Suggestions for building a Galton quincunx (which I have done, once):
The best quincunctes I've seen use fine steel shot, which are not
stacked one wide but poured into tubes or channels. This allows
thousands of balls to form one column of reasonable length. These need
to be vertical, requiring a transparent side window to hold the shot
in.) I don't think this is feasible unless you're set up to cut & glue
heavy Plexiglass. Try your local physics dept.
Wood, nails, and marbles or ballbearings are, however, well within most
people's capability. Whence:
(a) Make a jig to position one row of pins accurately above and between
the previous one. A strip of 1x2 with saw notches in (measure twice, cut
once!)
will do nicely.
(b) Don't build too wide or too short. A ten-wide storage rack will need
9 levels of Bernoulli trials, and an average of 256 marbles to get one
into an end lane. In the mean time about 126 marbles will have
accumulated in each middle lane (about 5 feet of them!)
(c) Use marbles unles you have a very cheap source of ballbearings.
(d) Buy more marbles than you need and gauge them, for more uniformity
in size. One ought to be able to do this nicely with a sloping and
gradually-widening track, spreading by one mm or so over half a meter,
with a box with partitions underneath. Balls fall through when the rails
get too far apart. Two metersticks
and a dozen taped-together cereal boxes should work here.
(e) Make the board three-legged with one side foot on a threaded rod to
permit
calibration/levelling. Buy a cheap spirit level (dollar store) and glue
it to the backboard once you've got it levelled to make relevelling
easier.
(g) Some sort of reset mechanism would be nice, to pour out all the
balls on command. I think I've seen a sealed "hourglass" with two
quincunctes end-to-end.
(h) (Advanced) If you use the standard "diamond nails" design, run lots
and lots of marbles through it and verify using chisquare testing that
its performance is *not* normal. The problem seems to be that the
marbles come through with a bit of
momentum in the existing direction of travel, creating correlation &
heavy tails.
A very close nail spacing (needing careful ball calibration) should
cause multiple bounces [but slower passage] making this problem go away.
Better designs (needing fancier jigs) would be the "hexagon nails"
design:
: : : :
: : : : :
in which the second row of nails enforces a vertical drop, or the
"hexagon blocks"
design in which a stick of wood is first ripped or planed to a hexagonal
cross section, then sawn into haxagonal tiles that are glued down:
/\ /\ /\
| | | | | |
\/ \/ \/
/\ /\ /\ /\
| | | | | | | |
Again, a good positioning jig, getting the clearance between hexes very
little over a ball diameter and the rows centered, is key. This design
has the advantage that the output columns are well over a marble
diameter apart and can be separated by sturdier structures. One could
even go wide enough to permit a 2-marble-wide bar (or, better, a 1 1/2
marble wide bar, as at left below)
o o
o not o o
o o
o o o
as the pattern at right is how a 2-marble-wide bar will in fact fill
unless pins are put up the middle...
-Robert Dawson
.
.
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