h a l f b a k e r y"Not baked goods, Professor; baked bads!" -- The Tick
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The system consists of two parts - a series of sets of rails and a double cone transport unit.
If two cones are joined at the bases, and then placed on a set of diverging rails they will roll along, even if the rails are uphill. It was first described by William Leybourn in 1694.
The idea is to
have two hollow cones joined like this, and inside them place a sphere with some seats inside it. Fill the inside of the cones with clear oil, and the cones can rotate whilst the seat compartment can stay upright, floating in the oil. Make it all from transparent materials and you can see out.
As the rails are inclined you simply make as many sets as you need to get to where you want to be - the cones roll up one set and drop onto the next, roll up again, drop onto the third, and so on until you reach your destination.
A little bumpy but it's free transport.
Double Cone in action
http://plus.maths.o...ill/index-gifd.html
How it works [Dipstick, Mar 12 2008]
Double-cone transport system from 1829
http://www.lhup.edu.../museum/impract.htm
About halfway down the page [Srimech, Mar 29 2008]
Brachistochrone curve
http://en.wikipedia...iki/Brachistochrone
for [david_scothern] - weird things about rolling balls and slopes (see also the tautochrone link) [neutrinos_shadow, Aug 27 2009]
[link]
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It's only free transport if you're going downhill and have a sufficiently wide cone (with equivalent space between the tracks). |
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All you need to do is put a series of slightly curved rails in a circle (or enough straight ones to encircle the planet) and you have a perpetual motion machine. |
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You realize of course that such a device cannot infact raise you above your starting point. Even though the rails are sloped upwards the device itself has to fall in order for motion to occur. So such a device would only move you downhill. |
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The system seems to roll up hill because the center of mass of the cone system is dropping. The rails are inclined but the angle of the cones is greater so the system drops. In your system, the cones would not drop to the next as the cones would hit the next set of rails. |
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Notice: No one with an IQ over 75 may ride the ride. |
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Welcome, [Dipstick]. We don't take well to perpetual motion here. But posting the link is nice of you, and indicates you aren't serious. |
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You should be able to design the system to eliminate bumps. |
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Not even remotely serious. I liked the idea of peering dismally through mineral oil on your way to work and it grew from there. |
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Change it to two concentric spheres and design all towns to be like giant pinball machines, complete with crowd controlled flippers (NOW, Jemima!), and we could get about quite nicely. |
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I came across a description of almost exactly this idea on the linked website. Might you have been subconciously aware of it? It's a very nice site for halfbakers, anyway. |
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This reminds me of something I saw in the Tokyo Science Museum, recently. It was in the children's section, and I couldn't explain it. There were three tracks. Each was made from two pieces of wire with a fixed gap between them.
The first track was straight, and sloped down. A ball would roll from the top to the bottom, and my daughter had great fun in doing so.
The second had one dip, like a roller coaster, but the final level was the same as track one.
The third track had two dips, but also ended up at the same height.
All tracks started at the same height, had the same horizontal length, and finished at the same height.
Three balls were supplied, all the same, and there was a mechanism that allowed all three to be set off at once. Three bells were placed at the other end. |
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The thing I couldn't work out was this: the ball that ran down two dips finished first, by some margin. The ball that ran down one dip came in second, and the ball that ran down a continuous slope came in last. Now, each ball had the same potential energy and kinetic energy at the start, but clearly different kinetic energies at the finish (but still the same potential energies). Where the hell did the extra energy come from? Less friction? It didn't seem likely, since the ball that ran down two dips had further to go. The only explanation is friction, or stored energy in the inertia of the balls, but I couldn't fathom it. |
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The dip can be considered to be superimposed on a steady slope. Thus the ball arrives at the dip going as fast as its steady-slope counterpart, is accelerated down into the dip, and decelerated as it comes back out. When it reaches the end of the dip, it will have decelerated back to the speed of its steady-slope companion. In between, though, more KE has temporarily been made available to it and so it has gone faster. Thus its average speed is higher. A hump would have the opposite effect. |
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Higher losses incurred as a function of higher speed will mean that the fastest ball overall will arrive at the bell at the slowest speed. |
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Not sure how two dips are better - were all the dips of identical dimensions, i.e. two dips = twice as much time at higher speed? |
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The point is that at the end of the dip, the ball was going faster and was ahead of the steady slope counterpart. All dips were equal, as far as I could tell. |
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The steady slope ball will accelerate down the entire length of the slope. When a ball comes out of a dip, it is ahead of the steady slope ball, so has converted more potential energy to kinetic, so should be moving faster. When the steady slope ball reaches the same point on its slope, it may be expected to be moving just fractionally faster than was the ball that passed through a dip, _at the same position_. |
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If the dips are all identical (sorry, puts me in mind of food...) then all we're seeing with two dips is the same effect twice. A single dip of double length would be even more effective. |
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This is a great idea, but I think it would be improved if you hooked up a chain or cable to pull the double cone uphill. The cable would be powered by a machine at the top of the hill, like a ski lift. And instead of a cone, you could put the seats on the cable, much like a ski lift. |
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