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You are confusing forces, acceleration, momentum, and energy all into one single mess. Incoming air gets deflected, which means momentum is being transferred from wings to air. That means there is force acting on the wings, which is lift. It also slows the air down. And that's drag. There is no lift without drag. But drag is not, usually, equal to lift. For a good airplane, drag is about 10 times less. For a high quality sailplane, it can be over 70 times less. The reason it all works out in terms of energy is because air is already moving at high speeds relative to the airplane, and energy is proportional to the square of the velocity, while momentum is linear with velocity.

ÃŽâ€L = ÉI = mvr

Because you don't use 100% of energy to do work against asteroid. You use almost all of it to accelerate exhaust off into space. What you should be looking at is angular momentum and torque. I'm getting something like 2.2 tons of fuel with the above parameters.

Because rocket moves very small amount of mass at high speeds. An airfoil moves a very large mass of air at a very small speed, which is proportionally more efficient.

This might be a cliche, but I still haven't found a better text on fluid dynamics that deals with general cases, rather than simplify it all down to incompressible/inviscid. Landau Lifshitz: Fluid Mechanics - Not familiar with this particular translation/edition, though.

The net effect of all stress-energy in universe is actually repulsive. The universe is inflating at an accelerated rate. But everything points to pressure terms providing repulsion, rather than negative energy.

I'm picturing this cycler as a modular station, so it could be built with modern lifters, but SLS would make it easier. Radiation shielding is a problem. But Solar radiation is mostly charged particles and gamma, which are much easier to shield from than, say, a nuclear reactor which produces a lot of neutron radiation. Having a few layers of scintillating and conductive materials should do the trick on shielding, I think. I should do the math on this at some point to be certain, though.

CUDA is awesome. And with modern cards, you don't even need a TESLA to handle fluid simulations. You can run something like this on most modern nVidia GPUs.

Even if you know the velocity field, Bernoulli only gives you correct lift at low mach numbers. The reason is that you have to take pressure differential outside of boundary layer, and at high mach numbers, pressure gradient across boundary layer is very high. So pressure in the region where Bernoulli applies doesn't agree with pressure on the wing's surface. If you have velocity field, just use Kutta-Joukowski. That's what it's for. I don't think there is a way to prove that viscous flow gives rise to Kutta condition, but it is possible to show that inviscid flow is laminar, and that it results in no separation layer. So yeah. No viscosity, no Kutta condition, no lift.

You are thinking of mass as a real value in Newtonian Mechanics. That's not how mass behaves in real physics. In field theory, mass behaves as a length. Specifically, it's the length of the 4-momentum vector. In natural units pμpμ = m². Can you put a negative value in there? Sure. But it's irrelevant. The relevant quantity is m², which ends up being the same sign regardless of whether m is positive or negative. But what of the gravity, you might ask. Nothing. It has nothing to do with mass. Gravity is determined by the quantity called the stress energy tensor, which tells you how much energy and momentum is concentrated in a point in any coordinate system. And from that, you can work out the amount of mass there, but same amount of mass can have different gravitational effects depending on the state that mass is in. Ultimately, mass itself doesn't determine anything. So questions of "negative mass" are absolutely silly. Whether you picture mass as positive and negative or all positive, the universe stays exactly the same. Negative energy, on the other hand, that has interesting implications.

Even with boost to LEO, moving a simple station built out of light, modern materials feels like way less effort than shifting an orbit of asteroid of comparable size even a little. ISS is what, about 100m across? An asteroid of the same diameter would be well over 1M tons.

Well, yeah. That's what length contraction in special relativity is all about. But it's not all that crazy. Think of it as measuring a height of a brick. It all depends on which end it stands on. Same deal with length being a frame-dependent quantity. Relative position of any two points in space-time involves time and space separation. So it's only natural that you need to first decide which direction is time and which is distance before you can measure length. And that's frame-dependence in a nut shell. General Relativity is only further complicated by the fact that frames are only really defined locally. Just because you've decided on which direction is time in your immediate vicinity doesn't mean you don't have choices for everywhere else in the universe. This leads to all sorts of silliness, until you realize that overall coordinate choices don't matter. What matters is how these things transform as you gradually move along a particular trajectory. And that depends only on local curvature along your path. So all of the ambiguity of time and space is reduced to local differential geometry. It's still crazy math, one which takes a while to fully grasp, but it hasn't caused anyone to jump out of a window yet, that I'm aware of.

As explained above, Bernoulli Effect does not produce any force on the wing. It is, however, part of what shapes the airflow around the wing. And 100% of the lift corresponds to deflection. Newton's 3rd, etc. What you can say is that majority of the deflected air is not swept by the wing directly. Again, see the illustrations of flow patterns around the wing to see how much air is actually being deflected in the flow. Not really. Plain flaps reduce critical AoA. However, they give you higher CL at the same AoA at the cost of increased CD and reduced glide ratio. Furthermore, they typically have higher AoA at the same attitude, so you don't have to flare nearly as much during approach. Leading edge flaps, slats in particular, can be used to increase critical AoA, but they typically reduce CL, so they are only ever really used on large airliners together with Fowler flaps, because the later dramatically increase wing area compensating for a CL drop. Naturally, all of that comes at a cost of a lot of drag, but that's what the airliner's engines are for.

Cycler transfers are going to be time-consuming. You don't want cycler to pass near LEO. In fact, you don't want it even clipping the Hill Sphere. So we are talking days if not weeks of transfer from LEO to cycler. Ditto transfer to a Mars station. So realistically, we're still looking at something like Apollo or even Orion capsule. On the other hand, cycler isn't limited to just your typical orbital facilities. Since people would need to spend 7-8 months at a time on an Earth-Mars cycler, I'd strongly advise something with artificial gravity. Probably something along the lines of a living module connected by light, extendable walkway/umbilical/tether to a massive power and life support system. A small hub in the center can house solar arrays and a docking port/airlock. Not having to deal with drag and tidal forces gives a cycler a whole lot of advantages over an LEO station. Ability to spin without any problems is one of them.

There is some basis in fact behind it in that a "bubbles" in fields behave as if they have negative energy. Casimir Effect is an infamous example. Similarly, superfluid vacuum is a fringe hypothesis that does have place to be. And, in principle, it would explain Casimir Effect as bubbles in superfluid. The rest of the statement is nonsense.

No, but this argument tends to happen frequently wherever enthusiasts and some professionals gather. Unfortunately, aeronautical engineers are frequently responsible for the worst nonsense in such discussions. There are a lot of very well qualified engineers out there who, unfortunately, do not understand the difference between, "This is a very good model that approximates behavior," and "This is why it works."

I agree that if you treat air as almost inviscid, almost incompressible fluid, you can get good approximation for lift by using Bernouli near airfoil. And this works for low mach numbers. But saying that Bernouli principle is the cause of lift is fundamentally wrong. It is wrong precisely because you cannot take it past boundary layer. And taking flow to be perfectly inviscid takes away separation layer. Lift of a foil in perfect inviscid flow is exactly zero.

Bernouli effect across the airfoil is zero, because boundary layer is stationary. Bernouli effect is not responsible for lift That is a very naive view. It is one of the components that set up an air flow around the foil. That, along with separation layer and continuity will result in a pressure differential in boundary layer.

Yes. This is a known result from electrodynamics as well. Electrostatic interactions work the same way. If Sun was to accelerate, however, that change would arrive 8 minutes late. As I have mentioned earlier, it is really changes that propagate at light speed. That is also what carries information. On the topic of straight parallel lines. There is no such thing in GR. The lines of the grid only look straight in that coordinate system. I can chose another, and that grid will look all sorts of warped. Yet, all physics will remain exactly the same. Likewise, lengths cannot be compared without taking time into consideration. Ordinary lengths are frame dependent. One must look at total distance in space and time.

No. In this picture the distance around any circle is defined as 2pi r, because this is how r is actually defined in Schwarzschild coordinates.

Ball on a trampoline is a false analogy. Do not rely on it too much. For starters, ball on trampoline cannot recreate black hole condition. While changes on trampoline surface do propagate at a finite speed, these are not affected by self curvature. Gravitational waves are. If we insist on decomposing interaction into virtual particle exchange, it is better to look at electrostatic interaction. After all, black hole can have electric charge, and we can actually do Quantum Electrodynamics in curved space. Here, the trick is to realize that virtual particles can follow space-like curves. They are not bound by speed of light rules. There is a big difference in force propagation and propagation of change in force. Later carries information and is limited to c. Former, might as well be instant. Of course, "instant" is a frame dependent concept. It is all just math trickery when we describe forces as particles.

In simplest terms, the information "gets out" before stuff actually falls into the black hole. The total mass of the black hole, and its effects on its vicinity, is the same for extra mass being inside the event horizon or just at the event horizon. And black hole itself is expressed as series of conserved quantities (mass, charge, angular momentum, etc) just as if it was an elementary particle. So where the mass enters black hole is absolutely irrelevant. This kind of goes back to the Sun changing mass 10x question. It can't just suddenly change. That mass has to come from somewhere. And that has a lot of interesting consequences in relativity. Yes, gravity propagates at the speed of light, but a lot of things wouldn't change even if it was instant. P.S. Yes, if you want to describe gravity in terms of gravitons, you end up having trouble with black holes. But then again, you end up with a whole lot of problems even before that, because quantizing gravity is not a trivial task.

No, it does not. It does not expand like the balloon that you inflate. It expands like a surface of the balloon that you inflate. Except, it's not an embedded object. All that exists is that surface whose area is getting larger.

So, for starters, any console exclusives don't count. Now for cross-platform development. I only have experience with Windows/XBOne cross-development, but seeing how similar these environments are, I can't imagine how it would apply less to PS4 or Wii U titles. Almost all of the situations where a graphics hardware-specific bug arises, it's either due to some very specific feature, which is going to be different between PC and console versions of the chip, or even more frequently, due to the problem with the drivers. In either case, the fix for console rarely applies to PC, and vice versa. The only cases of bugs that are caught more frequently on XBOne that have helped fixing PC version are race conditions and memory stomps. Simply because timing and memory layout can be different, making it more obvious on one platform over the other. None of these, obviously, have anything to do with graphics hardware. Now, shader bugs this might help with. I haven't really had to touch these a whole lot around here, so I honestly have no idea how many shader bugs we get on each platform. I suppose, it's possible that XBOne/Windows dev on these gives a certain advantage to AMD. I'll ask around. It's an interesting possibility.

I'm talking about hardware statistics on games I'm actually working on. Steam hardware survey shows Intel for any system that has Intel GPU, which is basically anything with a modern Intel CPU. You need to subtract off nVidia and AMD from 100% to get an estimate for Intel share.