Attempt 3
方法三
Let 8217;s dispense with the bows entirely and give our archers arrow-firing Gatling bows. If they can fire 70 arrows per second, that adds up to 110 square meters of arrows per 100 square meters of battlefield! Perfect.
我们还是完全放弃手动射箭，转而给这些射手每人都配备一把加特林射箭器。如果他们每分钟能射出70支箭，这样每100平方米的战场就能射出截面积110平方米的箭阵。真是完美！
But there 8217;s a problem. Even though the arrows have a total cross-sectional area of 100 meters, some of them shadow each other.
但这里有个问题。虽然所有的箭加在一起截面积有100平方米，但其中有些箭是互相重叠的。
The formula for the fraction of ground coverage by a large number of arrows, some of which overlap each other, is this:
计算一大堆互相重叠的箭覆盖的地面面积百分比的公式为：
With 110 square meters of arrows, you 8217;ll cover only two-thirds of the battlefield. Since our eyes judge brightness on a logarithmic scale, reducing the Sun 8217;s brightness to a third of its normal value will be seen as a slight dimming; certainly not “blotting it out.”
总截面积110平方米的箭只能覆盖三分之二的战场。由于我们的眼睛是以对数形式衡量光的亮度，因而把阳光亮度减弱到三分之一在肉眼看来只是有一点点暗淡，完全达不到“完全遮蔽”的效果。
With an even more unrealistic fire rate, we could make it work. If the guns release 300 arrows per second, they would block out 99 percent of the sunlight reaching the battlefield.
如果我们把已经不切实际的射箭速度进一步提高，最终还是可以达到完全遮蔽的效果。如果加特林射箭器每秒能够射出300支箭，那么它就能阻断战场上空99％的阳光。
But there 8217;s an easier way.
但其实还有更简单的办法。
Attempt 4
方法四
We 8217;ve been making the implicit assumption that the Sun is directly overhead. That 8217;s certainly what the movie shows. But perhaps the famous boast was based on a plan to attack at dawn.
之前我们进行的计算隐含了一个条件，那就是太阳在我们的正上方。在电影中当然是这样，不过也许那句著名的夸口说的是凌晨进攻的计划。
If the Sun were low on the eastern horizon, and the archers were firing north, then the light could have to pass through the entire column of arrows, potentially multiplying the shadow effect a thousandfold.
如果太阳刚从东边的地平线上升起，而射手们向北射箭的话，阳光必须要穿过整个“箭云”才能抵达地面，这样的遮蔽效果会是之前的几千倍。
Of course, the arrows wouldn 8217;t be aimed anywhere near the enemy soldiers. But, to be fair, all they said was that their arrows would blot out the Sun. They never said anything about hitting anyone.
当然了，要是这样射箭的话，就别指望它们落在敌军附近了。可是问题里说的是射出的箭挡住了太阳，他们并没有说要不要击中任何人。
And who knows; maybe, against the right enemy, that 8217;s all they need.
而且谁知道呢，也许面对合适的敌人，只需要挡住阳光就足够了。
1 Rule of thumb: One person per square meter is a light crowd, four people per square meter is a mosh pit.
1． 经验法则：每平方米站1个人算稀疏人群，而每平方米站4个人就跟在夜店狂舞区一样拥挤了。
2 Strictly speaking, they were Uruk-Hai, not typical orcs. The precise nature and origin of the Uruk-Hai is a little tricky. Tolkien suggested that they were created by cross-breeding humans with orcs. However, in an earlier draft, published in The Book of Lost Tales, he instead suggests the Uruks had been born from the “subterranean heats and slimes of the Earth.” Director Peter Jackson, when deciding what to show on-screen in his film adaptation, wisely went with the latter version.
2． 严格来说他们并不是典型的半兽人，而是强兽人。强兽人的准确起源和特性有些难以捉摸。托尔金曾表示他们是人和半兽人杂交而成，但在发布于《失去的传说》上的更早的草稿中，托尔金表示强兽人生于“地球泥沼和地下热量之中”。导演彼得•杰克逊在翻拍时机智地选择了后者作为呈现在银幕上的内容。