This isn’t where the community is supposed to have ended up. If rationality is systematized winning, then the community has failed to be rational.
Great post, and timely, for me personally. I found myself having similar thoughts recently, and this was a large part of why I recently decided to start engaging with the community more (so apologies for coming on strong in my first comment, while likely lacking good norms).
Some questions I’m trying to answer, and this post certainly helps a bit:
Is there general consensus on the “goals” of the rationalist community? I feel like there implicitly is something like “learn and practice rationality as a human” and “debate and engage well to co-develop valuable ideas”.
Would a goal more like “helping raise the overall sanity waterline” ultimately be a more useful, and successful “purpose” for this community? I potentially think so. Among other reasons, as bc4026bd4aaa5b7fe points out, there are a number of forces that trend this community towards being insular, and an explicit goal against that tendency would be useful.
Fun nerd snipe! I gave it a quick go and was mostly able to deconfuse myself, though I’m still unsure of the specifics. I would still love to hear an expert take.
First, what exactly is the confusion?
For an LOX/LH2 rocket, the most energy efficient fuel ratio is stoichiometric, at 8:1 by mass. However, real rockets apparently use ratios with an excess of hydrogen to boost Isp[1] -- somewhere around 4:1[2] seems to provide the best overall performance. This is confusing, as my intuition is telling me: for the same mass of propellant, a non-stoichiometric fuel ratio is less energetic. Less energy being put into a gas with more mols should mean lower-enough temperatures that the exhaust velocity should be also be lower, thus lower thrust and Isp.
So, where is my intuition wrong?
The total fuel energy per unit mass is indeed lower, nothing tricky going on there. There’s less loss than I expected though. Moving from an 8:1 → 4:1 ratio only results in a theoretical 10% energy loss[3], but an 80% increase in products (by mol).
However, assuming lower energy implies lower temperatures was at least partially wrong. Given a large enough difference in specific heat, less energy could result in a higher temperature. In our case though, the excess hydrogen actually increases the heat capacity of the product, meaning a stoichiometric ratio will always produce the higher temperature[4].
But as it turns out, a stoichiometric ratio of LOX/LH2 burns so hot that a portion of the H2O dissociates into various species, significantly reducing efficiency. A naive calculation of the stoichiometric flame temperature is around 5,800K, vs ~3,700K when taking into account these details[5]. Additionally, this inefficiency drops off quickly as temperatures lower, meaning a 4:1 ratio is much more efficient and can generate temperatures over 3,000K.
This seems to be the primary mechanism behind the improved Isp: a 4:1 fuel ratio is able to generate combustion temperatures close enough to the stoichiometric ratio in a gas with a higher enough heat capacity to generate a higher exhaust velocity. And indeed, plugging in rough numbers to the exhaust velocity equation[6], this bears out.
The differences in molecular weight and heat capacities also contribute to how efficiently a real rocket nozzle can convert the heat energy into kinetic energy, which is what the other terms from the exhaust velocity help correct for. But as far as I can tell, this is not the dominant effect and actually reduces exhaust velocity for the 4:1 mixture (though I’m very uncertain about this).
The internet is full of 1) poor, boldly incorrect and angry explainers on this topic, and 2) and incredibly high-quality rocket science resources and tools (this was some of the most disconsonant non-CW discourse I’ve had to wade through). With all the great resources that do exist though, I was surprised I couldn’t find any existing intuitive explanations! I seemed to find either muddled thinking around this specific example, or clear thinking about the math in abstract.
… or who knows, maybe my reading comprehension is just poor!
Intense heat and the dangers of un-reacted, highly oxidizing O2 in the exhaust also motivates excess hydrogen ratios.
The Space Shuttle Main Engine used a 6.03:1 ratio, in part because a 4:1 ratio would require a much, much larger LH2 tank.
20H2 + 10O2 → 20H2O: ΔH ~= −5716kJ (vs) 36H2 + 9O2 → 18H2O + 18H2: ΔH ~= −5144.4kJ
For the fuel rich mixture, if we were somehow able to only heat the water product, the temperature would equal the stoichiometric flame temp. Then when considering the excess H2 temperatures would be necessarily lower. Charts showing showing the flame temp of various fuel ratios support this: http://www.braeunig.us/space/comb-OH.htm
See the SSME example here: https://www.nrc.gov/docs/ML1310/ML13109A563.pdf Ironically, they incorrectly use a stoichiometric ratio in their calculations. But as they show, the reaction inefficiencies explain the vast majority of the temperature discrepancy.
Equation 12: http://www.nakka-rocketry.net/th_nozz.html The rough numbers I got where 4,600m/s for 4:1 and 3,800m/s for 8:1