does not exist in Ancient Greek infantry, they always wore a mixture of cloth and metal. 

They did not use bronze upper body armour at this time, but that of leather or linen

Bronze!!!  This is the Iron Age silly, the bronze age ended centuries before this point so all the armour, shields, weapons and arrows are now made of steel.  Here is why that matters, heavy infantry rule the Iron Age but not the Bronze Age because of basic physics; the metals involved have got stronger but the men wielding the metals have not. 

the Greeks' wooden shields (sometimes covered with a very thin layer of bronze) and bronze helmets deflected the arrows...

...In 1939, archaeologist Spyridon Marinatos, excavating at Thermopylae, found large numbers of Persian bronze arrowheads on Kolonos Hill

When we take two substances of the same strength and hit one substance (the armour) with a second substance (the weapon) all the damage done to the first substance is the extra force added to the equation by the person or missile thrower.  While hitting bronze armour with a bronze weapon does not involve more force than with steel weapons+armour in absolute terms, in relative terms the difference in the extra power on the side of the weapons vs the armour is greater with bronze than with steel so the armour takes more damage.

So what you're saying is; the harder the material, the less it deforms from external pressure. Congrats, you have successfully described hardness.

That is why I said that if Bronze Age people had longbows, nobody would ever have used any other weapon.  Bronze arrows against bronze armour is much more effective than steel arrows against steel armour.  It is for that reason that heavy infantry becomes dominant in the Iron Age.  In the Bronze Age masses of archers are used as front line troops and chariots are used to counter them, chariots are of a dubious effectiveness compared to cavalry in an actual charge but their dominance is because they provide cover against missile fire; even if you kill the horses with arrows the chariot itself provides cover for advancing infantry.

Your argument still relies on the idea that the longbow provides enough force to pierce plate, which I already provided evidence against. Sure it'd probably do more damage to bronze plate, cause steel is harder than bronze, but the steel was literally just scratched by a close range shot. At best, from the same range, I'd wager bronze plate might get slightly dented. Feel free to test it out, or find someone doing so online.

The Persian armies unlike the Greeks were mostly archers, the Spartans at Thermopylae were not fighting heavy infantry like themselves; they were fighting hastily converted archers while is why they did so well.  The Persians archers were useless, so they were forced to use them in melee but the Persians did not realise the uselessness of archers because their tradition of warfare did not take into account that the physics of warfare had changed by the transition from bronze to steel.  They thought (like you) that archers were still effective at the front line and like you they were wrong. 

They had a lot of archers, yes, but that wasn't all they had, and they certainly didn't hastily arm their archers with melee weapons and send them in. Some lessons in Persian army composition:

Xenophon (Cyropaedia 6.4.1; 7.1.2) describes the guard of Cyrus the Great as having bronze breastplates and helmets, while their horses wore bronze chamfrons and poitrels together with shoulder pieces which also protected the rider’s thighs. Herodotus, instead, describes their armament as follows: wicker shields covered in leather, short spears, quivers, swords or large daggers, slings, bow and arrow. Underneath their robes they wore scale armour coats

The sparabara, meaning "shield bearers" in Old Persian, were the front line infantry of the Achaemenid Persian Empire.[1] They were usually the first to engage in hand-to-hand combat with the enemy. Although not much is known about them today, it is believed that they were the backbone of the Persian army who formed a shield wall and used their two-metre-long spears to protect more vulnerable troops such as archers from the enemy

Not as well equipped for melee as the Greeks, sure, but certainly not hastily converted archers.

Also they were both still using bronze, I've already given you a source for that. Their bronze helmets and bronze-plated shields still protected them from the arrows, so bronze isn't as flimsy as you think, nor were people so quick to abandon it when a cool new metal was discovered.

[thompson]

I've decided against posting this under a new suggestion as I simply don't have time at the moment to give this topic the attention it deserves. Ranged weapon combat is really one of the weaker points of the game, but I'd rather wait for it to be done properly than have some half-measure implemented before a full rewrite is ready.

I've given the matter some thought and have devised a system of equations to govern bow and crossbow combat where the properties of the bow and crossbow are determined by the properties of the materials the weapons are made from. I had proposed a more simplified system earlier, but in retrospect, I feel it was grossly inadequate.

Bows
Bows essentially work by storing energy in the bow itself while drawing, and releasing it by letting go of the string. The energy is stored in the form of elastic potential energy both in the front of the bow (which is elongated, so experiences tension), and the back (which is compressed). For the sake of this discussion I will approximate a bow at rest as a straight rod of length L, with a constant cross-sectional area A, and radius r. When the string is pulled back the bow will curve. For simplicity, let's assume the bow deforms the shape of an arc of a circle of radius R. Upon deformation, the radius of curvature of the front edge of the bow will be R+r, and the back edge R-r. The degree of elongation of the front edge of the bow will therefore be:

2pi*(R+r) / (2pi*R) = 1+r/R

Similarly, the back will be compressed by 1-r/R.

Note here that the behaviour of the front and rear sides of the bow are different. Often the wood of a bow will be cut such that the front side will be made of sapwood (which has excellent tensile properties) and the rear heartwood (which performs better in compression). Bowwood is therefore a natural composite. Actual composite bows are usually made with sinew on the front and horn at the rear. These have excellent properties and can be made with a similar draw length to longbows despite often being much shorter. They can be less durable, however, and early resins used to glue the components together were not always water proof.

Enough of that. To determine how effective a bow is we need to calculate the energy (and velocity) of the projectile. This is done by integrating over the force that is applied to the arrow as it is released from the bow. So, we need to calculate this force, and how it changes as the bow is released. If the materials are elastic, the force will be approximately given by Hooke's law, where:

F=-kx

where k is a constant and x the elongation. We therefore need to estimate k, and define the boundaries of our integral over F. The minimum displacement will be 0 (string fully restored to initial position). The maximum value is what we call the draw length. I will represent this with the letter D. We therefore need to determine how far the string comes back as the bow is bent.

For a bow of length L that is deformed into an arc with a radius of curvature R where both ends are bound together by a taught string of length L (which is linear, and not curved), the displacement of the back of the arrow relative to the middle of the bow can be determined from geometry. It works out to be:

x = R - R*cos(L/(2R)) + sqrt((L^2/4) - R^2 * sin(L/(2R))^2)

This term is a little problematic as (to my knowledge) DF uses integer arithmetic in its calculations, while we need a square root and two trigonometric functions which tend to require floating point arithmetic. This isn't a deal-breaker as there are workarounds, but we can do better than this. Rather than allowing the string to be straight, we can assume it has the same curvature as the bow instead such that:

x = 2R * (1 - cos(L/(2R)))

This isn't a very realistic assumption, but it doesn't really matter as all bows will be similarly affected. Also, note for small angles:

cos(x) ~ 1 - x^2 / 2

This approximation is reasonable if you impose a maximum angle L/(2R) = pi/2 for our bow. This would correspond to a bow bent into a semicircle (the angle corresponds to half this semicircle). Therefore:

x = 2R * (1 - 1 + L^2 / (4*R^2)) = L^2/(2R)

This is a much nicer expression to work with and works trivially with integer values. The draw length D of the bow will be the displacement of the string x at the minimum radius of curvature for the deformed bow. So, what is this value?

The DF raws define a number of elastic material constants. The part of the bow that is stretched will need the tensile modulus, while the part that is compressed needs the compressive modulus. These values can be calculated from the values already in the raws¹. Let's call the tensile/compressive modulus of the material Y. The force required to change the length of the material by a fraction a is:

F = -YAa

Different parts of the bow will actually have different degrees of elongation and compression, so strictly speaking we need to integrate over the cross-sectional area of the bow to determine this force. We can make life easier for ourselves by approximating the bow with a rectangular cross-section of thickness 2r such that the average elongation of the bow once it has been deformed to an arc with a radius of curvature R is given by:

a = r / (2R)

The restoring force from the bow is therefore:

F = -YAr / (4R)

We divide by another factor of 2 because only half the cross-sectional area will be in each compression or tension. In DF the actual strength of a creature is proportional to its strength value (T) multiplied by its size (S). The maximum force an archer should be able to apply should therefore be given by:

F = TSk

Here k is an arbitrary constant. The maximum compression/elongation the creature will be able to induce in the bow will be:

a = 2TSk / (A * (Y_compression + Y_tension)

This gives us a radius of curvature:

R = rA(Y_compression + Y_tension) / (2TSk)

If we take the bow to have a square cross-section, A = 4r^2. Alternatively, r = sqrt(A) / 2. Thus:

R = A^1.5 * (Y_compression + Y_tension) / (4TSk)

This gives us a draw length of:

D = L^2 * TSk / (Y*A^1.5)

The draw weight (i.e. maximum force) will be the maximum force of the creature: TSk

Kinetic energy E can be found by integrating the force over the draw length as the arrow is released, giving:

E = (LTSk)^2 / (2*A^1.5 *  (Y_compression + Y_tension))

E = Mv^2 / 2

M is mass, v velocity. The velocity is therefore:

v = LTSk*A^-0.75 * sqrt(1 / (M* (Y_compression + Y_tension))

Velocity is the property the game currently uses, so at this point we are almost done. There will also be some maximum force a bow can sustain based on its material properties. For a material with a tensile or compression yield stress U, the maximum force the bow can sustain will be:

F = -UA / 2

The defining value will be determined by the smaller value of the compressive or tensile yield stress. This gives a maximum velocity:

v = UL*A^0.25 * sqrt(1/(2M*(Y_compression + Y_tension)))

And that's it for the maths. The ONLY new value we need in the raws for this is a cross-sectional area of the bow A, which would be defined in the bow raws.

However, things could be taken much further. Composite bows could be introduced that use different materials to optimize tensile and compressive properties. I'll follow up another day with some of these other possibilities.

¹The elastic properties for wood appear to be a placeholder value in the raws at the moment, so significant changes would need to be made to improve this. Otherwise, all wood would have bows of equal properties, which isn't really what we want.

WARNING: The final velocity equations could be out by up to sqrt(2), depending on whether I correctly carried all the 2's. I'll check it all later.

[GoblinCookie]

Due to fallout from an incident on the discussion forum I was unable to post for the whole of last week; I apologise. 

We also have to account for troop formation density, and the fact that in your mind longbows are basically railguns so a hit to the armour still counts.

And no, this was not the situation created by crossbows and longbows in the middle ages, infantry still existed and made up the bulk of most armies, even during battles on open fields.

Infantry is a term that covers archers, light infantry, heavy infantry and pikemen.  By heavy infantry I mean heavily armoured footmen with shields, think roman legionaries as a pure version of that and Greek infantry as a form of hybrid between heavy infantry and pikemen, with the pikemen side of things prevailing over times (Macedonian Phalangites vs hoptiles) as cavalry goes into greater use. 

I figured I should source my arguments, since if you try to do the same you might realise how wrong you are.

If I had said what you think I said I would have been wrong but I did not.

As the middle ages progressed (and beyond) heavy infantry which prevails in the earlier middle ages (so viking/sakon infantry with their axes) are phased out, infantry tend to be a mixture of pikemen and archers.

Good part about sourcing your arguments is that you can find out when you're wrong; the pope did outlaw crossbows (or rather the use of them against christians) because of ease of use and armour penetration, you were right about that. However if you look up the dates, that law was made in 1139, and the first proper plate armour since the fall of western Rome was made in 1420 (presumably this is why DF plate armour seems very hoplite-y). The armour penetration was likely in reference to maille armour, which, when unriveted was totally penetratable by more or less anything stabby, and when riveted was still suceptible to quite a few ranged weapons.

Perhaps this is because plate armour was invented to counter the effectiveness of longbows/crossbows at penetrating the armour used before?  It was invented for use by armoured knights on horseback, not for use by the kind of heavy infantry that prevailed in earlier eras.  When in the later middle ages they needed such infantry, they tended to dismount their knights to fight on foot rather than having a dedicated force of heavy infantry as they did in earlier eras. 

In some kind of alternative history where gunpowder did not exist it is conceivable to think of mass-produced platemail equipped heavy infantry coming dominate the battlefield, but they never had the opportunity to make plate armour cheap enough to equip massed formations with it before they had guns.  The question is did they have such armour armour at Agincourt, I would probably bet on this *not* being the case, at least for the majority of the knights. 

As for your actual argument in this post, it entirely relies on your railgun long/crossbows being real, since I completely agree that horses charging at you will reach you fast. I'll just leave this here.

I have already demonstrated with historical evidence that longbows were quite capable of killing heavy cavalry before said cavalry reached them.  This is pretty scary since such troops are the rock-paper-scissors answer to archers in all previous eras. 

If you're strong enough to use a longbow properly they take the same amount of time as any other bow, the motion is the same, the distance you pull the string back is the same, it just takes more power. They did tire out faster than people using lower poundage bows, obviously, and would have paced themselves so they didn't exhaust themselves before they exhausted their arrow supply, but it was a negligable difference, especially when compared to the massive range advantage they had compared to the lower poundage bows.

With a firing rate of three – five volleys per minute they were however no match for the English and Welsh longbow men who could fire ten – twelve arrows in the same amount of time

That was English & Welsh longbowmen vs Genoese crossbowmen at the Battle of Crécy. 5-6 seconds to pluck an arrow out of the ground, load it, draw, and loose as a volley with all the other archers, is not slow by any means. I can't find a figure for other bows, but they'd have to be pretty damn fast to have their speed be a big advantage over the longbow

As for the armour piercing comment, I refer back to the link in the previous section.

The more power it takes to pull the bowstring back, the slower the rate of fire is. 

I already covered the issue of the differential rate of fire of the two weapons.  The reason that people use crossbows is that the materials needed to make longbows are very specific, while crossbows can be made out of most materials.  The French did not have access to the needed woods to make longbows, while the English did in large quantities.  This gets back to the basic problem of this thread, why have crossbows?

I provided a source. If you think my source is wrong, provide me with a more reliable and up-to-date one, rather than simply making the baseless claim that my source is wrong.

I spent the last several pages demonstrating why your source is wrong.  The way that warfare works in the ancient world points very much to the absence of longbows and crossbows, because the introduction of such weapons revolutionizes warfare by obsoleting the heavy infantry that dominate the ancient world. 

Or maybe it's because Greek armies had lots of training, enough for the crossbow's advantage of being easy to use to be irrelevant, because plate armour actually works.

You cannot train people to not die when you shoot them with missiles that can go through their armour. 

Here's a video of faulty replica plate armour still working against functioning replicas of crossbows from the century after the armour was used. Makes some dents and small holes, but never actually hits the "body" underneath until the plate is removed. Also note that the crossbows have those metallic limbs that you claimed wouldn't work.

The first arrow to hit the target does not need to go through, only one does; the armour does not fix itself.  But as we already discussed, plate armour was invented to counter the crossbows and longbows that obsoleted earlier forms of armour.  It was invented too late before gunpowder to ever have been mass-produced.

In rock-paper-scissors, there is no situation in which scissors turn into rock, so already you've gone against your own analogy, but there's also some other questions it raises, like what happens when your cavalry has bows? If infantry is rock and cavalry is scissors, why were cavalry charges into infantry formations so common? Where does siege equipment fit in? Since numbers afford an advantage in warfare, how many pairs of scissors does it take to cut a rock?

It does if the environment is simply swapping one role for another.  In effect a heavy cavalryman bogged down in the mud is closer to a heavy infantryman than to a cavalryman in normal situations, so we can determine that heavy infantry are completely countered by archers at this point. 

We actually need these kind of scenarios because people tend to avoid obviously suicidal confrontations.  We are not going to have a heavy infantry VS archers fight once the archers can reliably penetrate their armour, since nobody will actually order such a charge at that point anyway. 

noun

• the act of fortifying or strengthening.
• something that fortifies or protects.
• the art or science of constructing defensive military works.
• Often fortifications. military works constructed for the purpose of strengthening a position; a fort

Stakes driven into the ground to protect against cavalry charges, under these definitions, are indeed fortifications as they are constructed for the purpose of strengthening a position. Small fortifications when compared to most others, but fortifications none the less. Boats on the other hand are not built for defence. Some boats do have fortifications on them, but Rome used polyremes, rather than defensive fortifications, they had offensive rams that were used to puncture the other ship's hull and sink it.

Stop quoting the dictionary at me when I have already clarified that by fortifications I mean things that actually prevent the enemy from making physical contact at all without special equipment.  So a boat is very much like a castle wall in this setup, you cannot engage the folk on the other boat without special equipment (a ramp to do so).  Yes the degree to which different boats take advantage of this varies, but all boats however have a primitive function as fortifications in the sense we are talking about, not in the dictionary definition. 

the trireme was essentially a ship built for ramming

Also why are you bringing up the testudo again? I agreed with you, it's used for sieges, because shields are quite good at stopping arrows, but the troop is left very open to flanking due to poor visibility, and has little to no oppourtunity for retaliation to melee attack without breaking formation.

Shields are not inherently good at stopping arrows simply because they are shields.  If the romans had tried to use the testudo formation at something like Agincourt, they would have been shot down because the arrows would have simply gone through their shields.  The formation's very effectiveness derives from the lack of armour penetration of contemporary missiles. 

I wasn't the one making claims though. You said that there was a thing that definitely never happened, I asked how you knew that, explaining that absence from Roman records isn't a reliable way to draw that conclusion, then you called me a conspiracy theorist. The burden of evidence lies firmly upon you.

No it doesn't, because this is a double negative.  That Romans do not have longbows is a negative claim, you would normally have to prove that they do.  However for them to *not* have longbows when we have proof that cave men had longbows, the negative implies a positive claim (that the human race at some point forgot how to make longbows).  I however also would presumably have to prove this claim, but it is a positive claim (something that happened) implied by a negative state being so.  You cannot prove they had longbows and I cannot prove that the event when longbows were forgotten happened either.

So we have actually run across an unusual situation where the burden of proof does not work. 

Because war is not rock-paper-scissors, good archers don't always beat heavy infantry.

If the heavy infantry has no archers, artillery or cavalry backing them up then yes they do.  Because the heavy infantry cannot catch the archers and they can always get more arrows, especially if said archers are on horseback.  Even if it takes a thousand arrows to take down a single guy, they will win since they can always get more arrows as long as their enemies cannot catch them.  The problem for ancient archers is that the Greeks and Romans did have cavalry.

They did not use bronze upper body armour at this time, but that of leather or linen

'Clever' people are actually gullible enough to believe that was actually so? Will modern intellectuals believe anything however ridiculous?

Since Persian soldiers are equipped with scale armour, the idea that the Athenians won at Marathon wearing armour made entirely of linen by their usual hoplite tactics is insanity. 

the Greeks' wooden shields (sometimes covered with a very thin layer of bronze) and bronze helmets deflected the arrows...

...In 1939, archaeologist Spyridon Marinatos, excavating at Thermopylae, found large numbers of Persian bronze arrowheads on Kolonos Hill

Thermopylae had been a key strategic point and battlefield for centuries (Herodotus backs me up).  The bronze arrows are from an earlier battlefield from the bronze age fought at that location.  People want it to be from THE Thermopylae, but there were lots of them. 

So what you're saying is; the harder the material, the less it deforms from external pressure. Congrats, you have successfully described hardness.

Not just that.  The important thing is that a harder material takes less damage from an equally hard material given the same force than a softer material does an equally soft material.  It is why punching people is so effective.   

Your argument still relies on the idea that the longbow provides enough force to pierce plate, which I already provided evidence against. Sure it'd probably do more damage to bronze plate, cause steel is harder than bronze, but the steel was literally just scratched by a close range shot. At best, from the same range, I'd wager bronze plate might get slightly dented. Feel free to test it out, or find someone doing so online.

The plate armour used in the very late middle ages is considerably better than the plate armour used by ancient greeks; it was also invented to counter such weapons.  There is also the issue that we are using modern metallurgy to make ancient armour, the steel we are using is of better quality that was used back then.  We need sufficiently rubbish steel to test this, since modern steel is just too good.

They had a lot of archers, yes, but that wasn't all they had, and they certainly didn't hastily arm their archers with melee weapons and send them in. Some lessons in Persian army composition:

Xenophon (Cyropaedia 6.4.1; 7.1.2) describes the guard of Cyrus the Great as having bronze breastplates and helmets, while their horses wore bronze chamfrons and poitrels together with shoulder pieces which also protected the rider’s thighs. Herodotus, instead, describes their armament as follows: wicker shields covered in leather, short spears, quivers, swords or large daggers, slings, bow and arrow. Underneath their robes they wore scale armour coats

Cyrus is long dead by this point, he ended up as a head inside a waterskin full of blood when he invaded the wrong people's land.  We are talking about Darius and Xerxes which come several generations later.  Again the Persians rose to power when bronze was still the basis of warfare, this is why they had a force that emphasized archery so much, the problem was that the Greeks equipment better suited the iron age and the Persian tactics were obsolete. 

I am basing my understanding of the Persian armaments off Herodotus, whose works I have access to and have read.  Bows and arrows are described as part of their troops basic equipment, so yes they are archers.  Said archers are also capable of fighting in melee as (fairly) light infantry.  So yes the Spartans were fighting archers at Thermopylae in melee combat.  It is just that the Persian archers were to a mediocre degree equipped and trained for such combat, which I guess is why they also won eventually. 

Not as well equipped for melee as the Greeks, sure, but certainly not hastily converted archers.

Also they were both still using bronze, I've already given you a source for that. Their bronze helmets and bronze-plated shields still protected them from the arrows, so bronze isn't as flimsy as you think, nor were people so quick to abandon it when a cool new metal was discovered.

Granted they were archers with some melee capability (and some light armour).  But archery was clearly the main use of Persian soldiers not fighting in close combat. 

The cool new metal is both lighter AND stronger than bronze.  There is no reason to use bronze whatsoever as soon as steel is available at a reasonable cost.  As a Dwarf Fortress player you should know that this is the case.  That means that they are not using bronze shields at this point, they using steel shields and steel everything.  Because they are not stupid enough to jeopardize their lives by using metals that are inferior in every relevant sense.