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