Enthalpy

Pasting regularly a supposedly sound version of the system has serious drawbacks, because you always have new settings, software installation... that you want to keep. By the way, malware exists for the Bios, against which a system reinstallation doesn't protect. Though, the capabilities of a Bios malware must be limited.

From http://en.wikipedia.org/wiki/ADSL With commonly deployed ADSL over POTS [hence not in Germany]... 138 kHz – 1104 kHz is used for downstream communication [...] further divided into 4.3125 kHz channels called bins. Wiki doesn't tell it, but since ADSL transmits more than 1Mb/s, these bins must use some special modulation, probably a constellation http://en.wikipedia.org/wiki/Quadrature_amplitude_modulation#Rectangular_QAM

Converting nuclear energy to electricity that accelerates ions is quite inefficient. One better uses alpha radioactivity to expel directly the helions or the remaining nucleus. This has already been proposed, by coating a thin film with an alpha emitter. Or even more efficient, let fission expel a half-nucleus, and catch the other half to obtain thrust. Though, no convincing setup has been proposed for that one. Worry: even with such methods, travel to the nearest stars remains very long, and these engines have unacceptable drawbacks with all imagined setups. A fission half-nucleus gets 100MeV or c/24 in random direction, so the original nucleus brings c/95 specific impulse. So if the spaceship attains quickly c/100 (and brakes upon arrival, which leaves 1/8 of the inital mass) it still takes 500 years to the nearest star - using technology known to be impossible to us now. Fusion isn't much better. Only antimatter would improve, among the forms of energy we imagine - but no-one can even propose a research direction to try to store it in any amount. At c/100, which is still too little, hydrogen and chemical fuels, slingshot and Oberth effect, Solar thermal engines and Solar sails are insignificant.

Esc-A, Ariane V's upper stage, has too much dry mass; now Esc-B is rumoured at 5650kg - shattering 200kg per ton of propellants. This hampers missions to geosynchronous orbit (Gso), one goal of Esc-B, and precludes missions beyond Mars. Worse: Ariane 6's upper stage inherits from the Esc-B, but dry mass hampers more a smaller launcher, and claims for Gso performance have disappeared. Maybe the extruded skin brings something, or maybe not: http://www.scienceforums.net/topic/60359-extruded-rocket-structure/ Also, if Esc-B controls roll by hydrazine and tetroxide pressure-fed in Verniers, it would be time to switch to hydrogen and oxygen pumped electrically. DLR has 500N engines on the shelf. I propose here to add over the Esc a small hydrogen-oxygen stage, easier to develop thanks to electric pumps, which enables deep-space missions and improves the Gso performance. At D=5.4m it fits the Esc-B, Esc-A, Ariane 6, and can also propel probes, say for capture at remote planets. It burns up to 6747kg of 720:100 hydrogen and oxygen at 25 bar, expanded to 125Pa in six 0.9m nozzles to achieve isp=4658m/s=475s. 29kN thrust permits 3300m/s in one perigee burn, to send 4.1t to Jupiter from a near-escape ellipse, reached by a first 548m/s burn from the 12t at geosynchronous transfer (Gto) provided by the Esc-B. The Esc-B alone would be marginal here, like 1.9t to Jupiter. ----- The hydrogen and oxygen tanks have 50µm of brazed steel, 20mm and 30mm foam to evaporate 15kg and 19kg in 10mn before launch, 10 and 20 plies of multilayer insulation to evaporate 1kg and 1kg per 10h in vacuum, and polymer belts to hold at the truss; they weigh 58kg and 77kg. The truss of welded AA6005 tube weighs 200kg. Add a loose polymer fabric or net against falling objects, plus separation belts: the structure and tanks weigh 390kg, and they need no internal pressure to hold the payload. The nozzles shall weigh 115kg, the chambers 40kg, actuators and pipes 15kg, for a 170kg passive engine; the hydrogen and oxygen screw pumps 30kg and 15kg, their motors as much, both inverters 10kg, summing to 270kg for the pumped engine. The Li-poly battery weighs 158kg. Transmissions, sensors, steering, controls count as 200kg, unlisted items 100kg. The electric-pumped dry stage weighs 1118kg. Centrifugal pumps would enlighten, a good car fuel cell also, and turbopumps further. ----- For lower energy missions, I consider the Esc-B is filled less to keep its start mass. To 4500m/s above Earth's gravity, for instance for my Solar thermal rocket engine, the stage would deliver 8.0t: worthy of the heavy launcher. To geosynchronous orbit, 8.4t instead of optimistic 7t for the Esc-B alone. Marc Schaefer, aka Enthalpy

I wouldn't follow the analogy with concrete, because - concrete is fragile while acceptable alloys are ductile, so the failure mode is radically different - joints aren't very dissimilar to grains in alloys. Neither would I make any parallel with carbon nanotubes, first because their behaviour in significant amounts is widely unknown. Spreading the stress despite bends and dissimilar lengths is what makes an acceptable rope, and nanotues have still to show their fitness. Expect to lose a factor of 5+ in tenacity provided nanotubes behave as well as adequate fibres do, and then carbon ropes won't be very good. Comparisons up to now are made between single nanotubes and complete polymer ropes, which is extremely unfair. Checking against single polyethylene or carbon fibres show that nanotubes aren't a revolution, and they still have to show their capability as a rope. If nanotube ropes get usable, their performance won't probably enable space elevators for instance.

Atlas' capability on escape trajectories is less than I estimated, here a new attempt: Mass at all steps of the mission can be multiplied by 0.78 or 0.78 - or take an Atlas V heavy. Because the Esc-A stage weighs fat 4540kg, Ariane V underperforms Atlas V 551. The Esc-B is rumoured near shattering 5650kg after removing the equipment case, so Ariane V ME would but outperform Atlas V 551. Even the specially-designed Esc-B weighs 200kg per ton of propellants and Ariane 6 shall use a similar stage - the competitors have 112kg/t at the antique Centaur and develop composite tanks. Time to wake up maybe?

Hidden variables were a consistent interpretation of QM, in competition with Conpenhagen's interpretation. Bell showed how experiments would choose between both interpretations. http://en.wikipedia.org/wiki/Hidden_variable_theory#Bell.27s_theorem and according to the experiments only, the Copenhagen interpretation won and is considered standard QM. This is exactly one case where several sub-theories, or interpretations, were logically possible and where experiments told which one was better.

Crystal deformation works by moving dislocations. Good single-crystals tend to be very hard and brittle. They're a very bad model to understand metals, whose behaviour fully depends on crystal imperfections. In a dislocation, some atoms have a less-than-perfect position in the crystal. When the dislocation moves, these atoms get a better position (for their bonds) but their neighbours get the worse position. This is energeticaly neutral, and the energy hill is small, so it happens at room temperature. http://en.wikipedia.org/wiki/Dislocation By the way, dislocations are easily seen at the surface of a good single-crystal. I once scratched the rear side of a monocrystalline silicon wafer to mark it, insisted a bit, and the markings were visible at the front side. This was not a plastic deformation, which is impossible with silicon.

Think back to the proposal of hidden variables. It was consistent with the rest of the theory then. Only experiments proved it false. What we may call "one standard QM" was not standard then, but only one possible interpretation, and wasn't a logical necessity.

OK, the cornetto overblows, my mistake. Whether an octave or a twelvth: these are ideal cases. All intervals exist, preferably inaccurate ones. Getting proper intonation over two or more modes is difficult and needs experiments, among others because the embouchure has a strong influence on pitch.

I wouldn't say that there is one standard quantum mechanics. It's still evolving, and under the constraint of experiments, not as a logic consequence of its consistency. Look at the uncertainty relations between entangled particles: some time ago the entanglement could have been considered perfect, and experimenters checked the bounds of the uncertainty relations in entanglement. So you may wish to say "QM is unique and standard", but then it's our interpretation of it that is multiple and evolving... Experimental results are puzzling: we shall agree.

Hi Ludovic, welcome here! (Priko?) The maximum amount of water that can be extracted is easy. The efficiency of the collector is difficult to predict, but you can try to make it good. Water has a vapour pressure that depends on the temperature [...of the water, but let's forget that]. Below 100°C this pressure is well under 1 atm (that's why water doesn't boil) but it contributes to the composition of the atmosphere as a partial pressure. Compare it with 1 atm, you have the maximum proportion of vapour (in volume) that air can contain. Multiply by the relative humidity, you have the volume proportion of vapour. When you don't forget that water weighs 18g per mole and air around 29g, you even get a mass of contained vapour per air volume. Then the collector shall cool all the contained vapour to be efficient which means more or less all the air, and here nice physics becomes nasty technology. But if you cool all the air to 10°C an leave no liquid water in the outgoing air, then you leave only the vapour corresponding to the partial pressure at 10°C. The difference gives the (ideal maximum) collected water. http://www.engineeringtoolbox.com/water-vapor-saturation-pressure-air-d_689.html Marc

Maybe you'd like an explanation more detailed than electromagnetism provides. Within electromagnetism, "moving charges create magnetic fields" is a fundamental law (mathematicians would say: an axiom) which has no explanation more fundamental, but serves to explain more things. A set of equations, for instance Maxwell (or an equivalent set, like Biot and Savart plus others) have been agreed on because they explain observations. Compare with taste: the ocean is salty, an oyster is salty, but how does salt taste? ...salty, and no better description. So: no explanation like "the movement lets the sensor vibrate" or "it spans a spring" is to be expected. But the set of electromagnetism laws explains many things properly (...when applied well, which is not trivial). Unified theories for electromagnetism and for the weak force would be even more fundamental, but these are even more abstract, and won't provide the kind of answer you apparently hoped.

Presently the force between neutrons, between protons, between protons and neutrons is little understood nor modelled - far less complete nuclei. With a proper understanding of it, we might for instance fuse deuterium with deuterium (without demanding tritium that ruins the hope of clean fusion energy), possibly even in machines more reasonable than the thingies Mankind tries to develop now (15G€ for Iter). That wouldn't be bad. Even a better understanding of the seemingly simpler weak force would be nice. Imagine if we could provoke at will the desintegration of 40K: we have plenty of it, reasonably easy to isolate, clean products. Or producing some radio-isotopes without the need of a special nuclear reactor would ease medicine. What we do presently is so primary and brutal! Use a huge neutron flux, expose a material, and from the resulting incredible dirt, try to extract the useful result, bring it within two days to the hospital on a different continent. Finding efficient, targeted and clean synthesis ways would be nice - but how, without understanding nuclear forces to develop different machines? Thanks! As predicted by one of the competing sub-theories or interpretations... The one that is taught subsequently. Think a bit backwards, entanglement itself was questioned by brilliant people. So was the minimum delay or comparison possibility between remote detections of entangled particles: experiment decided, not theory, and theory was oriented in one direction after that. The same happens presently with erasers and with partial detection. But if you prefer to call it "our imperfect understanding or interpretation of the perfect theory", which supposes that a theory exists outside our understanding, I won't question it - that's philosophy.

Few years ago, the answer was simply: observe a photon means destroy it. So if it's observed at one slit, you won't see it later, neither as fringes nor as anything else.

That sounds like a provocation... My impression is that intrication is unclear enough even to QM specialists. When they publish some hermetic experiment, other specialists stare at it bluffed . Though, an intuitive understanding of intrication - or call it a good mental image, or whatever you want - would help thaaaat much in developing quantum computers, which are a hot research topic, and are possibly some sort of technological future (or not). Than you could spend a compassionate thought at all poor guys who would desperately need a clear and intuitive (hence creative) understanding of QM to apply it, despite being specialists for other topics: chemists, semiconductor engineers... Such people can cite a few aspects less than perfectly clear , at least for them. And what about progress in some aspects of QM we still lack today? Say, solutions for THREE particles instead of two, that come from something more usable than a computer simulation? In fact, we would need a proper quantum description of a system of 1023 electrons in a metal, and then maybe we'd have a good theory of superconductors. Other QM topics are perfectible. Generally, books excel in formal representations and transformation, and in reproducing ONE result obtained by one genius a century ago (say, the spectrum of a neutral isolated hydrogen atom, in case someone meets one some day) but fail over any useful question, like the spectrum of a hydrogen molecule to begin with, or the life expectancy of an excited state, or a prediction of Van der Waals' forces, or or... For all these questions, we may perhaps get a questionable result from simulation software, but maybe not, and generally rely on case-by-case experiments. Developments of QM that would produce simple applicable methods would be welcome.

Crystallography and the like use to give answers of limited usefulness for the user and even the producer of alloys, so I haven't invested much in it, sorry for that. It's complete books of theories not easy to check experimentally, and when you need a simple answer they don't give it. Worse, there are so many possible processes and explanations that crystallography explains equally well everything and its opposite. Resembles a viscous fluid: time and speed have only a secondary (but real) importance in the flow of solids, while they're paramount in liquids. As well, flows of solids show thresholds that simple liquids don't have - though many liquids aren't just linear. The behaviour of an alloy under strain depends fundamentally of said alloy and its thermal and deformation history. This contrasts with a liquid. Austenitic stainless steel, commonly used for cold bending and deep drawing, gains much strength through deformation; this makes places already deformed more resistent, so the ongoing deformation affects in priority the other places, and the global deformation is evenly spread. Other alloys behave differently and aren't as good for cold bending. Simple deformation models, independent of the alloy, can't tell that. Also important, deformation can change the metallurgical state, typically from austenitic to martensitic in stainless steel. Some people wrongly believe it's the only cause of hardening. Poisson near 1/2: no! That would leave the solid's volume unchanged under uniaxial stress, which is not the case. Most alloys are near 1/3 (...though reasoning would imply 1/4).

For a slingshot as we use to understand it, the spacecraft should come from outside the Solar system - more accurately, its energy should suffice that it is not bound in the Sun's gravitation well. So aliens sending a craft from a different solar system could take advantage from the different speed of our Sun for a slingshot. It would need patience. Escape a galaxy by slingshot : this is the astronomical model for some objects observed outside any galactic gravitation well. Smaller objects get speed and are ejected. Same story for a globular cluster, which can eject an object from time to time. ----- What can be - and is - used by us is the Oberth effect, including at our Sun. http://en.wikipedia.org/wiki/Oberth_effect It tells that near a massive body, when you add a small speed to the minimum that allows to escape this body's gravitation, you keep a big speed after escaping, because speed sums act through their square as an energy. That's daily life when sending probes far from Earth, and it's used from our Sun as well: "for instance" the Pioneer, Voyager and New Horizons keep much speed after escaping Sun's gravitation. As a special case, Solar sails near our Sun would benefit both from the Oberth effect and from more intense light, so their Sun escape scenarios involve to first dive near the Sun and accelerate there. ----- (Every?) probe we sent farther than Jupiter used the slingshot effect at Jupiter, because our chemical propulsion is too weak for the Sun's gravity. In some cases we could make direct shots, but this would mean huge launchers and tiny probes. In other cases like Ulysses escaping the ecliptic plane, or Messenger going to Mercury http://en.wikipedia.org/wiki/Ulysses_(spacecraft) http://en.wikipedia.org/wiki/MESSENGER the energy is out of our reach with chemical engines only and demands a slingshot. Solar sails woud have done Ulysses' mission better and faster, if they were available. Some missions (Cassini to Saturn) even pass by Venus and Earth before Jupiter to further save mass. http://en.wikipedia.org/wiki/Cassini%E2%80%93Huygens In this case, the initial hydrogen rocket for the shot to Jupiter was cancelled, but the indirect trip permitted a less efficient solid rocket. As a drawback, Jupiter's period around the Sun is 11 years, so the window opens only from time to time. Better propulsion like my Solar thermal engine would bring this flexibility.

This state or a similar one must be possible, as are around 6*1023 more. Since eddy currents exist in metals, some states resembling this one must exist. As does the one that rotates in the opposite direction. And because both have the same energy, both are occupied or not without external influence on the metal. Though I doubt one gets the eddy current through a sum of such 2p orbitals. A phased sum of any orbital is at least as good.

Yes, I am. The doughnut is only one possible shape of a 2p orbital. The peacock, with one side positive and the opposite negative, is an other. Chemists use to take the peacock shape to think at molecular orbitals. A peacock is a sum of two doughnuts, a doughnut is a sum of two peacocks. Just like exp(ikx) is a sum of cos(kx) and sin(kx) - from where the oriented impulse is absent, be happy - and cos(kx) is a sum of exp(ikx) and of exp(-ikx).

The masses in my last message are wrong. Atlas V 551 can inject only some 5.1t in transit to Mars. And as an excellent practice, the unsterilized launcher shall not collide with Mars. Consequently, the probe must correct its path, which cost Mars Science Laboratory 14% of its mass. So a direct comparison wouldn't be fair. MSL innovated with its "guided entry" which used an unbalanced capsule (like Apollo) that rolled to adjust its path, to compensate for atmospheric fluctuations, for wind, and other perturbations, in order to land precisely. The petals I propose give stronger means of action, and their stability looks more reassuring. They weigh a lot, but MSL ejected 150kg to unbalance the capsule before aerobraking, later 150kg again to recover balance. The parachute weighs also. This makes the petals more aceptable.

I see. You were clear, I'm just a bit stubborn. Cornetto, serpent, ophicleide... http://en.wikipedia.org/wiki/Cornetto_(musical_instrument) http://en.wikipedia.org/wiki/Serpent_(instrument) http://en.wikipedia.org/wiki/Ophicleide Wiki's articles are heavily biassed in favour of these horrible instruments. The cornetto doesn't overblow, the serpent I believe doesn't, while the ophicleide does badly. All have horrible intonation, a bad range, a dull sound that varies an awful lot depending on the note... Why the hell should you want to play them? Any toy instrument is better than that! It's just that tone holes do not fit with a brass mouthpiece. They fit a reed, but a brass mouthpiece demands valves or a natural instrument. Worse: except on the ophicleide, the tone holes are ridiculously tiny. ---------- What instrument makes call "resin" instruments aren't generally made of epoxy but of PMMA, ABS or PP. These are not so unhealthy for humans, especially PP is considered harmless. Makers must consider "resin" to look more luxurious that "plastic" or "polymer", but they're just thermoplastics. Personnally, I wouldn't be afraid of blowing in an experimental epoxy instrument through a metal mouthpiece. But I would not sell one. ---------- To produce experimental bells, you could make an inner mould of clay on a potter's wheel, then cover it with nickel, or epoxy and glass fibre, or layers of MMA that you polymerize... then separate from the mould. ---------- Have you seen the price of instruments that probably work a bit, as opposed to a cornetto? At eBay.com, just the first answers when looking for "bugle": item 350712757879 sells for 30 dollar item 200938513000 sells for 60 dollar they can overblow as you wanted, and at this price, you can bore overblow holes if you want. Variant: you buy such a horn, preferably short, and add a cylindrical tube between it and the mouthpiece. This makes an approximate baroque trumpet, where you can add overblow holes if desired.

As an example, an automatic probe shall aerobrake and land on Mars. The body has 4m diameter or 12.6m2, the eight 1.5m*8m petals cumulate 98m2. This fits in Ariane 5's fairing, Atlas V and Delta IV as well. Atlas V 551 achieves 8900kg in tilted Gto, so is shall inject 6227kg at 3262m/s above Earth's gravity; Ariane 5 Me achieves a bit more. The slightly accelerated transfer (roughly 200 days) arrives with 4235m/s above Mars' gravity and plunges to 6559m/s little near Mars' surface. Aerobraking over straight 2*190km (no downlift) needs only 40m/s2 (smoother than the launch) or 249kN, beginning and ending at 30km above datum, with the middle at 24.7km. Fine, that's higher than Olympus Mons, and the mean free path is still <1mm at 30km. Here's my estimate of the atmosphere's density, fitted at 0km and 21km; adjust the braking height if you have real data - this may need real-time measures because of Mars' variability. I take the hypersonic drag as density*area*tilt*Ch*V2 with a Ch~0.8. 6559m/s and 0.22g/m3 at 30km need area*tilt=33m2: petals 1/5 active. Efficient braking could hence begin earlier. 5051m/s and 0.78g/m3 at 24.7km correspond to the body: petals just 1/30 active. 3542m/s and 0.22g/m3 at 30km need 113m2: petals fully active - but keep some angle. This is the speed of a circular orbit, though a capture would have sufficed. The wide tunability permits a softer brake and, together with some up- or downlift, can compensate some variation in Mars' atmosphere. The petals keep the probe stable. All this is easier than with a lifting body. The probe can even adjust its path to the landing site. The petals open to 30° short of flat for the descent, so the probe shows 97m2; with transsonic Cx~0.9, the speed drops to 192m/s near the ground (14.4g/m3 and 3.7m/s2). No parachute threatens to fall on the probe. A rocket shall brake to the soft touchdown. If pushing 3.7+10m/s2 it costs 263m/s performance. For comparison, hovering and manoeuvring over the ground at 5m/s2 during 60s also costs 300m/s. One simple autonomous touchdown algorithm could be: With all petals-feet moderately down, descend gently until one touches, then stabilize the height. Lower the other petals-feet until all touch, then stop the rocket. But if the feet don't touch after a reasonable stroke, then take off and try again 300m farther. One 150+150m hop with 3.7+10m/s2 push costs 91m/s performance, one 30s descent attempt 120m/s. Braking plus three landing trials cumulate 805m/s. At isp=340s it takes 1336kg propellants. If the tanks and engines weigh 140kg it leaves 4751kg. The dirty used heat shields are dropped on the ground and the probe walks away, with 20m span giving a nice clearing capability. But if dropping the shields isn't clean enough, the petals and all shields plus the rocket propulsion can belong to a crane that lowers a rover before separating itself and flying away, as the Mars Science Laboratory did. Marc Schaefer, aka Enthalpy

Hello dear friends! Here I plan to describe automatic spacecraft and manned spaceships that aerobrake at celestial bodies like Earth and Mars, and have big movable control surfaces in order to adjust much the braking force, provide stability, and when needed provide downlift. They look roughly like a capsule fitted with big movable petals, which can be behind the capsule for weaker braking, or extended for stronger braking. The same petals are useful as a parachute at lower altitude and speed, and possibly as legs to land and to move the spacecraft. This may save some mass, and limits the risks of unwanted interactions. Drawings are in the pipe and should make it clearer. Marc Schaefer, aka Enthalpy =========================================================================== Here's how the petals' position meet various needs, here to aerobrake and land; other missions like an aerocapture would follow a different sequence. The petals have (strong) actuators for several movements. Downlift needs it, and also the roll control (which can require additional control surfaces), walking on the soil as well. A taller spacecraft that requires downlift might have a tiltable heat shield. A numerical example is to follow. Marc Schaefer, aka Enthalpy

You're perfectly right that simple math alone won't make a decent instrument, and even the best acousticians have produced, err, perfectible instruments. Therefore, you need a way to test many designs. Plastic is less than optimum for a wind instrument, even a brass, but the ease of fabrication determines your choice. As for wood: only the densest ones (and most expensive) have a chance to survive the humidity variations of a wind instrument: blackwood, grenadilla... You can really forget all others: they will split very quickly. ----- A wind instrument's bore can have steps. This has been theorized, experimented, and the instruments work. I heard and played a bamboo saxophone that sounded like a softer sax. (Bamboo or) cane would be a candidate for your trumpet experiments if you can get many diameters with thin walls that fit in an other. Though, the steps introduce more losses which, due to their positions, act differently on the notes. This is a serious drawback for a brass instrument, which needs equally easy notes to be playable. Long smooth transitions would be much better. To the very least, the sections must be shorter than a quarter wavelength of the highest note, and even of its harmonics - this is very short on a baroque trumpet! These aerodynamic losses are also non-linear. The bamboo sax I tried could play pianissimo but not fortissimo, pity for a trumpet. ----- Would you access a rapid prototyping machine? More and more amateurs have their own, this would make you one prototype per night with arbitrary shape. If you access a lathe, you can turn the inner diameter of the straight instrument, with wax loaded with talc adhering on a central metal tube, then cover it with glass fibre and epoxy, and remove the wax. I made rocket noses that way, with steps of 0.2mm. Though, a straight baroque trumpet will be very long! Only the prototype? And how to access the overblow holes? A very nice alternative: let cover the wax with nickel instead. Honiba had a patent, expired meanwhile, to make the walls with a metal wire winded on a (wooden?) shape, then join the wires with solder. Nice for prototypes! ----- 13mm inner diameter is already much for a baroque trumpet! Have a look at manufacturers' catalogues, for instance Yamaha. What taper shape? That's the difficult part! A complete cylindrical bore does work. It's not very good for a brass, I suppose because of impedance matters. The frequency multiples (only odd available) are widely spaced, which is what you don't want on a baroque trumpet. But at least the modes are properly aligned in a first approximation; keep the flare very short (very few cm) and the mouthpiece transition as well. A strict straight cone works well and gives all frequency multiples (odd and even). It is used in the Alpine horn to give a really nice sound, unique among brass instruments. It precludes pistons which need a cylindrical portion, but you don't want pistons on your baroque trumpet anyway, so it's very possible. You could roll a sheet of brass and braze it. Previous conical designs like the ophicleide had tone holes instead of pistons. The diameter for a high-pitched trumpet would resemble an oboe. The sound will differ much from a trumpet. ----- The usual flares have no algebraic solution. They are essential to the sound quality of each instrument and its ease of playing. They offer a cylindrical section where to put the pistons. This cylinder de-tunes the fundamental mode, but the higher modes not too much. The "reason" is that for a half-wave, a cylindre is as long as a cone; only the last quarter-wave is longer in a cone. The precise flare compensates for the approximation, and a cylindre plus cone won't work well enough for a music instrument (I hear 0.1% pitch). This also means that a baroque trumpet, which won't use its second mode but starts at its third (or fourth?) can have a long cylindrical portion and a short flare. This is even necessary in order to reflect the high frequencies, so the air column resonates on high notes instead of just radiating. There is some choice for the length of the flare: short on a trumpet, it lets high frequencies resonate and gives a brilliant sound; longer on a cornet with its softer tone; very long on a flugelhorn for the warm mellow sound. This also makes higher or lower notes easier to play, but the mouthpiece contributes to it. For a baroque trumpet with a real standard flare, I'd take the flare length and shape of an existing trumpet of the same pitch, or scale it according to the pitch. I'd favour an even shorter flare, because the longer tube of the baroque trumpet will make the tone softer and more distant. Before this flare, I'd just lengthen the cylindrical section. This will de-tune the second and third modes, but they aren't used anyway.