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January 15

Physical interest/meaning of a certain Bernstein function

A quick question: consider the Bernstein function f(x):=-ln(1-exp(-x)), for x>0. Is this function any interest, or has it any meaning in Mathematical Physics, or more generally in some area of Physics? --151.29.234.2 (talk) 11:17, 15 January 2017 (UTC)[reply]

As a Mathworld link notes, completely monotonic functions occur in elasticity where Hooke's law

F = kX

applies to the special case of small deformations that exhibit Linear elasticity, and in larger deformations that are non-linear functions of applied strain, but not after non-reversible yield occurs. Blooteuth (talk) 14:37, 15 January 2017 (UTC)[reply]

Feynman Lectures. Lecture 44. Ch.44-4 The efficiency of an ideal engine [1]

...
Now we shall see how this universal law could also be obtained by logical argument, without knowing the properties of any specific substances, as follows. Suppose that we have three engines and three temperatures, let us say T1, T2, and T3. Let one engine absorb heat Q1 from the temperature T1 and do a certain amount of work W13, and let it deliver heat Q3 to the temperature T3 (Fig. 44–8). Let another engine run backwards between T2 and T3. Suppose that we let the second engine be of such a size that it will absorb the same heat Q3, and deliver the heat Q2. We will have to put a certain amount of work, W32, into it—negative because the engine is running backwards. When the first machine goes through a cycle, it absorbs heat Q1 and delivers Q3 at the temperature T3; then the second machine takes the same heat Q3 out of the reservoir at the temperature T3 and delivers it into the reservoir at temperature T2. Therefore the net result of the two machines in tandem is to take the heat Q1 from T1, and deliver Q2 at T2. The two machines are thus equivalent to a third one, which absorbs Q1 at T1, does work W12, and delivers heat Q2 at T2, because W12#W13-W32, as one can immediately show from the first law, as follows:
W13−W32#(Q1−Q3)−(Q2−Q3)#Q1−Q2#W12.(44.8)
We can now obtain the laws which relate the efficiencies of the engines, because there clearly must be some kind of relationship between the efficiencies of engines running between the temperatures T1 and T3, and between T2 and T3, and between T1 and T2.

— Feynman • Leighton • Sands, The Feynman Lectures on Physics, Volume I

First, I don't understand why W₃₂ is negative and why is calculated as Q₂−Q₃ and not Q₃−Q₂.
Mathematics must be correct in all cases, even if we don't know is the work done on or by the machine 2.

Second. How to calculate efficiencies? I try next:
$\eta _{\text{machine 1}}={\tfrac {W_{13}}{Q_{1}}}$

$\eta _{\text{machine 2}}={\tfrac {W_{32}}{Q_{2}}}$

$\eta _{\text{machine 3}}={\tfrac {W_{12}}{Q_{1}}}$
$W_{12}=Q_{1}-Q_{2}$
$W_{13}=Q_{1}-Q_{3}$
$W_{32}=Q_{2}-Q_{3}$
$(W_{13}-W_{32}=W_{12})$
So we have 6 equations and 9 unknowns. The system is unsolvable. Username160611000000 (talk) 12:55, 15 January 2017 (UTC)[reply]

we have 6 equations and 9 unknowns. The system is unsolvable. - I will just "answer" that part, because I think you can genuinely profit from it.

The ideal gas law states that

P=\rho R_{\text{specific}}T

. That is a "system" of one equation and three unknowns (pressure, density and temperature), hence unsolvable. So what? Tigraan^{Click here to contact me} 18:32, 16 January 2017 (UTC)[reply]

Tritium tube concentration and pressure for brightness

When tritium is put into one of those glowing glass tubes is it put in at 100% concentration or could it be concentrated to make them brighter? If the tube was made from a thicker or different material could it be put in at higher pressure in order to make the tube brighter? --78.148.97.148 (talk) 14:27, 15 January 2017 (UTC)[reply]

It's 100% concentration of hydrogen at a couple of atmospheres pressure. It's generally easier to make and fill vials at above atmospheric pressure than below. The brightness is controlled by the phosphor coating, the lifetime of the tube by the tritium fill. It's easy to make a new vial maximally drive the phosphor, but this gets harder as the tritium decays. Tritium's half life is 12 and a third years, Betalights are usually specified for a fifteen year lifetime and are usefully visible for maybe two halflives (thus a quarter of the original activity, possibly with degradation of the phosphor too). The brightness of the tube depends on the surface area, the activation power and the lifetime from the tube's volume. So the ratio between volume and area (i.e. tube radius or disc thickness) is important - a narrow tube may need a "powerful" fill. The "tritium" fill is never pure tritium as that's hard to arrange and of no real use - some will just be protium (vanilla hydrogen). If a tube is quite large but doesn't need to be especially powerful, then the gas pressure is usually kept the same, but there's a mixture with less tritium in it.

The radioactivity of the complete vial is usually limited by paperwork: most are kept to 1GBq, larger ones up to 10GBq are also used. Over 10GBq does need paperwork per device - so they're used, but discouraged, especially for civilian purposes. Andy Dingley (talk) 15:48, 15 January 2017 (UTC)[reply]

Agree with AD. The phosphor coating can only release a fixed amount of photon energy after being excited. So when the tritium concentration is higher enough to re-excite the phosphor atoms the moment they return to their rest state, no extra luminance is going to be forth coming. Therefore, the only option is to increase the surface area. Best way to do that is to use lots of very thin tubes as the ratio of surface area is greater for any given volume. Of course, if it were possible to get the pressure high enough and the gas hot enough it would get suddenly very bright indeed – at the same time as lowering the local real-estate values around where you live (or that should be in the past tense -lived). Aspro (talk) 18:52, 15 January 2017 (UTC)[reply]

The article Tritium illumination describes the construction of "beta lights" that consist of a glass tube with its inner surface coated with a phosphor and filled with Tritium a radioactive isotope of hydrogen. Having with a half-life of 12.32 years, tritium lights lose half their brightness in that period. The more tritium that is initially placed in the tube, the brighter it is to begin with, and the longer its useful life. Installing tritium at higher than atmospheric pressure can increase brightness and useful lifetime but at higher cost, require a thicker tube for strength, and possibly raise safety concerns since escaped tritium is a radioactive hazard. Blooteuth (talk) 19:50, 15 January 2017 (UTC)[reply]

"tritium lights lose half their brightness in that period."

But they don't. Nor are "lots of very thin tubes" a good or economical idea.

Tritium lighting is mostly used for self illumination. But a decade or two ago, before useful LED torches, when tritium was still sometimes used to make torches usable for map-reading, these were discs rather than tubes. The diameter of the disc controlled the brightness, the thickness controlled the life. Andy Dingley (talk) 23:45, 15 January 2017 (UTC)[reply]

Our article tritium illumination says that there are "several thousand" times more tritium in a nuclear weapon than in a keychain. I assume this is a slight underestimate... :) Some folks above sound like they are familiar with the topic - can someone put an actual sourced number for that difference in the article? Wnt (talk) 17:54, 16 January 2017 (UTC)[reply]

Article should be renamed as Tritium luminance. As anybody whom did the 101 knows 'illuminance' is the light falling upon an object etcetera., not the light emitted by the source (which is the luminance). Heard it said, that the amount of hydrogen needed to boost a nuclear device is no more than that which would fill a child's party balloon ( at standard temperature and pressure) which if one considers, that volume is well over a thousand time more than a keyring light. The Hydrogen then gets confined in a 'small' titanium bulb within the core. Extra tritium can be provided by the transmutation of lithium, once fusion has started. Would love to build one but don't know of anyone with a big enough back-yard to test it in. Mind you... Kim Jong-un appears to have a similar amateurish interest and has a very large range of unpopulated land. Does anybody have his email address? Lastly. A disc is very inefficient as approx half the energy is lost on the obverse face.--Aspro (talk) 21:34, 16 January 2017 (UTC)[reply]

Tritium radioluminescence might be justified as a redirect, but as many tritium illuminators are used for illumination of signage as are used for luminescence. They were originally developed as dial illuminators and the name stuck. Also we're under COMMONNAME, not just waving around personal erudition.

As to nuclear weapons, tritium and lithium, then you're confusing the two (boosting vs. secondaries).

If discs aren't used for Betalights, then you might like to inform Betalight themselves [2]. When used one sided, they're usually painted white on the back face. Andy Dingley (talk) 21:54, 16 January 2017 (UTC)[reply]

Where did I say they were not used. Talked about efficiency. Tritium radioluminescence seem very acceptable though. As for COMMONNAME, there are some nomenclatures that as an encyclopedia we should get right. ! Otherwise 'we' would be contributing to positive feed-back (think audio howl). Said that "Extra tritium can be provided by the transmutation of lithium" so of course it is secondary so don't see why you think I'm confused by any of what I said.--Aspro (talk) 23:34, 16 January 2017 (UTC)[reply]

I looked up hydrogen bomb and was amazed to read that the fusion fuel is actually lithium deuteride, not tritium at all! It didn't give a quantity - a non-reliable source [3] estimates up to 10,000 kg in the largest fusion bomb but I doubt they had their math right. I don't think it's a party balloon but honestly I should admit I don't know. It seems like every time I look up nukes they seem to operate a completely different way... I get the feeling that there's been a lot of misinformation spread around. Wnt (talk) 21:58, 16 January 2017 (UTC)[reply]

Having said that. Beta touches are almost exclusively used by the US military and as the US tax payer picks up the bill there is really no need to consider efficiency nor cost. If Walmart started selling them however, the design and construction may very well change. --Aspro (talk) 21:48, 16 January 2017 (UTC)[reply]

They're hardly used by the US military. The UK have always been bigger users. Also I can't speak for Walmart, but plenty of outdoor dealers carry small ones, and used to carry the larger torches (obsoleted by LEDs). [4] Saunders-Roe sell them mail-order too - the shipping boxes are great for terrifying the postman. Andy Dingley (talk) 21:56, 16 January 2017 (UTC)[reply]

That link appears to go to a Swiss company (you know, those folks that invented the cuckoo clock) and they don't seem to declare their NATO reg. May say MOD Patt. But that can just be sales and marketing puffery. Other companies proudly show their NATO. As far as I'm aware the British Army still relies on a good old box of Swan Vesta. Failing that, they just rub two boy scouts together [5] ;¬) .--Aspro (talk) 22:55, 16 January 2017 (UTC)[reply]

NSN 6260-99-965-3582 Andy Dingley (talk) 23:26, 16 January 2017 (UTC)[reply]

Andy Dingley is right (dam him). This company does supply products to NATO standards. However, I'm still going to stick with my Swan Vesta's (Vesta was the goddess of something or other and one can't go wrong with a woman behind you.) --Aspro (talk) 00:52, 18 January 2017 (UTC)[reply]

Vesta (mythology) was "the virgin goddess of the hearth" amongst other things. See also Vesta case and indeed Swan Vesta. You might have thought that England's Glory might be more appropriate (and safer if you work with explosives). Alansplodge (talk) 18:16, 18 January 2017 (UTC)[reply]

Helicopters and drones on Everest

There are apparently a lot of touching movies about lunatics who follow the siren song of Everest and K2, and the hardships they suffer because everything has to be carried up with great effort and no medical rescue is possible. Looking around on the Web, it seems like this is still the case, even in 2016. For example, I see that helicopters can barely make the second base camp at 20,000 feet (i.e. 50% shy of the summit) and supplies are still being carried over a dangerous ice fall by teams of Sherpas, though at this lower altitude helicopters might compete.^[6] Now, I can't knock them for making a living, especially if that's what they have to do to do so, but still, well, if Everest is a mountain of dreams, then it makes me dream that if I were a big shot at a company like Starbuck's I'd want to arrange drones to fly over and drop off and ideally assemble all the components and supplies for a large made-to-order hot cappuccino machine at the summit. Or at least try to hit the occasional downed climber with a falling oxygen bottle. And the funny thing is, I look them up and I see that drones are flying over, mapping glaciers,^[7] making lovely photos.^[8] At lower altitudes in the Himalayas they drop supplies now.^[9] So I gotta ask:

a) Why haven't drone supply operations more or less totally taken over all the big Himalaya climbing routes?

b) Is it possible to make a helicopter that reliably carries a full load to the summit of Everest? With modern technology, could you put in computer stabilization so that even an inexperienced pilot can tell it to resist the wind and keep it flat and level under adverse weather conditions? For that matter, if you were willing to blow enough money on construction and fuel consumption (and what do Himalayan climbers do but blow money) could you make a helicopter that can fly against the wind in a class 5 hurricane, hover right amid the flames of a burning World Trade Center tower, and safely board people on and off over a gangplank in the process losing no more than a bit of scorched hair? Or is there some theoretical limit as to what can possibly be stabilized against, no matter how good the electronics? Wnt (talk) 20:03, 15 January 2017 (UTC)[reply]

Well if a vulture can fly at 37,000 feet I'm sure it must be possible to build a helicopter to get to 29,000 feet - just it hasn't been in anybody's interest to do so. It is easier to get things that fly rapidly to fly higher - but vultures don't tend to go very fast. Making a drone that goes that high might be a bit easier than convincing anyone to make a helicopter. Dmcq (talk) 23:55, 15 January 2017 (UTC)[reply]

Not only is it possible, it's already been designed and built, and almost 40 years ago, too: Aérospatiale_SA_315B_Lama 89.120.104.138 (talk) 13:37, 16 January 2017 (UTC)[reply]

Nope, about 12,000 feet short. 2601:646:8E01:7E0B:F88D:DE34:7772:8E5B (talk) 09:42, 17 January 2017 (UTC)[reply]

"on 21 June 1972, the type established a helicopter absolute altitude record of 12,442 m (40,814 ft)", type certificate limits for safe commercial operation notwithstanding. 89.120.104.138 (talk) 09:08, 18 January 2017 (UTC)[reply]

I bet they stripped it down to the airframe (and the bare minimum of fuel needed for safe flight) for the record attempt, and used thermals just like Didier Delsalle -- and besides, they probably used translational lift the whole way (i.e. no hovering)! 2601:646:8E01:7E0B:F88D:DE34:7772:8E5B (talk) 09:23, 18 January 2017 (UTC)[reply]

Yes, see here: https://www.thisdayinaviation.com/21-june-1972/ . Also, the Everest summit is some three miles down from record altitude. MHO, you need evacuatin' from the Everest summit, a SA315 or similar (enclosed cockpit, space frame fuselage, lightweight construction, stripped down to the essentials) is the tool for the job. 89.120.104.138 (talk) 10:32, 18 January 2017 (UTC)[reply]

Odd, I'd think it would be worth it to the Chinese just to hear some Nepalis say "thank you for maintaining an airbase in the Tibet Autonomous Region"... Wnt (talk) 00:25, 16 January 2017 (UTC)[reply]

Didier Delsalle. --Hillbillyholiday ^talk 00:29, 16 January 2017 (UTC)[reply]

Well, a drone with just a mini-camera is one thing, but a full-size chopper for carrying supplies is another thing entirely -- a bigger payload requires more lift, which requires a bigger machine, which means still more lift -- and that means that the gross weight increases faster than the payload, until you reach a practical limit. And in the case of Everest, the high altitude compounds the problem -- thinner air means (1) less engine power, and (2) less rotor efficiency (these things compounding each other once again, meaning that the service ceiling decreases disproportionately as the gross weight increases). Now, you could try to overcome this in 4 ways -- you can try making the rotor bigger, but then you make it heavier, and above a certain size you'll run into problems with resonance; you can add more blades, but this also adds weight, and when you have more than 7 blades you start getting diminishing returns from each additional blade; you can use 2 rotors, but that also adds weight (not just the rotors, but the additional transmission shafts and gearboxes, and also additional structure for carrying the rotors) and mechanical complication; or you could spin the rotor(s) faster, but above a certain rotor RPM you'll run into advancing blade stall (which also occurs sooner at 29,000 feet than at sea level, because of the lower speed of sound). So, carrying a payload to the top of Mount Everest is in fact a very hard engineering problem -- not that it won't be solved someday, just not any time soon. 2601:646:8E01:7E0B:115A:F5FE:40F5:A40A (talk) 02:34, 16 January 2017 (UTC)[reply]

Another problem with manned helicopters is that to fly to that height they need to be pressurized, and this means the crew can't just jump out when they land and load in a patient to be evacuated, they would need people on the ground to load the patient into a sealed nacelle pod, and that pod would need to slowly increase the pressure from the starting pressure to that of the landing level pressure, so it can be opened when they arrive. Even an evacuation drone would still need that second part. StuRat (talk) 07:35, 16 January 2017 (UTC)[reply]

A helicopter has landed on the peak of Everest - see Didier Delsalle. This needed the helicopter to be stripped back to the bare minimum (no extra seats, for instance) and very careful thermal riding to get to the summit. A helicopter has never been usefully to the summit, but Sudarshan Gautam was rescued pretty close to it at 7,800 m (25,590 ft) (see Eurocopter AS350 Écureuil#Operational history). So it is possible - so why isn't it common? This article is a pretty good summary: The problem is that it's only barely safe at the best of times - in good weather, the engine can just grab enough oxygen to keep you airborne, but good weather isn't exactly common on Everest, and Nepal doesn't exactly have a good track record for air safety - without good regulation, when there are multiple companies all competing to be the cheapest and highest-flying, safety goes out of the window. Smurrayinchester 08:23, 16 January 2017 (UTC)[reply]

The Delsalle case is interesting - it says that the weight was trimmed to increase the one-hour fuel range of the helicopter. So there actually is some kind of a physical limit here, though it also involves the breadth of the mountain and not just its height. But I don't know whether that limit can be evaded by making a much larger or a much smaller helicopter with proportionally much more fuel storage; I suppose in concept a more energy rich fuel might be used, or an in-flight automated refueling system, etc. The prospect of trying to steal a great pilot's skill and implement it standard in the helicopter computers, including some more effective imaging of winds, also seems interesting. Wnt (talk) 12:24, 16 January 2017 (UTC)[reply]

Re a): Something not so far addressed – doing it as much as possible (including the preliminaries) without machine assistance is kind of the point of the whole exercise. I mean, I've crossed the English Channel/La Manche a number of times by ferry (and gone under it several via the Chunnel), but some people still want to do it the hard way. {The poster formerly known as 81.81.230.195} 2.122.62.241 (talk) 12:15, 16 January 2017 (UTC)[reply]

The problem with that idea is that I'd expect those following it not to use fixed ropes on the ascent, for example, but to not care whether the supplies they find at Base Camp N were taken up by Sherpas two weeks before or by a bunch of little drones. Wnt (talk) 12:24, 16 January 2017 (UTC)[reply]

Probably not. But why would they want to use drones? In the short term, it's not likely to be cheaper, considering pretty much no one is doing anything remotely like that (see Delivery drones, there are a few minor trials but mostly it's just talk). And while there are perhaps some minor advantages in doing it somewhere like Everest (a lot less crowded than some other proposals and possibly the world media is less likely to care if you injure or kill a Sherpa then if you do so to some rural Japanese person), there are as mentioned above and should be obvious a lot more challenges. And you'd piss the hell out of the Sherpas who you still need as guides, to set up the ropes etc. Heck it seems doubtful that either they or the Nepalese government would allow it. (Well for the later, perhaps if you bribe the right people but you aren't exactly helping the business case with that.) It's not like there aren't already serious disputes [10] [11] [12] and ironically IIRC one of the people attacked was actually a helicopter pilot sometimes or often involved in rescue flights. All in all, this seems a lose lose proposition for everyone involved. To put if a different way, if Starbucks really think a coffee machine (which they'd also have to design, probably with pressurisation etc) on Everest is a good marketing stunt, they could just hire a bunch of Sherpas and find someone involved in the company to accompany it. At least then it's only going to backfire because people comment on more junk on Everest rather also because of the drone stuff. Nil Einne (talk) 16:13, 16 January 2017 (UTC)[reply]

Helicopters (drone or not) must hover, and this is hard at high altitude. You need to hover to retrieve people or stuff, but not to deliver it. You can deliver using controllable parachutes from a fixed-wing aircraft. Of course, if this were done routinely, the mountain would soon be festooned with parachutes. You could probably work out a system that delivers heavy loads by a parachute that has some sort of balloon/drone combination to bring unloaded system back down to base. -Arch dude (talk) 04:32, 17 January 2017 (UTC)[reply]

Personally I wonder why a person would want to use a drone. What is the point of climbing Everest if it is not a challenge and there is no danger? One might as well have a pressurized funicular railway and a cafe selling cappucinos and Mount Everest souvenirs at the top. Dmcq (talk) 09:47, 17 January 2017 (UTC)[reply]

But before anyone invests in a tourist railway to Hotel Miyolangsangma, note that a funicular would need a system of Airlock doors to protect occupants against the 3x air pressure difference between sea level and the summit 8848 m higher. Any idea of stepping outside is not for general unequipped public. Only cold coffee is available outdoors. Blooteuth (talk) 15:30, 17 January 2017 (UTC)[reply]

Note that the lower air pressure could be somewhat countered by increasing the oxygen percentage, which would certainly be simpler to do (people just wearing oxygen tanks would do it). However, some people suffer other problems from the lower pressure alone, and these are sometimes fatal. So, maybe you could go halfway up with just oxygen supplements, but then it would be a good idea to pressurize the cabin if going higher. With a 2-stage system, people could get out of the oxygen supplemented funicular, and step into the pressurized one, perhaps after they take a rest stop, eat a meal, etc., on the way up, then do the reverse on the way down. StuRat (talk) 16:40, 17 January 2017 (UTC)[reply]

Well, ideally, people run a highway from Kathmandu to Lhasa that tunnels deep below grade, at least enough not to exceed the elevation of the latter city, and then visitors just ride an elevator up from it to a pressurized crystal sanctuary in the sky high above the summit. If they want they can depressurize, or preferably, wear some more comfortable technically advanced pressure suits, and walk along the gangplank from where the near-invisible stalk of the restaurant hangs in one of the triskelion voids of the mountain to the traditional ascent trail, where they can make those few last halting steps that induct them into the proud fraternity of those who have conquered the mountain. Wnt (talk) 16:55, 17 January 2017 (UTC)[reply]

Well I think Wnt has a point that a lot of people are already getting a lot of support, and yes not without controversy for numerous reasons but the fact remains they are doing so. But as I mentioned above, you'd still need a reason why the drones are a better choice than Sherpas doing the same work (presuming they can but it would seem they can for stuff Wnt suggested), and probably a reason they agree with. Given the current state of drone technology, I don't see how that's the case. Nil Einne (talk) 15:38, 17 January 2017 (UTC)[reply]

@Wnt: Do we have to use a helicopter rotor (or something similar) for lift? Drones don't have to be conventional quadcopters, right? Wouldn't an airship-like drone that contains a lifting gas that is lighter than air be a good idea? See also Atmospheric satellite, Geostationary balloon satellite, High-altitude platform station, Superpressure balloon and even Aerobot. Transporting a person is difficult, but transporting oxygen tanks or parts of a cappuccino machine seems more do-able, but we have self-heating cans so I don't think cappuccino machines are really necessary. (((The Quixotic Potato))) (talk) 00:32, 19 January 2017 (UTC)[reply]

Well... airships can have trouble. On a legendarily turbulent mountain with strong updrafts and downdrafts, probably a lot more trouble. I would not rule out that Miyolangsangma breaks wind so often on account of eating too many airships that didn't agree with her. ;) Wnt (talk) 01:25, 19 January 2017 (UTC)[reply]

@Wnt: But it doesn't have to come anywhere near the mountain, does it? I mean, we can drop payload (e.g. oxygen tanks) on parachutes, and we can launch the thing a relatively safe distance away. Remotely controlled parachutes that help steer the payload would be kinda cool (powered or unpowered), but I don't think that that is necessary. The air that is near the mountain is probably quite turbulent, but perhaps that turbulence decreases if you stay a bit farther away from it (e.g. a bit higher). If you design the payload (and its parachute) correctly then it won't get blown too far off its intended target. The sherpas would still have to collect the payload (and assemble the parts of your cappuccino machine), but perhaps that is easier than bringing every single piece with them. It may be useful to have a cable that guides the descent of the payload (which may or may not touch the ground). (((The Quixotic Potato))) (talk) 01:28, 19 January 2017 (UTC)[reply]