A few G4s ago, someone exchange gifted 3D-printed helic(oid)ally bisected screw-apart sintered plastic cubes. It would be interesting to determine the dimensions, for a given pitch, of a helic(oid)ally bisected cylinder that maximize torsional stiffness. Probably, the fatter the better. Alan Adler tells me stiffness scales with the cube of thickness, so gluing two planks together makes them eight times stiffer than letting them slip at the interface. (Extreme case: a ream of paper.) I think I once mentioned here that horizontal tree limbs often fail gradually by splitting internally along a horizontal plane through the axis. This ought to reduce their breaking strength fourfold and their stiffness eightfold. Perhaps sagging or too-slowly-swaying trees could be flagged in this age of near universal video surveillance. I don't understand the need for a transparent slide rule component, except for maybe a sleevelike cursor. I wonder if Shapeways can work tungsten, which is surprisingly cheap. I was shocked that the Mars rover dumped 330lb of tungsten ballast before landing. Remember the incredulity when Sputnik-1 claimed to weigh 184lb? Depleted uranium is pretty stiff and abundant, but its mechanical properties are complicated. (John McCarthy once considered trying to corner the DU market in anticipation of the the eventual acceptance of breeding, and found that the supply was inexhaustible.) McCarthy also collected stories of untimely inventions, e.g. the non-guttering candle, but I'm not sure he digitized them. --rwg -------------

On 8/31/2012 10:53 AM, Allan Wechsler wrote:> Don't cut the pieces out of a hollow cylinder. Cut them out of a> solid cylinder. I bet George Hart can just print out the pieces for> you...

mrob>You still get two helices, with no solid core because the "C scale" and "D scale" pieces meet each other at the axis. I think it would still be springy enough to cause excessive error, unless it were solid diamond or tungsten (-:, and you still have to solve the axis alignment problem (making sure the two helices remain co-axial) which is much more easily solved by the transparent concentric hollow cylinder solution that I mentioned at the end. On 8/31/12, George Hart <george@georgehart.com <http://gosper.org/webmail/src/compose.php?send_to=george%40georgehart.com>> wrote:> [...] A cursorless helical slide rule that doesn't "spring"> could be designed using a two-color process to make the inner cylinder> solid with the scale of a contrasting color, and the outer (hollow)> cylinder using a clear material for its background color. (The scale> markings could be above the line for one and below the line for the> other.) However, the technology is not yet as accurate and inexpensive> as one would like for two-color 3D-printing processes. Wow, 3-D printing the whole thing, that's an approach I wasn't willing to consider. I'd be asking how we make the end product snug enough to keep the two helices co-axial. Clearly you'd print them as two pieces, smooth off the mating surfaces, then screw then together -- but how do you smooth the inner surface of the transparent outer piece, whilst keeping it transparent? I guess I'm getting rather far afield of math-fun here, unless we start citing relevant formulas. -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 -mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com