THX-1138

HallsofIvy: I didn't say the plane was normal, I said the perspective was normal. But I'll allow as how it was ambiguously stated, though not inaccurate. The 'other way of putting it' should have removed the ambiguity. And I see no way the continuous smooth curve could possibly be a cycloid. The first reply makes sense to me; yours does not. Now, successive question: can a sine wave, or portion thereof, be closely approximated using cubic or quadratic Bézier curves or elliptical arcs? I want to represent the curve in SVG and those are the only curve commands available. So far all the SVG representations of sine curves I've found have been done in terms of lots of short line segments.

If you project a helix onto a 2D plane from a perspective normal to its axis, what type of curve is the result, and what formula describes it? Another way of putting it: If I want to draw a side-view of a twist drill bit, how do I draw the flute? Thanks!

The brass rod stock I have from an old SmallParts order; it's typed as 'C-360.' The aluminum stock is from a local hardware store, and I haven't the least idea of its metallurgical properties.

I need to machine an arbor for a gear-cutting tool. It will look something like this, but small -- the head diameter will be around 10mm. The cutting tip will protrude beyond the head's diameter by a variable amount, and only on one side, so the stress won't be radially balanced. It will be used to machine soft metals -- like brass and aluminum. I have rod stock of the appropriate size in both aluminum and brass. Which would be a better material to a) tolerate the torsional stress, and b) keep the threads for the set-screws intact for longer?

Yes, I studied the Wikipedia article, but either it didn't answer my questions or else I'm too thick to understand how it did answer them. (Actually, the section on Semi-latus rectum and polar coordinates makes it clear that a 'tilted circle' is, in fact, a proper ellipse. One down..) Thinking about this some more.. Given a tool diameter d, the foci would be d - 12mm apart, in order to give a 6mm distance from the nearest focus to an endpoint of the major axis. How to turn that into an angle measurement is still something I've not figured out, although the same section gives a clew. Figure out the eccentricity and the angle is easily calculated. (I'm probably not awake enough to figure out what I'm doing wrong, but I'm also deducing that the constant sum of the distances to the foci is always equal to the length of the major axis.) I went back to the Wikipedia article after a massive caffeine infusion, and I think I got a bit closer. If the cutting tool is 50mm in diameter, and I want the least distance from a focus to an endpoint of the major axis to be 6mm, then using the formulae in the article we get: [math]\varepsilon = \frac{c}{a} = \frac{(\frac{50}{2} - 6)}{25} = \frac{19}{25} = 0.76[/math] [math]\varepsilon = \sin{\psi} = 0.76[/math] [math]\psi = \arcsin{\varepsilon} = \arcsin{0.76} \approx 49.46\,^{\circ}[/math] [math]b = \sqrt{a^{2} \cdot (1 - \varepsilon^{2})} = \sqrt{625 \cdot (1 - 0.5776)} = \sqrt{264} \approx 16.25mm[/math] Which is a nice step along the way. However, the above will result in the semi-latus rectum (who says mathematicians don't have senses of humour?) being [math]l = a \cdot (1 - \varepsilon^{2}) = 10.56mm[/math] so the width of the groove if it is 6mm deep will be 21.12mm. That's much too wide; the cylinder will roll around in it like cavemen carrying an egg (see the film Caveman ). Obviously I need to futz around with the diameter of the tool, the depth of the groove, and the eccentricity of the ellipse. (Since the cylinder is going to be soldered into the groove, it needn't mate perfectly -- just 'good enough.') Apologies for 'thinking out loud' here, but perhaps this will be useful to someone else in the future.

I have a machining problem that I am trying to solve, and it appears that math may be of assistance. Basically, I have a 12mm cylinder and a piece of 10mm brass bar stock, and I want to cut a groove in the bar that approximates the curve of the cylinder fairly closely. Unfortunately, I don't have any tools that can work with a diameter as small as 12mm, so I thought that perhaps using a larger diameter circle, 'tilted' at an angle so it intersects the bar as an ellipse, might get me close enough. (Of course, I never thought before about any formulae relating a 'tilted' circle to the defining particulars of its cross-sectional view based on the angle. Does viewing a circle at an angle result in a proper ellipse?) That's probably incredibly unclear, so let me see if I can depict it. The attached images are, in order: the cylinder and the bar (with the desired groove marked in blue); the cutting tool (variable diameter, but not small enough); a top view of the tool and the bar; and an end-on view of the tool and the bar. Obviously this method will only yield an approximation of the groove I need. The question is, however, what diameter and angle to use for the tool to get something 'good enough.' An ellipse with one focus 6mm from the end would probably do for starters.. Plus I learn a bit more about geometry..

Propane torch it was. Most everything came loose, but the fumes from the PCB sent me fleeing a few times.

Well, I managed to get someone from Data Translation on the telephone, and the basic answer was, 'We can't give you the specs for individual components; that unit was on a PCB we manufactured.' Fortunately I still had the PCB to hand, and was able to give her a serial/part number. Eventually she found a reference to it and noted that it had been out of production for more than twenty years. (No surprise, really.) She opined that anything that old would be unlikely to still function. I don't see why a sealed solid-state component should suffer terribly from the ravages of time, so I took the brute-force approach and pumped +5VDC into the inputs. And got ±15VDC at the outputs. So it works. I'm guessing that as long as I keep it under about 1A it'll probably be close to immortal.

It's a residue -- essentially dust. 0.1mm wide at the largest, most much smaller. And around m0.005mm maximum thickness at a guess. Small enough to be strongly affected by Brownian motion. And actually, no, they aren't quite distinct. At 15X, which is rather stronger than a hand lens, I've manually separated most of the obvious bits -- but there are plenty of UNobvious ones. Thanks for the suggestions for alternate procedures, but I'd also like to pursue my original idea of using chemistry rather than mechanics.

In salvaging some [very] old PCBs, I came across an interesting little item: a 50mm × 50mm × 10mm DC-DC converter: 5VDC to ±15VDC. Perfect for op-amp breadboarding.. The same board had several socketed DT201A chips (outsized DIP-24) that probably also relate to power conditioning or the like. It's labeled a "DATA TRANSLATION DT15150" and I can find lots of references to that online in the surplus parts categories. However, so far I haven't found anything that defines its specs. I'd like to know what the voltage and current limitations are, but short of disinterring an old hardware design lab I'm not sure where I'd find 'em. The 'Data Translation' company as such doesn't respond to email questions about it, not even to say whether it's one of their old parts or not. The DT201A chips are likewise interesting, but too small to have tantalising legends printed on them. Anyone ever heard of one of these, know anything about them, or have a pointer? Thanks!

Perhaps not the best forum, but I couldn't find a better one.. I remember from my younger days that there were some things you weren't supposed to do with magnets, including heating and jarring them. The explanation at the time satisfied me. One thing I've wondered about off and on ever since, though: Is placing (and keeping) two opposed magnets (N-N or S-S) in proximity detrimental to their long-term magnetism? TIA..

I have about 2cc of 0.1mm particles (and smaller), some of which are flakes of placer gold but most of which are common mica. I want to separate these. A centrifuge would be useful -- if I had one, which I don't. The particles are small enough, as is my skill in the technique , that panning is suboptimal. So I'll try falling back on straight chemistry to remove the mica threads from among the gold. Short of HF, what would be good for dissolving the mica fragments? YT2095 says that heated solutions of some common hydroxides (NaOH, KOH, LiOH) will attack glass (and I'm extrapolating to hope they'll go after other silicates), but my first attempt -- glass in boiling NaOH solution -- yielded no discernible effect. Perhaps I didn't meet the necessary criteria, or perhaps the effect is too small to be useful in this case. DrDNA suggested aqua regia or piranha, but aside from being things I want to avoid, they won't help -- both are safely stored in glass, and aqua regia would dissolve the gold and leave the dross. So, any alternative ideas for something that will dissolve mica but leave gold and a nickel or carbon crucible untouched? (Yes, I realise I'm not talking about putting the mica into solution, but 'dissolve' gets the idea across adequately, I think. ) TIA..

The NaOH YT suggested cleaned the beaker adequately, and the discussion moved on a bit from there. I haven't the least desire to get with twenty metres of either aqua regia or piranha. I'll start a new thread on the 'getting rid of silicates' bit. Thanks!

Well, I tried boiling a bit of glass tubing in a concentrated solution of NaOH for twenty minutes, and there was no discernible effect. I examined it at about 100X. Mmph. I guess I'll try to get some LiOH and try that.

Are you serious? I'm not sure how my Significantly Better Half would react to the aroma..

And regardless of the device creating the effect, it's not likely to be the sort of 'hologram' you can walk through (e.g., the operative in Serenity). At least not and retain perfect health..

I have a bunch of old circuit boards I've collected over the years, and the sheer mass has grown to the point that I need to do something about them. I saved them either because I could use them elsewhere (e.g., power supplies) or because I wanted to reclaim some of the parts (connectors, gang resistors, etc.). Almost all of the parts in which I'm interested are heat-tolerant. Unfortunately, getting the little buggers loose is turning out to be more of a chore than I anticipated -- I think primarily because the pins are soldered through the boards and not just to the pads. I've had limited success in using a solder-sucker to clean it up. I used to have some solder-wick around somewhere, but I'm not sure it would do the job, either. Any solvent able to work on the substrate or the solder itself would doubtless cheerfully consume the interesting bits as well. The boards themselves are expendable, so slicing them up to get the parts on their own little bits of PCB is tolerable. Anyone have any suggestions for getting these things loose from their tenacious boards and solder?

A little empirical test here.. a little aqueous NaOH in the beaker, some agitation, a thorough rinsing, and the residue seems to be pretty much gone. So I would guess that it was, in fact, undecomposed silicic acid, and not silica gel as I mistakenly thought and originally stated. Thanks again for leading me to take a closer look. (I'm still trying to find an explanation of the hyphenated notation, though, so I can try to trace the actual reactions.) Very interesting! So hot NaOH might be the ticket for removing some tiny mica flakes I have in another situation. Brilliant! Thanks!

I'm not following you. I didn't add NaOH to anything. An aqueous solution of Na2O-2SiO2 (sodium silicate) was one of the primary reactants. An aqueous solution of HCl was the other. Unless you're suggesting that I add NaOH to the residue in the beaker in order to reverse it to sodium silicate and then wash it out..? Which would seem to imply that NaOH would attack quartz, as well as laboratory glassware, which is certainly foreign to my experience..

I believe you're mistaken. From the Encyclopaedia Britannica: silica, also called SILICON DIOXIDE... silica gel, a highly porous, noncrystalline form of silica See also http://en.wikipedia.org/wiki/Silica_gel, http://en.wikipedia.org/wiki/Silicic_acid, and http://en.wikipedia.org/wiki/Silicon_dioxide (Yes, I know Wikipedia isn't always a reliable source, but in this case it's supported by the Britannica, which I do regard as reliable and authoritative.) An aqueous solution of sodium silicate treated with a strong acid (like HCl) yields silicic acid.. and some other byproduct(s). When you heat a silicic acid, it decomposes into silica gel and H2O. I'm not sure which silicic acid was formed, though, and even if I assume the simplest I'm not familiar with the hyphenated notation to be sure I evolve the reaction correctly. What I have in my beaker is the residue of that reaction after being allowed to mostly dry, a substantial amount of water re-added (to dissolve any of the soluble byproducts, which I was expecting to be NaCl), the precipitate filtered out, and the beaker inadvertently left to dry completely. Upon review, I did in fact fail to heat the precipitate to drive out the water, so what I've got (in another container) is probably silicic acid that hasn't been decomposed. And what's in the beaker is probably the same. Both potentially contaminated by other byproducts of the first reaction.

NaOH? What reaction are you postulating? From a quick glance at mixing Na2O-2SiO2 + HCl, I was anticipating salicic acid (not sure which one) and NaCl... And why would NaOH etch borosilicate glass? By the way, I'm unfamiliar with that hyphenated notation. Is it equivalent to Na2O(SiO2)2 ? Also, since silica gel is silicon dioxide, I wouldn't expect HCl to touch it under pretty much any circumstances..

I recently made up some silica gel, and I inadvertently allowed the beaker to dry without cleaning it thoroughly. So now there are traces of it on the glass, and they're proving a right bugger to get out. I don't think anything short of hydrofluoric acid is going to touch it chemically, and that wouldn't be such a good idea in a glass beaker anyway. Any suggestions for getting the last traces out? TIA..

I'm not up on recent technology, but for many years water heaters included a rod of magnesium used as an anode, which was essentially sacrificed to preserve the steel of the tank. (I assume because things that would normally corrode the steel will operate on the much more reactive magnesium instead.) This isn't high-grade magnesium by any means; among other things, the anodes I've salvaged have always had a thin steel rod at their centre (again, my assumption is so that at advanced stages of corrosion bits at the bottom of the anode will stay on the rod rather than falling off because the magnesium above them has corroded away). I expect it's actually an alloy of some sort. However, if you don't need 100% purity, this might be good enough. Shavings and filings from such an anode ignite nicely. You can buy these anode rods online, or take a good-sized adjustable wrench to a junkyard or dump. The anode is usually the large hex (or four-sided) nut with no apparently purpose, located in a recessed dimple on the tank top, about half-way between the centre and the edge. You'll probably have to whack at it a bit because they commonly get somewhat corroded in place. A little penetrating oil might be good to bring along. I don't recommend cutting it loose with a torch.

I finally managed to phrase my search in such a way as to find something useful: http://www.chembuddy.com/?left=concentration-questions&right=mass-percentage-to-molarity-q1. Given that, and the best MSDS I could find for this bottle of Rooto drain opener, and assuming the solvent is H2O, and that the figures on the ChemBuddy site are accurate, and linearly interpolating the density of 93.2% H2SO4, I get this: m[sub]H[sub]2[/sub]SO[sub]4[/sub][/sub] = 98.07848 d[sub]H[sub]2[/sub]SO[sub]4[/sub][/sub] = 1.821761 (interpolated) c[sub]M[sub]H[sub]2[/sub]SO[sub]4[/sub][/sub][/sub] = (10 × 93.2 × 1.821761) ÷ 98.07848 = 17.3114537 The only figure there that's accurate is the molar mass of H2SO4; the density is interpolated from a w/w concentration that may or may not be accurate. However, the result of approximately 17 molar seems about right to me. Did I do this correctly, or did I screw up somewhere? Now on to figuring out the pH..

Which I've seen mnemonicised for the layman thusly: 1st law: You can't win. 2nd law: You can't break even. 3rd law: You can't even get out of the game.