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Making a wooden cyclotron?
You need two D's, half-circular dishes. A marble starts near the center, and needs to be
accelerated every time it crosses the gap. You do this by moving the D's up and down such that
when the marble arrives at the gap, it is higher than the opposing D. You need a ramp across the gap.
Because the marble is accelerated, the radius of the orbit in the dish will be bigger every time,
and eventually the marble will leave the accelerator. In a cyclotron, the time it takes to make one
revolution is constant, and in order to achieve this in the wooden model, the slope needs to increase
with radius as follows (balance gravity with the centrifugal force):
4*pi^2*r
-------- = tan(alpha)
g*T^2
where r is the radius, g is the acceleration of gravity, T is the (fixed) time for one revolution, and
alpha is the angle of the surface at radius r. So for an orbit time of 1.5 seconds, and a dish
of about 2' diameter, the angles would be like this:
| r (cm) | angle (degrees)
| 
xxx xxxxxxx xxxxxxx xxxxxxxx xxxxxxxxx xxxxxxxx xxxxxxx xxxxx
| | 0 | 0
| | 5 | 5.1
| | 10 | 10.2
| | 15 | 15.0
| | 20 | 19.7
| | 25 | 24.1
| | 30 | 28.2
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Since the slope (tangent) is linear in r, the shape of the bowl is a parabola. Here is a table of
orbit time, dish depth, maximum velocity, for a dish of 60cm diameter.
| orbit time (s) | dish depth (cm) | max velocity (m/s)
|
| 1.0 | |
|
| 1.5 | |
|
| 2.0 | |
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| One of these ramps needs to be attached to each of the dish halves. The drop is equal for all radii,
and the drop is s-shaped so that it smoothly matches the surface of the dishes.
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| To operate, crank the handle up and down. There should be stops (not shown) so that the
surfaces line up nicely in both the up and down positions.
The D's ride up and down on vertical 1" dowels mounted on the base, over which plastic sleeves ride smoothly.
(also not shown.
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A little chute near the center with a latch/release launches the marble with just the right velocity onto
its first orbit. Then you crank until the marble gets accelerated right out of the top edge of the dish.
If you surround the dish with a rim that prevents the marble from flying off in a random direction, and which
has one hole in it so tha marble can escape in a pre-defined direction, you can aim at a gong. This would loudly
announce when you have successfully achieved full acceleration. Bingo!
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Ask Mr. Science
Why do you cet carsick?
I made a model of the balance organ of the inner ear out of 1" (ID) tubing,
bent in circles and joined with a short coupling. I made three of these, tied
together with twist ties at right angles to each other. I filled 2 with water, in which
I also put some washed-out coffee grounds, representing otoliths, and xxx (more to come)