K^2

The rocket doesn't need to sit tight with the muzzle. Plunger will push it mechanically just fine and to the same effect.

If you can formulate specific questions, I can go through the code and find out for you. I need to know very specifically where you see the numbers being reported, so I can find the GUI code that handles the particular menu or HUD item and trace it through the routines to whichever function actually computes it. I was able to use this to resolve many questions with drag and ISP curves for engines.

There are times in that video when machine isn't running. Average on that gives a more reliable neutral position. Albeit, at the cost of increasing the error.

Yeah, I forgot about aerobraking. Luna to LEO should be doable in under 100m/s, then. No need for VASMIR, you're right.

There is really no reason to use NERVA for that. It's absurdly expensive for the task. If you are going to be sending a lot of stuff from Moon to Earth or LEO, you should build a magrail on the surface. Launches to Earth can be done directly from surface, requiring only minor corrections along the way. Launches to LEO would be better done by using a VASMIR tug. In this scenario, cargo is launched by mag rail, uses chemical rockets to circularize and meet the tug, and the tug takes it to LEO gradually in the following weeks.

Why isn't that an attraction at water parks yet?

That is a more interesting pattern of movements than I expected. I'll see if I can set up a small program to track that dot automatically to verify N_las' results.

M Drive, in the most general terms, what you need to do to be able to swing on a swing set is alter moment of inertia about the pivot in a cycle that matches frequency of oscillations. You might be able to do that with gyros using a simpler cycle than without. If that's what you are getting, it's still really cool, but doesn't get you anywhere closer to propulsion. In order to start moving in free space, total momentum of the system must change. I hope you won't argue with that. Your idea is that we can alter momentum without applying an external force. Id est, momentum need not be perfectly conserved. That's not actually all together impossible, but it would imply broken symmetries which we ought to have observed with far, far more sensitive experiments that have been done already. But if you wish to verify your device's operation, ultimately, you still need to show a change of net momentum. And that's where gravity and pendulum come in. Gravity is an external force, so it results in change of momentum. Indeed, if you drop something, it accelerates. The string on which the object is suspended, also is a force, and also results in momentum change. If the string is perfectly vertical, the two cancel each other out. Net momentum change of object is zero. If the suspended mass is swinging, then on average the momentum changes are canceled. But if there is an average deflection, there is a net momentum flow. So if your system is capable of maintaining average deflection, then we know that it would be able to accelerate in vacuum. Swinging back and forward, in contrast, only tells you that your system has been able to build up angular momentum. Which as I've said, is already pretty cool when you can do it with a very simple system, but as you yourself point out, it's something little kids can do on a swing. So it's not groundbreaking. Nor does it contradict the well established principles of conservation of momentum and conservation of angular momentum. (Both are transferred via pivot and gravity, rather than created/destroyed.)

You don't need fuel to get off the Moon. Moon's no Earth. It doesn't have an atmosphere or anything else to prevent you form launching things with magrail. The actual problem with lunar surface base is that there is no way to obtain enough of everything you'd need for habitation. Not with current tech and without deploying entire city-worth of industrial equipment. So you will have to bring stuff down to the surface. And landing on the Moon is going to be very expensive. We do not have what we need in place for this kind of spending to have any advantage.

V = (4/3)pi r³ The formula you used is for surface area. Always check your units. r² has units of m², and volume is m³. If you kept units through all of your operations, you'd see that you aren't getting radius in meters.

Yes, definitely. In fact, if you replace string with a rigid rod and remove gravity, a machine that can move around to any place in a circle can be built. This is why gravity is important here, and why only average deflection would show deviation from expected behavior.

I bet someone said something similar about wooden ships to the people who set out to colonize the New World.

The fact that costs are impossibly high and there is no way to get sufficient quantities of any kind of materials for this are pretty much a given. If we ask a truly practical question of, "How big we can build it, given budget constraints," then the answer is, "About the size of ISS," because that's all we've been able to build given the budget constraints. So I've disregarded that aspect of it completely. On the subject of cyclical stress, yes, of course there is always going to be some. But it's going to be very small compared to the constant load. To be honest, though, I don't know at which point we need to start considering it as a serious threat.

Firing engines while in the barrel will increase the pressure, potentially, beyond what barrel can handle. This can be avoided with a delay, though. I'm also pretty sure the whole thing violates model rocketry regs in the States. Whether that causes any legal problems is up to jurisdiction. I have no idea how that works in Canada, but you might want to check. That said, forget electrical ignition. This is practically a mortar to begin with, so there is no reason not to make it more like one. Use some of that dowel to make a plunger with a firing pin. Put a primer cap from a rifle shell at the base of the engine.* This can work with or without a delay fuse, depending on whether you want the engine to fire in the barrel. * Again, I don't know how readily ammunition is available where you live, but you can usually get some short .22 rounds used for biathlon pretty much anywhere. Otherwise, primers aren't that hard to make. The home made ones just aren't going to be as reliable and stable.

I address that case in second to last paragraph of this post in this very thread, including conditions under which such a system is self-balancing. And yes, on a real washing machine, this is going to be the case. If you read that entire post, you'll see that I've addressed all other peculiarities of both systems as well.

I've jumped the gun on that 9GPa figure. You can get that from a perfect lattice under tension as a matter of theoretical limit, but not from a real world steel wire, you are right. But you can definitely do much better than 1GPa if you are interested in just raw tensile strength. Resulting alloy will be brittle, and so structural steel is usually much less, yeah, but you should be able to get up to 2-3GPa if you really have to. I agree that it's probably not a good idea. And yes, I've pointed out as well that this is ignoring any safety margins. Cyclic stress you don't have to worry about. The whole thing will be under very consistent load. But you don't want it to be too brittle or too close to limits, so even if something somewhere breaks, the whole thing doesn't fall apart. But that's why I used just a raw torus as a basis. Throwing some suspension cables down from the hub would already greatly reduce stress on the main structure. If you want to be more elaborate, you can build a support structure with multiple inner rings connected with cables. That will allow you to support even more of the station's "weight" suspension bridge style. And, of course, you don't have to build from steel. In fact, in space, composite materials are probably a better choice. And you can get much better UTS/weight with these. So I still say that 100km is a very safe bet. There should be no reason, in terms of materials and engineering, that we couldn't build a 1G station that big. As you go larger, it gets worse rather rapidly, so the real cutoff with materials we know might not be that much larger.

Oh, yeah. Equal Transit-Time Fallacy. Not only has it been demonstrated wrong, but it is trivial to show that Equal Transit implies zero circulation, which, by Kutta-Joukowski Theorem implies zero lift. Not only is it wrong, but where it true, winged flight would be impossible. The fact that there are still people out there who believe that nonsense is rather sad.

There is only one universe in Many Worlds. They like to call observer/observed pairs "worlds" to help intuitive understanding, but there is just one wave function. Same as with Copenhagen. Except, Copenhagen adds a wave function collapse statement. Many Worlds does not. So if you want to go with Ocam's razor, MWI is a simpler interpretation of the two. More importantly, as I've said, they are completely indistinguishable. It's not like Universe really works the way a) and not , but we don't know it yet. No. To say that, there has to be some way to distinguish the two, even if we can't carry out the experiment. There is no way. They are mathematically equivalent. So one cannot be right while the other is wrong. And if it makes you feel better, both are almost certainly wrong. Starting with the fact that they are based on measurement axioms which don't play nice with the gauge freedoms of the Field Theory and just many-particle QM in general. And then there is the fact that superposition principle, which both take for granted, does not work on large scale. Meaning that "worlds" cannot be completely independent, and collapse just leads to contradictions outright. Ultimately, you should view QM as a tool. It's not how the world actually works. QM is a tool that helps you interpret and work with the underlying field theory. But quantization of the field theory is not required. We make perfect use of Gravity without quantizing it, because it's a fairly straight forward field theory. Similarly, we can do full description of Electrodynamics without employing Quantum Mechanics, so long as particle fields are not involved. It's only when you introduce particle fields into both and try to look after all of the interactions, that the underlying field theory gets too complex to even interpret, let alone try and make computations with. That's where quantization comes in and saves the day. But it's just what we use to describe the system with much simpler algebra. Which is not the same thing as actual physics of the thing being that.

Without the spokes, cross-section has to support 1/À of its own "weight". So diameter is equal to the longest homogeneous structure you can suspend in 1G. Steel has density of about 9g/cm³ and can support about 9GPa at a maximum. That's almost exactly 100km at 1G. Since there are a number of things you can do to improve on that, I'd claim 100km as the most conservative estimate. Between adding spokes, using carbon nanotubes, perhaps some other fancy materials, and doing some clever fractal design, 1,000km wouldn't be fantasy. But I don't know if you could make it safe. I think, going larger would require materials we have not discovered yet, but given sizes of typical cities, and ability to "stack" Stanford Tori *, from perspective of material science and engineering, we can build a large enough station to fit any existing metropolis. Naturally, from perspective of resources, this is far beyond our capability. The limitations, however, are purely in getting construction materials, workers, and equipment to the required orbit. Advances in asteroid or Lunar mining might be able to change that rapidly. * Stacking rotating stations isn't as trivial as it may seem. Having them rotate on independent hubs would allow any slight wobble in each to shake the structure apart. Building a rigid connection, in contrast, can result in instabilities. Specifically, a station whose two principal axes of inertia are very close may start to tumble, which would be catastrophic. However, stacking a "few" rings with rigid connection is fairly straight forward, so long as you look after possible resonances. It's a little hard for me to tell exactly which part is causing problems, but here are a few things to consider. First, there are no external forces. So center of mass of the station cannot accelerate, no matter how fluids slosh around inside. That means that the station can only rotate around center of mass. (Any other rotation causes accelerated motion of CoM.) So if there is more fluid on one side of the station, the center of rotation will be shifted there. That leads immediately into the most simple way to get a general idea for the effect. The polar plot of a circle of radius R plotted around a point shifted by d from center of the circle is given by the following expression. r(θ) = Sqrt(R² + d² - 2Rd cos(θ)) Plot this from -À to À as a regular plot to see that it has a minimum at 0. Since the centrifugal force is going to be purely radial, this means that the point closest to CoM on the ring is the one that's "highest" in terms of artificial gravitational (centrifugal) potential. So fluid is going to tend to flow to the side opposite of the CoM, trying to shift CoM closer to geometrical center. The more abstract of seeing this is by recognizing that total angular momentum is conserved, so the total rotational kinetic energy, E = L²/(2I), is minimized whenever the structure has maximum moment of inertia, I. If the fluid is distributed along the floor of the station in a "thin" layer (compared to size of the structure), then around center of rotation, moment of inertia is same as for the ring, MR², regardless of how fluid is distributed. Here, M is the total mass of ring and the fluid. Now, there is a theorem that states that moment of inertia around arbitrary point is greater by Mr² that moment of inertia about center of mass, if the point is located distance r from center of mass. So if center of mass is located distance d from geometric center, and what we just computed is moment of inertia about geometric center, then about center of mass, moment of inertia is given by the following. I = MR² - Md² This is trivially maximized for d = 0. So if at all possible, the system will try to tend towards that to minimize energy. All of the above assumes that station is in perfect balance if you remove the liquid. It turns out, that adding liquid can actually help reduce wobble of a slightly unbalanced station. But this requires more complex considerations. The simplest example, however, is balancing in rotors and drums of washing machines. If there is a spring trying to keep drum centered, then the whole problem is of a driven damped harmonic oscillator given by r'' + 2ζÉ r' + É0² r = d eiΩt. Here, Ω is the drum's rotation speed. If you solve this equation, you'll find that stead state has a wobble in the opposite direction to the center of mass shift whenever Ω >> É. So if you ever wondered why the washing machine's drum has such a soft spring, it's to reduce É, allowing it to self-balance at lower RPM. If you remove the spring, the effect isn't quite perfect. The liquid will never remove wobble completely. But it can help reduce its effects, because again, the station will rotate around the center of mass, which will cause fluid to "prefer" the opposite end, helping shift center of mass a bit towards geometric center.

Thing is, from perspective of observer, the two are indistinguishable. There are theorems stating as much. Honestly, take your pick. But I recommend everyone to understand both, and understand them well, because many things intuitive in one are completely counter-intuitive in the other. Having both interpretations at your disposal will let you sort through problems that much quicker.

There are branches of both where I'm going to be pretty lost, and there are definitely a few members on this board who can teach me many things on these. Oh, and I don't mind arguments and questions. Everyone is going to learn something from a well structured argument. I just get a little cranky when people are snarky about it.

The SO(2) is isomorphic to U(1), which is an imaginary exponent. So yeah, of course I can write everything down as a linear combination of exp(ix) terms, but that doesn't make it any less weird, or that weirdness any less relevant to structure of SO(2). But SO(2)/U(1) is about as simple as non-trivial Lie Groups get, I'll give you that. At least, SO(2) is Abelian. All of my work is in SU(3)xSO(1,3). SU(3) is non Abelian, and has 8 generators. Eight. That means I have eight self-interacting gauge fields to deal with. Particle physics is really, really weird. And while they rarely show up directly, this weirdness is closely related to weirdness of trig functions. And hyper trig functions. Hey, at least my SO(1,3) is global. Stochasty deals with local SO(1,3) on top of all of the above, if I recall correctly. I think, my main point is that there is a very deep hole you are staring down when you start asking questions about derivatives. But you can take it a step at a time with some guidance.

Why would you put your sensors on the rotating ring? Ring should only contain the habitat and work stations. Maybe life support, if it's more convenient. Propulsion, power generation, comms, and sensors should all be on the hub. There just isn't any reason to do it another way. There is also no reason for larger ship to have an exposed bridge. Whether for protection from possible attack, or just in case of collision with debris or asteroids, bridge should be well protected, located as deep inside the rotating ring as possible. All of the information, be it visual, radar, or other sensor data, can be relayed to the bridge from the hub. So from perspective of the bridge, there is going to be no rotation, and absolutely non problems related to rotation.

I think, step one would be an either Perturbation Theory or simulation of an H-H-bar "molecule". I have no doubt that hydrogen and anti-hydrogen are going to interact. If they form a bound state, that's useful information. If they end up repelling, then we learn something too. Once we know how this system behaves, it's going to be a lot easier to understand how two chunks of matter and antimatter interact. Whether they tear into each other, or almost harmlessly bump into each other, with a small burst of radiation.

Actually, I have, and my laundry machine has loose bearings in the outer ring specifically to self-balance. The reason clothes don't self-balance is because they get stuck to the walls and each other. Anything that's free to move around the perimeter, however, will improve balance. I can tell you more, given a spring, such as wheel suspension, there is a minimum spin speed at which the system self-balances. But in free space, any rotation with free flowing liquid or other free-moving mass is going to self-balance. Would you like to see derivation of that from the first principles? There are a lot of things you might know better than me, but mechanics isn't one of them, trust me. I'm happy to explain further to satisfy your curiosity, but you ought to leave any hope of proving me wrong on this at the door.