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270977 | James DuPrie <jbn.duprie@g...> | 2020‑05‑23 | odd question: Gravity well (read for oldtool content - its really there) |
You know those vortex-type things that you roll a coin or ball down, and they take forever to spin down the hole in the middle? Apparently, they are called gravity wells, I've been asked to build one. Out of wood. The actual task isn't all that daunting - plane a bunch of stock flat, glue it up, and spin it on the lathe. The one bit I can't figure out is: what is the formula for the curve of the "funnel". Any ideas or input? It seems to me it should be something like an asymptote (y=x^2/(x^2-1) or maybe an exponential curve, but its enough work to make the blanks that I don't want to just do trial and error. Any thoughts? Now, for the oldtool bit: I'll be building at least 2 of these (assuming the proof of concept works the first time around). The proof of concept one I'll build out of standard (cheap) dimension stock. I'm planning on about a 20" diameter disc, so here's the process: rip stock into 1.5" strips. (no-name rip saw, about 4 TPI) Cross cut into sections that match the depth of the curve ( another no name saw, but set up for crosscut at about 8TPI). I'm still pondering this one. Since I'll be building up the disc, I might save some stock and lathe time by actually building the curve as I glue it up, then use the lathe to just smooth out the lumps. That will make glue up an absolute B**ch, but make everything else a lot easier. Various bench planes to get 2 sides of each blank flat and parallel. Glue up into rows. Plane flat and parallel and glue into block. Basically building a butcher block more-or-less disc, Use large compass to scribe circle, and coping saw to round (more or less) the blank. I use a a brace and bit with a hex adapter to drive in the screws to hold the face plate on. Nothing like a good bit of torque to make it easy... The lathe is unmentionable, but suffice it so say that it spins thing really well. I KNOW the easy answer is to refer him to someone with a CNC router or lathe, but the challenge is something I just can't walk away from. What could be cooler. I'm thinking that if I can make the prototype work, I'll use beech for the final product, probably with end grain for the surface. He says he's using 1" stainless steel ball bearings, so I want something that won't get grooves worn into it. Of course, the idea of using something with a bit more grain is tempting. I'm guessing that a curve like that would make for a real pretty showing... Maybe if it works well I'll play around with some lighter balls and see if I can get one to work with a ping pong ball or a super ball, then see about some fancy grain.... Anyway, if you have any thoughts on what that curve should be - or have any other thoughts - I'd love to hear them... -Thanks! -James |
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270978 | Ed Minch <ruby1638@a...> | 2020‑05‑23 | Re: odd question: Gravity well (read for oldtool content - its really there) |
Sounds like you have it covered. Seems like a simple lathe job if you ignore that 20” dimension What does your lathe look like? Seems simple enough to make a cardboard negative shape to hold up against the curve as you develope it. You could also make a carboard shape for the outside and use a drawknife or big gouge to get close. There is one at the Franklin Institute in Philly that is about 5 feet across made of fiberglass and not very fair (is lumpy in other words). You put a coin in a slot and drop it and the coin rolls on its edge all the way around and down into the hole - a way to make donating fun for kids. The math escapes me Ed Minch |
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270979 | "yorkshireman@y..." <yorkshireman@y...> | 2020‑05‑23 | Re: odd question: Gravity well (read for oldtool content - its really there) |
Wow - more a challenge than a commission, but hen, aren’t they all. A fellow member of the IWCS used to make segmented bowls. He cut accurate segments of a circle and glued up within a PTFE ring (circle of yellow gas main) I would attempt something similar to construct an open cone void. Even using only 6 or 8 segments, you are able to cut the blanks so as to form the rough interior shape, then refine on the lathe. You may need some form of inserted centre to provide stability whilst roughing off the first part of the material. 30 degree angles for the essentially coopered construction are no harder than 45 for a corner, and you then join up in pairs for octagons, or threes for a hexagon, so you can check and refine the mating joints as you complete each gluing. As for the curve itself, can you gain access to an existing one and make a template? otherwise it will be t’internet. I have no ideas. I might suggest a hard lacquer finish somewhat against my principles as the final finish. Enjoy! Richard Wilson locked down under grey skies in Northumberland. |
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270980 | Erik Levin | 2020‑05‑23 | Re: odd question: Gravity well (read for oldtool content - its really there) |
James asked about the coin funnel: I believe you want to look at: https://www.spiralwishingwells.com/guide /physics.html">https://www.spiralwishingwells.com/guide/physics.html Near the bottom is the equation (it is a surface of revolution) and near the top of a dimensioned sketch of an actual device. I get the impression that it isn't that critical in practice, and the friction between the coin and the surface have a stabilizing effect, in the same way that the friction between the tire and the road helps stabilize a bicycle (the geometry makes it possible, but the friction makes it happen) *** This message was sent from a convenience email service, and the reply address(es) may not match the originating address |
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270981 | Ed Minch <ruby1638@a...> | 2020‑05‑23 | Re: odd question: Gravity well (read for oldtool content - its really there) |
And I also forgot to mention that since it looks like there will be end grain showing, the ball should not wear a groove for a long log time Ed Minch |
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270982 | Tom Dugan <tom_dugan@h...> | 2020‑05‑23 | Re: odd question: Gravity well (read for oldtool content - its really there) |
Wow, a question where I could actually put my astrophysics degree to use, and beaten to the punch. In any case ... Gravity is a 1/r-squared equation, and the curve is a paraboloid - a parabola rotated about an axis. And of course you're approximating a 3-dimensional phenomenon in 2D. Another common way to model gravity is to stretch really stretchy fabric across a frame and drop a weight into it. The fabric approximates a paraboloid and allows you to roll lighter balls into/around the well. Not as elegant as a hard surface though. Easy enough to find and print an image of a parabola to make Ed's template. Scaling it up beyond the limits of a typical lathe seems to be the hardest part. Let us know how it goes! -T Get Outlook for Android<https://aka.ms/ghei36> ________________________________ From: OldTools |
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270983 | Claudio DeLorenzi <claudio@d...> | 2020‑05‑23 | Re: odd question: Gravity well (read for oldtool content - its really there) |
> > Hey Tom Roy Underhill shows how large press screws etc were cut using a paper > template in one of his books. Try to find a copy because I think it's sort > of similar to your project. I think he was making a a large apple press > (apple cider press) or something with a 10" or maybe a 12 inch diameter > cylinder blank of close grained wood. He was using straight lines to plot > a even thread pitch which is slightly different to your need of a > progressive pitch. Do you need a double pitch? Do the tracks also have to pitch along the z > axis to keep the rolling objects inside as they accelerate? I guess the > track would be horizontal at the top and totally vertical at the very > bottom? I would make a prototype out of bendy weldable gluable plastic > board first to work out the bugs. Or did I totally misunderstand that? Are you making a paraboloid bowl > and shooting the balls down a chute to get them to roll around the walls of > the bowl on the way to the bottom? Cheers Claudio |
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270984 | Claudio DeLorenzi <claudio@d...> | 2020‑05‑23 | Re: odd question: Gravity well (read for oldtool content - its really there) |
D'oh, why do I always read the latest post first! Great link Erik! -- Claudio On Sat., May 23, 2020, 8:35 a.m. Erik Levin via OldTools, < oldtools@s...> wrote: |
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270985 | Kirk Eppler | 2020‑05‑23 | Re: odd question: Gravity well (read for oldtool content - its really there) |
Tom is fighting the urge to design a black hole for James to use, I'm sure if it. On Sat, May 23, 2020, 6:07 AM Tom Dugan |
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270988 | James DuPrie <jbn.duprie@g...> | 2020‑05‑23 | Re: odd question: Gravity well (read for oldtool content - its really there) |
OK, parabola it is.... thanks to everyone for some excellent references and input. For those that had questions: I'm trying to turn a 'gravity well' as seen here: https://www.spiralwishingwells.com/guide/physics.html. They claim to use Y=-1/|x|, which would be a parabola, so I guess that's one more confirmation. I glued up rounds 2 and 3 today (1.5" thick was the first one, these are 3" and 6"). The 6" should be plenty deep for a full parabola. the plan is to have the outside edge be level (horizontal). There will be a 'wall' around the outside to hold the ball bearing until it slows enough to start falling towards the center. The curve will progress to the center, where the surface will be vertical. My guess is that friction and spin will mean that I might end up doctoring the curve a bit, but then, the chances of generate a perfect mathematical curve are pretty unlikely anyway, so it will be a start... I'm thinking I'll try both the parabola and the asymptote and see which works better. And maybe an exponential one too..... -James |
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270989 | Erik Levin | 2020‑05‑23 | Re: odd question: Gravity well (read for oldtool content - its really there) |
Pedantic moment: y=1/x is not a parabola, but is a hyperbola. A parabola looks roughly U shaped and has no asymptotes. If you are using ball bearings, rather than coins, the exact shape doesn't much matter, as long as it has smooth transitions in curvature. You can bend a spline as a guide in shaping and it will be fine. As a historical note, back when I was but a wee lad, and in school, we would mount rubber sheets in what was basically an embroidery frame and push and pull points up and down to form hills and valleys. Dropping bb's, or similar small metal balls, randomly on the surface would give a good approximation of what electrons in a tube would do. Of course, I am young enough that tubes were already out, but it was still part of one course and lab. We had no end of fun tossing a bb tangentially to get the orbits like you are making up. whooosh, whooosh, whooosh, whoosh, whoosh, whosh, whsh, whsh, whsh, wsh, wsh, wsh, wsh, whs, sss, ss, ss, ss, s, s, ziiiiiip *** This message was sent from a convenience email service, and the reply address(es) may not match the originating address |
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270990 | Mike Lynd | 2020‑05‑23 | Re: odd question: Gravity well (read for oldtool content - its really there) |
whooosh, whooosh, whooosh, whoosh, whoosh, whosh, whsh, whsh, whsh, wsh, wsh, wsh, wsh, whs, sss, ss, ss, ss, s, s, ziiiiiip Yay! Superb! 8o) On Sat, 23 May 2020 at 21:15, Erik Levin via OldTools < oldtools@s...> wrote: |
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270991 | "yorkshireman@y..." <yorkshireman@y...> | 2020‑05‑24 | Re: odd question: Gravity well (read for oldtool content - its really there) |
ASCII art in surround sound! Who knew? R |
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