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Re: The development of bubble sextants
From: Hanno Ix
Date: 2009 Aug 14, 16:40 -0700

Brad, George:

First, I am sorry I have confused you:

My previous topic was the measurement of LON by the time differences of transits of Sun and Moon at the local meridian. Here I interjected myself into an entirely different discussion: the dynamic of spirit levels. While both are ultimately aimed at determining position they are aimed at the same time at quite different issues within this field.

To the pendulum comparison:

Often one can choose from several models to describe a system. I chose a pendulum because its the best comparison I personally know of. Let me describe other systems but quite similar to the spirit level. You will see the similarities immediately. And you will, I hope, agree, that the pendulum analogy is valid.

Assume a rail that is bent to a circular arch and has a groove at the inside of the arch so that a tiny ball can roll in that groove along the arch. The rail is mounted on a table such that it rests with its deepest point on that table. You set the ball into the rail and give it a tiny push. Of course, the ball will roll back an forth on the arch, slightly diminishing the amplitude of the cycles until it comes to rest at the center.

If you can neglect the energy of the rotation in that ball, I assure you, it will move just parallel to a pendulum with the same length as the radius of above arch and if started at the same time and with the same elongation. In reality, after several periods their movements might actually get out of sync, mostly because of different friction in both systems.

The only difference is that the trajectory is enforced by an circular arch in one system, and by a thread of the length of the arch's radius on the other. A first order analysis yields the period as equal to 2*pi*sqrt(r/g) for both cases. ( r ist the radius of above arch/length of the thread, and g is the constant of gravitation). Please note: The period is independent of the mass of the "lens", and no hint of the type of

You construct a third system: You tie a helium balloon to a string of the same length as we used above. Because helium is lighter than air this time the "lens" of this "pendulum" will swing above the suspension point. Nevertheless, the period will be close to the above. Friction again will cause the difference we might see in actuality.

Again a new sytem, our last: You build an circular arch from a hollow tube and fill it with liquid, say with spirit. However you leave some space, so that a bubble is created. Since the bubble is lighter than the medium of its environment it will act just like the above ballon.

All four systems have in common a circular trajectory, an equilibrium point and a restoring force nearly proportional to the instantanous ( ~sinus of ) elongation. They will also have friction, or damping, somewhat proportional to the instantous speed. That is the reason they behave so similarly.

Because of this simularity I can also use the more general analogy of a low pass filter in all the mentioned cases, particularly to the spirit level. I hope to draw from it insights of how to improve the stability if the bubble.

I also hope I have demonstrated to you the validity of the analogy between spirit level and pendulum.

Best regards

--- On Fri, 8/14/09, Brad Morris <bmorris@tactronics.com> wrote:

From: Brad Morris <bmorris@tactronics.com>
Subject: [NavList 9515] Re: The development of bubble sextants
To: "NavList@fer3.com" <NavList@fer3.com>
Date: Friday, August 14, 2009, 1:48 PM

The patent originally referred to by Hanno requires that the optical device be pendulously
suspended in the tube, such that vertical is maintained. How would he know if the device he constructed
was then plumb? This may be the reason why Hanno is now looking at spirit levels.

If the device were to be constructed by Hanno, it would need be checked by reference to some
other well understood device. Hanno will not prove that his device is plumb by reference to
a spirit level. That would required somehow referencing the spirit level (horizontal) to the
optical axis (vertical), a difficult task without highly accurate metal machining. I believe
that Hanno suggested wood, an in-appropriate material for constructing this type of device.

The NavList has recommended that Hanno obtain a theodolite, which would be the standard method
of taking these meridian crossing measurements. Once calibrated and certain, then Hanno can
compare those measurements to his device measurements and determine statistical variation.
Naturally, there will be much work in just establishing the practice of the method with
the standard device, let alone the construction and calibration of the new device to the old.

And by the way, a pendulum takes advantage of the acceleration of gravity, where the spirit
level takes advantage of the buoyancy of the bubble, with the viscosity of the fluid providing
dampening. A spirit level is NOT a pendulum turned upside down.

Best Regards
Brad

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