K^2

Enthalpy of Hydrazine is 50.63kJ/mol at molar mass of 32g/mol. So I'm getting ~1.5MJ/kg. And yeah, kerosene is about 46MJ/kg, so it's actually close to 30x difference. However, a lot of it is due to oxidizer coming from air. The stoichiometric ratio of kerosene to pure oxygen is about 1:3.276. So the net specific energy of kerlox is only about 11mJ/kg, and that's "only" 6-7 times better than Hydrazine. The reason for the difference is because you're using Hydrazine as monoprop. So all you get out of it is enthalpy of the fuel, with products being N2 and H2 gasses, which have enthalpy of zero by definition. On the other hand, were you to burn the hydrogen, the enthalpy of water vapor is -241.8kJ/kg, and you'd get two moles of that for every mole of hdyrazine. This is why anything with hydrogen in it makes for such a fantastic bipropellant fuel. If you were to burn hydrazine with oxygen, the net specific energy is going to be 8.3MJ/kg, and that's only 20% less than kerlox. But yeah, monoprops are pretty pitiful in their performance compared to bipropellant fuels.

Monoprop is definitely worse. But why are you using that, and not fuel/ox mix?

While sitting on the ground, a Cessna 150/152 will have about 15kN at effective ISP of about 20,000s. This will vary a bit with the engine, but it's in the ballpark. However, it's not going to be able to get to anything close to mach 0.4. Even a variable pitch prop will lose thrust and ISP rapidly as it picks up the speed. I would expect about half the thrust and ISP by the time a variable pitch prop gets up to these speeds, assuming the whole thing is designed to operate like that in the first place. A fixed pitch prop will be just chopping air by about mach 0.2. Turboprops are designed to operate into transonic regions, but even their ISP will drop to something in the 5,000-6,000 range by that point. So if you want to go for something almost ridiculously Kerbal, I'd go with 20,000s at mach 0, 10,000s at mach 0.5, 5,000s at mach 1, and 0s at mach 1.5. Thrust should scale the same, keeping fuel consumption constant. You can add second scaling on altitude, which will not impact the ISP, but will scale thrust proportionally to air density.

That's a warning statement in and of itself.

Not if you heat it to supercritical temperature. At that point, as the supercritical steam expands, and becomes sub-critical steam at some point, it remains above boiling point, so it exits as 100% steam. The effective ISP of a steam rocket is still surprisingly not bad. Under ideal conditions, starting from critical point, you can get about 30s out of it, which is about the same as black powder. The downside is that you need a tank that can hold a little over 22MPa, or just under 220 bar, which means you'll have a fairly heavy tank. For reference, a quick look up of steel diving cylinders, aluminum will simply melt, for 232 bar gives 15L and 16.5kg. At critical point, this will hold about 4.8kg of water. And that will get an empty tank up to over 170mph, which isn't bad, even if it's a far cry from 500mph that this guy is aiming for. Earth is more spherical than a billiards ball. Significantly smoother as well. When people point out that it's, in fact, a geoid, they are being unnecessarily pedantic. Deviation of Earth from perfect sphere is less than 1% between polar and equatorial radius.

Anything in science is subject to critique, but I should point out that theory that yields EFEs is the most robust, most scrutinized, and most well tested, both numerically and quantitatively, theory that we have for anything. We have tests of General Relativity and Quantum Electrodynamics to 12 digits, and both of these arise from the same underlying principles. I also would like to point out that while gravity is not really a force in Classical sense, neither is electrostatic force. Both of these are gauge forces of symmetry groups. The difference is that gravity is a gauge force of an extrinsic degree of freedom, and all other forces are due to intrinsic DoF symmetries. This means that gravity can be viewed as a fictitious, or inertial force of the frame of reference, with no such analogue existing for intrinsic DoFs. Strength of gravity in early history of the universe, and we're talking tiniest fractions of a second here, is in the fact that gravity is highly non-linear, and density of the early universe was rather high. And while we have no closed form expression for Quantum Gravity, beyond being able to write down the Lagrangian, which causes the worst kind of divergences, we do have effective field theories that describe it adequately on all length scales significantly above Plank's length, and all of these are consistent with our expectations of early universe expansion. Dark energy and dark matter... *sigh* Let me just say that it's much easier to believe that there are yet-undiscovered matter fields responsible for that, be they WIMPs or something else entirely, than to think that the theory itself is fundamentally broken. The later is, of course, a possibility, and a number of teams are probing various ways in which it can be wrong, but nobody seriously expects a discovery more shattering than, "Oh, looks like there is another degree of freedom that we haven't realized existed." A more interesting question is why the fundamental symmetries exist. But once we agree that they do, Lagrangian we have in Standard Model is the only possible one, and all of physics neatly follows as a matter of rigorous mathematical theorem. So the only possibilities are that the fundamental symmetries are broken in ways we haven't detected yet, that there are more symmetries we haven't discovered yet, or that we got all of the physics right, and the rest is just math. We have really good scientists looking at all 3 possibilities.

No. You need to melt salt for it to undergo electrolysis. That is done, and is one of the ways of acquiring metallic sodium, but you'll have to heat salt to about 800°C for it to melt. In solid form, salt is an excellent insulator and will require voltages far greater than these available in the outlet to cause a breakdown across any significant distance, and even then, only a narrow ion channel will be formed. The other problem is that electrolysis, if that's your goal, requires DC current. What you get out of an outlet is AC. So you'll need a transformer and a rectifier bridge. If you apply an AC voltage to molten salt, current will flow, but no net production of sodium or chlorine will follow. P.S. NOTE: Chlorine gas is extremely corrosive and toxic. I'm realizing that with sufficient motivation, it's easy enough to heat salt to a melting point, and I should put in a warning that salt electrolysis should not be carried out without a fume hood and proper training in operating one. Id est, don't do this at home, for crying out loud.

No, that's not true as a general statement. A sub-critical flow will speed up to compensate, resulting in almost exactly the same mass flow rate. That's the whole point of having a throat in the nozzle in the first place. Only once you've reached the critical speed does reducing throat size further will start reducing the mass flow rate.

That's really not how hydrodynamics of a nozzle works. Reducing the throat actually speeds up the flow, keeping mass flow rate constant. This will go on until you hit the critical speed (AKA speed of sound) and only at that point you'll start actually reducing the flow rate. But it also happens to be the point where you can start expanding the nozzle to get more energy out of the fluid. As the result, the cross-section of the nozzle is not designed for a specific flow rate. It's the other way around. The cross-section of the throat is completely determined by the diameter of the combustion chamber, chamber pressure, and chamber temperature. If you want more flow, you have to either increase temperature or size of the combustion chamber, and resulting throttle diameter is something you just compute from a formula at that point.

Um... Maybe not on Proton. They don't have the best flight record.

One of the simplest schemes for course corrections in real control loops is known as PID controller. The 'P' and 'D' portions of the acronym are effectively the to-course and on-course corrections respectively. The difference is that they are computed continuously, so that you never switch from one to the other. The 'I' is the integral portion which corrects for any continuous action trying to move you off course. Such as, if there is a constant current trying to carry you off course. It's a bit like having an experience helmsman who doesn't take the ship fully on-course to counter that current and not require another to-course correction later. So while computers let us do all of this with more precision and more frequent updates, the basic ideas haven't changed much.

While I agree that this should be the base assumption for any pair of sunglasses, this statement is not technically true. Glass, real glass, is an excellent filter of the UV rays. This is why we've had such a thing as sunglasses long before we had fancy UV-blocking polymer coatings. And if you happen to have a pair of sunglasses made with thick, heavy glass lenses, they will give you significant protection from Sun's UV rays. Sun happens to be bright enough that even with perfect UV filter, it will physically burn your retina, because it's exactly like putting a magnifying glass next to a sheet of paper. But amount of time it takes to cause permanent damage with and without UV filtering is substantial. This by no means goes into category of, "Go ahead and look." Because it's still horrible for your eyes, and because you can't be certain what your shades are made out of despite what it says on the label, and you should never look at the sun through the shades. But if we are talking about academic truths, some glasses do make it less harmful.

Of course!

I'm in the region that's going to get 75% cover. Was hoping to drive out to Oregon to be within totality, but my health betrayed me. So I'm planning to build a simple camera obscura today to watch the Sun safely as it gets partially blocked by the Moon. As a public service reminder, do not look directly at the sun. Unfortunately, partially obstructed disk isn't as painful to look at, but just as dangerous. Watching for 30 seconds can leave you blind, and even shorter exposure can lead to irreversible eye damage. Regular sun glasses will not protect your eyes sufficiently. Most will not block enough UV to completely protect you.

The gravity turn begins almost immediately. Although, a big part of it is to get the rocket down-range early in case of an accident. All else being equal, better if debris fall into the ocean/desert than on the launch pad. But it also works out from optimization that it gives you no advantage to ascent directly up even early on. You always want at least a little bit of an angle. In general, ascent profile can vary quite a bit between different rockets. Your main criteria are aerodynamic heating, dynamic pressure, and fuel use. On one hand, you want to be out of the atmo as quickly as possible, on another, you don't want to be moving too fast. And the sweet spot will never be exactly the same for two designs.

Model rocket engines aren't nearly consistent enough for a guided landing. Take it from somebody who've spent a lot of time trying to build a multi-engine model rocket. Getting it to fly straight was a task I eventually gave up on. There is just too much variation in thrust profile from one motor to the next, even in the same batch. Any home-built solid motor won't do any better. You have to build a hybrid with very sophisticated control system to even have a chance. So lets see. You need to understand how a hybrid motor operates, including the relationships between pressure, oxidizer flow rate, fuel burn rate, and thrust. All of these things mutually influence each other, and all you really get the control over is oxy flow. You don't have to worry about complex nozzle, so you're off the hook on fluid dynamics, but you still need to understand combustion, thermodynamics, and non-ideal gas laws at rocket science levels. Now, if you manage to not mess up the engineering part of it, we're next moving into building the control system. Throttling a real rocket is nothing like throttling one in KSP. The delay between change in valve position and thrust output is significant. Meanwhile, you have multiple sensors with very noisy input. So we get into control theory and filters here. There are fairly standard solutions that ought to work here, like PID and Kalman Filters. But at a minimum, you need to know how to implement them on your hardware of choice. I would recommend starting much, much simpler. If you want to build a self-landing rocket, try building one in KSP first. All of the parts necessary to build a Falcon-like booster core in KSP are stock. On top of it, install kOS mod and write a script from scratch that lands the rocket safely at predetermined location. Make sure it can do so even if you vary the initial payload and ascent trajectory. Once you have that done, you'll know that you can at least handle the control portion in near-realistic scenarios. You still need to adjust for delays and noise in the real rocket, but that's definitely a doable task if you understand how to make automated landing in KSP. If you get that far, you can start looking at what it'd take in terms of an engine build.

There will be no fish on Titan. The available energy flux is nowhere enough for that level of competition. We're talking colonies of very slow, very simple bacteria in the best case scenario. I still think that makes Titan the most important exploration target in the Solar System. A place where life is definitely possible, as far as we know, and where if we find it, it would confirm two distinct origins of life forms in a single star system. And if we find nothing interesting there at all, it will help us better define our understanding of what is and is not habitable.

That's not true. Not even all elementary bosons are massless, and none of the fermions are. More than 99% of the mass of the matter is dynamic, as you describe, but there is still some amount of inherent rest mass associated with individual fields. Also it's a bit more complicated than "relativistic mass from velocities," since a stationary electron still has a very high self-energy compared to the bare mass, but that's getting into details of Quantum Field Theory.

If only CO2 was just a little more soluble.... A bottle rocket with constant 5 bar would have ISP of up to 100s. That's seriously not bad for something you can build at home. Unfortunately, not enough gas dissolves in water at 5 bar to sustain the pressure, not to mention all the gas you'd be losing in "exhaust". So if you wanted to build a good bottle rocket, you still want to fill it with air and water, with the air that's already there doing most of the work. But carbonation would improve the efficiency of a bottle rocket by a notable margin. If anybody wants to try a menthos/cola assisted bottle rocket and compare it to plain air/water, I'd be curious to see the results.

Conservation of momentum is a direct consequence of relativity. The details vary depending on which kind of relativity we are talking about. In Special Relativity and Galilean (Classical) Relativity there is a global translational symmetry, which leads to total momentum being a conserved quantity per Noether's Theorem. In General Relativity, there is a local Poincare Symmetry, which leads to a conserved current which momentum factors into. So it's entirely valid to say that reactionless drive violates Special/General Relativity. That is where relevant conservation laws come from. But yeah. Electromagnetic radiation, i.e. photons, has momentum. So all relevant quantities are conserved in a photon drive/rocket. You just need an obscene amount of power to get any useful thrust, and you still get a finite ISP, because energy has mass too.

I've been kind of wanting to write a generic optimizer that takes a file containing any KSP rocket, makes an educated guess on when to trigger stages, and computes an optimal ascent profile for it. It wouldn't shave off much, but custom profile will always be better than generic. Unfortunately, this involves considerable amount of work which I don't have time for.

This formula gives losses to drag and gravity during optimal vertical ascent to escape velocity for old KSP aerodynamics. It was purely an observation that it tends to give a correct ballpark estimate for losses during a normal ascent to orbit. Since they changed the aerodynamics, this formula is almost useless. You could use it as a very generous upper bound, but in practice, your losses will be a lot smaller. Likewise, terminal velocity used to be really easy to calculate with the old system. Now, it will be very different for different rockets, so it's almost not worth bothering with. Basically, with new aerodynamics you have two options. 1) Proper simulation, integrating all relevant forces over particular ascent profile. 2) Just winging it.

Sort of. AFAIK, the closest people got is taking blood, centrifuging it to separate out the plasma, then introduce artificial red blood cells. I don't know if it's done as a procedure, but we have this capability. This is rarely necessary though. There are few cases where you can't get the right blood type these days. The one case where incompatible blood types can be a very serious issue is in mother/fetus incompatibility. It's rare that it causes issues, but when it does, they can kill both mother and child. And in this particular case, in vitro fertilization with gene therapy can solve the problem, making child's blood compatible with mother's. It is currently illegal almost everywhere, but hopefully, we'll start doing that in the near future.

The only advantage of this method is the fact that it keeps track of the cross-terms for you and, if you consider it an advantage, the fact that you don't need to remember multiplication table. Once you go to numbers with larger digits, however, the counting and larger carries make it completely impractical. That's why we have column multiplication in the first place.

Sure. But the concept isn't terrible. With casing and proper nosle, a playdoh rocket is completely doable. Of course, it is far from ideal due to low melting point, but for short burn time it should hold shape well enough. For cheap home built engine, plexiglas (acrylic) works impressively well. It has enough strength to forego casing. You do still need a nosle, though. Can't beat carbon for that. @munlander1 Yeah, hybrid motor.