What does Spider-Man eat for breakfast?
蜘蛛人要吃什麼當早餐？
作者／洛許(Mark Lorch,英國赫爾大學生物化學系講座教授)
譯／吳京
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| Credit:Krassy Can Do It |
While stuck in a hotel room I got sucked into watching the 2002 Spider-Man movie. And it struck me that Peter Parker must have an enormously high-protein diet to generate all that spider silk he goes through. So being the geek that I am, I wondered what his protein consumption has to be to sustain his villain-beating lifestyle.
I think we can work it out with a bit of school-level physics, maths and some basic biochemistry. We will need to work out the strength of Spider-Man’s silk, calculate how much force Spider-Man would exert on the silk and then figure out how much and what kind of protein will be needed to enable Spider-Man to do his stunts.
Let’s assume Spider-Man produces silk that has the same characteristics as dragline silk produced by the European garden spider Araneus diadematus. That means it ought to have tensile strength – which is the largest stress that a material can withstand before breaking – similar to that of a piano wire.
讓我們假設蜘蛛人的絲和在歐洲很普遍的十字園蛛(Araneus diadematus)所吐出之曳引絲相仿，也就是說絲的張力強度可比擬鋼琴弦，張力強度(tensile strength)是指一個材料在被拉斷前所能承受的最大應力。
A piano wire has the tensile strength of 1.1 billion Pascals. Pascals is a unit of measure for pressure, which is force per unit area.
According to Marvel’s directory, Spider-Man weighs 75kg. Applying Newton’s first law, we can figure out the downward force that Spider-Man exerts. It would be mass times the Earth’s gravitational acceleration, which works out to be about 735 Newtons.
These two values allow us to calculate the cross-sectional area of spider silk by dividing the force exerted by the tensile strength of the silk. Without going into the tiny calculations, it turns out that Spider-Man could hang from the ceiling on silk that is less than 1mm thick.
有了這兩個數字後，我們用向下力道除以絲的張力強度，就可以算出絲的截面積。不用算得太精準，結論是厚度不到1公厘的絲就可讓蜘蛛人吊在天花板上。
From the time of Spidey’s fall, we can calculate that he fell about 240m (wow, that’s one high balcony). Plus, assuming the silk stretches to its maximum, a stopping distance, it will be a fall of about the height of the Eiffel Tower. The impact force on the silk rope as they slow down would be about 35 times their weight.
Which is about six times greater force than when Spidey is just hanging around on the end of his line of silk. But taking into account the length of the fall (240m) and the extra force, he will need 1.3 kg of silk to catch his fall. So I reckon he must have had about 900 eggs for breakfast that morning, just to have enough silk for that one scene. I think Aunt May might have noticed.
當我悶在某間飯店的客房時，2002年版的蜘蛛人電影讓我看到入迷。一個想法閃入腦海：彼得帕克一定得吃極大量的高蛋白質食物才能產出所有被他用掉的蜘蛛絲。身為一個科學宅，我想知道他到底消化了多少蛋白質來維持這種打擊犯罪的生活形態。
I think we can work it out with a bit of school-level physics, maths and some basic biochemistry. We will need to work out the strength of Spider-Man’s silk, calculate how much force Spider-Man would exert on the silk and then figure out how much and what kind of protein will be needed to enable Spider-Man to do his stunts.
我想憑著中學等級的物理、數學及生物化學的基礎知識便可得到解答。我們要求出蜘蛛人的絲有多強韌、計算蜘蛛人會施加多少力量在其絲上，之後就可得知讓他飛簷走壁需要何種蛋白質及其數量。
Let’s assume Spider-Man produces silk that has the same characteristics as dragline silk produced by the European garden spider Araneus diadematus. That means it ought to have tensile strength – which is the largest stress that a material can withstand before breaking – similar to that of a piano wire.
讓我們假設蜘蛛人的絲和在歐洲很普遍的十字園蛛(Araneus diadematus)所吐出之曳引絲相仿，也就是說絲的張力強度可比擬鋼琴弦，張力強度(tensile strength)是指一個材料在被拉斷前所能承受的最大應力。
A piano wire has the tensile strength of 1.1 billion Pascals. Pascals is a unit of measure for pressure, which is force per unit area.
According to Marvel’s directory, Spider-Man weighs 75kg. Applying Newton’s first law, we can figure out the downward force that Spider-Man exerts. It would be mass times the Earth’s gravitational acceleration, which works out to be about 735 Newtons.
These two values allow us to calculate the cross-sectional area of spider silk by dividing the force exerted by the tensile strength of the silk. Without going into the tiny calculations, it turns out that Spider-Man could hang from the ceiling on silk that is less than 1mm thick.
一根鋼琴弦的張力強度為11億帕斯卡，帕斯卡是量測壓力的單位，即每單位面積上的力。
根據漫威字典，蜘蛛人的體重為75公斤，再依牛頓第一運動定律，我們可以計算他所施加的向下力道約為735牛頓，即體質量乘地球的重力加速度所得的質。
有了這兩個數字後，我們用向下力道除以絲的張力強度，就可以算出絲的截面積。不用算得太精準，結論是厚度不到1公厘的絲就可讓蜘蛛人吊在天花板上。
Now we need to figure out how much volume this total silk fibre would represent, if Spider-Man’s pre-lunch world-saving session requires 100m of it. Silk is slight heavier than water, which means that 100m of the wire would weight about 87g.
There is about 6g of protein in an egg. So it looks like Spidey only needs about 15 eggs for breakfast if he plans to use 100m of silk. That’s not too bad.
現在我們要來算算所有絲纖維相當於多少量了，如果蜘蛛人在午餐前這段拯救世界的班表中需要100公尺的絲，而絲稍重於水，可算出100公尺的絲約為87公克。
現在我們要來算算所有絲纖維相當於多少量了，如果蜘蛛人在午餐前這段拯救世界的班表中需要100公尺的絲，而絲稍重於水，可算出100公尺的絲約為87公克。
每顆雞蛋約有6公克的蛋白質，如此看來，如果蜘蛛人打算用100公尺的絲，他只要吃約15顆的雞蛋，這看起來不算太糟。
But spider silk consists predominantly of a protein call fibroin. Proteins are made from different amino acids, and fibroin is about 42% glycine. While egg consists of just 10.7% glycine and serine (I’m counting serine because it can be easily converted to glycine). So really Spidey needs to consume four times more egg protein than the silk protein he plans to use. So actually he needs 60 eggs for his 100m of silk.
但蜘蛛絲的主要成份為一種特定的蛋白質，稱為絲素蛋白(fibroin)。不同蛋白質由不同成份的胺基酸組成，絲素蛋白中約有42%的甘胺酸(glycine)，雞蛋則只含有10.7%的甘胺酸及絲胺酸(serine)(我把絲胺酸納入計算，因為它可以輕易地轉變為甘胺酸)。所以事實上蜘蛛人從雞蛋攝取的蛋白質必須高於造絲所需的四倍以上，如此他實際上要吃60顆雞蛋才能造出100公尺的絲。
But spider silk consists predominantly of a protein call fibroin. Proteins are made from different amino acids, and fibroin is about 42% glycine. While egg consists of just 10.7% glycine and serine (I’m counting serine because it can be easily converted to glycine). So really Spidey needs to consume four times more egg protein than the silk protein he plans to use. So actually he needs 60 eggs for his 100m of silk.
但蜘蛛絲的主要成份為一種特定的蛋白質，稱為絲素蛋白(fibroin)。不同蛋白質由不同成份的胺基酸組成，絲素蛋白中約有42%的甘胺酸(glycine)，雞蛋則只含有10.7%的甘胺酸及絲胺酸(serine)(我把絲胺酸納入計算，因為它可以輕易地轉變為甘胺酸)。所以事實上蜘蛛人從雞蛋攝取的蛋白質必須高於造絲所需的四倍以上，如此他實際上要吃60顆雞蛋才能造出100公尺的絲。
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| 更多蛋，謝謝！ Credit:Tonymadrid Photography |
That’s not really the end of it either. After all what happens if he leaps from a building to save a falling Mary-Jane and deploys his webslingers to save the day, as he does about halfway through the movie.
In the scene, Spidey leaps from the balcony and falls for seven seconds before his silk starts to arrest his fall. He has caught M-J so let’s say their combined weight is 125kg. How much silk is he going to need here?
然而故事還沒結束，畢竟蜘蛛人還要從高樓上跳下去救瑪麗珍並且射出保命蜘蛛網來轉危為安，電影演到一半時他就是這樣幹的。
In the scene, Spidey leaps from the balcony and falls for seven seconds before his silk starts to arrest his fall. He has caught M-J so let’s say their combined weight is 125kg. How much silk is he going to need here?
然而故事還沒結束，畢竟蜘蛛人還要從高樓上跳下去救瑪麗珍並且射出保命蜘蛛網來轉危為安，電影演到一半時他就是這樣幹的。
在那一幕中，蛛仔從陽台躍出，經過7秒後蜘蛛絲才抑止了下墜之勢。他還要抓著一個瑪麗珍，我們就說總重為125公斤好了。光這個動作就要多少蜘蛛絲啊？
From the time of Spidey’s fall, we can calculate that he fell about 240m (wow, that’s one high balcony). Plus, assuming the silk stretches to its maximum, a stopping distance, it will be a fall of about the height of the Eiffel Tower. The impact force on the silk rope as they slow down would be about 35 times their weight.
從蛛仔下墜的時間算來，大約是落下了240公尺(哇！好高的陽台！)。此外，假設蛛絲延伸一段減速停止的距離才來到最大長度，這落下的距離就跟艾菲爾鐵塔一般高了。為了緩衝下墜而施加到絲索上的衝擊力道則大約是35乘與他們的體重。
Which is about six times greater force than when Spidey is just hanging around on the end of his line of silk. But taking into account the length of the fall (240m) and the extra force, he will need 1.3 kg of silk to catch his fall. So I reckon he must have had about 900 eggs for breakfast that morning, just to have enough silk for that one scene. I think Aunt May might have noticed.
這比蛛仔吃飽太閒地懸掛在蜘蛛絲上的力量還要高出6倍(譯註：(35*125)/(9.8*75) ≅6 )。把墜落距離(240公尺)和額外力量一起考量，他需要1.3公斤的絲才能接住這次下墜。所以我估算他那天早餐必須吃上900顆蛋才有足夠的絲完成那一幕。我想梅嬸應該早就注意到了吧！
資料來源(Source of the materials)：
原文於The Conversation網站公開授權轉載
譯文部份屬館主的自我練習，請翻譯的前輩及同好不吝指教。
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