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    Re: The development of bubble sextants
    From: George Huxtable
    Date: 2009 Aug 14, 19:55 +0100

    Hanno likened a classic spirit level to a pendulum, stating- "You have a
    system that has one degree of freedom and suspended such that its center of
    gravity is below the suspension point."
    
    I ask- in a classic spitit level, just where is that "suspension point",
    then?
    
    Hanno has answered my question about his aim. It's not a forlorn attempt to
    make it insensitive to horizontal accelerations, it's pleasing to note. It's
    an attempt to filter out shorter-term "tilt", including those virtual tilts
    caused by local accelerations, by introducing a low-pass filter into its
    response. To achieve that end, if it was worthwhile, I had suggested
    replacing the spirit by something more treacly.
    
    The trouble is, it won't work. What a sextant bubble has to do is to
    respond, in short order, to the various tilts and rolls of the instrument
    itself, as the observer does his best to compensate it against the motion of
    his environment, in aircraft or ship. To that end, a quick response is
    needed: short compared with the period of those tilts and rolls. But the
    sideways buffetting, by waves, at sea (I don't know about aircraft) is on a
    very similar timescale to those pitches and rolls. So I don't see how you
    could filter out one, by (effectively) adjusting the viscosity of the
    treacle, without degrading the response to the other. Same applies to
    accelerometers with electronic filtering applied. What value of
    time-constant would Hanno suggest, for that purpose?
    
    I can't see, for the life of me, how Hanno's proposed torus geometry will
    help him to achieve his aim.
    
    .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 6:08 PM
    Subject: [NavList 9511] Re: The development of bubble sextants
    
    
    George:
    
    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 quite similar.
    
    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 spirit level.
    
    
    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
    pass filter!
    
    None of all this, though, proves my original proposal.
    
    Regards
    
    
    
    
    
    
    
    
    --- On Fri, 8/14/09, George Huxtable  wrote:
    
    From: George Huxtable 
    Subject: [NavList 9510] Re: The development of bubble sextants
    To: NavList@fer3.com
    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. 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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