I beg to disagree in a particular point you brought up:
Actually, a pendulum IS a good model for the classic spirit level: You have a
system that has one degree of freedom and suspended such that its center of
gravity is below the suspension point. If the friction is not too bad you can
actually make it oscillate!
Answering another question of yours:
With "more stable" I mean the behavior of a "low pass
filter" as used, for instance, in stereo amplifiers, car suspensions,
water distribution systems, etc. This might not be obvious but the math is
Also, the physical size of the thought model does not speak for or against
its correctness. Should the model be correct and useful we could find methods
to adapt it to practice.
I say, the resonance frequency of the classic spirit level seems too high and,
therefore, it follows external disturbances too quickly. Therefore, I am
searching for a method to control its resonance frequency. Also, I am going
to choose the losses in the system such that oscillations decay "just
right": not too much overshooting but not too slow a response either.
However, the sensitivity of the spirit level can still be maintained as is -
if so needed! So far, though, sensitivity has not been my concern.
I do not know if such considerations were used in the design of bubble sextants.
I once used one, and the bubble seemed to have been very quirky.
In passing let me observe:
Accelerometers are being used in inertia navigation systems to model a system
that resembles, in part, the behavior of the bubble. There, the math is implemented
by electronic integrators, amplifiers, etc. The difference is you can give
the electronic model nearly ideal properties that cannot implement in a
A gyro compass implements a system with a very low pass-band frequency. That
is why it has been built. And, strange as it may sound, the surface of water
in a big tank could be used as a spirit level of sorts if it acts as a low
None of all this, though, proves my original proposal.
--- On Fri, 8/14/09, George Huxtable <firstname.lastname@example.org>
From: George Huxtable <email@example.com>
Subject: [NavList 9510] Re: The development of bubble sextants
Date: Friday, August 14, 2009, 8:21 AM
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.
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
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.
contact George Huxtable, at firstname.lastname@example.org
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" <email@example.com>
Sent: Friday, August 14, 2009 6:16 AM
Subject: [NavList 9506] Re: The development of bubble sextants
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
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
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.
We surely can the dent "right": we can put of the spirit's mass to
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.
--- On Thu, 8/13/09, firstname.lastname@example.org <email@example.com> wrote:
From: firstname.lastname@example.org <email@example.com>
Subject: [NavList 9491] Re: The development of bubble sextants
Date: Thursday, August 13, 2009, 12:03 AM
Thanks for this most interesting paper.
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