Wikipedia:Reference desk/Archives/Science/2013 November 22

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November 22

Big Xbox is watching you?

Trying to ask this question without sounding like a loon, so here goes:-

Is it technically possible for Them (CIA/MI5/whoever your local Them are) to use Xbox One's controversial new Kinect faciliy to watch and record you in your own home wihthout your knowledge?

Just curious about the technological side of it - not trying to advance any conspiracy theory here. Needless to say, They will probably find some way to watch you anyway, if They are interested in your activities, wheteher or not you happen to have an Xbox One in your home. Thanks. --146.90.108.78 (talk) 00:01, 22 November 2013 (UTC)

• While there are plenty of conspiracy folks speculating on this topic, there are some legit sources that express concerns (e.g.: [1]).

You might have better luck regarding specific tech details here: Wikipedia:Reference desk/Computing; but, I am certain that if it could be done, it will be done. See also: PRISM (surveillance program) ~E:71.20.250.51 (talk) 01:07, 22 November 2013 (UTC)

A web-connected camera and microphone can be accessed by third parties without any real trouble by people in the know for these kinds of thing. It is absolutely possible. Is it happening? I don't think They care that much about you, but it is technically a thing that could happen. Norton explains possibilities for webcams here, and I have no reason to think Xbox is not vulnerable. Mingmingla (talk) 01:32, 22 November 2013 (UTC)

The companies aren't even trying to hide the spying any more. Just look at any set of Terms and Conditions, any company - for example, Kinect. [2] You don't own it, you can't examine it, you can't export it anywhere that allows people to look at it, you don't have any claim to privacy, you don't have any access to the courts, and they can do whatever they want to you at any time. The bottom line is that the only security you have with any computer equipment (so long as you are allowed that) is to physically disconnect things, preferably by never taking them into your home. We are far, far beyond the level of technology that our social mores are able to sustain, and there will be a reconciliation of the overall tech level on one side or the other. Wnt (talk) 01:58, 22 November 2013 (UTC)

"They" have always had the technical ability to spy on you through any web-connected camera (see Webcam#Privacy), provided they are able to inject code into your machine. My own privacy concerns (over stupid trolls, rather than the government) has always led me to disable the webcams on any computers I buy, or receive from my employer. Someguy1221 (talk) 02:02, 22 November 2013 (UTC)

• Anyone who has a camera or microphone permanently enabled on an internet-connected device is completely crazy in my opinion. I'm not even particularly paranoid, but it scares the sh*t out of me. Why would you even take the remote chance that some pervert or lunatic could spy on you in your home? I don't understand how people can be so blasé about it. I'm not happy unless the camera is physically disconnected or covered when not in legitimate use. Unfortunately, in-built microphones are harder to physically disable because even covering them won't completely block the sound. 86.169.185.129 (talk) 04:04, 22 November 2013 (UTC)

What's the difference between a Kinect and every laptop and cell phone sold in the past 10 years? It seems like there are hundreds of millions more of those devices compared to a gaming console that just launched. Yet no one seems particularly paranoid about them. Why is a Kinect any different? --209.203.125.162 (talk) 23:49, 22 November 2013 (UTC)

What you want is a white noise machine and an earbud. Still, better keep up with the happy thoughts, just in case. InedibleHulk (talk) 04:35, 22 November 2013 (UTC)

Those who have nothing to hide have nothing to fear. This is the high-tech equivalent of Will Rogers' axiom, "Live your life so's you wouldn't be ashamed to sell your parrot to the town gossip." Just in case, though, you could disable the camera by simply placing a piece of electrical tape over it. ←Baseball Bugs ^{What's up, Doc?} carrots→ 12:32, 22 November 2013 (UTC)

A quick question, what's your banking account and password? Oh and a list of the numbers, CVVs, expiry dates, full name, addresses, sample signatures and PIN numbers for any credit or debit cards you own would be great too. Nil Einne (talk) 13:24, 22 November 2013 (UTC)

Well you're at it, I want to know what your sexual habits are, and what you look/sound like when having sex. Creeped out? You should be. --Bowlhover (talk) 15:24, 22 November 2013 (UTC)

I don't do bank accounts or credit/debit cards - I operate strictly on a cash basis. As for the other thing, just picture the typical rabbit during mating season. Creeped out? You should be. >:) ←Baseball Bugs ^{What's up, Doc?} carrots→ 21:11, 22 November 2013 (UTC)

That's fine then. You don't sound like you're extremely poor, so a quick question where you store your spare cash (specific locations, e.g. if in your house under your mattress specify that level of detail as well as a full address preferably including GPS coordinations to a 10 metre or so range)? Can you also let me know where you store any keys etc required for access for any of said locations as well as any passwords, pin numbers etc for safes, combinations locks, secured guards, whatever. Oh and don't worry if my friend visits these locations sometime soon, they're just checking this stuff out, ignore them since you have nothing to fear. Nil Einne (talk) 15:46, 23 November 2013 (UTC)

The "you have nothing to hide" thing isn't true. To take a real example - my local neighborhood has a problem with people letting their dogs poop on the sidewalk. I proposed to our home owners association that we provide free poop bags at stations around our neighborhood and needed to research the cost. So I Googled for people selling those bags. Unfortunately, I accidentally clicked a "sponsored link" instead of just a regular search result. Consequence: For the last month, I'm plagued with adverts for dog-poop cleanup devices on just about every freaking web page I visit! Even to the point that I'm trying to find a recipe for a dish at thanksgiving - and when I print it out for my wife, it has TWO dog-poop-related adverts on the printout! Aaaaarrrrgggggh!

Privacy is a huge issue. Big businesses want to know as much as possible about you so that they can target you with adverts and other things that will entice you to spend more money with them. There is strong evidence that people like Amazon dynamically vary their prices depending on what they know about you. There is a very strong possibility that something you do online (thinking you're doing it in private) will result in them jacking their prices up when next you go to buy a book or something from them. Dunno about you - but I'd rather that didn't happen!

SteveBaker (talk) 15:51, 22 November 2013 (UTC)

While your response is correct, I don't think you have looked far enough forward to grasp the full problem. A merchant might say that his knowledge of you might entitle you to a discount instead; that's the first step. What about when they start saying that your Facebook/Twitter status determines the attractiveness of your online persona? What about when you're told that you have to have a degree in Microsoftology if you expect to be hired anywhere? What about when failing to be filmed for a few hours of your life is treated the same way as a ten-year gap on your resume is treated now, and they treat you like a terrorist? It is possible that the Revelation of John provides as good an insight as is to be had on such society, and on the fate of those who fail to comply with its dictates. Wnt (talk) 18:20, 22 November 2013 (UTC)

Steve, you might be able to fix the flood of dog poop adverts by clearing the cookies from your browser; or am I being naieve to the reach of the dog poop or big brother? Astronaut (talk) 20:05, 22 November 2013 (UTC)

Snakebite

If you get bitten by a venomous snake, is it possible to suffer permanent damage? This is NOT a request for medical advice. 24.23.196.85 (talk) 01:42, 22 November 2013 (UTC)

Well, yes, such as death (I assume the science reference would consider death permanent). Check out the article snakebite for some other long term effects. (In that article there is a picture of a particular injury that may be upsetting. Proceed with caution.) 88.112.41.6 (talk) 01:52, 22 November 2013 (UTC)

Definitely. The Hemotoxin bites in particular can cause huge wounds that may never fully heal. Google and you'll see lots of awful pictures. Shadowjams (talk) 03:13, 22 November 2013 (UTC)

Power required for hovering

Hi, please see the question here which I asked a quite a while ago. Returning to this problem, I could not remember how I had worked it out, so I tried to do it again. However, this time I get the answer Power = (M g)^(3/2)/(2 sqrt (rho A)), which is different by a factor of sqrt(2). Although the original answer was said to be correct by one respondent, I now doubt whether it was. Can anyone adjudicate as to which (if either, I suppose) is correct? 86.160.221.246 (talk) —Preceding undated comment added 03:52, 22 November 2013 (UTC)

The problem is under-constrained. There are literally an infinite number of correct answers. I gave a very technical answer, with citations and specific examples, when this was asked again in "Hover," in November 2012. "Helicopter flight is characterized by aerodynamic work against a non-conservative force. What this means in practice is that the amount of energy or power required for a maneuver depends on the helicopter's configuration. A helicopter pilot can independently control the collective, the cyclic, and also throttle the engine rpm. The pilot can also change the attitude of the helicopter to maintain a hover at many different engine settings and aircraft attitudes."

If your "ducted fan" has fixed blade pitch, your problem becomes a little bit better constrained; but you still need to completely define the angle of attack and the profile of the "fan" blade airfoil shape. Nimur (talk) 04:32, 22 November 2013 (UTC)

In a real-life helicopter there are masses of other considerations beyond what I am trying to calculate in my highly simplistic model. Forget all those. I believe that what I am trying to calculate is well-defined. It is just based on the amount of kinetic energy that must be imparted to the air in order to generate the right force to keep the mass hovering. 86.129.18.115 (talk) 12:15, 22 November 2013 (UTC)

Correct, but because of the way that physics works in the real world, there are many ways to put different amounts of kinetic energy into air, and achieve the same effective net force. Ultimately, the problem with your approach is that you are trying to apply conservation of energy, but you want to "conveniently ignore" the numerous ways that energy can manifest in air: as turbulence, as cyclic flow, as heat, as convective flow, as laminar flow, as a compression or pressure perturbation, and so on. Because the engine performs no useful work (when hovering, the force is exerted over no net distance upward), you must use a model that considers the energy lost to lossy terms like aerodynamic drag and turbulent flow and heat. These are not "optional" parts of the equation.

The real work - force exerted over a distance - is performed horizontally, against the air in the form of the rotating fan-blades pushing against the air as it turns. Work is performed against the drag term. How much work? Depends on the drag - which depends on the airfoil shape, the angle of attack, an| the parameters of the air, like density and viscosity; and on non-ideal terms that characterize turbulent flow.

If you can't quite grok how there can be an infinite number of correct solutions to a physical equation, it's time to review the theories covered in advanced algebra or ordinary differential equations. There are an infinite number of correct answers, but that is not identical to saying any solution is correct. Nimur (talk) 12:41, 22 November 2013 (UTC)

Yes, I do want to conveniently ignore all the other complexities. I know that the answer obtained will have little to do with the amount of power needed by a real-life helicopter. All I want to do is confirm the answer to the question "how much power to impart sufficient kinetic energy to the air to keep hovering", ignoring absolutely everything else, no matter how unrealistic it is in the real world. 86.129.18.115 (talk) 12:51, 22 November 2013 (UTC)

Let's replace air with a solid material, then, since you are choosing not to treat it a fluid - you are intentionally ignoring the most fundamental and critical properties of air ("it can flow"). So, the amount of energy required is zero. The hovering machine rests on a solid material, exerting a contact force equal to, and exactly countering, its own weight. No work is performed, because no force is exerted through any distance. This model is only accurate as long as we can ignore the properties of air as a fluid. Nimur (talk) 13:00, 22 November 2013 (UTC)

Or, let's take the other hypothetical extreme, treating air as a fluid that is so perfect that it never exerts any aerodynamic drag, nor ever exhibits any turbulent motion. The fan blades begin to spin, and lose no energy to the air! But there's a problem... the blades pass effortlessly through the air. They just ... go right through the air molecules, in total contraindication to all prior physical intuition! Because the fan blade cannot even feel the air, it cannot exert a force to push any air downward. (That would require drag and shear force to direct the rotational flow downwards). The fan keeps spinning, and keeps spending energy against its own internal friction, but air never flows, and the vehicle cannot hover.

Maybe you're starting to get the intuition that these "idealizations" are not only unrealistic - they're useless, ...and they aren't even consistent with any theory we could contrive if we started with first principles of physics, solving the kinetics for one single gas molecule, and then extrapolating statistically to billions and billions of other gas molecules. We need to deal with terms like shear force and viscosity. Those terms describe the way air really behaves, whether we observe it in a lab or if we model it with the kinetic theory of gases. If you choose to ignore those terms, you aren't writing "simplified" equations about your problem: you're just describing something else entirely.

We use drag coefficients and similar aggregate parameters so that we don't have to solve the harder, full-form analytic equations that describe fluid flow as an absolutely immense n-body problem with n=6.022x10²³. It's already in a "simplified form!" But if you just leave out these terms, you're going to get answers that are so incredibly wrong that they predict perpetual motion, or free energy, or zero energy, or something else totally ridiculous. Nimur (talk) 13:18, 22 November 2013 (UTC)

I see that there is a complete failure of communication here, in terms of me conveying the problem that I am actually trying to solve. If it helps, forget air. Forget fans. Forget all the complexities that are plaguing you. Imagine a device being fed sand. It has to fire a stream of sand downwards at sufficient rate to keep hovering using some imaginary mechanism that wastes no energy. The density parameter is the density of the stream of sand emanating. 86.129.18.115 (talk) 13:42, 22 November 2013 (UTC)

Even then, the answer is still underconstrained. A smaller amount of sand at higher velocity can accomplish the same task - providing identical impulse - as a larger amount of sand at lower velocity. The power expenditure depends on how you feed sand into the machine: are you constrained by mass flow rate? Are you constrained by maximum sand-pump power? None of these? Then, if you have a control system to ensure the craft hovers, you still have one unconstrained variable, so the engine can run at any power setting; a different amount of sand needs to flow at a different velocity depending on the power setting. That has to be controlled independently of the power setting. Your control system must calculate and match power- and flow-rate, (maybe it "opens the sand valve" to the desired level, at the same time it throttles the engine power to the desired level; alternately, the engine power can be set, and the "sand valve" is opened or shut); or else the craft won't actually hover. Again, because you're choosing to ignore energy loss terms, you've left open the prospect that we can, for example, take a 200 horsepower engine and use it to impel one single grain of sand at some preposterous hypersonic velocity every second, thus levitating the vehicle. A real engine cannot actually apply its entire power to drive a single grain of sand. Nimur (talk) 14:12, 22 November 2013 (UTC)

The power expenditure does indeed depend on the flow rate of sand. That is accounted for by the cross-sectional area and density parameters. You are correct, the resulting equation would in theory work with a tiny flow rate and extreme speed. That is as expected. 86.129.18.115 (talk) 14:17, 22 November 2013 (UTC)

...so, power is force times velocity, which is just "weight times sand-velocity" in this case. Interestingly, that's the gravity-burn equation I linked for you... nearly the first answer you got, back in 2011! But, explain again why cross sectional area limits the sand velocity? Perhaps you mean to say ... the flow is choked, because it is non-ideal? Fascinating, that we would need to model non-ideal parameters for a simplified problem like this! Nimur (talk) 14:20, 22 November 2013 (UTC)

(edit conflict × 2) In the first round Dragons flight spoke of the air being incompressible; note that your sand idea is at odds with this (because obviously sand grains can be brought closer together with no energy). That said, the equations I can see here are $F=Mg={\dot {m}}\Delta v$ (conservation of momentum, and a sand supply separately suspended at your altitude), ${\dot {m}}=A\rho v'$ (note that this depends delicately on the issue of compressibility), and $P={\dot {m}}(v'^{2}-v_{0}^{2})/2$ (rate of kinetic energy deposition). For sand, we can suppose that $v_{0}=0$ (a horizontal conveyor feed), so $v:=\Delta v=v'$ and we can simplify to $Mg=A\rho v^{2}$ and $P=A\rho v^{3}/2={\frac {(Mg)^{3/2}}{2{\sqrt {A\rho }}}}$, which is what you have this time around. At least three of these four equations are separately wrong for a fluid: a fluid exerts pressure forces in addition to reaction forces, has a compression-dependent flow rate, and is moving when it arrives at the impeller. (Of course, if Dragons flight has a derivation of the older form, let's hear it; as Nimur says, this is treacherous ground.) --Tardis (talk) 14:28, 22 November 2013 (UTC)

Thank you so much for understanding what I was asking! It looks like last time I was off by a factor of sqrt(2), as I suspected. 14:39, 22 November 2013 (UTC) — Preceding unsigned comment added by 86.129.18.115 (talk)

Tardis, you didn't apply the product rule on your derivative to compute "rate of deposition of kinetic energy":

${\frac {d}{dt}}{\frac {1}{2}}mv^{2}={\frac {1}{2}}(v^{2}{\frac {dm}{dt}}+2mv{\frac {dv}{dt}})$... surely you don't think we can idealize away that velocity term? And that's why your answer for power totally lacks a term proportional to exhaust velocity. I'm not so very good at following equations, but I can spot an error a mile away if it forgets a term that has physical significance... and in this case, you left off v_E. Not that it's important, it's just where the majority of the energy is getting put! It also makes for a catchy song lyric... udv +vdu, you left off vE... something wasn't quite right about it... Nimur (talk) 15:11, 22 November 2013 (UTC)

I don't know whether this answers your question, but in my working-out the exhaust velocity gets accounted for in the form v = sqrt(F/(A rho)). 86.129.18.115 (talk) 18:05, 22 November 2013 (UTC)

I'm not quite sure which of those two terms I'm omitting: the first is appropriate if you consider the "object" to be the slug of falling sand, which (neglecting gravity on it since we don't have to pay for that) is moving at a constant velocity but has a growing mass (yielding $P={\frac {1}{2}}v^{2}{\dot {m}}$: here v is a constant, so is your $v_{E}$), while the second is appropriate if you consider an infinitesimal mass — but then you need to integrate over the time during which the impulse is applied, giving $dE=dm\int _{0}^{t}v{\frac {dv}{dt}}dt={\frac {dmv_{E}^{2}}{2}}$ so $P={\frac {dE}{dt}}={\frac {v^{2}}{2}}{\frac {dm}{dt}}={\frac {1}{2}}v^{2}{\dot {m}}$ (where I have again taken $v:=v_{E}$). (There are, I'm sure, some very technical arguments that could be made about integrating and then differentiating with respect to t in two different senses, but the rigorous approach of considering the simultaneous distribution of energy parcels of mass that are at different points in their acceleration will yield the same result because of linearity.)

Anyway, I didn't think of it with that equation at all. I simply said that each parcel of material changes from 0 velocity to $v:=v_{E}$, so its specific kinetic energy change is just the final value ${\frac {v^{2}}{2}}$. Since it is at a rate ${\dot {m}}$ that we dole out that specific kinetic energy, the power is just the same product from before.

You're quite right that specific impulse is relevant. However, here it is constrained by the known $\rho$ and A, whose product is a linear density. It is an entirely fair objection that $\rho$ at least is not known a priori, but must be found by equation of state considerations from the flow and varies non-trivially over space and time. However, our trivial "sand conveyor" case is reduced to one parameter in a physically plausible way (though the engineering is absurd) by the specified density. A different question would be "how can we minimize the power required by changing the output density?", to which the trivial answer is of course "make the density as large as possible to mimic a solid support where the power is 0". --Tardis (talk) 01:39, 23 November 2013 (UTC)

I believe that the solid support case is qualitatively different, and cannot be approximated or approached by making density large. 86.128.4.176 (talk) 14:29, 23 November 2013 (UTC)

I think the best "qualitative" interpretation I have is that the first term reflects energy added to the slug of sand to move it through the impeller, and the second term reflects the energy added to each slug of sand to accelerate it through the impeller. It's not really physically meaningful to distinguish between these components of the equation, except in the infinitesimal sense: there is an instantaneous change in energy associated with the velocity, and another term associated with the acceleration, for each infinitesimal unit of mass. Nimur (talk) 09:01, 24 November 2013 (UTC)

Your question has no reasonable answer. The energy required is entirely dependent on the nature of the fluid you're pushing downwards.

• An object can sit on top of a block of concrete indefinitely using no energy whatever - the power is zero.
• I have a desk ornament of Dr Who's Tardis that floats effortlessly in the air using magnetic levitation - again, zero power consumed.
• Work done is force through a distance. If the object is perfectly still - with a perfectly efficient mechanism, the distance travelled is zero and the power is zero. Ergo, any power that is needed is "losses" due to a less than perfectly efficient levitation scheme...so the amount of power required depends only on the relative efficiency of the machine.
• A hovercraft needs some power to keep it's soft skirt inflated - but otherwise is sitting on a block of air.
• Consider a helicopter, which needs much more power than a hovercraft because the air isn't contained and is continually leaking out of the sides.
• Even in a helicopter, the numbers are drastically different between a 'ground-effect' hover and a high altitude hover or a hover beneath an overhang (eg hovering underneath a bridge).
• Those water jet packs keep someone hovering very nicely with very little power because their working fluid is water - but regular rocket packs need huge amounts of power because they are exhausting hot gasses.
• A rocket hovering in a vacuum needs different amounts of power than one hovering in air - which is different again to a jet motor doing the same job.

Anyone who claims to have a simple formula for such a general question is talking nonsense. I think this was adequately explained to you the last time you asked this. One person gave you some equation or other - but it was incorrect, please don't latch onto that as "The One Good Answer That I Got" - it wasn't...it was the one complete bullshit answer you got!

If you can narrow things down more specifically to precisely how this "levitation" is being performed, we'd have a chance at getting a better answer for you.

SteveBaker (talk) 13:55, 22 November 2013 (UTC)

Please read my last message. The question that I am posing is well-defined and has an exact answer. 86.129.18.115 (talk) 14:11, 22 November 2013 (UTC) Also, ignore ground effects. If any other real-life complexity occurs to you, IGNORE IT. 86.129.18.115 (talk) 14:13, 22 November 2013 (UTC)

There's some out-of-order posting here, (which is okay, just a little confusing). I've responded above. Your new problem restatement is still underdefined. Nimur (talk) 14:16, 22 November 2013 (UTC)

I completely understand that you're asking for a spherical cow kind of answer - and I can tell you that the equation for that is "P=0". Gravity is a "force", not an energy source - so in the abstract "spherical cow" universe, producing an equal and opposite "force" requires no energy whatever - which is why magnetic levitation consumes no energy and this little TARDIS on my desk hovers so effortlessly - or why we could place an object at one of the "Lagrange points" and it would just sit there without falling.

Power equals force times distance moved...if the distance moved is zero, then the power/energy-consumption is zero too. The problem is that 100% of the energy consumed in a practical machine is in producing that force in a situation where there is nothing solid to push against. The details and losses that you're trying to ignore are 100% of the resulting power requirement - so you don't get a simple abstract answer. Many people here are trying to tell you that - they know the answer and you don't (which is why you asked them!) - so stop arguing with them and listen! I'm sorry, life sucks, there isn't always a simple answer to even the simplest question. SteveBaker (talk) 14:35, 22 November 2013 (UTC)

The question that I am asking is well-defined and has an exact answer that is not zero. It is not difficult to solve for anyone with a knowledge of physics. For me, however, it is on the margins of what I can work out. The biggest difficulty appears to be explaining to other people what the question actually is. 86.129.18.115 (talk) 14:42, 22 November 2013 (UTC)

I'm sorry - but you say that you don't know what the answer is - but you somehow do know that it's not difficult and you know that it's not zero and you know that it's well-defined? Well, if you know so much, how come you don't know the answer? The truth is that you know none of those things - really - you don't. Everyone here is telling you that. Ask yourself what information you have that tells you that there it's "not difficult to solve"? How do you actually know that? The answer is that you don't...you're guessing that it's easy to solve, that it's well-defined and so forth - and we're telling you that your guess is incorrect. So, you asked us a question - we've told you the answer. Stop arguing and listen! SteveBaker (talk) 15:36, 22 November 2013 (UTC)

No, you listen. "We" have done nothing. At least one person understands what I am asking. The fact that you can't grasp it is your problem, not mine. 86.129.18.115 (talk) 18:00, 22 November 2013 (UTC)

See the article on thrust, specifically https://en.wikipedia.org/wiki/Thrust#Thrust_to_power. --Modocc (talk) 15:02, 22 November 2013 (UTC)

Hey, is that the same as my equation??!! 86.129.18.115 (talk) 18:34, 22 November 2013 (UTC)

Or see this pdf: www.aerostudents.com/files/aircraftPerformance2/helicopters.pdf‎ (notice the square root of 2, so your old answer was correct). This is a typical physics introduction handbook problem, one that a highschool student should be able to answer. Judging by the reactions you got, most people here would have flunked their physics exam. Ssscienccce (talk) 18:58, 22 November 2013 (UTC)

Here's another one: FTM106: U.S. Naval test Pilot School Flight Test Manual chapter 5 Hover performance Power required assuming an ideal rotor: equation 5.24 Ssscienccce (talk) 19:26, 22 November 2013 (UTC)

And we even have an article on it: momentum theory Quote:

For a stationary rotor, such as a helicopter in hover, the power required to produce a given thrust is:

$P={\sqrt {\frac {T^{3}}{2\rho A}}}$

Ssscienccce (talk) 19:32, 22 November 2013 (UTC)

Do you have any idea why the formulas here and here seem to differ by the same factor of sqrt(2)? My working-out was based on my pretty sketchy knowledge of some basic physics equations, and I did not consult any of these references, yet spookily I seem to have produced two differing equations that match the two differing equations in the articles. Unfortunately, I cannot now remember how I arrived at my original equation, so I cannot see where the reasoning diverges. 86.129.18.115 (talk) 20:05, 22 November 2013 (UTC)

The formula in the thrust article would be valid for a rocket, not for a helicopter (you best ignore the comment in that section about incoming air). To quote A review of rotor induced velocity field theory (Office of Naval Research, 1954) "this was one of the most important features of momentum theory. It showed that the induced velocity at the disk was one-half its value in the ultimate wake." It can be derived with the Bernouilli equation, but to put it simply, you're not just pushing air away from the rotor, you're also pulling air towards the rotor. Look at it this way: the rotor creates a pressure difference between top and bottom, and the upward force is equal to (Pb-Pt)A . Pb will be higher than ambient pressure, Pt lower. Pb-Pa = Pa-Pt = (Pb-Pt)/2, so the upward force is 2(Pb-Pa)A. With a rocket, the upward force is only (Pb-Pa)A. Ssscienccce (talk) 21:57, 22 November 2013 (UTC)

Note that real rotors will require more power to achieve the required trust. The calculated power will only produce T*FM thrust, with FM being the figure of merit of the rotor. Values between 0.7 and 0.8 represent good hovering performance, while state-of-the-art rotors may reach 0.82. The actual required power is P/FM, this is the power that the rotor must receive, doesn't include transmission losses between engine and rotor. Maybe add 10% for those losses and you get a value that, assuming good design and optimal conditions should suffice to hover without ground effect. Ssscienccce (talk) 05:05, 23 November 2013 (UTC)

A very similar factor explains the difference between the OP's two answers: since the fluid must already be moving when it reaches the impeller, its change in kinetic energy is larger ($\Delta (v^{2})=(v_{0}+\Delta v)^{2}-v_{0}^{2}=(\Delta v)^{2}+2v_{0}\Delta v$). --Tardis (talk) 01:39, 23 November 2013 (UTC)

A bit of searching turned up this power point presentation on propeller thrust: [3]. --Modocc (talk) 03:14, 23 November 2013 (UTC)

I would like to momentarily go back to the "sand conveyor" simplification, which eliminates all the issues of fluid behaviour. Assume that the sand is made available to the device at zero velocity and zero cost. My method of working out the power requirement is as follows. (I know that this probably should be done with calculus but I want to stick with exactly what I have if possible, to avoid getting lost, as my grip on this is pretty tenuous.)

F is the force (thrust) required to be produced
v is the ejection velocity of the sand
m is the mass of sand ejected in each timestep of Δt
P is the power needed
A is the cross sectional area of the ejected stream of sand
ρ is the density of the ejected stream of sand

From basic principles:
(1) m/Δt = vAρ
(2) F = mv/Δt ⇒ m/Δt = F/v

From (1) and (2):
(3) F/v = vAρ ⇒ v = sqrt(F/Aρ)

From kinetic energy equation:
(4) P = (mv^2/2)/Δt

Substitute (2) and (3) into (4):
(5) P^2 = F^3/(4Aρ)

Now, what I would like to know is whether it is possible to adapt this method with just a small tweak in order to produce the forumula at Momentum theory, or whether a different method altogether is needed. I believe that in my original result from several years ago I may have had v = sqrt(2F/Aρ), but I can't figure out now how I arrived at that. 86.128.4.176 (talk) 00:12, 24 November 2013 (UTC)

As you have set up your equation, power is the dependent variable. You have set up an equation to calculate the power as a function of thrust. You specify the thrust (e.g., set it equal to vehicle weight), and you assume that some valid configuration exists for which you can deliver that thrust. You have (intentionally) ignored that some thrust values are impossible to achieve; and some power values are impossible to achieve; and that thrust and power are coupled in a real engine. Those are acceptable simplifications. It's all legal, but it's a little weird, because usually power is the variable we can actually control, and thrust is a result, not an input. You're sort of solving an inverse problem.

But there are still some flaws in your approach. Equation 1 assumes an incompressible fluid; that's also fine. You are in good company when you make that assumption.

Equation 2 is incorrect. It's just flat out wrong. Force is not "mv/Δt". Force is equal to the total change in momentum with respect to time. So, F = d(m v) /dt = (m dv/dt + v dm/dt). This is called the product rule for differentiation. In your approach, you are entirely neglecting one of these terms, which means you are failing to account for a significant amount of power. In order to calculate this term, you must provide some constraint equation. How do you accelerate each element of mass? Typically we could use the properties of a fluid (or sand) to constrain this term. But, I already know you don't want to bring those details into play, and you're happy to sacrifice physical accuracy. That's fine... you can constrain this term by some other method - by decree, if you like: dv/dt = 1. But you can't just leave it out of the equation. That would be mathematically incorrect.

Equations 3 and beyond are invalid because they depend on Equation 2. Equation 4 makes a similar mathematical error.

If you want to solve physical dynamics problems like this one - even if you choose to abstract some details away - you must become better acquainted with the correct applications of differential and integral calculus. These tools are not optional. Nimur (talk) 10:47, 24 November 2013 (UTC)

First, I disagree that this "inverse problem" is "a little weird". It is entirely reasonable to ask how much power is needed to hover a certain mass. Second, the basis of F = mv/Δt is simply F = ma. Over a time interval Δt, a mass m (of sand) is accelerated smoothly from 0 to v. Therefore a = v/Δt and the associated reaction force is mv/Δt. I would like further opinions on the validity of this please. I don't understand why it is wrong. 86.169.36.80 (talk) 12:30, 24 November 2013 (UTC)

It's legal to solve inverse problems; they are a central consideration of control theory and engineering. But they are frequently ill-conditioned, which means that you must use absolutely flawless mathematical rigor when calculating solutions. In your specific problem, you are considering power and force to be totally independent. Is this valid? Well, sure, if you drop the terms that relate the two! And then you are left with an equation that is wrong. Surely by now you've seen those mathematical jokes that prove 2+2 = 5 by cleverly hiding a division by zero somewhere in a simple-looking equation? Those are the consequences of incorrectly solving ill-conditioned problems. Nimur (talk) 16:17, 24 November 2013 (UTC)

(Disclaimer. I'm just another guy on the web that likes to seek relevant references too). From our Impulse (physics) article we have $d(m\mathbf {v} )\,=(dt)\mathbf {F} \,=d\mathbf {J} \,=(dm)\mathbf {v} _{e}\,$ which justifies the derivation given in the article on thrust which is essentially the same as yours. These derivations glosses over the some of the finer detail that Nimur is trying to constrain/define when he takes the derivative, but I see nothing inherently incorrect with your approach either (I may not have had enough sleep, and my maths can suffer when that happens). The power required is proportional to the jet velocity, see [[4]] but that means its better to propel larger masses when using lower exhaust velocities. The difference I see between what you have now and before is the difference between the forces produced by the rockets and helicopters that others pointed out above. Propellers have an incoming velocity added in addition to the exhaust velocity because the force is doubled (its a push pull system). A similar result (with a doubling of an upward force on the hand) can be obtained by dribbling a basketball. --Modocc (talk) 13:30, 24 November 2013 (UTC)

Let's be sure there is no confusion about the meaning of m. In my derivation, m is, as explained above, the mass of a chunk of sand propelled out over Δt. It is not the mass of the vehicle. In my concept dm is zero (or is not a relevant measurement). The sand is available in the "milieu" at zero cost and does not need to be carried by the device (this is obviously unrealistic in the case of a rocket which must carry its own fuel, but is intended to be analogous to the air in the case of a propeller). That being said, do you feel, then, that my derivation above can yield the equation at Momentum theory just by applying a factor of 2 at the relevant point? This is the part I really can't get my head around. 86.169.36.80 (talk) 13:48, 24 November 2013 (UTC)

The equation at Momentum theory can be obtained from the powerpoint presentation's equations that I provided earlier (you can simplify those by first setting the plane velocity to zero and then combine the equations for thrust and power). When you do that, you will see that for a given air velocity the thrust is twice that of the rocket. To understand that, envision a car with two props, one underneath expelling air from its interior and another one on top pulling it in, so you have left out half the force. --Modocc (talk) 14:12, 24 November 2013 (UTC)

Yeah, thanks, I looked at that before but I can't understand it unfortunately. That is why I just wanted to stick with what I had worked out and make a small change, if at all possible. I'm puzzled that my formula, P^2 = F^3/(4Aρ), actually needs less power for given thrust than the Momentum theory one, P^2 = F^3/(2Aρ). If I am somehow "missing half the force" then shouldn't it be the other way around? 86.169.36.80 (talk) 14:32, 24 November 2013 (UTC)

The problem is that your entire equation is wrong: it states an incorrect relationship between power and force; and you are still trying to draw conceptual conclusions from it. If you make unphysical equations, you get unphysical results: 2 = 5, perpetual motion, faster-than-light sand conveyors. The least of your worries is a scale factor of 2. Your continued attempts to make these problems go away by substituting sand for air belies that you are not understanding the fundamental problem. Flow equations work equally well for grains of sand and for microscopic gas molecules. You still need to define shear terms, viscous interaction terms, ... it's almost as if the Navier-Stokes equation was written without loss of generality!

Hey, what's this? An entire textbook chapter of correct physical equations, available at no cost, from a reliable source? It's almost stunning that nobody linked to this already! Except, that I did, twice before. You can download the entire textbook, at no charge, from the FAA; or you can buy a paper copy for about $15. I can recommend some good physics and calculus books if you need those, but the Helicopter Handbook uses engineering-charts instead of calculus-based derivations, so the math is quite simplified.

Have a look at chart 2-32. See how many parameters go into the power equation? The power required depends on the interaction between the impeller, and the fluid that is being impelled. The very same applies, whether we consider a rotor in air, or a conveyor belt pushing sand, or a ship propellor in seawater. The parameters are different, but you cannot ignore that required power is coupled intricately with the messy details of the motion of the fluid (or sand). Nimur (talk) 17:49, 24 November 2013 (UTC)

An actuator disk accelerating a fluid flow from right to left

Woeps, I should have paid more attention, wasn't as simple as straight forward as I thought, ignore what I said previously about rocket versus helicopter. What's missing is the continuity equation: we assume the air is incompressible, so the volumes above and below the rotor have to be the same. Since the velocity of the air under the rotor is higher than above it, the diameter of the air flow must contract to comply with the continuity equation. That's what you see in the figure: the rotor accelerates the flow to the left, the rotor is at point S, and you see that the air flow contracts, and the velocity increases up to the "ultimate wake". So the air doesn't exit the rotor at maximum speed, the pressure differential between the rotor and point S1 accelerates the air, and only at S1 will it reach the maximum velocity. On the right of the rotor, the same thing happens. Instead of using the velocity of the air exiting the rotor to calculate the kinetic energy, you have to take the ultimate wake velocity, which is larger, that's the reason for the higher power requirement. The ultimate wake velocity comes from momentum theory, that's why one handbook said: "this was one of the most important features of momentum theory. It showed that the induced velocity at the disk was one-half its value in the ultimate wake."

This also explains why the sand analogy can't be used, because pressure difference play an essential role.

I'll post a more decent overview later Ssscienccce (talk) 18:14, 24 November 2013 (UTC)

Here goes: Air far above the rotor is at ambient pressure p_a and zero velocity, far downstream it's at wake velocity V_w and at ambient pressure p_a again (we assume inviscid and frictionless fluid, so the wake and the surrounding air don't mix). Directly under the rotor, the velocity is V_d and the pressure is p_d.

The thrust delivered is equal to the change in momentum with time, so (with dotted m meaning the mass flow rate):

$T={\dot {m}}V_{w}$ (why V_w and not V_d? Because at V_d there's an additional pressure component)

The power delivered by the rotor is

$P={\tfrac {1}{2}}{\dot {m}}V_{w}^{2}\quad or\quad P={\tfrac {1}{2}}TV_{w}$

But at the location of the propeller disc, the power is equal to the work done by the thrust:

$P=TV_{d}$

So

${\tfrac {1}{2}}TV_{w}=TV_{d}\quad or\quad V_{d}={\tfrac {1}{2}}V_{w}$, the velocity under the rotor is half of the ultimate wake velocity.

The mass flow rate is:

${\dot {m}}=\rho V_{d}A$

We can write the thrust as:

$T={\dot {m}}V_{w}=\rho V_{d}AV_{w}={\tfrac {1}{2}}\rho AV_{w}^{2}$

This gives us Vw in function of the thrust

$V_{w}={\sqrt {2T \over \rho A}}$

So the power becomes:

$P={\tfrac {1}{2}}TV_{w}=T{\sqrt {T \over 2\rho A}}$

That should be it, I think... Ssscienccce (talk) 13:53, 25 November 2013 (UTC)

So the essential thing to remember is: the air leaves the rotor at speed V_d, but the pressure difference with the ambient air continues to accelerate the air, so the thrust is actually mV_d + p_d (p_d being the overpressure under the rotor) Ssscienccce (talk) 14:16, 25 November 2013 (UTC)

It's all very clever to point out that there is a ${\frac {dm}{dt}}$ term that arises from the product rule. You can even use that term (in my "slug of sand" case earlier). But there's a reason that students are taught $F=ma=m\Delta v/\Delta t=mv/\Delta t$ (further expressions appropriate in the case of constant acceleration (or average force) and zero initial velocity, respectively); you can always work merely with that expression. (The common cases where people use the ${\frac {dm}{dt}}$ analysis, like pushing a cart that's simultaneously being filled with material, can instead be interpreted using the normal second law if you consider that you are applying the force (perhaps indirectly) to the added material: its instantaneous velocity change times its mass flow rate yields the correct force.) (In reply to your comment higher up in response to me, to simplify things:) Acceleration requires work because it changes kinetic energy. Mere movement does not, unless it is in a potential field. Here, we can ignore the effects of gravity on the sand, because we can take it to be at zero velocity (and otherwise supported) until disbursed and to be irrelevant afterwards. --Tardis (talk) 21:44, 24 November 2013 (UTC)

About the only thing the derived thrust equations for the helicopters and rocket (which is nothing more than a souped up version of a sand blaster :-)) have in common exactly is their mass flow, and the change in volume elements with the helicopter's flow does not effect that. In addition to what I interpret to be a force $mv/\Delta t$ being applied twice (once during the inflow and secondly during the outflow), the induced power Tv that is dumped into the helicopter's wake is also twice that of the rocket Tv/2, thus the rocket is more efficient, producing an equivalent thrust with less power as the OP pointed out and, in any case, the difference between the relations turns out not to be very large and is simply the cube root of 2. -Modocc (talk) 00:11, 25 November 2013 (UTC)

Let me try to rephrase: the quantity of energy conveyed away by the exhaust, during each unit of time, is a conceptually distinct amount of power from the power necessary to generate said exhaust. The former is purely derivable from a kinetics calculation, while the latter depends on things like engine efficiency. Even idealized engines have maximum efficiencies. Consider, for example, the Carnot cycle. An ideal rocket in a no-net-motion gravity burn is one limiting case, where all the momentum is carried away by the exhaust, and all the useful power is conveyed to the exhaust gas. But that is not the only power we need to consider: the original ask was for the power required to hover - not the subset of that power that gets wasted in exhaust gases; nor the subset of power that corresponds to only the kinetic energy of the rotor wash; nor the subset of power that corresponds to the kinetic energy of moving sand. When you fail to account for the lossy process by which an engine converts potential energy into kinetic energy, you are describing a perpetual motion machine. At that point, we may as well "further idealize the problem," connect the exhaust nozzle to the engine intake, and use perpetual motion to hover with zero energy input. Lots of power goes through, but no new energy gets put in by the engine. Everybody who keeps "simplifying" these equations is performing exactly this flawed process.

The ask was for how much power is needed to hover. That is asking how much new energy the engine must add, per each unit of time. The ask was not how much power denotes the rate of energy exchange in the airflow. The ask was not how many ways can we play with dimensional analysis to yield a term whose units are measured in terms of energy per unit time. The ask was "how much power is needed to hover." To answer that, we need to know how efficiently the engine converts input energy into useful work. Whether the engine is a rocket impulse engine, or a helicopter rotor, or a sand chute, the laws of thermodynamics still apply. If you want to calculate the energy conveyance for each granule of sand, and set up an n-body problem, you can do so, but what you cannot do is assume a magical sand conveyor belt that is perfectly efficient, has no friction, yet still performs useful work accelerating sand.

Think of it conceptually! If the conveyor belt has no friction, it cannot move the sand, because there is no traction. This is exactly analogous to a viscous drag term in a conventional fluid. You can not evade thermodynamics, no matter how many simplifications you make. You must account for how the conveyor belt exerts force on each sand granule. And you must integrate each differential unit of work over all n-gazillion sand grains. And did you remember to conserve angular momentum for each granule of sand with respect to (n-gazillion minus one) other grains? Oh, woops, you forgot? No problem, it's only that angular momentum is a fundamental property of the universe, whose conservation is more fundamental than the conservation of energy... not like anyone would notice if we totally use wrong physics to constrain the motion! We can just throw out one conservation principle so that it's easier to calculate the other one, right? Besides, each grain is so small that it has almost no momentum... how much different would our answer be? There's only n-gazillion very small errors... Or, you could use a bulk approximation that is physically accurate in the statistical ensemble, ergo, applying regular fluid flow equations. If you don't use the correct physically-guided equations, your answer is wrong. Period. Nimur (talk) 18:19, 25 November 2013 (UTC)

I see you are trying to teach the OP something he didn't even ask about. How do you know he hasn't already figured that some processes are more losy than others? Did he ask for the power needed to hover with a balloon? No. He asked about some specific derivations regarding thrust and you don't seem to have a problem with the P(T) derivations nor their utility. -Modocc (talk) 18:57, 25 November 2013 (UTC)

I understand perfectly well that all real machines are lossy. None of Nimur's obfuscations seem to be any help in deriving or explaining the formulas at Momentum theory and Thrust#Thrust to power, and they may be just a smoke-screen to disguise his early failure to recognise what seems to be a fairly standard equation. 86.161.61.128 (talk) 17:51, 26 November 2013 (UTC)

• @Ssscienccce, thank you for your derivation above. I need to spend time working through it to see if I can get my head round it. I wonder, if you have time, whether you could cast your eye over my "sand conveyor" workings above (piece starting 'I would like to momentarily go back to the "sand conveyor" simplification') and give your opinion on whether this is correct within its own ambitions. Nimur keeps insisting that it is flat wrong but I am not so sure. What do you think? 86.161.61.128 (talk) 18:11, 26 November 2013 (UTC)

You are working with an equation so non-standard that it cannot be cited in any textbook or paper! But you believe your equation anyway, ...because some other anonymous Wikipedia contributor wrote a bunch more equations you barely understand! So tell me, when you read the article on thrust and power, which type of power do you think it is referring to? The Pilot's Handbook of Aeronautical Knowledge (yet another free physics textbook for you) doesn't seem to have your "standard" equation in it. Actually, it states this, about comparing power and thrust:

“ It is possible to compare the performance of a reciprocating powerplant and different types of turbine engines. For the comparison to be accurate, thrust horsepower (usable horsepower) for the reciprocating powerplant must be used rather than brake horsepower, and net thrust must be used for the turbine-powered engines. In addition, aircraft design configuration and size must be approximately the same. When comparing performance, the following definitions are useful:

• Brake horsepower (BHP)—the horsepower actually delivered to the output shaft. Brake horsepower is the actual usable horsepower.
• Net thrust—the thrust produced by a turbojet or turbofan engine.
• Thrust horsepower (THP)—the horsepower equivalent of the thrust produced by a turbojet or turbofan engine.
• Equivalent shaft horsepower (ESHP)—with respect to turboprop engines, the sum of the shaft horsepower (SHP) delivered to the propeller and THP produced by the exhaust gases.

”

That comes from... what's this? A whole chapter on comparing different types of power between different types of engines. Oh! How relevant! It looks as if a group of experts on aerodynamics got together, wrote a physics book, and explained your problem very thoroughly! Were I to actually trust my life to an aircraft designer, I would sure hope they use that procedure, instead of "some equation from Wikipedia!" But, I'm sure you guys will be able to work through the small bug in your math. While you and your fellow contributors work through some more equations and conduct original derivations in total contravention of Wikipedia's standard policy, and in complete defiance of standard, published, approaches to solving this problem, I'll be out flying; the weather is great today. Nimur (talk) 19:17, 26 November 2013 (UTC)

If you believe that strongly that the P(T) derivation at thrust is incorrect and needs a citation, tag it, it was added over a year ago by some other guy... and if you didn't realize that we have been talking about two different equations (neither of which were the OPs although he has derived both independently apparently), then please reread this thread to see what you missed. --Modocc (talk) 19:44, 26 November 2013 (UTC)

Nimur, I am getting very tired of your worthless and irrelevant rants. I would prefer it if you made no more contributions to this thread. 86.179.114.69 (talk) 19:57, 26 November 2013 (UTC)

Unless his contributions are disruptive or violates WP:NPA he is still welcome, its the wiki-way, so please bear with it. --Modocc (talk) 20:17, 26 November 2013 (UTC)

Arbitrary break

From the article on thrust we have $\mathbf {P} ^{2}={\frac {\mathbf {T} ^{3}}{4\rho A}}$. From momentum theory we have $P={\sqrt {\frac {T^{3}}{2\rho A}}}$ or $\mathbf {P} ^{2}={\frac {\mathbf {T} ^{3}}{2\rho A}}$.

The OP's equation using sand is exactly the same as the thrust article's equation. Thus, whether or not the OP used a rigorous derivation, if his thrust equation happens to be incorrect then the article's equation is also incorrect and would need to be removed. Apparently, Nimur snubbed a poorly written article, unless he was under the false impression that the two articles' equations were identical (and he would have misinterpreted much of what I and others have written about it). When Nimur says it "...doesn't seem to have your "standard" equation in it." emphasis mine, I'm not sure if he is referring to the article's equation, the OP's equation or both. -Modocc (talk) 20:53, 26 November 2013 (UTC)

It may be correct for sand (as far as I can see it is), it's not correct for air: sand will leave the accretion disk at it's ultimate speed because there's no force acting on it (ignoring gravity). Air that leaves the propeller is still accelerated until the pressure drops to ambient. So the velocity at the disk is correct for the mass flow (density * area * velocity), but for the thrust and power, the wake velocity must be used. That's the main result from momentum theory, and every source repeats it:

• http://www.aerostudents.com/files/aircraftPerformance2/helicopters.pdf‎ page 1: The ideal power of the helicopter now becomes equation (2.3)
• FTM106: U.S. Naval test Pilot School Flight Test Manual chapter 5 Hover performance page 5.16: The power required to accelerate the air mass through the disc, induced power, assuming T ≅ W at a hover, is equation (5.24) (T is thrust, W is weight of the helicopter)
• "Rotorcraft Aeromechanics" By Wayne Johnson, page 41: equation (3.5)

Every time the same equation, $P={\sqrt {\frac {T^{3}}{2\rho A}}}$ Ssscienccce (talk) 22:05, 26 November 2013 (UTC)

Instead of moving air downward with rotors, the model used with momentum theory, one can build rockets with pressurized air, so same fluid but different equations. The OP was correct the first time for rotors, and has simply gotten our article's rocket equation the second time. But we've already pointed this out to the OP though, but I'm not sure if Nimur will agree that the P(T) equation at thrust is correct, so we will likely need to quote or locate a reliable source for it. -Modocc (talk) 22:33, 26 November 2013 (UTC)

I agree, it would be good to find a source for that. It says here that P = Fv/2, which spookily enough is an equation I have written down on the pad in front of me where I did the workings-out. If we could also validate that F = Aρv^2 then that would seem to nail it. 86.179.114.69 (talk) 00:14, 27 November 2013 (UTC)

fluid mechanics

how to know flow analysis of fluid — Preceding unsigned comment added by 213.55.110.123 (talk) 13:37, 22 November 2013 (UTC)

After you've exhausted the information in our article on fluid mechanics, you might be able to ask a more specific question, or more clearly define your request.

Do you need help finding information in a different language? We have thorough articles in German, Italian (it:Fluidodinamica), and Arabic, and even a stub in a stub article in Oromo. There are related articles in many other languages. Nimur (talk) 13:40, 22 November 2013 (UTC)

Fluid mechanics is one of the tougher subjects out there (and one of the least well-understood ones). There is simply no way to contain all that you need to know in a response here - or even in a full encyclopedia article. You're going to need at least a good book on the subject - and possibly some college-level courses to properly get to grips with it.

The mathematics behind it is complicated - and even with the best math available, we need gigantic wind-tunnels or wave tanks to properly confirm the results of mathematical/computer estimations.

I can perhaps sketch out one approach to this in computers that may prove helpful to you:

• Divide the volume of fluid we're interested in into tiny imaginary cubes - producing a three-dimensional grid.
• Divide time into tiny steps.
• Within each cube we'll approximate the flow as a linear motion through the cube and the temperature and pressure as being constant throughout - clearly that's not true in the real world - but if we make the cubes small enough, it may be good enough.
• Now, we can formulate a relatively simple equation using the temperatures, pressures and kinetic energies of all of the adjacent cubes to figure out how they influence this cube during one tiny time-step. We figure out heat transport and fluid flowing into or out of this one - which gives us a new temperature, pressure and flow rate through this cube at the end of one tiny time step.
• Some cubes have boundaries that face the object we're interested in testing - so their equations have to take that into account.
• We start with all of the cubes being identical with the fluid flowing through them being stationary and the temperature and pressure being uniform throughout them all.
• Armed with those equations, we can have a computer run that equation for each of the cubes of fluid for one tiny time step - then move onto the next time step and do it again. You can then tell the cubes at one end of this massive grid that there is fluid being injected into them and gradually, after many more time-steps, the system starts to look more like how fluid flows in the real world.

Unfortunately, this misses a lot of real-world effects - but for some applications, it produces enough insight into the fluid flow to be useful. Sadly, to model something like an airplane flying, you'd need a mesh of cubes maybe a centimeter or two on a side - and there would be perhaps billions of them. The time step might need to be a fraction of a second - so even the fastest computers would take days to calculate anything useful. In many cases, these systems have to run on giant super-computers in order to get useful and realistic results.

Of course my description misses many subtleties of how this is really done - and there are certainly other ways to approach it.

SteveBaker (talk) 14:22, 22 November 2013 (UTC)

For reference, Steve is basically explaining the idea behind a finite element method to solve the PDEs governing fluid flow. More at Finite_volume_method_for_unsteady_flow. He's right that this is a difficult subject. Though some engineers can learn how to manage some simulations in undergrad, the real nuts and bolts of the theory are usually reserved for graduate level mathematics and physics instruction. On the flip side, we do have a system of equations that can answer most of our questions, the Navier–Stokes_equations, but no general solutions are available (as of yet), and so we tend to approximate solutions with numerical methods, as outlined above. SemanticMantis (talk) 14:44, 22 November 2013 (UTC)

Don't forget about the finite volume method, which is also popular for CFD. --Tardis (talk) 02:24, 23 November 2013 (UTC)

For how many percents stress can raise the glucose in the blood?

I'm looking for an accurate information about that. It's interesting me because last week I saw someone that the EMTs cheeked her glucose and her levels was high (320) and the EMT said that it because the stress. I doubt if that true too much (because I know that the normal levels are between 80 -140 14:07, 22 November 2013 (UTC) — Preceding unsigned comment added by 5.28.171.111 (talk)

You're not going to get a good answer here because there are some people doggedly enforcing policies against "medical advice" in a very broad sense. Note that an EMT may not give local busybodies a full medical history of people they are working on. We're hard pressed (and not supposed) to diagnose a patient who knows his history, so you're pretty much SOL for an "accurate" answer. If you're interested in the topic I encourage you to explore blood glucose, information from health organizations, etc., but that won't tell you what was going on in a specific situation. Wnt (talk) 18:12, 22 November 2013 (UTC)

Ok, let's make order, I wouldn't want a medical edvice or somthing, so let's be relax... I would only like to understand the topic of the influences of the stress on the glucose in the blood, that all. I'm not talking about specific case, what I told you, it was only as an example. I came here because this issue of "stress influences on the level of the glucose" is a new for me and I'm looking for that some information. I think that we exaggerate sometimes when we take the warning about the medical advice - too much even to the place that we shouldn't need that at all and then people like me lose information. Although, I definitely understand you so Thank you. 19:45, 22 November 2013 (UTC) — Preceding unsigned comment added by 5.28.171.111 (talk)

This is not medical advice, this is a list of references that address the general topic of stress and blood glucose. Here are two links, to authoritative sources that confirm that stress can increase glucose levels (though they don't say by how much). Mayo clinic ([5]), and the American Diabetes Association ([6]). I see that WnT has supplied one of these links already. If you want quantitative information, you might have luck searching google scholar for /stress blood glucose/, like so [7]. If you cannot access these articles, you might try the same search at your local library. SemanticMantis (talk) 21:56, 22 November 2013 (UTC)

Also, since people react differently to stress, I'd also expect their blood glucose to respond differently. StuRat (talk) 22:05, 22 November 2013 (UTC)

As per our article on stress hyperglycemia, "the glucose [due to the stress of illness] is typically in the range of 140–300 mg/dl (7.8-16.7 mM) but occasionally can exceed 500 mg/dl (28 mM)." - Nunh-huh 22:28, 22 November 2013 (UTC)

Projectile penetration

If a projectile hit the same target at 400 m/s and 800 m/s, the penetration doubles or became four times higher (i.e. the penetration of projectile is directly proportional to momentum or kinetic energy?)?95.246.215.102 (talk) 21:21, 22 November 2013 (UTC)

Impact depth is the relevant article. If the speed of the projectile is great enough for elastic deformation in the target to be neglected, the penetration depth is directly proportional to the momentum, so doubling the speed will double the depth. Tevildo (talk) 21:53, 22 November 2013 (UTC)

(ec) I doubt if it's as simple as either. A faster projectile has the ability to concentrate the pressure more on the point of impact, while a slower object gives the material which is struck time to respond, and distribute the force over a wider area. The also depends on other factors, like the material and temperature. If you look at video of a high speed bullet striking a rubber sheet, for example, it seems to shatter, not bend, just as it would if frozen of it made of a brittle material. (The difference between my answer and the previous one is that I did not assume that we can neglect deformation.) StuRat (talk) 22:00, 22 November 2013 (UTC)

Penetration depth depends on the shape of the projectile, whether it's subsonic, supersonic or hypersonic (relative to the speed of sound in the target material, not in the air), the velocity range when it's subsonic, and lots of parameters like unconfined compressive strength. A range of penetration depth formulas exist, most of them similar to one of these forms (V is velocity, a, b, c, d, e are various parameters or constants):

• a.log(1+bV²)
• a.(b.V-c.log(1+e.V))
• a.V^1.8+b
• a.log(1+bV²) for V < 200fps, c.(V-d) for V > 200fps

An in-depth overview of penetration depth formulas can be found here (master thesis, 85 pages). Too bad that they only did five actual impact tests: velocity in m/s, corresponding depth between brackets in m: 277(0.173) 410(0.31) 431(0.411) 499(0.48) 567(0.525), so three times the depth at twice the speed.

A U.S. Army Engineers report on penetration in rock gives some data from tests, between 300 and 800 m/s. In that range, twice the velocity results in 2.4 to 2.9 times the penetration depth.

Experiments on porous rock with projectile speeds between 18 and 42 m/s showed "penetration depth quadratically related to the initial projectile kinetic energy" ( "quadratically related"? is that a convoluted way of saying it was proportional to the speed?) with dry rock, but proportional to the kinetic energy when the rock was saturated with kerosine (so double the speed, four times the depth).

See also a blog about slingshot tests here

All the test results mentioned are subsonic, at supersonic speeds penetration depth should be proportional to kinetic energy, so double the speed, four times the depth. Ssscienccce (talk) 00:04, 23 November 2013 (UTC)

I would say that the penetration, if the material is homogenous and doesn't have any particular properties, should be directly proportional to the square of speed: this because the material resistance can be regarded as a strong form of friction, and if an object double the speed, appling the same force, the drake distance became four times higher. 95.246.216.236 (talk) 18:23, 23 November 2013 (UTC)

Yes, your model is based on fibrous materials or other situations where friction is the main stopping force. It is very different from Newton's model (linked above by Tevildo). In practice, I suspect that reality will lie between the two models for most materials. Dbfirs 21:38, 23 November 2013 (UTC)

Yet another room temperature superconductor prediction notable?

Is this wild guesstimate:

http://www.sciencedaily.com/releases/2013/11/131121135635.htm

Notable enough to include under High-temperature superconductivity? Hcobb (talk) 22:27, 22 November 2013 (UTC)

This question would probably be better on the article talk page, but Physical Review Letters is an impeccably reliable source, and I see no reason not to include the reference. Tevildo (talk) 23:12, 22 November 2013 (UTC)

Topological insulator might be a better place. They are related though. --DHeyward (talk) 08:58, 23 November 2013 (UTC)