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Everything posted by Enthalpy
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Hello you all! It is known, but not universally, and intriguing anyway: an RC network can amplify a voltage. No power gain of course, here a low impedance drives the network and a high impedance observes the output. The example network on top right here does that: It is best understood as a three-cell lowpass RC, as on top left, where the output was moved to other terminals, between what was the usual output and what was the input. The reasoning is valid because the implicit low-impedance generator stays at the same place. If, at some frequency, the network has some amplitude at the usual output with a phase between 90° and 270°, that is, it shows a component in phase opposition, then the voltage between the input and the usual output exceeds the input voltage. The component in phase quadrature adds even more voltage. On the diagram, I compute the frequency for phase opposition (which becomes in-phase at the new output) and compute the gain there, but other frequencies bring more gain. The high-pass shows the same behaviour. More than three cells would bring more gain. Higher R and C impedances near the usual output, too. This was enough unexpected to me that I built both circuits at the diagram's bottom, and both oscillated immediately and quietly. As a result of the small loop gain, the waveform was a rather clean sine, at a frequency nearer to zero phase than to maximum gain. Pretty useless I guess, but I find it puzzling. Marc Schaefer, aka Enthalpy
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Why is it hard to whistle with a dry mouth?
Enthalpy replied to Ken Fabian's topic in Other Sciences
Yes, that's exactly what I was thinking at. I want for years to think and model that, have some ideas, but it's damn difficult. I had even imagined that "whistling" was a cover-up for the more important theme of wind instruments, figure that. Having tried all the symphonic woodwinds and played several of them, I confirm that warming the instrument up is vital. More important for the more sensitive instruments, that is, the flute. Whether is results from the temperature or the humidity? Present theories, with which I'm not pleased, claim that the temperature gradient down the air column must match the one for which the instrument was optimized. That would then matter for the alignment of the harmonics: a gradient different from the one used during optimization would detune the harmonics and make emission more difficult. But of tiny is the difference of frequency shift between fundamental and harmonics in a nearly cylindrical instrument? I doubt. I also fear that, being presently an armchair inventor, any model I'd propose may be radically wrong. It would be much healthier to experiment first: distinguish the temperature from the humidity, build an instrument with purposely misaligned harmonics, dry the tube often or cool it permanently, measure the Q-factor, and so on. -
Energy contained in the magnetic field
Enthalpy replied to Danijel Gorupec's topic in Astronomy and Cosmology
Yes. So the electrostatic interaction has a mass, easily measured when considering the interacting particles together. But when explaining the measured energy levels in hydrogen-like atoms, the mass of the nucleus-electron attraction can't be attributed to the electron. Not all, not one half, not even 1%. These figures are brutal. That's why I disagree that the energy and the corresponding mass would be an attribute of the interacting particles. There is something fishy there. There is exactly zero proof in that link. Said expert supposes that the energy of the magnetic field resides in the vacuum, and that light would respond to this energy like observation tells it responds to the mass of a galaxy. But, sorry, we have observations for galaxies and our Sun only. Bending light with a kilogram of iron was never observed. We ignore what makes the mass of a galaxy, and gravitational lensing was observed where galaxies have no visible mass. Even claiming "only protons, neutrons and black matter bend light" would be consistent with our observations. And we have observations that the Earth changes the pace of time. This is nicely consistent with light bent by other masses, but is not a proof. The rest of the explanation by the "expert" is a mere consequence of his supposition, writing some Relativity equations as if bending by the magnetic field were sure. Don't let some equations reproduced from a book impress you. There is absolutely nothing convincing in the link. It's a supposition with good-looking writing. Don't misinterpret me: I make the same supposition. -
"Gamma" is often used for "energy higher than X-rays", but "originating from nuclei" is more correct, sure. However, cosmic rays make nuclear reactions easily. If lightning electrons, rather than cosmic rays, create the MeV rays by some process to be determined, then they do have the energy to excite nuclei. One excited state of 40Ar is just 1.46MeV above the ground state.
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Piano hammers are heavier than the shortest strings. This slows down the rebound and may let us perceive the note too low because it is. As measured on a Yamaha upright piano, the three strings for highest C have D=0.9mm and L=48mm so they weigh 0.72g together, of which 0.36g moves. The lighter hammer heads there have about 8mm*8mm*30mm Fagus Sylvatica (Beechwood) weighing 1.4g. The hammer is 4* as heavy as the strings and the first half-period 2.2* slower, as the strings' elasticity move more mass until they have repelled the hammer. This affects more the high notes whose sound is shorter and strings are lighter. In the joined archive, ToingMake.txt feeds Toing.exe to write Toing.wav that plays four times F=2794Hz and the highest C=4186Hz. F decays in 50ms and C in 10ms. C's first half-period is normal in the first two occurrences and slowed down by 2.2 in the last two. Toing.zip I hear lower the C with slower half-period. Not much, but it resembles the perception of a piano. Felt that covers the hammerhead to sound softer must slow down the rebound and first half-period further. 4µm/N would be as stiff as the strings, felt against thin strings must be softer. Marc Schaefer, aka Enthalpy
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Here's an other way to add undertones to the piano's highest notes to help the listener perceive the height, as an alternative to the construction of Apr 21, 2018 here. The soundboard transmits a part of the hammer's percussion to the other part of the strings whose length is a multiple of the struck one. Separate tuning is needed if the strings rub too much at the soundboard. Damping at the longer part of the string attenuates the undertone as quickly as the note. Marc Schaefer, aka Enthalpy
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Here on December 30, 2018 05:13 PM I suggested to lay a few graphite fibres on the plates as bracings. I suppose the composite damps less than spruce does, but then a well adjusted mix of aramide and graphite fibres would tune the damping at will. Aramide fibres are horrible to cut. The mix offers more tuning possibilities than wood, nice. Marc Schaefer, aka Enthalpy
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Why is it hard to whistle with a dry mouth?
Enthalpy replied to Ken Fabian's topic in Other Sciences
I've had somewhat similar thoughts but not for whistling. I need much more time thinking at it, and the physical model and maths aren't trivial. If someone knows an answer, I'd be interested too! -
Do a violin's table and bottom radiate efficiently? I try to estimate the radiated power from the vibration pattern on Martin Schleske's fantastic website: schleske.de For instance at the 409Hz resonance, the vibrating zones are ellipses about 100mm*50mm. Lambda/4=209mm, so the 5.6mohm*F2=0.9kohm radiation resistance of a small source isn't too wrong here. Average arbitrary 1m/s rms in one such zone pushes 4dm3/s air to radiate 14mW rms. The zone's mass, about 3.5g, takes 9N and reactive 9W to accelerate. Radiation contributes 0.15% to 1/Q while losses are 1.5% in Schleske's measures. At 884Hz, the small source resistance would be 4.4kohm but the observed individual zones are about 100mm*60mm while lambda/4=97mm so the resistance would be bigger. Though, the pattern is a quadripole, 75mm=0.19*lambda and 160mm=0.41*lambda, and the 0.19*lambda reduce the individual resistance. I just keep the 4.4kohm per zone, should be good enough for the qualitative conclusion. Again 1m/s lets each zone radiate 98mW and absorb reactive 30W so radiation contributes 0.3%. At 2060Hz, the zones are about 60mm*45mm but lambda/4=42mm so the small source's 24kohm and 0.1W are less wrong than a wide piston's 0.9W, while the multipole's spacing of 70mm=0.42*lambda changes little. Each zone's 1.9g absorbs reactive 25W so radiation contributes 0.4% while losses are 3% as deduced from the resonance peak width. Picea abies' (spruce) reported losses are typically 0.8% lengthwise at acoustic frequencies. Luthiers seek exceptional wood and excel at avoiding other losses. The violin's table and bottom radiate rougly 0.1* the power received from the strings. That's better than expected but it would usefully improve. It's my reason to seek lighter tables and bottoms, with bracings. A pizzicato sound is much shorter when pressing the string against the fingerboard than with an empty string. This tells that the finger (and fingerboard) absorbs most of the string's power, even before the power has a chance to reach the table and bottom. But an instrument with frets would not be a violin. Marc Schaefer, aka Enthalpy
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How to decide whether lightning is triggered by cosmic rays or produces X and gamma rays? wikipedia versus other processes, for instance wikipedia already discussed here scienceforums A laser beam, shooting concentrated and in brief pulses from the ground to the clouds, could already trigger lightning. A brilliant mind nicknamed Sapo proposed to install X- and gamma-ray detectors around the laser: If ionizing rays are detected, they are produced by the jolt. If none is detected, then they usually result from cosmic rays that trigger the jolt. Unless theories propose the production of gamma rays only if the jolt progresses slowly, or a similar subtlety. The original place of this proposal is inaccessible now, and I feel the idea shouldn't get lost.
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Instruments of the violin family have arched tables and bottoms. This brings stiffness at precise locations with no added mass. Could bracings replace the arched shape?. This works for the guitar, whose table is flat and 1mm thin, a value that would be difficult to attain by carving arched plates but is usual for flat material using industrial tools. The higher pitched violin would need bracings stiffer than the guitar, and stiffer than in the previous estimate whose plates are arched. If the spruce table is 1mm thin, a typical distance between bars drops to <30mm, and the bars are taller - to be experimented, for instance with Chladni patterns, possibly after varnishing. Reinforcements seem necessary at the plates' rim, continuous but possibly of several overlapping glued parts - or shall all bars and the rim but shaped from a single plate? The instruments needs also taller ribs to keep the volume, and a taller bridge to give the bow a way. Marc Schaefer, aka Enthalpy
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Energy contained in the magnetic field
Enthalpy replied to Danijel Gorupec's topic in Astronomy and Cosmology
No, that's wrong. The energy of an electron in a hydrogen-like atom (1 electron, many protons) is properly computed with the relativistic mass correction and without the mass correction of the electrostatic attraction. This correction would be much bigger than the experimental accuracy, so the electron and the nucleus don't bear the interaction mass. We had already this discussion. Problem is, I ignore where the interaction's mass is. Or worse, it exist for some observations but not for some others, even for one single observer if I grasp it properly. That would be fantastic. Swansont computed the magnetic energy to me much smaller than the neutronium's mass, but the magnetic field has a very strong pattern, shrinking to zero at some positions. If the distribution of the neutronium's mass is even enough, or has a distinct shape, maybe the effect of the magnetic field can be distinguished. With (how much?) chance, a magnetar exists that bends light from two farther sources passing very close and less close to it. Then the comparison of the wobbles would tell if all the mass-energy that bends the light is below the surface... except that we probably don't have the necessary accuracy. -
Church bells at the height written for Parsifal are too big. Wagner wants E G A C where C is the height of the 20t bell on Vienna's Stephansdom, so the E would weigh 80t. Bells of that size were made, but not moved on a stage. Wagner later let build a "Glockenklavier" for that, a kind of grand piano with four notes of many strings each, hit by wider hammers moved by the fists on big keys (I've found no equivalent sites in English) Glockenklavier at de.Wiki hear the instrument qUfo1szjPIc at Youtube br-klassik.de but orchestras aren't pleased with the power nor the sound, so they still experiment wiener-staatsoper.at this isn't solved yet. ========== For notes less low, orchestras investigate alternatives to church bells with a decent sound FaxGwZRKpao at Youtube, sounds at 0:54, 2:16, 3:10, 3:27, 3:47, 4:06, 4:50 or they buy authentic church bells from traditional founders, possibly over a store 2MaoAOhxbdQ at Youtube, sounds at 0:09, 1:52 schlagzu.com so if electroforming is cheaper, a market exists.
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Energy contained in the magnetic field
Enthalpy replied to Danijel Gorupec's topic in Astronomy and Cosmology
Every energy has an inertia, and attracts massive objects, and is attracted my massive objects, so at least conceptually, the magnetic field would change the path of nearby stars, of light, and so on. One banal example, but with the electrostatic field, is the mass of heavy elements. As more nucleons compose a nucleus, from hydrogen to iron and beyond, the strong force releases attraction energy, and iron is lighter than expected from a sum of protons, electrons and neutrons. But as more protons (and neutrons) are added beyond iron, the electrostatic repulsion between the protons increases, and atoms get not-so-light per nucleon as iron. This mass resulting from the electrostatic field is commonly measured on decent scales, or by electromagnetic deflection. Still very obscure to me: the inertia of the interaction energy doesn't count when we compute the acceleration of the particles due to that interaction. So this mass depends on the observer and possibly on the use he wants to make of it. There would probably be practical difficulties to an observation using the magnetar, as our knowledge of its mass "without the magnetic field" is supposedly too imprecise to check if the magnetic energy makes a difference. Besides gravitational effects, strong magnetic fields might act on light by other means. Experiments on Earth, with limited human technology, have shown none, to my limited knowledge. -
Happy new year to all and each of you! Bonne année ! Frohes neues Jahr! ¡Feliz año nuevo! Feliz ano novo! Felice anno nuovo!
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I suggested in this thread on December 16, 2018 06:30 PM to add bracings to the tables and bottoms of the violin family, to make the plates thinner, lighter, and hopefully lounder and more responsive. The thinner shell adds resonance modes between the bars, so these must be close enough to eject to modes to high frequencies. A violin can play more or less a B at 3951Hz on the fingerboard (a bit higher by playing so-called harmonics): the lengthwise flexural half-wave in 1.5mm thin spruce is 40mm, and this shall be the distance between the bars. Irregular spacing helps further. For comparison, a guitar table is 1mm thin. ViolinBracings.zip This spreadsheet computes the EI/rho of plain wood (spruce for the top plate) and a thinner shell with bracings. To obtain the resonant frequencies of 2.5mm plain spruce from a 1.5mm shell, 1.1mm thick and 3mm wide spruce bars spaced by 40mm suffice in the R direction (they ar cut from the stiffer L direction), while those stiffening the L direction are 2.4mm thick. The resulting table would weigh 0.70* as much as plain 2.5mm. The plates' curvature adds stiffness, hopefully in the same amount with thinner shells and bracings. The bars stiffening the R direction could be cut thicker from the R direction to keep its damping. A CNC milling machine could carve them from thicker wood together with the shell in one part, much like isogrid construction in aluminium. A few preimpregnated graphite fibres laid on the shells' inner faces might replace the added wood bars, but their damping differs and they seem more difficult to adjust. The sketched bracings are by no means an optimum nor the only possibility, as guitars show, and they will need adjustments beyond a spreadsheet's possibilities. At best, they may guide the first experiment, to check if the idea has potential. Since violin-like instruments alternate the resonances among the top and bottom plates, both plates should be modified to keep the balance. Marc Schaefer, aka Enthalpy
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Many string instuments use Picea abies and Acer pseudoplatanus (Norway spruce and sycamore) Picea abies and Acer pseudoplatanus on wiki for which Voichita Bucur and other sources measured the elasticity: Data spreads much, as expected from a natural material. The experiments need careful interpretation, as for instance the small shear modulus can reduce a beam's flexural stiffness. Elasticity must also depend on the frequency, so static or ultrasonic data may be inaccurate for music instruments. Good news: all the sources I've seen agree on the axes L, R, T. Attempts are reported from time to time to replace wood by man-made materials: aluminium, graphite fibres, 3D printed polymers... Wood outperforms them by far because it propagates flexural waves faster, as is known to instrument makers and to academic researchers. For a given resonance mode, faster waves enable a bigger soundboard that radiates better. Or at identical wave speed, the soundboard can be lighter to couple better with the strings. Also, when flexural waves are faster than pressure waves in air they pass efficiently to the air; this happens above a frequency reached earlier with wood. The equation for 1D flexural waves is (2piF)2*rho*e = k4*E*e3/12 where the wave speed and the soundboard's mass depend on E*e2/rho and e*rho for which Picea abies brings EL~10GPa, ER~1.6GPa, rho~400kg/m3. Compare with aluminium alloy: E=72GPa rho=2740kg/m3. To match spruce's flexural wave speed in the L direction, aluminium would be as thick and 6.5* as heavy, ouch. To match the R direction, aluminium would be 0.4* as thick and 2.6* as heavy, yuk. So what about graphite fibre composites? They can achieve rho=1550kg/m3, EL~150GPa, ER~20GPa: to match spruce's flexural wave speed, graphite would be 0.5* as thick and 2.0* as heavy. So while graphite fibres may compose some day the radiating body of a good string instrument, they can't mimic a spruce or sycamore soundboard. Sandwich construction may be the path to fast flexural waves. Or the radiating body better uses compression waves somehow. Marc Schaefer, aka Enthalpy
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Alternators have been used at radio transmitters, long ago, between spark-gap and vacuum valves. What ol' Nikola did, I ignore it. They had big numbers of pole pairs relatively prime at the rotor and the stator, so that for a given rotation frequency, the stator and rotor poles that just began to overlap passed quickly from one pair of elements to an other. Well done. While this scheme is efficient at removing the current components at low frequencies, it doesn't amplify the desired radio frequency, it only keeps it. So the field at the pole edges had to be very sharp, with edges at the metal and a very thin airgap. Imagine 100m/s rotor speed, difficult enough then: 1mm transitions in the field could produce AC current with strong components up to roughly 2*10µs or 50kHz, reaching the LW. But any pole length over 1mm was waste, producing components at lower frequencies removed by the relatively prime scheme. Poles 1mm long would have been more efficient but impossible to produce. I had thought at modernizing the alternator. Silicon can rotate at 500m/s, with patterns and gaps few 10nm small. The alternator could be electrostatic rather than electromagnetic. The achievable frequency is the same as the read throughput of a mechanical disk drive, that is, 200MB/s=2Gb/s would achieve 1GHz energy conversion - or rather less for a significant power hence facing area. But magnetrons do that better.
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Researchers let fungi chew some components of Norway spruce and sycamore to lighten them researchgate.net their goal is to build bowed string instruments, but if fungi can lighten balsa wood, sandwich materials improve. I proposed a graphite-balsa-graphite sandwich for the walls of the solar sail's booms, in this thread Mar 15, 2015 but such sandwiches have many uses. The paper reports on figures 3a (axial) and 3b (radial) 15% mass gained after 20 weeks chowing on Norway spruce (-19% E modulus matter less here). If balsa too gets 15% lighter, a 10-segment sail is 30kg lighter. That's one science instrument more. Merry Christmas! Marc Schaefer, aka Enthalpy
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Trying to imitate the allegedly stiff but lighter wood grown during the Maunder minimum and used for bowed instruments by Guarneri, Stradivarius and Guadagnini, researcher let fungi consume some components of Acer pseudoplatanus (sycamore) and Picea abies (Norway spruce) researchgate.net with varied effects on the density, Young's modulus and damping, depending on the wood, fungus and duration. While the effect on bowed instruments remains to see, damping *1.5 to 1.8 could improve bassons and contrabassoons built of Acer pseudoplatanus, easing the high notes. In figures 4a (axial) and 4b (radial), page 8 of the Pdf, 6 weaks chewing by Xylaria longipes reduce E by 17% but rho by 8%, which is a limited drawback for a bassoon and can become an advantage if building and constant mass, that is thicker. I wondered why players of Heckel-system bassoons found high notes difficult while I achieved the conventional high G after one week. The narrower French system surely helps, the hard reeds too, but the denser harder wood may very well ease the high notes. My 1915 instrument, as thick as recent ones and heavier, is probably of Dalbergia latifolia (rosewood), twice as stiff as Acer pseudoplatanus. Merry Christmas! Marc Schaefer, aka Enthalpy
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The baritone "sarrusophone" provided by Uriel Rodriguez S. on his Youtube page T_hwbf3lOlY at 1:10 is not a sarrusophone but a saxophone, very well played by Yasuto Tanaka RVOBQBamjDA I have been abused. My sincerest apologies to all readers. This obviously raises doubt about the other "sarrusophone" records provided by Uriel Rodriguez S., as the instruments are even rarer than the Eb baritone, and I've seen no single other record of them on the Web. They too can be saxophones, using a weak reed for the alto and the tenor. Okir_ItyEgQ Sopranino at 1:10 vAZJfRdVOEo Soprano at 1:10 xP2UHG51l1U Alto at 1:10 (and the picture is from a tenor) WWcz1kL00H4 Tenor at 1:10 This is a real sarrusophone, better played than usual, looks like a Eb contrabass DZFf_j80tX8
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My opinion about the "wavefunction collapse", measurements, and particles "deciding" has evolved. The collapse was introduced long ago as an ad hoc addition to QM, with nor firm basis nor formulation. More recent experiments, like "quantum erasers", tell that interactions don't reduce the possible states of a particle. A measurement being an interaction (followed by many interactions), it shouldn't reduce neither the possible states. It's only that apparatus are built to indicate a reduced set of possibilities - give certainty. This results from the decorrelation among the other possible states, which is extremely difficult to avoid in macroscopic states (making quantum computers difficult), and the decorrelation makes the other possible outcomes unobservable from a state that observes one outcome. So all possible stories do happen, they interfere and this can sometimes be observed, but decorrelation gives the observer the states that observed A the impression that he doesn't exist in the states that observed B. No collapse at all. Only an illusion. Some funny experiments tend to rule out that the observer's spirit makes the collapse. For instance with light emitted by stars long before the observer was born. I don't know in detail what the specialists' opinion is, but the kind of experiments they make suggests that they have already taken this step. The idea needs only time to percolate the science community. What relation with entanglement and the EPR paradox? Both photons (or whatever you want) are emitted with any polarization: all the possible stories happen. But the only possible stories link the polarization of both photons. Both detectors see a photon or not, consistently with the possible pairs of states. No collapse at the detectors and the measurement: the detectors, the apparatus, the observer exist in all the possible states that result from the possible photon pair stories. The photons, the detectors... don't need to transmit any information, neither slowly nor quickly. In very possible state of the experiment and the observer, the photons are correlated because all possible stories want it. Some state of the photon pair at the detectors, say "seen and seen", results in many possible states of the experiment and observer, depending on every collision with an air molecule for instance, and the sum of these many states is small as a mean and non-repeatable, so this set of many states has no effect on any state of the experiment and observer that resulted from a "missed and missed" state of the photon pair at the detectors. This gives the illusion of a wavefunction collapse.
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Beware newspapers need to catch the public's attention. When Angela Merkel said "I can imagine that no car with an Otto or Diesel engine is sold in 2030", in some newspapers it became "Merkel decided to ban Diesel cars in 2030". You believe electric cars are unrealistic... But humans have this ability to make unexpected things possible. For electric cars there is a very strong incentive. Think at LED lamps. Based on the ruinous tiny things just capable of telling "on-off", I thought all plans of LED lighting were foolish. But recently I replaced all my lamps by LED, because they work and are better. Companies have invested billions in that technology. One key is that it suffices when a few people (at the right place!) believe a progress is possible and useful. Never mind if 99.99% of Mankind don't believe it. This is a superiority of a free country, where people can explore new direction and are allowed to fail, over a dictatorship where one single person decides everything and can only try to catch up what was done abroad. Batteries are already good enough to move cars. In California, in Norway, electric cars sell very well. Trucks may be the next big market. Companies invest billions to develop batteries, they will improve. Whether the next ones will use lithium (which isn't expensive nor scarce), zinc or sodium, I don't know. It's impossible to predict 10 years in advance and with limited data. You know, all companies have long thought through before their heavy investments, and they made different decisions. My preferred one is liquid hydrogen at 1atm with vacuum insulation. Decent density, and the tank is only as heavy as the hydrogen. I'd have nothing against adsorption, but it seems to need a high pressure, which makes it less attractive. Aeroplanes will use hydrogen soon, much more so than batteries, and their tanks will spread to cars.
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Yes. On the other hand, I just compare what can be done with the existing stuff. Tugplanes presently in activity were designed 50 years ago and built 40 years ago. No newer design with a combustion engine replaced them, despite fuel to operate these antiques costs a lot. So to imagine if an electric tugplane has a chance on the market, I compare it with with the present fleet, rather with an alternative inexistent option. Pessimism would let say that if newer thermal designs didn't get through, the electric one won't neither. But an electric tugplane has some advantages. If willing to compare a new electric design with a new combustion engine design, we might forecast that power is 3* cheaper with electricity, maintenance is much faster, and construction looks cheaper (far from obvious, because combustion engines are often modified car engines). But this is only extrapolation and gut feeling, as neither one nor the other exists.
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Some chips progressed from mid-2016 to end 2018. Processors have stalled. 14nm finfet then, 12nm finfet now. Intel's Xeon Phi got a minor update to the Knights Landing. nVidia's Titan V provides as many 64b GFlops using as many watts as the Knights Landing. Waiting for 7nm processors. Dram chips have still 1GB capacity. Their throughput increased thanks to parallelism and new bus standards, not to faster access to the cells. But Flash memory did improve: Imft (Intel-Micron) made a chip, nonvolatile but not flash, that is fast that draws too much power for my goal here Samsung brought its Z-Nand (Slc V-Nand) to around 20µs read and write latency. The chips are not documented, but as deduced from the Ssd, they could each hold 25GB and read or write 200MB/s. This is fantastic news for a database machine and also for a number cruncher with good virtual memory. Better: this throughput seems to access one single 4kB page, so each processor could have its own 200MB/s access to its part of the Flash chip. 50* the Dram capacity, read or write the complete Dram to virtual memory in 0.3s, that looks sensible again. How much does a chip cost? How much does it consume?