Enthalpy

Example of a rotating-wing craft powered by fuel cells (click for full-scale). This one has six rotors to transport three people, according to the previous message; other numbers and patterns are possible. The surrouding truss includes a landing sledge which holds the cabin by its floor. The truss has healthy angles and offers some protection to the tank and cabin. For sight, access, aspect, the truss would better lift the cabin by the top. The six rotors and the truss suggest a compact de-assembled craft, easing transport and storage. Marc Schaefer, aka Enthalpy

This time I shall disagree, exceptionally. Solids get deformable once their yield strength is exceeded, which is by very far the case deep in Earth, even if the temperature were low. At just 1000km depth, the isostatic pressure is already ~5GPa, exceeding the hardest tool steel. A hole there would make the stress no more isotropic (zero stress perpendicular to the hole's surface) and let collapse the hole. It's the same yield strength that lets an ammunition round deform nearly without resistance upon impact with a armour. Experts compute such a hypervelocity impact using zero yield strength, as if the metal were a liquid, because the impact stress overwhelms any strength.

It is equivalent to the bijection question only if adding "almost all" others are transcendental, as Mathematic did properly.

For decades, students learned the Gold and Bondi cosmology, where matter was to be created from nothing to keep the Universe at constant density despite the recess of galaxies. Before the neutrino was proposed, observers of beta radioactivity were ready to abandon the conservation of energy. The Universe is said to have created matter for free during the inflation period, as the gained gravitation energy compensated the matter "cost". ... looks like not everyone clenches to conservation law that hard. As of laws of the Universe... we ignore them. We make models and observe to what point they hold. Some models, including the conservation of mass+energy, hold damned well.

North Korean build a new cooling tower to restart the Yongbyong nuclear reactor that produces weapon-ready plutonium from natural, hence little controllable, uranium. http://www.bbc.co.uk/news/world-asia-22763278 http://en.wikipedia.org/wiki/Yongbyon_Nuclear_Scientific_Research_Center In this context, I feel better not to help over the Internet about the splatting of water drops in finer droplets, which is a key technology in cooling towers.

Mine will be a more general answer not based on the supplied graph - sorry for that. As warmer air rises because the atmosphere's temperature gradient with altitude is big enough, it reaches a height (unless exceptionally dry) where the contained vapour condenses. The resulting dense liquid water droplets make air more dense than light vapour does, but vapour's condensation heat also let the containing air cool less, and this tends to make the air bubble lighter than the surrounding. When the first effect (liquid water dense) outweighs, the air bubble gets quickly denser than its surrounding. It produces a cumulus, whose base is flat (=condensation altitude), and the ascension stops. When the second effect (vapour condensation keeps air warm) outweighs, the air bubble stays lighter than the surrounding air, or even, gets increasingly lighter than the surrounding, and produces a cumulo-nimbus where the bubble loaded with liquid water continus to rise, up to the stratosphere's base where the tropospheric temperature gradient stops. The typical conditions for cumulo-nimus is a cold front, where denser cold air moving forward tops lighter air kept back by the ground. The abnormally denser surrounding air helps the rise of the bubble.

Yes, are "all others transcendental" was the original question. sin(pi*x) a bijection between rational x and algebraic sin was an assertion, not the question: Trig functions with arguments a rational multiple of π are algebriac numbers. ----- As for sin(pi*n/d) being algebraic: - Because sin(pi)=sin[d*(pi/d)] is rational and is a polynom of sin(pi/d), this latter is algebraic - sin([n*(pi/d)] is a polynom of sin(pi/d) hence is algebraic.

NBR is already a copolymer. What about adding one momomer more that would introduce sequences edible by bio-agents? Sorry if I put nonsense, I'm weak on chemistry.

Man, the importance of relativistic mass on orbital energy is in every course about orbitals... The question was not about relativistic versus rest mass, but whether the photon's energy absorbed by the atom can be attributed to the electron. And for the kinetic part of this energy, the answer is a clear "yes, essentially to the electron", because essentially the electron moves, the nucleus far less so.

Positive charges, that is atom nuclei, make no significant contribution to electromagnets, permanent magnets, nor magnetic materials. Only electrons do, which are the negative charges. Each electron creates a small magnetic field, through its spin and through its orbital momentum. This ultimately makes the field in a ferromagnetic material, and it needs no movement by the electrons, at least not a movement a usually conceived. Most electrons in matter come in pairs, which cancels out both sources of field, spin and orbital. That's not even random. In some materials (iron, oxygen...) a few electrons are not paired and create individual magnetic fields. In the ferromagnetic subset of these materials, the nonpaired electrons interact strongly enough that their orientation is not random. More surprisingly, this interaction can result in a net global field instead of a global cancellation. One simple case: the material alternates regularly stronger and weaker individual magnetic fields (hence of orbital origin). Magnets side-by-side align spontaneously in opposite directions, but if strong and weak magnets alternate, it can result in all strong ones pointing in one direction, outwhelming all weak ones pointing in the opposite direction. In this case, the material gets spontaneously magnetized. Though, this works only in microscopic volumes called Weiss domains. At a bigger scale, the Weiss domains orient randomly or even against an other to cancel out the field. Now, in some materials called permanent magnets, they don't cancel out. Or in the core of an electromagnet, the external influence of the current in the coil lets the well-oriented Weiss domains grow, taking volume from the badly-orientated Weiss domains, so that the the core is magnetized as long as the external current flows. This is a ferromagnetic material. Depending on how easily Weiss domains can grow and shrink (or equivalently, the Bloch boundaries who separate them can move), the material is "magnetically soft" (electromagnet's core: easy to orient, but loses this orientation) or "magnetically hard" (permanent magnet: hard to orient, but keeps the orientation). There is no clear limit between both, with some materials being semi-hard; as well, soft materials still keep some little remanence, in a variable amount very important to transformers or motors. Magnetic hardness depends a lot on the composition, thermal history and deformation history of the material; for iron, magnetically hard goes with mechanically hard - hence the name - but not for all materials.

That would surprise me. Since electrons are much lighter than the nucleus, we can and do observe the effect of the change in relativistic mass of the electrons. The mass change introduces a correction in the orbital energy, which is well measured sice it depends on each orbital and has different effects on the wavelengths of each transitions - and we can measure them with astonishing precision. At least for the hydrogen atom, accurate solutions are known, and they fit the measures to many digits - but only half as many digits if the electron's relativistic mass change is neglected. And as expected from the energy levels, this change depends on the orbital. So it looks logical to me that the electron's relativistic mass changes with the orbital, that we can attribute the kinetic energy change to one particle mainly (the nucleus gets a bit as well, in a proportion easy to compute). For the electrostatic part of the absorbed energy, a distinction between electron and nucleus would make little sense, since it's an interaction.

More detailed figures about a quadcopter-like with hydrogen fuel cells. 3* 100 kg - - - One pilot and two passengers, with luggage, dress, seats 3* 100 kg - - - Three Honda fuel cells of 100kW each 150 kg - - - 70kg of liquid hydrogen in one tank 6* 100 kg - - - Six rotors of D=3.8m in stators, with motors and electronics 70 kg - - - Cabin armour and floor 30 kg - - - Windshield 150 kg - - - Truss 80 kg - - - One parachute for the aircraft 40 kg - - - Shock absorbing gear 80 kg - - - Unaccounted ========== 1800 kg - - - Take-off mass --------------------------------------- Six rotors permit one to fail. The opposing one is also stopped or reduced, the remaining four get all the power and steer like a quadrotor does. Four D=3.8m 60% efficient rotors accelerate together 1046kg/s air to 18.5m/s at sea level, lifting 19400N or 1.1g. http://en.wikipedia.org/wiki/Quadrotor Stationary flight (17700N) at sea level needs six rotors (68m2) to accelerate 1213kg/s to 14.6m/s, consuming 214kW. Two fuel cells shall provide this briefly to land if the third fails. The fixed-pitch rotors can't brake a powerless fall, hence the parachute. Mean 250kW provided by 60% efficient cells consume 70kg hydrogen in 3.8h. The single tank is lighter, three would add redundancy. Panels of extruded AA5083 sandwich (t1=t2=1mm, a=45°) welded together separate the cabin from the tank (more detailed previous description http://www.scienceforums.net/topic/60359-extruded-rocket-structure/ ) More of this material makes the tank's outer shell, as I described for aeroplanes http://www.scienceforums.net/topic/73798-quick-electric-machines/#entry738806 The passengers sit at the pilot's sides just ahead of the craft's middle, exiting to the prow, and the tank and fuel cells lay just aft. Metal panels make a wall and the cabin's floor, and wrap a bit the tank below, above and at the sides, leaving much open area to the aft. --------------------------------------- For silence, each rotor has eight 1.8m long fixed blades of 0.5m chord, running at variable 3.4Hz or 40m/s. Made of foam covered with 560+300g/m2 composite, each shall weigh 3kg. The outer streamlining stators weigh each 19kg of the same material. 30°/s craft roll or pitch rate result in peak 2m/s and 43m/s2 at the blade tips. The gyroscopic moment is 81N*m peak per blade or just ~12MPa in the composite skins, and 324N*m at the shaft or just 0.15m times the lifting force. 2*15° roll or pitch in 2*0.5s need at each rotor 8.4m/s2 or 838N change over 2950N. Accelerating a rotor from 3.4Hz to 3.85Hz in 0.5s takes 245N over mean 1670N. Each fast 50kW motor and its reducing belt, plus the shaft and bearings, shall weigh 57kg. I didn't check a slow motor. Stator blades don't look so useful. --------------------------------------- A truss of AA6082 D=150mm e=1mm tubes holds the rotors together and with the cabin. The landing gear's shock absorber might use my viscoelastic elements or not http://www.scienceforums.net/topic/71234-deployment-brake/ A sketch is to come. The aircraft is a simple assembly like toy quadrotors are, but optical features suggesting a high-tech aeroplane promote passengers' confidence. Marc Schaefer, aka Enthalpy

There are too few algebraic numbers! No function can take any real number as an argument - of which transcendentals outnumber algebraic ones - and take different algebraic values for each transcendental argument. You may refine the explanation a little bit by taking a subset over which the function is strictly increasing for instance.

Why not? An electron in a lower state in an atom absorbs an electron and goes to a higher state. The electron gets a less favourable electrostatic potential (say, it's farther from the nucleus) so its mass-energy must be higher. What would be wrong with that?

- Don't specialize too much. You'll have to change your activity half a dozen times in a career, as most people do. Learn as much as you can as long as this is relatively cheap and convenient! - Get a scientific and technical culture as broad as possible. This is one basis of creativity. - New energies for sure. Storage would be more useful than production, which is beginning to work now. - Nanotech yes... One word for completely different things, so the first task is to distinguish them. - Biotech! Love or hate it, but it's one predictable future, so one should learn biology... - Every engineer or researcher needs as much knowledge as possible about materials, mechanical engineering and production, languages, maths, computers.

http://www.britannica.com/EBchecked/topic/388166/molecular-ion looks like the same notion used by a different profession. Let's see what chemists say to that.

The very design of a hovercraft lets the whole area create lift, whose center is essentially independent of the blowers' location.

(1) You can't light a bulb at that distance, because of losses. The longest lines span very few 1000km with good efficiency but use 600kV DC or even 1MV DC (and cheaper aluminium, by the way). Not the slightest hope with 200V. (2) This distance is the limit where RC gives about the same delay as LC, so we may still take LC, that is the speed of light since overhead lines are air-insulated, to estimate the propagation time. After 3s, you get your nothing at the end of the line. (3) Propagation time does make a difference in electricity transport. The phase lags over the distance, but the whole network is synchronous over a continent. 1000km introduce 3.3ms lag and a quarter period of 50Hz is just 5ms. It has to be compensated.

The cost of such hydrocarbons must be compared with (1) The decreasing cost of renewables (2) The cost of bad weather that results from CO2 put in the atmosphere by burning fossil fuels, resulting in bad food production for instance. "The Tuvalu Islands are not shrinking and will not slip beneath the waves." And of course, all climate scientists are morons, all oceanographs as well, and you known it better. You know what? The credibility of such assertions is about zero on a decent science forum like here. There are plenty of more efficient places for such claims.

I'll make one single trial, since I'm less patient than John has been... Electrons arrange according to the outside influences. If the context happens to be a lonely iron core, they arrange in 2.8.14.2 indeed - more details there http://www.webelements.com/iron/atoms.html By the way, 8 is not the number that fills any shell. It depends on the shell, and they don't even fill orderly. The "periodic table" is not periodic. http://www.webelements.com/ Any other influence will change that. A simple external electric or magnetic field already deforms the orbitals and chenges their energies, as is seen from Zeeman effect http://en.wikipedia.org/wiki/Zeeman_effect As soon as a second atom passes the iron near enough, it makes a chemical bond (possibly unstable with a noble gas) which is a rearragement of the electrons on new "molecular orbitals" which are no more 2.8.14.2 - it's even worse with iron, which involves deeper electrons in its chemical bonds http://en.wikipedia.org/wiki/Transition_metal so even on Earth, you'll never meet an iron atom in 2.8.14.2 state, as they're all bound in molecules. The temperature of stars is strong enough to strip most or all electrons from an iron nucleus, so orbitals and shells mean very little. http://en.wikipedia.org/wiki/Plasma_(physics) Where density is low (say, lower than the solids we know on Earth) electrons are far away from the nuclei and are little influenced by them. Where density is similar to a solid or higher, new molecular orbitals appear to accommodate the electrons. Matter resulting from them may not be chemically stable, but stays in that density due to the attraction by mass. This can be called degenerate matter, especially if density is high and the temperature exceeds the binding energy of electrons, in which case attraction by individual nuclei is little important http://en.wikipedia.org/wiki/Degenerate_matter typically in a white dwarf. Only at higher density do electrons and protons combine into a neutron star http://en.wikipedia.org/wiki/Neutron_star there, electron shells have lost their significance for a looooong time.

The N-body problem is badly known. Few decades ago, all books still told "unstable" because Poincaré claimed it a century before, but recently planets have been observed around double stars, and around one star of a double system - both being unexpected from common belief. Old triple stars are known also. So presently, people are extremely coutious about the choas or stability of N-bodies. Looks like Poincaré botched it and everyone followed him for a century.

I vote in the same direction as Dimreepr, because of the skirt. A hovercraft has a surrounding skirt that deforms according to the terrain and spreads the air throughput. So the resulting thrust is not located at the fans but spread over the pressure area. Nor does the thrust result directly from air acceleration at the fans, since air then decelerates from the fans to the undercarriage, and accelerates again at the leaks under the skirt. The lateral stability of a hovercraft demands a (lossy) sectoring of the undercarriage, so that lift decreases on the side where the skirt is too high to follow the terrain. Standard hovercraft design rather puts all fans in common, then sectors the total flow in the skirt. Some reasons for such a design: - The overpressure acts on a bigger surface - Only a skirt achieves pressure with a limited throughput - This throughput, hence the fan power, is way smaller than computed from what fans would need to create lift - This is what differs between a hovercraft and a helicopter, and saves big power. ----- Fun : the first human-powered helicopter (Gamera) has flown recently. It relied fully on ground effect. But a human-powered hovercraft is much easier (obviously these guys don't have the power-to-mass ratio of the young lady who flew Gamera): http://vimeo.com/18859973

That sounds good. The center-of-mass can be known even when the internal details of an object are unknown, and even if ignoring the internal speeds, interactions, kinetic energies... (at a proton for instance), the composite particle gets a rest mass and a center-of-mass that summarize the sub-particles and energies. Thanks! Fun: as interaction energy has inertia (said to be the main contribution in a proton), we would need to know where the interaction energy resides in order to compute a center-of-mass.

My own frenzy about flywheels there http://saposjoint.net/Forum/viewtopic.php?f=66&t=1974 In short: - Made of steel, they look cheap and efficient enough to store electricity produced during night and restore it during day peak hours. From my evaluations, they would be cheaper than building oversized power plants just for the peak hours as is done presently. - The bearings can be magnetic but don't need to. Roller bearings and hydrostatic bearings suffice. - Vacuum looks possible but a bit difficult. I'd prefer operation in air, with my flow calmers.

Maybe it's just a matter of wording. How shall we call that mass that increases with speed? Since it is the one mass that limits accelerations and creates gravity, I was pleased with the short expression "mass" for that one, or if really necessary "relativistic mass", and "rest mass" for the constant one. There is a little bit more in it. We can't distinguish rest mass from kinetic and interaction energies, in some objects whose interior is imprecisely known. It is said to be the case for protons and neutrons, whose mass shall result essentially from movement and interactions between quarks and gluons. But when considering a complete proton, we say "mass" and even "rest mass" for it, despite its constituents are very far from rest. We can't do better, and don't need to because it makes no difference, despite said "rest mass" is essentially non-rest. So a distinction between rest mass and energy seems artificial to me, as both have the same effects, and in some cases we can't attribute them to one rather than the other. I'd prefer "mass" or "mass-energy" for the sum of both, which is the observable quantity. Or?