《那些古怪又讓人憂心的問題》第33期:牛排墜落(1)
STEAK DROP
Q. From what height would you need to drop a steak for it to be cooked when it hit the ground?
Q．從多高處掉下來的牛排才能在掉到地上時正好烤熟？-Alex Lahey
——亞歷克斯•萊希
A. I HOPE YOU LIKE your steaks Pittsburgh Rare. And you may need to defrost it after you pick it up.
A．但願你喜歡匹茲堡生牛排，撿起來之後別忘了解凍哦。Things get really hot when they come back from space. As they enter the atmosphere, the air can't move out of the way fast enough, and gets squished in front of the object-and compressing air heats it up. As a rule of thumb, you start to notice compressive heating above about Mach 2 (which is why the Concorde had heat-resistant material on the leading edge of its wings). When skydiver Felix Baumgartner jumped from 39 kilometers, he hit Mach 1 at around 30 kilometers. This was enough to heat the air by a few degrees, but the air was so far below freezing that it didn't make a difference. (Early in his jump, it was about minus 40 degrees, which is that magical point where you don't have to clarify whether you mean Fahrenheit or Celsius-it's the same in both.) As far as I know, this steak question originally came up in a lengthy 4chan thread, which quickly disintegrated into poorly informed physics tirades intermixed with homophobic slurs. There was no clear conclusion. To try to get a better answer, I decided to run a series of simulations of a steak falling from various heights. An 8-ounce steak is about the size and shape of a hockey puck, so I based my steak's drag coefficients on those given on page 74 of The Physics of Hockey (which author Alain Haché actually measured personally using some lab equipment). A steak isn't a hockey puck, but the precise drag coefficient turned out not to make a big difference in the result. Since answering these questions often includes analyzing unusual objects in extreme physical circumstances, often the only relevant research I can find is US military studies from the Cold War era. (Apparently, the US government was shoveling tons of money at anything even loosely related to weapons research.) To get an idea of how the air would heat the steak, I looked at research papers on the heating of ICBM nose cones as they reenter the atmosphere. Two of the most useful were “Predictions of Aerodynamic Heating on Tactical Missile Domes” and “Calculation of Reentry-Vehicle Temperature History.”
從太空中掉回來的物體會變得非常燙手。當它們進入大氣層時，位於前方的空氣來不及跑開，因而會在物體前方被不斷壓縮，同時溫度也會逐漸升高。一個簡單的經驗法則是，當速度高於2馬赫時，壓縮生熱的效應會逐漸開始明顯起來。（這也是爲什麼協和式飛機在機翼前端有防熱材料）當跳傘運動員菲利克斯•鮑姆加特納從39千米的高空跳下後，他在離地30千米的地方突破了音速。這個速度足以使空氣溫度升高幾攝氏度，但考慮到那個位置的空氣實在是太過寒冷，因而這幾攝氏度的差異可以忽略不計。（在他剛跳下的那段時間裏，空氣的溫度爲零下40度。這個溫度很神奇，因爲零下40℃和零下40℉都是同一溫度。）據我所知，這個牛排問題最初起源於4chan1上的一個長帖，但這個帖子的內容很快就演變成了長篇大論的蹩腳物理以及攻擊同性戀的混雜體，最終也沒有得出一個明確的結論。爲了得到更準確的答案，我決定進行一系列數值計算，模擬牛排從不同高度掉下來的結果。一塊8盎司（約250g）的牛排大小形狀和一個冰球差不多，所以我用《冰球物理學》（這本書的作者阿蘭•阿什用一些實驗室設備親自測量了各種數據）第74頁上的阻力系數來近似牛排的阻力系數。雖然牛排和冰球還是有區別的，但更加精確的阻力系數對最終結果沒有太大的影響。由於回答這些問題經常需要牽涉到分析極端物理條件下的非常規物體，因而相關的資料只能在美國軍方在冷戰期間的研究中找到。（很明顯，美國政府會往任何與武器哪怕只有一點兒聯繫的東西里投入大把的金錢。）爲了瞭解空氣會如何加熱牛排，我閱讀了研究彈道導彈再入大氣層時鼻錐被加熱的論文，其中最有用的兩篇文章是《戰術導彈整流罩氣動加熱的預測》和《再入大氣層載具歷史溫度的計算》。
