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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
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
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.
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)


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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
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  on behalf of Ed Minch 
Sent: Saturday, May 23, 2020 8:40:29 AM
To: James DuPrie 
Cc: Tools Old 
Subject: Re: [OldTools] 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

> On May 23, 2020, at 8:13 AM, Ed Minch  wrote:
>
> 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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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
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:
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  wrote:

> Wow, a question where I could actually put my astrophysics degree to use,
> and beaten to the punch.
>

Kirk in HMB, where the dang tourists are already swamping the neighborhood
by 830 am
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
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




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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:
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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