科学与数学nasa.gov
火箭方程的暴政（2012）
The Tyranny of the Rocket Equation (2012)
2014 — 2022，它一次次回到首页
黑点是上首页（≥ 50 分）的那次投稿，空心点是没冲上去的投稿，点越大分数越高。
导读
NASA 宇航员 Don Pettit 的科普文章，用齐奥尔科夫斯基火箭方程解释化学火箭为何受限于推进剂质量、能量和结构重量，并推演如果地球直径大 50%，人类可能几乎无法靠火箭进入太空。文章把航天工程的极限约束讲得直观，也延伸到行星引力井对文明太空能力的限制。
为什么经久不衰：它用一条简单公式揭示了航天被质量与能量约束的残酷上限，解释了为何化学火箭几十年改进有限，也让人重新思考地外文明与引力井。
HN 评论精选
化学燃料已接近极限，核动力曾被认真考虑但风险大，其他发射方式收益有限。
这早就为人所知。这正是火箭和 40 年前相比没有大幅进步的原因：化学燃料几乎已到极限，用化学燃料进行太空旅行只是勉强可行。20 世纪 60 年代，人们普遍认为太空飞行需要核动力；参与其中的人都知道火箭方程。阿波罗原计划包含核上面级，NERVA 发动机已建造并测试，卡纳维拉尔角还计划建核装配大楼。但因为目标太狭窄（“人、月球、十年”），最终选择的是用一座 50 层楼大小的一次性火箭把房车大小的载荷送上月球。核火箭坠毁会造成放射性污染，规模不及切尔诺贝利或福岛，但至少像一个小镇；从偏远岛屿发射会有帮助。人们尝试或提出过各种绕开火箭方程的方案：早期试过气球发射，维珍等仍用飞机发射，帮助有限。大气层内吸气、出大气层后转火箭模式的飞行器被多次提出，但兼顾火箭与飞机很难且增重很多；作为飞机必须达到高超音速才有意义，而造高超音速飞机非常难，至今只有少数小型验证机做到。
Animats查看英文原文
Right. This has been known for a long time. It's why rockets aren't much better than they were 40 years ago. Chemical fuels are as good as they can get. Space travel with chemical fuels is just barely feasible. In the 1960s, it was assumed that nuclear power would be necessary for space flight. Everybody involved knew the rocket equation. The original plan for Apollo included a nuclear upper stage. The engine (NERVA) was built and tested. A Nuclear Assembly Building at Canaveral was planned. But, because the goal was so narrow ("man, moon, decade"), the solution chosen was a disposable rocket the size of a 50-story building to send an RV-sized payload to the moon. The crash of a nuclear rocket would produce a radioactive mess. Not Chernobyl or Fukishima sized, but at least small-town sized. Launching from an isolated island would help. Various schemes have been tried or proposed to beat the rocket equation. Launching from a balloon was tried early. Launching from an aircraft is still used by Virgin Aerospace. It helps a little. A space vehicle that's an air-breather while it's in the atmosphere and transitions to rocket mode once out has been proposed many times, but making something that's both a rocket and an airplane is hard and adds a lot of weight. As an airplane, it has to go hypersonic to get up enough speed that it's worth doing this. Building a hypersonic aircraft is very hard; so far, only a few small demo craft have done it. The National Space Plane (hypersonic single-stage-to-orbit) was proposed in the 1980s. Ben Rich, head of the Lockheed Skunk Works and the designer of the SR-71's propulsion system, declined to let Lockheed bid on it. (His comment: "We used titanium (on the SR-71). You know anything stronger?") Remember, it has to be strong at a few thousand degrees. The same problems apply to launch track systems. Going hypersonic near the ground is possible; the Holloman AFB test track, 50,000 feet of very straight railroad track, has been used to reach Mach 8.6. The required acceleration is about 14g. Far too much for humans. The "space elevator" requires not only unreasonable strong materials but the ability to put so much mass in space that you wouldn't need a space elevator if you had that kind of launch capacity.
行星大小可能决定文明能否进入太空；航天是极限工程。
“如果我们的行星直径大 50%，我们将无法进入太空，至少不能用火箭运输。”我觉得从德雷克方程的角度看这很引人深思。据我所知，我们发现的类地行星似乎比地球大一些。也许如果那里有文明，他们会被困在一个几乎无法逃离的星球上；如果连发射哈勃望远镜都很难，他们也许就不会费心去做。另一点是工程：有个说法是，只有工程师才能做出刚好满足需求的东西。很多人不怎么做计算就盖房子，爱好者没有学位也能造车；这正是航天工程令人惊叹的地方。
lordnacho查看英文原文
"If our planet was 50% larger in diameter, we would not be able to venture into space, at least using rockets for transport." I thought this was quite though-provoking from a Drake Equation standpoint. From what I've gleaned, the earth-like planets we know of seem to be a big bigger than Earth. Perhaps if there's civilization out there, they are hampered by the misfortune of being on a planet that's practically impossible to escape from. If they find it hard to put up a Hubble Telescope, perhaps they'll just not be as likely to bother. My other remark is to the engineering. There's a quip that you have to be an engineer to make something that only just satisfies the requirements. Plenty of people build houses without much in the way of calculation. Even cars can be built by enthusiasts without degrees. This is what makes the space stuff such amazing engineering.
航天飞机外储箱是极限轻量化与储运工程的典范，难度堪比金字塔。
普通易拉罐按质量算 94% 是饮料、6% 是罐体；相比之下，航天飞机外储箱是 96% 推进剂、4% 结构。外储箱内部大到能办谷仓舞会，装着比绝对零度高 20 度的低温液体，加压到 60 磅/平方英寸（对这么大罐体是巨大储能），还能承受 3g 并以每秒 1.5 吨抽送推进剂。这种工程知识之惊人，堪比当年建金字塔。
edraferi查看英文原文
The common soda can, a marvel of mass production, is 94% soda and 6% can by mass. Compare that to the external tank for the Space Shuttle at 96% propellant and thus, 4% structure. The external tank, big enough inside to hold a barn dance, contains cryogenic fluids at 20 degrees above absolute zero (0 Kelvin), pressurized to 60 pounds per square inch, (for a tank this size, such pressure represents a huge amount of stored energy) and can withstand 3gs while pumping out propellant at 1.5 metric tons per second. The level of engineering knowledge behind such a device in our time is every bit as amazing and cutting-edge as the construction of the pyramids was for their time. That's awesome, I had no idea.
文章把动量与能量混为一谈不严谨；ΔV 与奥伯特效应说明速度线性、能量平方的差异很重要。
文章说这些变量“可以表述为能量”，这是错误的，而且影响重大。能量和动量并不相同：动量随速度线性增长，而能量随速度平方增长。一个能体现差异的例子是奥伯特效应：ΔV 衡量的是速度而非能量，这一点很关键。奥伯特效应说，航天器在轨道最低点、速度最快时点火最节能；更准确地说，反作用发动机在高速时产生的机械能变化大于低速时。加 1 m/s 总是需要相同的动量变化，但你速度越快，动能增加越多：2 公斤物体从 0 到 1 m/s 增加 1 焦耳，从 1000 到 1001 m/s 增加 2001 焦耳。
rocqua查看英文原文
> Although a momentum balance, these variables can be cast as energies. They are the energy expenditure against gravity (often called delta V or the change in rocket velocity), the energy available in your rocket propellant (often called exhaust velocity or specific impulse), and the propellant mass fraction (how much propellant you need compared to the total rocket mass). This is false, and in a meaningful way. Energy and momentum are not the same. Momentum scales linearly with speed, whilst momentum scales quadratically. One case where this difference matters a lot is the Oberth effect, where the fact that Delta V is a measure of speed rather than energy is of key importance. The Oberth effect states: "the most energy-efficient method for a spacecraft to burn its fuel is at the lowest possible orbital periapsis". Or, more accurately "the use of a reaction engine at higher speeds generates a greater change in mechanical energy than its use at lower speeds". It just turns happens to be that, in orbit, you are going fastest at the lowest point. This effect is a direct result of the scaling differences. Adding 1m/s will always require the same change in momentum, but the faster you are going, the more it will increase your kinetic energy. For a 2kg object, going from 0m/s to 1m/s increases kinetic energy by 1 joules. Going from 1000m/s to 1001m/s increases kinetic energy by 2001 joules. It is key here that, when expending reaction mass at a given exhaust velocity, it will always result in the same change in momentum, whilst resulting in a different change in kinetic energy. Delta-V is just the total speed change that can be achieved by all momentum generated through reaction mass. The rocket equation is about converting this momentum into a speed by compensating for the fact that a rocket gets lighter as it expends reaction mass, to get to Delta-V. If Delta V was a measure of energy, then it shouldn't matter where you use your delta V, you always get the same kinetic energy back. Luckily Delta V is a measure of momentum, which allows us to exploit the Oberth effect for more efficient orbital changes. As for exhaust velocity, _if_ your fuel is your energy source, the exhaust velocity and the energy density are indeed related. But consider an ion engine, where the reaction mass is just mass, and the energy comes from solar panels (or another source of energy).
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