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I don't really understand what Hanno is after in his attempt to redesign a
spirit level so that "it becomes more stable".

Is he trying to eliminate its response to horizontal accelerations so that
it responds only to gravity? In that case, I predict that he is doomed to
fail. The two are inseparable.

The "centre of mass" of the liquid plays no part in the operation. You could
attach a large tank, or tanks, filled chock-full of the liquid, by filled
pipes, to the spirit level as you wished, displacing the centre of mass of
the total body of fluid wherever you wished, and it would have no effect. A
spirit level is not acting as a pendulum, which I suspect is the concept
Hanno has in mind.

Another point. I don't know what is the sensitivity of the spirit level that
Hanno plans to improve. A sensitive level, such as might be found on a
theodolite, might have a surface curvature that shifts a bubble by about one
millimetre for 20 arc-seconds tilt. To emulate that curvature in a vertical
torus such as Hanno seems to be suggesting, he would have to give it a
radius of about 17 metres, according to my simple-minded estimation.

Perhaps Hanno is intending to "make it more stable", just by slowing or
damping its response. To do that might call for replacing the spirit with
some more treacly substance, Any moves in that direction would minimise the
response to short-term oscillations, but such increased sluggishness would
make it much less usable.

Perhaps Hanno will explain further, if I've misunderstood.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message -----
From: "Hanno Ix" 
To: 
Sent: Friday, August 14, 2009 6:16 AM
Subject: [NavList 9506] Re: The development of bubble sextants


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  wrote:

From: 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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