《那些古怪又让人忧心的问题》第93期:斯巴达勇士(1)
SPARTA
Q. In the movie 300 they shoot arrows up into the sky and they seemingly blot out the sun. Is this possible, and how many arrows would it take?
Q．在电影《斯巴达300勇士》中，斯巴达勇士朝天空中射箭，看上去阳光都被箭给挡住了。那么在现实生活中这种场景是否可能出现？如果可能的话需要用到多少支箭？——Anna Newell
——安娜•纽厄尔
A. IT'S PRETTY HARD TO make this work.
A．要做到这种效果相当困难。Attempt 1
方法一Longbow archers can fire eight to ten arrows per minute. In physics terms, a longbow archer is an arrow generator with a frequency of 150 millihertz.
长弓射手每分钟能够射出8～10支箭。用物理术语来说，一位长弓手就是一个频率为150毫赫兹的发箭机。Each arrow spends only a few seconds in the air. If an arrow's average time over the battlefield is three seconds, then about 50 percent of all archers have arrows in the air at any given time.
每支箭在空中停留的时间只有几秒。如果在战场上平均每支箭滞空时间为3秒的话，那么在任意时刻，仅有一半射手的箭在空中。Each arrow intercepts about 40 cm2 of sunlight. Since archers have arrows in the air only half the time, each blocks an average of 20 cm2 of sunlight.
每支箭都能挡住约40平方厘米的阳光。由于一位射手只有一半的时间箭是在半空中，因而平均每支箭能挡住20平方厘米的阳光。If the archers are packed in rows, with two archers per meter and a row every meter and a half, and the archer battery is 20 rows (30 meters) deep, then for every meter of width . . .
如果射手们站成方阵形状，每一行两人间距半米，两行之间相距1.5米，并且一个射击阵列有20行（宽30米），那么平均每1米的宽度……. . . there will be 18 arrows in the air.
……能有18支箭在空中。18 arrows will block only about 0.1 percent of the Sun from the firing range. We need to improve on this.
从有效射程以外看18支箭只会挡住约0.1％的阳光。同志还需努力！Attempt 2
方法二First, we can pack the archers more tightly. If they stand with the density of a mosh pit crowd,1 we can triple the number of archers per square foot. Sure, it will make firing awkward, but I'm sure they can figure it out.
我们可以让射手们站得更靠近一些。如果他们站得和夜店狂舞区那里一样近，1每平方英尺的人数就可以翻两番。当然，站这么近射起箭来肯定不舒服，但我确定射手们一定会想出解决方法来的。We can expand the depth of the firing column to 60 meters. That gives us a density of 130 archers per meter.
我们可以将射击阵列的宽度增加到60米，这样每米就有130名射手了。How fast can they fire?
他们能射多快？In the extended edition of the 2001 film Lord of the Rings: The Fellowship of the Ring, there's a scene where a group of orcs2 charge at Legolas, and Legolas draws and fires arrows in rapid succession, felling the attackers with one shot each before they reach him.
在2001年电影《指环王：魔戒远征队》加长版中出现了一个场景，其中一队兽人2朝莱戈拉斯猛攻，而莱戈拉斯连续不断地迅速拔箭射击，在兽人冲到他面前之前就一箭一个射倒了这些兽人。The actor playing Legolas, Orlando Bloom, couldn't really fire arrows that quickly. He was actually dry-firing an empty bow; the arrows were added using CGI. Since this fire rate appeared, to the audience, to be impressively fast but not physically implausible, it provides a convenient upper limit for our calculations.
扮演莱戈拉斯的演员奥兰多•布鲁姆在现实生活中没法以这么快的速度射箭，其实在拍摄时他只是假装在拉弓射击，并没有搭上箭，观众们看到的箭其实是后期通过特效加上去的。既然在观众看来，莱戈拉斯的飞快速度还没有到物理上不可能的程度，因此我们就以它为限来进行计算。Let's assume we can train our archers to replicate Legolas's fire rate of seven arrows in eight seconds.
假设我们能训练出许多像莱戈拉斯那样能在8秒内射出7支箭的射手。In that case, our column of archers (firing an impossible 339 arrows per meter) will still block out only 1.56 percent of the sunlight passing through them.
在这种情况下，我们的射击方阵平均每秒能够射出不可思议的339支箭，但即使这样也只能挡住约1.56％的阳光。
