I purchaced, some time ago from a science store, an accellerometer that consisted of a circular tube with a bubble just like you describe. (My daughter called it a "nerdometer.") It is mounted on a square plate about four inches square and it is marked in units of "G" and in degrees so it can also be used to measure angles above horizontal. It is meant to be use to measure the acceleration of your car, just hold it against the side window, rotate it so the bubble indicates zero, then punch the gas pedal. It helps to have an assistant read the position of the bubble while you watch the road! When I get home I will try your suggested modifiction.
gl
--- On Thu, 8/13/09, Hanno Ix <hannoix@sbcglobal.net> wrote:
From: Hanno Ix
<hannoix@sbcglobal.net>
Subject: [NavList 9506] Re: The development of bubble sextants
To: NavList@fer3.com
Date: Thursday, August 13, 2009, 10:16 PM
Gentlemen:
This is only for those who like physics!
I have been thinking about the physics of a spirit level. Have you ever seen an analysis of the dynamic behavior of a spirit level/bubble? I would like to study that. At the present level of my knowledge I believe, though, the spirit level in the sextant could be designed so that it becomes more stable. Let me explain.
For the sake of simplicity, lets assume here a tubular spirit level. A bubble has
two degrees of freedom for the bubble whereas a tubular spirit level has only one. This makes the analysis simpler.
Accelerating a horizontal spirit level along its long axis will make the bubble move in the direction of the acceleration i.e accelerating it forward will make the bubble move forward, and vice versa. Almost any translation or rotation of the sextant in the plane
that contains the axis of the level will cause such accelerations. Try it at home!
In simple terms: the acceleration will create a force in the opposite direction of the acceleration. When accelerated forward the heavier spirit will follow the force opposing the acceleration thereby moving its center of mass as far back as possible. This will be achieved by displacing the lighter air bubble as far to the front as possible.
Assume now we have a tubular spirit level and, rather than being closed on the front end and the back end, these ends are connected. A simple way would be to extend the ends by more tubing creating thereby a ring-shaped tube, or a tubular ring. Fill the ring with spirit until you have a bubble of the desired size.
Mount this ring shaped level to the sextant such that the its main plane is parallel to the main plane of the sextant and the bubble plays at the same location as it was before the
modification. So the optical function will be restored.
Because of the bubble, the center of gravity of the liquid will be slightly below the center of the ring putting the majority of the mass into the bottom half. This was the case in the original design, also. Therefore, when accelerated forward, the spirit would move back again , and, consequently, the bubble would move forward again.
Now, give the tubular ring a little dent at the bottom thereby moving the center of the spirit mass above the center of the ring. I predict we will see that now the bubble will move opposite to the acceleration, i.e. backwards.
We surely can the dent "right": we can put of the spirit's mass to the center. Therefore there will be exactly the same amount of spirit in both halves: there is no net force to move the spirit anymore, and the bubble will stay where it was before the acceleration.
This was just a mental model to justify my believe. I
have never built such a ring shaped level - and I could be entirely wrong!
I challenge you, though, to prove me wrong.
Best regards
--- On Thu, 8/13/09, engineer@clear.net.nz <engineer@clear.net.nz> wrote:
From: engineer@clear.net.nz <engineer@clear.net.nz>
Subject: [NavList 9491] Re: The development of bubble sextants
To: NavList@fer3.com
Date: Thursday, August 13, 2009, 12:03 AM
Thanks for this most interesting paper.
Bill Morris
Pukenui
New Zealand
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