This week we’re looking at a specific visual motif common in TV and film: the arrow volley. You know the scene: the general readies his archers, he orders them to ‘draw!’ and then holds up his hand with that ‘wait for it’ gesture and then shouts ‘loose!’ (or worse yet, ‘fire!’) and all of the archers release at once, producing a giant cloud of arrows. And then those arrows hit the enemy, with whole ranks collapsing and wounded soldiers falling over everywhere.

本周我们来讨论一种在电视剧和电影中非常常见的视觉套路：箭雨齐射。你肯定见过这种场景：将军命令弓箭手准备，他喊一声“拉弓！”，然后举起手做出一个“等一下”的手势，接着大喊“放箭！”（或者更糟糕的“开火！”），所有弓箭手同时放箭，形成一大片箭云。随后这些箭射中敌人，整排士兵倒下，到处都是受伤倒地的人。

From Alexander (2004) showing the Battle of Gaugamela. This bit is amazing because Darius III silently gestures and all of his archers draw their bows (also why are they kneeling? They’re shooting at a high angle! There’s no need to kneel!) and then at another silent gesture which they cannot see because Darius III is behind them, they all release at once.
And every part of that scene is wrong.

以电影《亚历山大》（2004）中表现的高加米拉战役为例。这一段很精彩：大流士三世默默地做了个手势，所有弓箭手就一起拉弓（顺便说一句，他们为什么跪着？他们是高角度射击，根本没必要跪下！），然后又在一个他们根本看不见的手势下（因为大流士在他们身后）同时放箭。
而这一幕里的每一个细节都是错的。

Now the thing that, in the last couple of decades, everyone has realized is wrong is that you don’t tell archers to ‘fire’ because their weapons don’t involve any fire. But the solution in film has been to keep the arrow volleys – that is, the coordinated all-at-once shooting – and simply change the order to ‘release’ or ‘loose.’ Which isn’t actually any better!

过去几十年里，大家逐渐意识到一个问题：你不应该对弓箭手喊“开火”，因为他们的武器根本不涉及“火”。但电影的解决办法只是把命令改成“放箭！”，同时保留“齐射”这种形式，其实这并没有任何改进！

Archers didn’t engage in coordinated all-at-once shooting (called ‘volley fire’), they did not shoot in volleys because there wouldn’t be any point to do so. Indeed, part of the reason there was such confusion over what a general is supposed to shout instead of ‘fire!’ is that historical tactical manuals don’t generally have commands for coordinated bow shooting because armies didn’t do coordinated bow shooting. Instead, archers generated a ‘hail’ or ‘rain’ (those are the typical metaphors) of arrows as each archer shot in their own best time.

弓箭手并不会进行这种协调一致的“同时齐射”，他们不会这样射击，因为这么做没有意义。事实上，人们之所以困惑将军到底该喊什么，正是因为历史上的战术手册里通常根本没有“统一齐射”的指令，因为军队本来就不这么干。相反，弓箭手会射出“箭雨”或“箭雹”（这是常见的比喻），每个弓箭手按自己的节奏射击。

More to the point, they could not shoot in volleys. And even if they had shot in volleys, those volleys wouldn’t produce anything like the impact we regularly see in film or TV. So this week, we’re going to walk through those considerations: briefly looking at what volley fire is for and why archers both wouldn’t and couldn’t do it, before taking a longer look at the problem of lethality in massed arrow fire.

更重要的是，他们其实也做不到齐射。即便真的齐射了，其效果也远远达不到影视作品中那种杀伤力。因此，我们将讨论这些问题：先简要看看齐射战术的用途，以及为什么弓箭手既不会也不能这样做，然后再更详细地分析大规模箭雨的真实杀伤力。

What Is Volley Fire For?
We want to start by understanding what volley fire is and what it is for. Put simply, ‘volley fire’ is the tactic of having a whole bunch of soldiers with ranged weapons (typically guns) fire in coordinated groups: sometimes with the entire unit all firing at once or with specific sub-components of the unit firing in coordinated fashion, as with the ‘counter-march.’ In both cases, the problem that volley fire is trying to overcome is slow weapon reload times: this is a solution for slow-firing but powerful ranged weapons. That has generally meant firearms, historically, but we do actually see volley fire drill with crossbows in China from a very early period as well (but, interestingly, there’s no evidence I am aware of that volley fire was ever done with crossbows in Europe).1

齐射战术是干什么的？
我们首先要理解什么是“齐射”，以及它的用途。简单来说，“齐射”就是让一大群使用远程武器（通常是火器）的士兵以协调的方式开火：有时是全体同时射击，有时是按队列轮流射击，比如所谓的“反向行进”。
无论哪种形式，齐射要解决的问题都是：武器装填速度太慢。这是一种针对“射速慢但威力大的远程武器”的解决方案。历史上这通常指火器，但在中国很早也出现过弩的齐射训练（不过有趣的是，在欧洲似乎没有弩进行齐射的证据）。

Volley fire can cover for the slow reload rate of guns or crossbows in two ways. The first are volley fire drills designed to ensure a continuous curtain of fire; the most famous of these is the ‘counter-march,’ a drill where arquebuses or muskets are deployed several ranks deep (as many as six). The front rank fires a volley (that is, they all fire together) and then rush to the back of their file to begin reloading, allowing the next rank to fire, and so on. By the time the last rank has fired, the whole formation has moved backwards slightly (thus ‘counter’ march) and the first rank has finished reloading and is ready to fire. The problem this is solving is the danger of an enemy, especially cavalry, crossing the entire effective range of the weapon in the long gap between shots. This, by the by, was the volley fire tactic that was being used in China with crossbows before gunpowder; I don’t know that anyone ever did volley-and-charge with crossbows, which lack the lethality of muskets.

齐射可以通过两种方式弥补火器或弩装填慢的问题：
第一种：持续火力覆盖
其中最著名的是所谓的“反向行进射击”战术。在这种战术中，火绳枪或火枪被部署为多列纵深队形（最多可达六排）。
最前排先进行一次齐射（也就是全体同时开火），然后迅速退到本列的最后方开始重新装填，让下一排上前射击，如此循环往复。等到最后一排完成射击时，整个队形已经略微向后移动了一点（因此称为“反向行进”），而最初的第一排也已经完成装填，准备再次开火。
这种战术要解决的问题是：在两次射击之间漫长的间隔里，敌人（尤其是骑兵）有可能穿过武器的有效射程，直接冲到面前。
顺便一提，这种齐射战术在火药武器出现之前，就已经在中国的弩兵中被使用了。不过，我不确定是否有人曾用弩来实施“齐射后冲锋”战术，因为弩的杀伤力不如火枪。

From The Fellowship of the Rings (2001). It’s a little hard to see in a still, but what these archers are doing is that each rank releases and then knees while the next rank shoots, which is wholly unnecessary, as you can see from the angles the bows are being held. Its also counter-productive: kneeling and standing again take longer to do than to just knock a new arrow and fire! This is a volley fire drill that is *slower* than just shooting normally!
The other classic use is volley-and-charge. Because firearms are very lethal but slow to reload, it could be very effective to march in close order right up to an enemy, dump a single volley by the entire unit into them to cause mass casualties and confusion and then immediately charge with pikes or bayonets to try to capitalize on the enemy being demoralized and confused. You can see variations on this tactic in things like the 17th century Highland Charge or the contemporary Swedish Gå–På (“go on”). By charging rather than waiting to reload, the attacker could take advantage of the high lethality of firearms without suffering the drawback of long reload times.

电影《护戒使者》（2001）里有一个类似场景：弓箭手一排一排轮流射击并跪下。但这是完全没必要的，从他们的射角就能看出来。而且这反而更慢：跪下再站起来比直接搭箭射击还费时间！
第二种：齐射后冲锋
由于火器杀伤力很强，但装填速度很慢，因此一种非常有效的战术是：部队以密集队形行进，接近敌人，在近距离由全体士兵齐射一轮，造成大量伤亡和混乱，然后立刻用长枪或刺刀发起冲锋，试图利用敌方士气低落、阵型混乱的时机扩大战果。
这种战术的不同变体可以在一些历史案例中看到，例如17世纪的Highland Charge，或同时期瑞典的Gå–På。

As we’re going to see in a moment, the lethality of bows or crossbows against armored, shielded infantry – even in close order – was pretty low at any given moment and needed to add up over an extended period of shooting. By contrast, muskets were powerful enough to defeat most armor and thus to disable or kill basically anyone they hit, limited of course by reload time: with a reload time of as much as 30 seconds for earlier matchlocks, a line of musketeers might only be able to fire a few times at an advancing infantry unit (which might take two or three minutes to walk through effective range) and given the limited accuracy of smoothbore muskets, only the last shots would hit at a high level. By contrast, a unit doing volley-and-charge is compressing probably close to 50% of the lethality of sustained shooting, devastating moment and then immediately charging.

正如我们稍后将看到的，即便是在密集队形下，弓或弩对穿着护甲、持盾的步兵的杀伤力也很有限，需要通过长时间累积射击才能形成实际效果。
相比之下，火枪足够强大，可以击穿大多数护甲，从而击伤或杀死几乎所有被击中的敌人，但当然受限于装填时间：早期火绳枪装填时间可能长达30秒，因此一排火枪手可能只能在敌方步兵进入有效射程的两三分钟内射击几次。而且，由于光滑膛火枪的精度有限，通常只有最后几发能有效命中。
而采取齐射+冲锋的部队，则能在极短时间内集中约50%的持续射击杀伤力，造成毁灭性打击，然后立刻冲锋。

Putting that much lethality into a singular instant was valuable from a morale perspective and of course it enabled a unit to quick march through the enemy’s effective range, stopping only briefly to fire and charge, limiting losses from steady enemy fire. But as we’re going to see, the lethality of bows (and, to a significant extent, crossbows) was much lower and so couldn’t be effectively compressed into that single, devastating, confusing moment.2

将如此高的杀伤力集中在短时间内释放，从士气角度来看是非常有价值的。当然，这也让部队能够快速通过敌人的有效射程，只需短暂停下射击和冲锋，从而减少敌方持续火力带来的损失。但正如我们将看到的，弓（以及弩）的杀伤力要低得多，因此无法有效地使用这个战术。

Why They Wouldn’t and Why They Couldn’t
But as you’ve hopefully noted, these tactics are built around firearms with their long reload times: good soldiers might be able to reload a matchlock musket in 20-30 seconds or so. But traditional bows do not have this limitation: a good archer can put six or more arrows into the air in a minute (although doing so will exhaust the archer quite quickly), so there simply isn’t some large 30-second fire gap to cover over with these tactics. As a result volley fire doesn’t offer any advantages for traditional bow-users.

正如你可能注意到的，这些战术都是围绕火器长时间装填设计的：熟练士兵可能需要 20–30 秒才能装填完一支火绳枪。但传统弓并没有这个限制：一个熟练弓箭手每分钟可以射出六支甚至更多箭（尽管这样会迅速消耗体力），所以根本不存在需要用这些战术来弥补的“30 秒射击空档”。因此，齐射对于传统弓箭手来说没有任何优势。

And so, as far as we can tell, organized volleys with bows weren’t done. We do have evidence in China for volley fire with crossbows, but of course crossbows, particularly more powerful ones, have all of the same reload-time problems that firearms do, so it is no shock to see the same tactics emerge. But historians have searched the ancient and medi sources for any hint of volley fire with bows and have come up wanting. Now, I should caution here that this is a topic where if you are reading sources in translation you are likely to be fooled: many translators will use the word ‘volley’ to describe things happening in the original Greek or Latin or Old French or what have you that are not volley fire, for the same reason that filmmakers keep putting archer volley fire in their movies: volley fire is a big part of how we imagine warfare. But as hard as it is to prove a negative, I will note that I have never seen a clear instance of volley fire with bows in an original text and so far as I can tell, no other military historians have either. And we have been looking.

据我们所知，弓箭手并没有组织过齐射。在中国，有弩的齐射记录，但弩尤其是威力较大的弩，也有和火器类似的装填问题，所以看到类似战术出现并不奇怪。
然而，历史学家查阅古代和中世纪的资料，想找到弓箭齐射的任何证据，却都未果。这里需要提醒一点：如果你看的是翻译资料，很容易被误导。很多译者会用“volley（齐射）”来描述原文（希腊语、拉丁语、古法语等）中发生的事情，而这些并非真正意义上的齐射，原因与电影中频繁出现弓箭齐射场面相同：齐射深植于我们对战争的想象中。
尽管证明不存在某件事很困难，但我可以明确指出：我从未在原始文献中看到弓箭齐射的确凿例子，而且据我所知，其他军事历史学家也没有找到过。我们一直在查找这些资料。

Of course the other reason we can be reasonably sure that ancient or medi armies using traditional bows did not engage in volley fire is that they couldn’t. You will note in those movie scenes, that the commander invariably gives the order to ‘draw’ and then waits for the right moment before shouting ‘release!’ (or worse yet ‘fire!’). The thing is: how much energy does it take to hold that bow at ready? The key question here is the bow’s ‘draw’ or ‘pullback’ which is generally expressed in the pounds of force necessary to draw and hold the bow at full draw. Most prop bows have extremely low pulls to enable actors to manipulate them very easily; if you look closely, you can often see this because the bowstrings are under such little tension that they visibly sway and wobble as the bow is moved. This also helps a film production because it means that an arrow coming off of such a bow isn’t going to be moving all that fast and so is a lot less dangerous and easier to make ‘safe.’

当然，我们可以合理确定古代或中世纪使用传统弓的军队不会进行齐射，另一个原因是他们根本做不到。你会注意到电影里的这些场景：指挥官总是先下令“拉弓（draw）”，然后等到合适时机才大喊“放箭（release）！”（或者更糟，“开火（fire）！”）。问题在于：拉弓并保持待射姿势需要多少力气？这里的关键是弓的“拉力（draw 或 pullback）”，通常以磅力（pounds）表示，即拉满弓并保持所需的力量。
大多数道具弓的拉力极低，以便演员轻松操作；仔细看，你常能发现弓弦几乎没有张力，随着弓的移动明显晃动。这对拍摄有好处，因为由这种弓射出的箭飞行速度不快，更安全。

But obviously actual bows are supposed to be dangerous.
And here folks will say, “ok, that’s prop bows, but I hold a hunting bow at full draw while lining up a shot all the time.” But there are two considerations here. The first is that many modern hunting bows are compound bows (note: compound, not composite), which is to say they use lever and pulley systems with wheels (‘cams’) which enable the energy at each stage of the bow’s draw to be controlled and are typically designed so that the energy necessary for the final bit of draw (that is, holding the bow at full draw) is relatively low. As a result, the strength required to hold a compound bow at full draw for an extended period is actually lower that what would be implied by its raw pullback.

但显然，真正的弓是危险的。
有人可能会说：“好吧，那是道具弓，但我打猎时经常拉满猎弓瞄准。”对此有两个问题。第一，现代许多猎弓是复合弓（注意是复合弓，不是复合材料弓），也就是利用杠杆和滑轮系统来控制拉弓各阶段的能量，并且设计上使得最后阶段的拉力（即保持拉满弓）相对较低。因此，长期拉满复合弓所需的力量实际上比它的原始拉力要低。

But also the pullbacks of hunting bows are much lower than those of war bows. Modern hunting bows generally feature pullback weights around 40-60lbs (going higher for compound bows but still generally topping out around 75lbs and typically being much less) and shoot lighter, thinner arrows than war bows. And that should make a fair degree of sense: deer cannot shoot back and do not generally wear armor. The military archer, by contrast, needs a lot of lethality and a lot of range because he is shooting at someone with armor and weapons who means to shoot back (or run up and stab him), although as we’ll see, even with extremely powerful bows the ability of war archers to inflict lots of casualties is pretty limited against properly equipped enemies. If your hunting bow mortally wounds a deer but does not disable it, that’s not ideal but the deer is going to run away, not charge at you spear in hand.3

第二，猎弓的拉力通常远低于战弓。现代猎弓一般拉力在 40–60 磅左右（复合弓可能更高，但通常上限约 75 磅，通常远低于此），且射出的箭比战弓的箭更轻更细。这个设计很合理：鹿不会反击，也通常不穿护甲。相比之下，弓箭手需要更高杀伤力和更远射程，因为他射击的目标装备了护甲和武器，并且可能反击或冲上来用矛刺击他。
不过正如我们将看到的，即便使用极强力的战弓，战场上的弓箭手对装备齐全的敌人的杀伤力仍然有限。如果你的猎弓射中了鹿造成致命伤但未能立即制伏它，这固然不理想，但鹿会逃跑，而不是拿着矛向你冲来。

As a result, the pullback weights of war bows tend to be higher. How much higher? We’ve actually run through this evidence before: at least in Afroeurasia, as far as I can tell, 80lbs pullback is about as light as a war bow will usually get. Draw weights anywhere from 100lbs to as high as 170lbs (see Strickland and Hardy, The Great Warbow (2005) for details) are known for the highest end bows like the English longbow and Steppe recurve bows. Which is to say that the pullback weight range of ‘old world’ war bows exceed at their lowest end the heaviest common draw weights of hunting bows and keep going up dramatically from there. The typical war bow was more than twice as powerful as the typical modern hunting bow. These war bows shot with enough force that they required specialized arrows with thicker, more robust construction to withstand the amount of energy being imparted.

因此，战弓的拉力通常要高得多。那么到底高多少呢？我们以前其实已经看过一些证据：至少在欧亚大陆，80磅拉力几乎是战弓的最轻拉力。像英格兰长弓或草原反曲弓等顶级弓，拉力可以从 100 磅一直高到 170 磅。也就是说，即使是磅数最低的古代战弓，也超过了常见的猎弓拉力，而且战弓的拉力还会显著增加。典型战弓的威力是现代猎弓的两倍以上。战弓射出的力量非常大，因此需要专门设计的箭，箭身更粗、更结实，以承受传递的能量。

Which neatly answers why no one had their archers hold their bows at draw to synchronize fire: you’d exhaust your archers very quickly. Instead, war bow firing techniques tend to emphasize getting the arrow off of the string as quickly as possible: the bow is leveled on the target as the string is drawn and released basically immediately. Remember back to our statistic that a good archer can put around 6 arrows in the air in a minute? Well, even the best archer can’t do that for very long. I often see folks asking about how many arrows an archer could carry, seemingly imagining archers shooting at their maximum rate for prolonged periods (like they do in video games), but if you imagine pumping a 150lbs weight as fast as you can, I think you’ll immediately recognize that you aren’t going to be able to keep that up for more than a minute or two (more on this as well in Strickland and Hardy, The Great Warbow (2005), by the by). Holding the bow at draw for any length of time is going to accelerate that exhaustion and thus lower the rate at which shots are made and the time that rate can be maintained.

这也很好地解释了为什么古人不会让弓箭手拉弓保持待射来同步射击：那样会很快让弓箭手疲劳。相反，战弓的射击技巧强调尽快将箭射出去：拉弓的同时瞄准目标，然后几乎立即松开弓弦。记得我们之前提到的统计数据吗？一个熟练弓箭手每分钟大约可以射 6 支箭？即便是最优秀的弓箭手，也不能长时间保持这个射速。我常看到有人问弓箭手能携带多少箭，好像想象弓箭手像电子游戏里一样长时间以最大速率射箭，但如果你试着快速举起 150 磅的重物，你会立刻意识到，你无法坚持超过一两分钟。保持拉满弓的姿势时间越长，疲劳累积越快，从而降低射速，也缩短了能够维持该射速的时间。

So the reason we have no evidence for archer volley fire is because they didn’t do it and they didn’t do it because it doesn’t solve a problem that exists with bows (whose rate of shot is fast enough not to require volley tactics) but it does cause all sorts of new problems (exhausting your archers).

所以，我们没有找到弓箭齐射的证据，是因为他们根本不需要齐射：弓的射速足够快，不需要通过齐射来解决问题；而尝试齐射反而会带来各种新问题——比如让弓箭手迅速疲劳。

But there’s a second related problem to these scenes: arrow lethality.
Modeling Arrow Lethality
Because when these arrow volleys arrive, the result is usually devastating, with large numbers of men falling all over the place (often being shot straight through their heavy armor).
But how lethal were arrow barrages? Well, the short answer is that we don’t know and it must have varied considerably. Teasing out the specific lethality of one part of an engagement from others is difficult even with modern warfare; for pre-modern warfare, we are often lucky to even have reliable estimates of total casualties in a battle, much less specific estimates of casualties caused by a specific source or weapon. Still, we have more than a few solid indications that the lethality of barrages of arrows, in some cases even over extended periods, could be quite low, which isn’t to say such weapons were ineffective.

但是，还有第二个相关问题：箭矢的杀伤力。
因为在电影里，当箭雨来袭时，结果通常是毁灭性的，大量士兵倒下（甚至直接穿透厚重盔甲）。
但是，箭矢齐射到底有多致命呢？简短的回答是：我们不知道，而且杀伤力很可能变化很大。即使在现代战争中，要单独分析某一环节的致命性也是困难的；在前现代战争中，我们甚至很难获得战斗总伤亡的可靠数据，更别提由特定武器造成的伤亡数据了。不过，有一些可靠的证据表明，箭雨的致命性，在某些情况下甚至在持续一段时间内，也可能相当低，当然这并不意味着箭矢无效。

Depending on the way the men in the target infantry formation are facing and the formation, in most fighting formations, upwards of 50% of the total horizontal space simply doesn’t contain and humans to hit and arrows plunging into that space are going to hit nothing but the ground. Now the vertical space is trickier: there’s going to be a lot of empty space between the ranks as well, though we are almost never informed about how much. One exception is the Macedonian sarisa phalanx, where we’re told (Polyb. 18.29) that the sarisa of the fifth rank extends two cubits beyond the first rank, which lets us calculate roughly a 90cm rank interval. Other formations might have been tighter or looser, of course. But the implication here is that an arrow shot on a flat trajectory (so at very close range) at least half of the target area is entirely empty space; for an arrow shot in a high arc, as much as 75% of the target area might be. And of course in this estimation, we’ve been treating our soldiers like they are large rectangular prisms (our army of gelatinous cubes will be very effective), but of course actual humans aren’t going to physical occupy a lot of the space we’re even giving them here (note the silhouettes below). So the majority of arrows are simply going to miss.

根据步兵队形的朝向和排列方式，在大多数作战队形中，多达50%的水平空间可能没有人存在，箭矢射入这些空隙，只会打到地面。垂直空间则更复杂：排与排之间也存在很多空隙，但我们几乎没有资料说明具体间距。一个例外是马其顿的长矛方阵，据记载，第五排的长矛比第一排超出两肘（约90厘米），由此可以粗略推算排间距。其他队形可能更紧或更松。
这意味着：如果箭矢平射（低弧线、近距离），至少有一半目标区域是空的；高抛射时，空区可能占到 75%。而且，在这个估算中，我们假设士兵像大型长方体一样占据空间，但实际上人类并不会占据这么多空间。因此，大多数箭矢实际上会落空。

But of course then our target infantrymen are also not unprotected. Let’s assume here an average infantryman who is roughly 170cm in height (5ft 7in, a touch on the tall side, but not unreasonable for pre-modern agrarian soldiers). The first thing he is likely to have protecting him is a shield. For the purpose of our arrows killing or disabling our infantryman, a decent shield is essentially perfect protection in the area it covers: even very light shields can ‘catch’ arrows effectively (and indeed, this is what very thin hide or wicker shields are for). The one risk we face is the arrow punching through the shield into the shield arm, which could certainly happen, but many shields have reinforced metal bosses over where they are gripped, making this less likely. But as we discussed with shield walls, shields often cover quite a lot of the body; shields could be quite big. So let’s draw that out with some example shields, to scale with a human silhouette (again, 170cm tall) and see how much of this relatively big fellow (by pre-modern standards) typical shields covered:

当然，我们的目标步兵也不是毫无防护的。假设步兵平均身高约 170厘米（5英尺7英寸，在前现代农耕士兵中算是略高，但并不离谱）。他最先可能拥有的防护就是盾牌。就箭矢的杀伤或削弱作用而言，一个合适的盾牌几乎可以完全覆盖它保护的区域：即使是非常轻的盾牌也能有效挡住箭矢（实际上，这正是薄皮盾或柳条盾的用途）。唯一的风险是箭矢穿透盾牌击中持盾手臂，这确实可能发生，但许多盾牌在握柄位置都有金属加强块，从而降低了这种风险。
正如我们讨论过的盾墙，盾牌通常能覆盖身体相当大的一部分；盾牌可以相当大。我们用一些盾牌与一个人形轮廓（仍然假设身高170厘米）进行比例对比，就能看到这些盾牌覆盖了步兵的大部分身体区域：

What you can immediately see is that just about any shield is going to massively reduce the target area of the body even if it isn’t moved. All of these shields are large enough to cover the entire trunk of the body, protecting all of the vital organs in the torso. Assuming our infantryman has crouched down a little and put his shoulder into his shield (and kept his weapon hand behind it), our archer has lost upwards of three-quarters of his target area (even higher for very large shields like the Roman scutum). Worse yet, the target area that remains is mostly legs where arrow strikes, while painful, are a lot less likely to be lethal and may not even be disabling.

几乎任何盾牌都能大幅减少身体的目标面积。所有这些盾牌都足够大，可以覆盖整个躯干，保护胸腹部的重要器官。假设我们的步兵稍微下蹲，把肩膀靠在盾牌上（并将持武器的手放在盾牌后面），弓箭手的目标面积已经减少了四分之三以上（对于像罗马方盾这样的大型盾牌，这个比例甚至更高）。更糟糕的是，剩余的目标主要是腿部，而箭矢击中腿部虽然疼痛，但致命性较低，甚至可能无法造成致残。

And of course these soldiers can move their shields, angling them up if the arrows are plunging downward or crouching behind the shield if they’re arriving on flat trajectories. Moreover arrows at range move slowly enough to be actively blocked and dodged, to the point that we know that ‘arrow dodging’ was a martial skill of some import in cultures that engaged in small-scale bow exchanges as part of ‘first system‘ warfare.5 Of course, if the incoming hail of arrows is dense enough, soldiers might be unwilling to put their heads up to try to spot incoming and block (at Agincourt we’re told the French soldiers angled their helmets into the arrow-rain, for instance), but infantry under lighter ‘fire’ might actively move their shield to block specific incoming arrows.

当然，这些士兵可以移动他们的盾牌：如果箭矢是俯冲而下，他们可以将盾牌倾斜向上；如果箭矢平射，他们可以蹲在盾牌后面进行防护。此外，远程射来的箭矢飞行速度足够慢，士兵能够主动格挡或躲避。以至于我们知道，在一些小规模弓箭交战中，“躲箭”是一项重要的武艺技能。当然，如果箭雨密集到一定程度，士兵可能不敢抬头去尝试格挡（比如在阿金库尔战役中，据说法国士兵会将头盔倾斜以迎向箭雨），但在较轻的“火力”下，步兵可能会主动移动盾牌去阻挡特定的箭矢。

And then behind that shield our infantryman is also probably wearing some kind of armor! Now a full plate harness is going to provide only extremely few points of vulnerability, but to give our archers a more favorable case, let’s stay in the ancient world and consider two ‘edge’ cases from the Hellenistic period: a mailed Roman legionary (the most heavily armored infantryman of the period) and a Gallic warrior (one of the less armored infantrymen of the period). By picking soldiers this early, we’ve given our archers a bit of a hand: these fellows don’t have fully enclosed helmets, or significant arm protection; later medi combatants, particularly with wealth, would have been much better protected, with things like aventails to cover the neck and fuller protections for arms and legs. The Roman has a mail lorica hamata, a Montefortino-type helmet (with cheek-flaps protecting much of the face) and greaves, while our Gaul has just the helmet and probably some thickened textile body protection. The coverage might look like this (please forgive my very rough efforts to draw out irregular shapes):

在盾牌之后，我们的步兵很可能还穿戴着某种护甲！全身板甲的防护几乎没有明显弱点，但为了给弓箭手提供更有利的战场模拟，我们先回到古代，假设两个极端例子：一名穿链甲的罗马军团士兵（当时的重装步兵）和一名高卢战士（当时的轻装步兵）。选择这些较早时期的士兵，相当于给弓箭手提供了一些优势：这些士兵没有全封闭的头盔，也没有手臂防护；而后期中世纪战士，尤其是富裕者，会有更完善的防护，如颈部防护和手脚的全面防护。罗马士兵穿着链甲、蒙特福蒂诺型头盔和护胫，而高卢战士仅有头盔，可能还穿着加厚的纺织防护服。

Once again, the human silhouette shape is via Wikimedia Commons.
Now as we’ve discussed, armor protection against arrows isn’t necessarily a binary. Armor often gets discussed as if arrows either always defeat it or never do and really only one of those is correct: arrows will not defeat good iron or steel plate armor at effectively any range. But for other forms of armor, the range and the power of the bow matter a lot. I’m going to summarize my previous estimates here (but I sure do wish we had more long-range bow-penetration testing!): at relatively long range (c. 200m) even powerful bows might struggle to reach the target with enough impact energy to penetrate mail and relatively weak war bows – which are still bows with 80lbs pullback (so our weak war bow is roughly 50% more powerful as a typical hunting bow) – may struggle to even penetrate a good textile defense with a solid hit. Even at moderate ranges (c. 100m), mail will probably sometimes defeat even the most powerful bows (but sometimes it will fail) and even a gambeson provides a degree of protection from the weakest (again, still 80lbs pullback bows).6

正如我们之前讨论的，护甲对箭矢的防护并不是简单的“能防”或“不能防”二元情况。很多时候人们讨论护甲时，好像箭矢要么总能穿透，要么完全无效，其实只有后一种说法部分正确：箭矢几乎不可能穿透良好的铁制或钢制板甲，无论射程多远。但对于其他类型的护甲，射程和弓的威力就非常关键。我在这里总结一下之前的估算：在较远距离（约 200 米）下，即便是强力弓，也可能难以以足够冲击力穿透链甲，而相对弱一些的战弓，也就是仍然有 80 磅拉力的弓（比普通狩猎弓约强 50%），甚至可能难以穿透一件质量不错的纺织防护服，即便击中也未必有效穿透。即使在中等距离（约 100 米），链甲也可能偶尔抵挡住最强弓的射击（但有时也会失败），即使是一件加厚衬衣也能在面对最弱弓时，提供一定防护（这里的弱弓仍为 80 磅拉力）。

What that means for our Roman legionary up there the good news is that very few arrows are going to accomplish much; the situation is worse for our Gaul, but actually not much worse. For the Roman legionary, he has upwards of 85% of his body covered by his giant shield. Should an arrow get around that shield somehow, to hit anything vital (except his face) it has to contend with his mail. Now powerful war bows, especially at short range can absolutely defeat mail, but not every shot is going to be the most powerful bow shooting a point-blank range shot hitting dead on and for the rest, a decent chunk of them are going to fail to split the mail rings or else expend so much energy doing so that they don’t penetrate lethally deep through the thick textile padding (the subarmalis) beneath the mail. Meanwhile, his lower legs below the shield are covered with solid bronze greaves which will almost always deflect an incoming arrow (they’re both solid metal, but also curved so an arrow is likely to glance off). His head and neck remain the big point of vulnerability, but something like three quarters of that space is covered by his helmet and his cheek-guards: an arrow slamming into a solid, 1.5kg bronze helmet is going to be unpleasant, but the arrow isn’t usually going to penetrate (though the impact may daze or even knock out the soldier).7

对于上文中的罗马军团士兵来说，好消息是，箭矢几乎无法造成实质伤害；高卢战士的情况糟一些，但也没有糟到哪去。罗马军团士兵的巨型盾牌覆盖了身体约 85% 的面积。如果箭矢穿透盾牌，想要击中致命部位（面部除外），还必须穿透链甲。强力战弓，尤其在近距离时，确实能击穿链甲，但并非每一箭都能做到必中。大部分箭矢要么不能完全分裂链环，要么在消耗大量能量后仍无法穿透下面的厚纺织衬里达到致命深度。同时，盾牌下方的腿部被坚固的青铜护胫覆盖，几乎总能将箭矢弹开（护胫不仅是实心金属，而且弯曲，箭矢通常会滑开）。头部和颈部仍是主要弱点，但大约四分之三的面积被头盔和面颊护片覆盖：一支箭射中实心 1.5 公斤青铜头盔会很疼，但通常不会穿透。

And if we start stacking these ‘filters’ for our arrows, we see the lethality of our barrage drops very fast against infantry. Maybe two-third to three quarters of our arrows just miss entirely, hitting the ground, shot long over the whole formation and so on. Of the remainder, another three-quarters at least (probably an even higher proportion, to be honest) are striking shields. Of the remainder, we might suppose another three-quarters or so are striking helmets or other fairly solid armor like greaves: these hurt, but probably won’t kill or disable. Of the remainder, a portion – probably a small portion, because of those big shields – are being defeated by body armor that they could, under ideal circumstances, defeat. And of the remainder that actually penetrate a human on the other side, maybe another two-thirds are doing so in the arms, feet or lower legs, many of them with glancing hits: painful, but not immediately fatal and in some cases potentially not even disabling.

如果我们把这些因素叠加，就会发现箭雨对步兵的杀伤力迅速下降。可能有三分之二到四分之三的箭完全落空，击中地面或飞过整个阵型；剩余的箭中，又至少有四分之三击中了盾牌；剩下的箭中，再有大约四分之三击中了头盔或其他坚固护具（如护胫），虽然会造成疼痛，但大概率不会致死或致残；再剩下的一部分箭，可能很少，因为盾牌太大，被护甲挡住，无法有效杀伤；最终实际穿透人体的箭中，约有三分之二击中手臂、脚或下腿，多为擦伤：疼痛，但通常不致命，有时甚至不致残。

After all of those filters, we’re down to an estimated arrow lethality rate hovering 0.5-1%, meaning each arrow shot has something like a 1-in-100 or 1-in-200 chance to kill or disable an enemy.

经过这些层层“过滤”，箭矢的杀伤率估计只有 0.5% 到 1%，也就是说每射 100~200 支箭，大约只有 1 支能杀伤或致残敌人。

Of course they wouldn’t be firing in volleys and numbers would matter. But we can extend our model a bit. Let’s assume an equal sized force of heavy infantry, advancing at the quick step (so a march, not a charge) against an equal sized force of archers. Bow shot is about 200m, which a quick march will cross in about 2-and-a-quarter minutes (quick step is 120 steps per minute, 75cm covered per step, roughly). Each archer can loose six arrows a minute, so each infantryman has, on average, 13.5 arrows to deal with. His chance of being killed or disabled by one of those arrows over the course of marching into contact (assuming our 0.5% arrow lethality) is thus about 6.75%. And that is under very favorable assumptions for our archers: our infantry doesn’t break into a charge, has no screening forces, the archers can shoot at maximum effective range, don’t tire out their arms and can all shoot effectively for the entire period (no return shots, no being blocked by friendly troops, etc). In practice, we should probably also impose a pretty sharp lethality ramp for these arrows: our 0.5% lethality figure is based on arrows loosed at pretty close range on flat trajectories, but of course the earliest shots in this scenario would be at much longer range, with less power and accuracy and so much less lethal; our 6.75% figure is thus something of a maximum. A 6.75% ideal disable rate is not going to stop the determined advance of heavy infantry: that infantry is going to march right on into contact and if those archers don’t have their own heavy infantry to meet it, they are going to be put to flight very quickly.

假设有一支同等规模的重步兵队伍，以快步前进（即行军，而非冲锋），面对同等规模的弓箭手。弓箭射程约 200 米，快步行军穿越这一距离大约需要 2 分 15 秒（快步每分钟 120 步，每步约 75 厘米）。每名弓手每分钟可以射 6 支箭，因此每名步兵平均要应对约 13.5 支箭。假设箭矢致伤率为 0.5%，那么在行军过程中被箭杀死或致残的概率大约为 6.75%。
而且，这还是在对弓箭手非常有利的假设下：步兵不发起冲锋，没有掩护部队，弓手都能在最大有效射程射击，手臂不疲劳，并且整个过程中都能有效射击（没有反击，没有友军阻挡等）。实际上，我们还应考虑射程对杀伤率的影响：0.5% 的致伤率是基于近距离平射的情况，而最早的射击实际上是远程射击，威力和精度都低得多，因此 6.75% 的致伤率实际上属于最大值。即使如此，这样的理想致伤率也不足以阻止重步兵坚定推进：他们会继续前进，如果弓箭手没有自己的重步兵迎战，很快就会被击退。

Conclusions
One of the challenges in understanding pre-modern warfare is in navigating between the extremes of ‘wonder weapons’ and ‘useless’ weapons. If bows were so powerful that they could mow down heavy infantry or invalidate cavalry, no one would have fought any other way. We know that, of course, because eventually a technology emerges – firearms – which was so lethal that it steadily pushed every other way of fighting off of the battlefield, save for a bit of light cavalry. Bows and crossbows existed for far longer and didn’t have this effect, because they weren’t that powerful: they simply lacked the tremendous lethality of firearms. The very strongest war bows might deliver at most around 130 joules of impact energy, slicing and piercing through a target. By contrast even relatively early (16th century, for instance) muskets could deliver one to two thousand joules of impact energy, with a projectile that didn’t neatly slice or pierce the target (it didn’t need too), but smashed through, shattering bone and shredding issue over a much larger area.

结论
理解前现代战争的一个挑战在于如何在“神兵利器”和“无用武器”的极端之间找到平衡。如果弓箭真的强大到可以轻易碾压重步兵或彻底废掉骑兵，那么显然没人会选择其他作战方式。当然我们知道情况并非如此，因为最终出现了一种新技术——火器，其致命性如此惊人，以至于逐步将几乎所有传统作战方式逐出战场，仅剩少量轻骑兵幸存。弓箭和弩存在的时间远比火器长，但并未产生同样效果，因为它们并没有那么强大：它们缺乏火器那种惊人的杀伤力。最强大的战弓，其冲击能量大约在 130 焦耳左右，可以切割或穿透目标。而相比之下，即便是相对早期的火枪（例如 16 世纪）也能产生一至两千焦耳的冲击能量，其弹丸不需要切割或穿透目标，而是直接粉碎骨骼、撕裂组织。