STEAK DROP
牛排坠落
Q. From what height would you need to drop a steak for it to be cooked when it hit the ground?
Q．从多高处掉下来的牛排才能在掉到地上时正好烤熟？
-Alex Lahey
——亚历克斯•莱希
A. I HOPE YOU LIKE your steaks Pittsburgh Rare. And you may need to defrost it after you pick it up.
A．但愿你喜欢匹兹堡生牛排，捡起来之后别忘了解冻哦。
Things get really hot when they come back from space. As they enter the atmosphere, the air can 8217;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 8217;t make a difference. (Early in his jump, it was about minus 40 degrees, which is that magical point where you don 8217;t have to clarify whether you mean Fahrenheit or Celsius-it 8217;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 8217;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 8217;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.”
从太空中掉回来的物体会变得非常烫手。当它们进入大气层时，位于前方的空气来不及跑开，因而会在物体前方被不断压缩，同时温度也会逐渐升高。一个简单的经验法则是，当速度高于2马赫时，压缩生热的效应会逐渐开始明显起来。（这也是为什么协和式飞机在机翼前端有防热材料）当跳伞运动员菲利克斯•鲍姆加特纳从39千米的高空跳下后，他在离地30千米的地方突破了音速。这个速度足以使空气温度升高几摄氏度，但考虑到那个位置的空气实在是太过寒冷，因而这几摄氏度的差异可以忽略不计。（在他刚跳下的那段时间里，空气的温度为零下40度。这个温度很神奇，因为零下40℃和零下40℉都是同一温度。）据我所知，这个牛排问题最初起源于4chan1上的一个长帖，但这个帖子的内容很快就演变成了长篇大论的蹩脚物理以及攻击同性恋的混杂体，最终也没有得出一个明确的结论。为了得到更准确的答案，我决定进行一系列数值计算，模拟牛排从不同高度掉下来的结果。一块8盎司（约250g）的牛排大小形状和一个冰球差不多，所以我用《冰球物理学》（这本书的作者阿兰•阿什用一些实验室设备亲自测量了各种数据）第74页上的阻力系数来近似牛排的阻力系数。虽然牛排和冰球还是有区别的，但更加精确的阻力系数对最终结果没有太大的影响。由于回答这些问题经常需要牵涉到分析极端物理条件下的非常规物体，因而相关的资料只能在美国军方在冷战期间的研究中找到。（很明显，美国政府会往任何与武器哪怕只有一点儿联系的东西里投入大把的金钱。）为了了解空气会如何加热牛排，我阅读了研究弹道导弹再入大气层时鼻锥被加热的论文，其中最有用的两篇文章是《战术导弹整流罩气动加热的预测》和《再入大气层载具历史温度的计算》。