《那些古怪又讓人憂心的問題》第93期:斯巴達勇士(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．在電影《斯巴達300勇士》中，斯巴達勇士朝天空中射箭，看上去陽光都被箭給擋住了。那麼在現實生活中這種場景是否可能出現？如果可能的話需要用到多少支箭？——Anna Newell
——安娜•紐厄爾
A. IT'S PRETTY HARD TO make this work.
A．要做到這種效果相當困難。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.
長弓射手每分鐘能夠射出8～10支箭。用物理術語來說，一位長弓手就是一個頻率爲150毫赫茲的發箭機。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時間只有幾秒。如果在戰場上平均每支箭滯空時間爲3秒的話，那麼在任意時刻，僅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.
每支箭都能擋住約40平方釐米的陽光。由於一位射手只有一半的時間箭是在半空中，因而平均每支箭能擋住20平方釐米的陽光。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 . . .
如果射手們站成方陣形狀，每一行兩人間距半米，兩行之間相距1.5米，並且一個射擊陣列有20行（寬30米），那麼平均每1米的寬度……. . . 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.
從有效射程以外看18支箭只會擋住約0.1％的陽光。同志還需努力！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.
我們可以讓射手們站得更靠近一些。如果他們站得和夜店狂舞區那裏一樣近，1每平方英尺的人數就可以翻兩番。當然，站這麼近射起箭來肯定不舒服，但我確定射手們一定會想出解決方法來的。We can expand the depth of the firing column to 60 meters. That gives us a density of 130 archers per meter.
我們可以將射擊陣列的寬度增加到60米，這樣每米就有130名射手了。How fast can they fire?
他們能射多快？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年電影《指環王：魔戒遠征隊》加長版中出現了一個場景，其中一隊獸人2朝萊戈拉斯猛攻，而萊戈拉斯連續不斷地迅速拔箭射擊，在獸人衝到他面前之前就一箭一個射倒了這些獸人。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.
扮演萊戈拉斯的演員奧蘭多•布魯姆在現實生活中沒法以這麼快的速度射箭，其實在拍攝時他只是假裝在拉弓射擊，並沒有搭上箭，觀衆們看到的箭其實是後期通過特效加上去的。既然在觀衆看來，萊戈拉斯的飛快速度還沒有到物理上不可能的程度，因此我們就以它爲限來進行計算。Let's assume we can train our archers to replicate Legolas's fire rate of seven arrows in eight seconds.
假設我們能訓練出許多像萊戈拉斯那樣能在8秒內射出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.
在這種情況下，我們的射擊方陣平均每秒能夠射出不可思議的339支箭，但即使這樣也只能擋住約1.56％的陽光。
