K^2

You don't get settling with power, because you need power for that, but you always have a vortex ring. When autorotating, it eats into your driven region. If you try to offset that with the collective, you stall your rotor. So your sink rate is going to be significantly higher if you don't have any horizontal motion.

No, you can't. You are trying to invent a perpetual motion device. Energy has to come from somewhere.

It depends a lot on the projection, but the picture you show is based on equirectangular projection, which makes the most sense for this sort of application. For an equirectangular projection, call the horizontal position (longitude) Æand vertical position (latitude) θ. (So we are looking to plot function θ(Æ).) For a circular orbit with inclination α, where α = 0 corresponds to equatorial orbit, the latitude is given by the function: θ(Æ) = sin-1(sin(Æ- Æ0) sin(α) / Sqrt(sin²(Æ- Æ0) + cos²(Æ- Æ0) cos²(α)) ) Where Æ0 is the latitude of the ascending node. For non-circular orbits, the formula will be quite a bit more complex. Edit: There, that should work. Though, it does not account for planet's rotation. If you want to throw that in, you'll need to figure out orbital period and adjust Æaccordingly.

No, you actually get different phase following different trajectories, and these add up either constructively or destructively. A much more familiar example is propagation of light. You can think of light as being absorbed and re-emitted as a spherical wave along each point in space. This is absolutely equivalent to light taking every possible path. But because the electric field in the source is oscillating, the strength and direction of electric field contribution from a particular path will depend on the path. At a given random point, the contributions from all possible paths are most likely to be random, and all of the contributions are going to cancel out. In contrast, there are special paths along which the phases match almost perfectly, so you could detect light there. Specifically, the phase depends on the length of time it took like to follow a path. If we consider the "shortest" path between two points, calculus of variations tells us that any tiny deviation from the path will not change its length. That means all of the paths in the neighborhood will have matching phases, allowing constructive interference. That means that in vacuum, light appears to propagate in the straight line. If you throw in some obstacles, or have materials with different optical densities, you end up with more interesting trajectories.

That's really the best way to think about it. Gravitational potential energy is going to contribute to free energy, so while clumping together around a planet reduces system's entropy, thereby increasing free energy, the reduction of gravitational potential energy offsets it. But only to a point. Which is why atmosphere isn't at the bottom of the oceans. The only draw back is that this requires basic understanding of entropy and free energy, which aren't the most intuitive topics.

These kind of go together. What I described is a 1-particle exchange. Two particles pass each other, one of them emits a photon/gluon/graviton, the other absorbs it, and they part ways. Again, which does emitting, and which does absorbing doesn't matter. What matters is that one particle got exchanged. But that's not what really happens. Or more specifically, that's not all that happens. There can be exchanges of 2, 3, 4, and any number of force-carrying particles. And they need not be absorbed in the same order that they are emitted. Worse yet, there can be particle-antiparticle pairs that form from vacuum, absorb one of these force-carrying particles, and then emit another one. There is an infinite number of categories of infinite number of possibilities to how two particles can exchange energy and momentum. And they all take place. Lets forget about interaction for a moment. Picture just one particle propagating through space. Since this is a quantum particle, it will have uncertainty in momentum and position. And so you can describe propagation of the particle as probability amplitude that changes in time. But alternatively, you can describe it as particle with precise location and precise momentum following one of precise trajectories. What you are uncertain of is which trajectory it follows. So instead of looking at it as particle being in many places at once, you look at it as particle following many paths at once. This is the Path Integral Formulation of quantum mechanics. While it tends to be fairly impractical in classical QM, it turns out to be indispensable in RQFT. Part of the reason is that it lets you describe interactions in terms of Lagrangian directly, and that looks after all the symmetries out of the box. Since all interactions are understood to be consequences of local symmetries, this is clearly useful. Same idea applies to many-particle systems. Not only can particles take all possible paths, but the interaction can follow all possible combinations of particles being emitted and absorbed. The main requirement is that all conserved quantities are conserved. Momentum is one of these. So it's often useful to go from coordinate representation of the dynamics to a momentum representation. Mathematically, what that means is that we take Fourier Transform of the Green's Functions, so that they become functions of momentum instead of functions of coordinate. As a result, each particle path we consider has a very specific momentum associated with it. And for every possible trajectory of all the particles, the momentum is conserved. So I can still carry out all of the operations in the previous post as if we are dealing with classical particles that have definite momentum.

Casimir Effect. Just because you are completely ignorant of the underlying theory, doesn't mean everyone else is equally ignorant.

You are confusing several things. "Jupiter" estimate comes from a modified metric, so it's already not strictly speaking an Alcubierre Drive. And Dr. White's estimate is 700kg. The only "football" reference has been made to the shape of the craft.

We don't have stations with centrifugal gravity, either. Doesn't mean that asking "what happens if I throw a ball on one," is a science fiction question, or something we can only guess on. We know how physics for a space station works. We just can't afford to build one right now. We also know how physics for AD works. There just isn't enough energy in the universe to build one. There are other warp drive configurations that we might, eventually, build. And they will work a little differently. But a question of whether an Alcubierre Drive can get out of a black hole is not something we have to guess on. We can answer it exactly. For any practical warp drive, that would be just an approximation, and something could go wrong. And maybe it's something we will have to do trial and error on, but we aren't just guessing. Neither was Von Braun guessing on his rockets. He had excellent understanding of fluid dynamics and rocketry. And he did a lot of math before he ever tried to build a rocket. Fact that you cannot account for absolutely everything and have to make corrections during development of a particular machine doesn't mean you go in blindly, or that you are just guessing until you build one. Only a complete fool would think so. That's how we get all of these crackpots with perpetual motion and reactionless drives. We do know what can and cannot work. And we know a lot about warp drives and can answer many questions about them without having to have built one yet. Just like Von Braun was able to answer questions about his rockets before he built one, or nobody would have given him money to build them.

No, not really. Exchange is symmetrical. If particle A emitted a graviton with positive energy that was absorbed by particle B, it's the same thing as particle B emitting a graviton with negative energy that is absorbed by particle A. Which happened first, absorption or emission, doesn't matter either. Lets work out an example. Suppose, you have two particles, both of mass m, that were traveling with momenta p and q, have exchanged a graviton with momentum k, and are now traveling with momenta p' and q'. All of these are 4-momenta, so they contain information about both energy and momentum. From conservation of 4-momentum: p' - p = k q' - q = -k And we know that before and after, the two massive particles were on the shell. p² = p'² = m² q² = q'² = m² I'm using natural units, where c = ħ = 1. Lets look at the mass of the exchanged particle. k² = (p'-p)² = p'² + p² - 2p'·p = 2(m² - p'·p) Lets look at that p'·p term. I can decompose it as p'0p0 - p'·p. Here, p0 is particle's energy and p is ordinary 3-momentum. For sake of example, lets suppose that the particle was at rest to begin with. (In fact, we can always choose a coordinate system where it was so. So this assumption can be made without loss of generality.) In other words, p0 = m, and p = 0. In that case, p'·p = p'0p0 - 0 = p'0m. This is interesting. Clearly, if particle is no longer at rest, its energy, p'0, has increased. In other words, p'·p > m². And that means, k² < 0. So a virtual exchange particle can have negative mass. And, in fact, this is normal for virtual particles, regardless of whether they carry an attractive or repulsive force. The corresponding energy, however, can be positive or negative, depending on whether particle's energy increased or decreased in interaction, and on which direction in time you consider the particle to be propagating. This will be frame-dependent, by the way. Energy always is. This should also give you some insight into why quantum gravity is so complicated. The fact that virtual photon in electrodynamic interaction has negative mass, or any mass at all, isn't a problem. Its always electrically neutral, so if you only consider electromagnetic interactions, photon will only couple to charged particles, making it pretty easy to account for all interactions. As a result, QED is pretty simple, as far as RQFT go. Then you can look at strong interactions. Well, gluons are much similar, but they carry color charge. So gluons can couple to each other. But there are only 8 gluon types, each carrying its own, constant charge, and so you can still account for most things. QCD is far more complex than QED, but manageable in a lot of ways. And then you look at gravity, and virtual graviton will have mass and energy, so it will be able to interact with other gravitons, and so gravitational interaction alters gravitational interaction, and the whole thing gets really bad really fast. In practice, what you actually end up with is a non-renormalizable field theory, which sort of means that everything is infinite, and there is no way to deal with it. There have been some great results from effective field theory approach lately, so we can build a very good approximation for quantum gravity, but it has limitations. Specifically, it doesn't tell us anything about physics at plank scale, which is really the biggest puzzle people hoped QG would resolve.

Alcubierre Drive is a certainty. Whether we can build one or not is an irrelevant question. We have all the math for it. We know exactly how it will interact with a black hole. Your statements are just a bunch of ignorance coming from somebody who does not understand anything about General Relativity.

We do know, actually. Albeit, graviton theory is incomplete, due to certain problems in quantizing gravity, we have a general theory for gauge bosons which covers this question. After all, it doesn't matter if it's supposed to be a graviton or a photon. Two opposite charges attract in a very similar way to two masses, and must also exchange photons that cary momentum the "wrong way". And the solution is actually quite simple. A classical particle has momentum proportional to its velocity. Any on-the-shell particle, which can freely propagate through space, must also have that property. But a virtual particle, does not. All forces are mediated by virtual particle exchange, and all of these particles can propagate one way, and carry momentum for a different direction. At that scale, energy and momentum behave more like a charge. In fact, energy-stress tensor, which is generalization of these concepts to a general coordinate system, is the conserved charge of the General Relativity, just like electric charge is a conserved charge of Electrodynamics. I could probably get into this a bit deeper, but understanding propagation of force carrying particles requires good understanding of Partial Differential Equations, Green's Functions, Fourier Transforms, and some theorems from Complex Analysis. The math on this is pretty hairy. P.S. I really like that this is turning into a community Q&A thread.

An Alcubierre Drive can, indeed, escape from bellow the event horizon. It has to be a supermassive balck hole, as people have already mentioned, because space-time around the bubble needs to be relatively flat, and there is a limit to how far bellow the event horizon you can go, which is directly related to how much faster than speed of light the drive is capable of going. The actual physics behind it is that bellow event horizon, all time-like geodesics lead to the center. So no matter can escape. But FTL ship follows a space-like geodesics, and there are some space-like trajectories that allow you to exit a black hole.

By then, hopefully, you have most of your orbital speed, and TWR isn't much of an issue, anyhow. Like I said, it does look good for orbital applications. But building an actual ascent rocket with it would have been more exciting.

It's not particularly hard to design an 8-bit or 16-bit MCU, but manufacturing one is a completely different matter. There are a few places that build custom chips, but it's not cheap. As Nuke says, you are probably best to go with an existing solution. Personally, I like the Microchip's PIC series. They are inexpensive, easy to code for, have great selection of features, and some of them come in tiniest packages. The drawback is fairly low clock speeds on most of them. So you need to make sure that the feature package matches your application very closely. Fortunately, it's possible to do more often than not. Edit: Come to think of it, there is one more option. There are some field-programmable controllers out there. It's going to be considerably more expensive, eat up more power, and probably be less flexible than stock MCU, but if it's just about having a project, and you absolutely must have a custom controller, that's an affordable option.

You can attach a module that would allow for stable artificial gravity. Not going to be very comfortable, because of low G and high RPM at that scale, but it's workable, and there has been proposals to send one up. Nautilus-X ISS demonstration module is probably best known of the above. It addresses most of the engineering challenges.

There are a lot of pipes, though. And I'm not sure what you mean by "purely space". Once in orbit, definitely. During ascent? I'm not so sure. I'm really annoyed at atmosphere. Especially that property where at certain altitude it's of no help, but it's still too thick to accelerate without losses. I really wish there was something we could do about that. Then we wouldn't need any fancy propulsion or power sources.

Yeah, that's definitely going to be too heavy to power the ship, unfortunately. A slower flying, purely lower atmo cargo plane, though, is still entirely within realm of possibility. But who knows. First reactors also were way heavier than they needed to be. Maybe this is something that can be miniaturized, or have its power output boosted by an order of magnitude.

Energy stored in the flywheel is mv²/4, as we've established. Kinetic energy of a ship traveling at v is mv²/2. So if we convert 100% of energy in a flywheel into kinetic energy, we get v/sqrt(2). That's about 210m/s for the flywheel we've been talking about. Make it twice as heavy to store twice as much energy, and you end up wasting twice as much energy to accelerate it. And we haven't even talked about mass of the ship here. Flywheel has no practical applications as energy storage system. Again, if it did, there would be actual applications. There aren't. Unless bearings get busted. If the flywheel is built incorrectly, you won't be able to even spin it up. And if a flywheel develops a crack, it explodes. Actually, practice shows that electrical systems are less likely to fail than mechanical ones. That's why we use them for just about everything now. NO! YOU!!!! See? I can do that too. Except it really does nothing except make you look both incompetent, and unwilling to even try and understand why you are wrong. But sure, have fun with this. I've been finding this whole thing immensely entertaining myself.

They you bring 3% more battery, and your ship is still 20x lighter. Are you really struggling with that concept? Again, electrical energy is converted into the same type of energy at a 3% loss. Heck, make it 10% loss. You want 50% loss? I'll give you that. Battery is still a more efficient storage. Again, if this weren't true, we'd actually be using flywheels for storage. We don't. Anywhere. Ever. Not since Lithium batteries became a thing. Have you ever seen a cellphone with a flywheel? Or a laptop? Or a satellite? Or a mass-produced car? Anything? Come on. Use your brain, please. First of all, so far you've been working with integers, not reals. There is an uncountable number of reals. You can't organize them into any manner of adding them together. What you've said applies to integers. Except, it just doesn't work that way. Consider the following way of adding all integers together. (0 + 1) + (-1 + 2) + (-2 + 3) + (-3 + 4) + ... Absolutely any integer will show up in one of these brackets. So by adding all of these numbers together, we add up all the integers. Except, each bracket adds up to 1. Exactly one, no matter how far out you go. So the above is just 1 + 1 + 1 + ... What does that add up to? Well, certainly not zero. Certainly not anything negative, either. Unless... What if I add them up like this? (0 + (-1)) + (1 + (-2)) + (2 + (-3)) + ... Same thing as above, except this is -1 - 1 - 1... Which is certainly not positive. But not zero, either. Moral? To find a sum of infinite series, you really need to understand what an infinite series is, and how it is defined via limits. Or it simply isn't a number. Which is the real case. You cannot multiply by infinity. You cannot add to infinity. You cannot perform any mathematical operation on infinity, because infinity is not a Real Number. Like I've pointed out, there are other algebras with slightly different definitions. And there are even some really creative ones where you can actually add infinities, but this has absolutely nothing to do with any mathematics you are familiar with. What you understand as numbers are Real Numbers. And what you understand as addition and multiplications are the binary operations on the Field of Real Numbers. These things are strictly defined in mathematics. People have thought really hard about some of the things you've brought up, and solved these issues over 100 years ago. And if you end up studying real mathematics, you will learn about all of this.

That's kind of why 7km/s. You need to get quite a bit of vertical velocity to get the thing high enough for TWR of 1 being sufficient to push the thing to orbit. So your first stage eats most of the atmo/gravity losses, but you'll need most of the orbital velocity to be gained by second stage due to gravity turn ending up being done so high up. Of course, I'm not sure you need such low TWR. Again, it depends on how heavy the reactor is. Also, I was trying to save as much of the weight as possible for the air-breathers. Which isn't necessary with a 2-stage design.

Electric to mechanical can be over 97% efficient with brushless motors. Again. You just throw out random claims without ANY numbers to back them up. You can typically get something like factor of 2x on streangth of the disk with that. You can probably get another increase with better materials. So maybe you can get 5x higher energy density by utilizing extremely expensive materials and manufacturing techniques. Cheapest LiPo batteries are still 4x better. Top of the line ones can be more than 10x better. And we're still making advances on these. For the second time, if gyros were actually good at storing energy, that's what we'd be using in electric cars, RC planes, drones, and so on. But for some silly reason, people just keep using LiPo batteries for these. I wonder if it has anything to do with the above numbers. Suppose that was so. You are going to prove what, exactly, with that? I thought you were going to use mathematics to prove your points. About flywheels, or maybe QTs. Or maybe you can actually derrive something for warp drives. But even your claim is absurd. Say it has numerical value. Call it x. Clearly, infinity + infinity is still infinity. So x + x = x. 2x = x. Divide both sides by x, which is a number according to you, and clearly not zero, so we can divide by it, and we get 2 = 1. Now, there is a concept of extended reals. Here, infinity is part of the set. But it has special rules for binary operations so that you don't end up with the silliness above. It's very useful in measure theory. You could go as far as claiming that infinity as a number this way. Specifically, that infinity is an extended real number. But the fact that you claimed that it has a "numerical value," really underlines the fact that you don't get the concept.

Specific fuel consumption of Williams FJ33 is cited as 13.8g/(kN s) @ 5.3kN. And specific energy of Jet A is 43.02kJ/g. Which gives me a bit over 3MW total. And the problem here is the mass of the engine. Adding motor isn't going to help that. I'd rather take a ~50% loss on compressor, because we have plenty of excess energy.

Not looking good on the jets. Cyrus Vision SF50 has a 140kg turbofan that consumes 3MW of heat from fuel to produce 5.3kN of thrust. Assuming linear scaling, this doesn't look good for an SSTO. There is simply no way to get enough thrust from air-breathing stage at anything like reasonable efficiency without bringing too much weight for the rocket stage to carry. So if you want to go orbital, or even suborbital, using arcjets, you'll have to go with two stages. Naturally, first stage can fly back to the point of origin as a conventional airplane. So this could still be a viable idea. I just need to know how heavy these reactors are, because I'm not familiar with polywell tech, and I'm not seeing anything useful on Wiki. Hydrazine is way cheaper than argon, is liquid at room temperature, and has a high density. No need for huge cryogenic tanks, which saves a ton of space. Something less toxic might be a good idea, though. Methane should work extremely well in an arcjet. It would require a bit of pressurization, but it isn't bad otherwise. Actually, if it's tuned right, anode shouldn't be hit with more than 2-3kK, so you could minimize erosion during normal operation. You'd probably have to swap them out pretty frequently anyways, but it doesn't seem like a deal breaker.

100MW should get you about 20kN of thrust from an arcjet rocket, with maybe 800-1000s of ISP. (Some rough figures from the top of my head.) That's with ammonia, I think, but hydrazine shouldn't be significantly worse. Anyways, with air-breathing arcjet to get you started, this should be enough for about 2T total mass, and about 7km/s to go. So your dry mass is going to be something like 400kg/450kg. That needs to include engines. Doesn't leave for much. How heavy is that 100MW reactor you're thinking of?