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    Re: The development of bubble sextants
    From: Hanno Ix
    Date: 2009 Aug 18, 15:30 -0700
    George:

    You wrote below:

    But now, with the shunting engine, start moving the flatcar backwards and
    forwards. The pivoted mirror will respond to the acceleration forces, and it
    will start swinging. To reduce that effect, you could add a sort of dumbell
    arrangement, like a see-saw, with its centre of gravity aligned with the
    pivot. tThat would act like a trapeze artist's balance pole, to increase the
    moment of inertia. Now you have a system with a long period. Its response to
    short-period perturbations will be reduced by the enhanced inertia. You can
    make the period as long as you like by increasing the dumbell weights, or
    decreasing the weight and spacing of the ballast.

    And you are totally right - so far. However: you cannot accelerate forever in the same direction, with the same amount. Pretty soon you will reach top speed and then there will be no more acceleration - other than gravity! The mirror will dampen its oscillations and go back to equilibrium - i.e the horizontal position - while the train keeps going with constant speed from then on. Until, of course, the train slows down with neg. acceleration - causing the opposite movement of the mirror.

    The trick is to find out what in the particular application the biggest acceleration is, and how long it can possibly last. I bet shipbuilders can give us rather good estimations of the roll/pitch frequencies of vessels from size boat to size oil-tanker. I guess, as I said before, we are talking about 1/10 Hz to 1 Hz with exceptions on both sides.

    If the cut-off frequency of the lowpass is low enough, say 1/10 of the roll/pitch frequency, the acceleration will barely have caused the mirror to move before accelerations in the opposite direction occurs, thereby cancelling almost the first one.

    Howver, there is one more problem: In our design the mirror will be deflected while the acceleration goes on. If the engine not simply accelerates, but it does so differently with each expansion of the steam, you will see the jerks in the mirror movement. Solution: put another lowpass filter in front of the first one. Ugly, but easy to understand: let the pivot of your pendulum slide softly on a rail that is attached to the car and oriented in the direction of the accelarations, here front to back. Connect the pivot with a soft spring to the point where is was fastened to before. Make sure this secondary system is sufficently damped.

    Now, short jerks cannot be transfered to the pendulum anymore, only those slower accelerations will be transferred that really affect the overall speed of the train. The mirror will move much slower and in a mode commensurable with the train movement, and it will, in average, maintain now its pointer much closer to the gravity vector.

    I think I correctly described the line of thought that leads from the original spirit level to the Bush patent.

    Please, forgive my lapses of precision in my explanations. I hope you can follow the argument nevertheless.

    Regards

    H




    --- On Tue, 8/18/09, George Huxtable <george@hux.me.uk> wrote:

    From: George Huxtable <george@hux.me.uk>
    Subject: [NavList 9569] Re: The development of bubble sextants
    To: navlist@fer3.com
    Date: Tuesday, August 18, 2009, 1:12 PM


    In [9565], Hanno asked-

    "Who was Vannevar Bush?"

    He became heavily involved in the politics of US science, particularly
    military science, during and after World War 2, after his participation in
    the atomic bomb project. Look him up on Google. I think he had respectable
    credentials. That doesn't mean that all his notions were worthwhile ones.

    Just because it was never actually made (or so we presume) doesn't mean that
    this stabilised mirror wouldn't work. Indeed, it might, but it would be a
    lot more convincing if there was an actual instrument for the inventor to
    point to, and say "There it is, it works, and its performance is so-and-so".
    Without that, it's really no more than a notion. Hanno has been convinced,
    but I am less credulous.

    The spherical geometry is needed to deal with all the accelerations and
    tilts that occur in three dimensions. That makes the construction of the
    instrument very complex. However, to investigate the principles involved,
    let me simplify the problem to just one dimension.

    Let;s imagine we have a smooth straight railway track, but with undulations.
    Just to pre-empt diversions about Coriolis force, put it on the equator,
    aligned East-West (though that's really unimportant). On this track we put a
    flatbed railway truck, and a navigator who wishes to take observations of
    the Sun, to his East, using a horizontal mirror as an artificial horizon.
    The rail track tilts as it goes over hills and valleys. Attached to the
    truck is a shunting engine. How do we mount the mirror, to make it
    insensitive to such motion?

    We could put a pair of knife edge bearings athwart the truck, and on those
    mount a platform carrying the mirror. That would have a ballast weight
    attached below it to supply a vertical reference. Then, whatever the tilt of
    the track, as long as the car was stationary, and had been so for a long
    time so that all oscillation had died out, we would have a good horizontal
    mirror.

    But now, with the shunting engine, start moving the flatcar backwards and
    forwards. The pivoted mirror will respond to the acceleration forces, and it
    will start swinging. To reduce that effect, you could add a sort of dumbell
    arrangement, like a see-saw, with its centre of gravity aligned with the
    pivot. tThat would act like a trapeze artist's balance pole, to increase the
    moment of inertia. Now you have a system with a long period. Its response to
    short-period perturbations will be reduced by the enhanced inertia. You can
    make the period as long as you like by increasing the dumbell weights, or
    decreasing the weight and spacing of the ballast.

    Even so, it will respond to those horizontal accelerations by tilting, to
    some extent, especially if those accelerations are long-lasting. And that
    will give rise to a slow swing, which will continue for a long time, as we
    haven't introduced any damping. So let's do so, by attaching a light vane to
    the platform, that dips into a bucket of water (or some more treacly fluid),
    that sits on the bed of the truck. Now the energy of those swings can be
    dissipated. We can arrange the damping to ensure that the swinging dies away
    fastest, to achieve so-called critical damping.

    But what have we done? By that damping vane, we have introduce a connection
    between the tilt of the railcar and the tilt of the platform, that had been
    absent before. Now, any sudden tilt of the car will produce an immediate
    tilt of the platform, which will due away with the long time-constant of the
    system, so it will continue for some time.

    What I've tried to show is the complex interplay, in such a system, between
    tilts and accelerations, in their combined effect on the mirror, and the
    unwanted side-effects of the necessary damping. It's by no means obvious
    that a system can be designed to eliminate such effects. Bush says nothing
    about the proper choice of such oscillation periods and damping constants
    for optimum effect.

    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" <hannoix@sbcglobal.net>
    To: <navlist@fer3.com>
    Sent: Tuesday, August 18, 2009 6:42 PM
    Subject: [NavList 9565] Re: The development of bubble sextants


    George:

    I simply assumed you would look up the rest of the patent yourself - which
    you did. So why attach it?

    I also assume you read it. His goal, you will agree, was to create a
    mechanical structure with a very low proper frequency and a well chosen
    damping. Simply, he anticipated results of modern signal theory.

    A practical example of a similar concept is the seismometer which of course
    has been implemented many times. It, too, is a lowpass filter just used
    differently!

    I claim, the idea, the concept, the line of thought of this patent is
    correct.

    Look, Charles Babbage' s invention was much more complicated than this and
    he could not implement it in his times. We found better means. And now, we
    both use the descendant of his idea at this very moment - because the idea
    was right.

    I am not an ME, but I agree with you about the complexity of the
    inventor's proposed implementation. But that alone means nothing in the long
    run.

    BTW: Who was Vannevar Bush?

    Regards




    --- On Tue, 8/18/09, George Huxtable <george@hux.me.uk> wrote:

    From: George Huxtable <george@hux.me.uk>
    Subject: [NavList 9561] Re: The development of bubble sextants
    To: navlist@fer3.com
    Date: Tuesday, August 18, 2009, 3:44 AM


    Hanno included 3 attachments with his last message, but without accompanying
    text.

    First, as a general request, can I ask that when contributors provide
    pointers or links for us to look at, a few words are added to the email text
    to say what's likely to be found there, so only those with an interest will
    be bothered to look.

    In my case, Hanno's attachments were rather rewarding. I found three
    diagrams from patent no 1912358 of 1929, by Vannevar Bush, a name that
    Americans of a certain age may well recognise. It can be readily located,
    from that number, within Google Patents. The patent referred to the use of a
    mirror as an artificial horizon, and a proposal for stabilising it against
    accelerations. It included several pages of text, omitted by Hanno, without
    which those diagrams would make little sense.

    An amazing proposal, which I greatly doubt could ever have been constructed.
    It shows a horizontal mirror suspended on springs within a liquid-filled
    transparent sphere, that floated on a bath of mercury within another
    transparent sphere. Clearly, the author relished complication. It put me in
    mind of those Eastern cosmologies in which the Earth was held by a comely
    maiden, who stood on the back of an elephant, which was then supported by
    the shell of a giant turtle, which swam in the ocean, and so on, combined
    with the concentric crystal spheres that carry the planets in the Ptolemaic
    universe. All with the idea of decoupling the mirror from the accelerations
    that it was being subjected to.

    Not for the faint-hearted to attempt constructing, then. It seems to have
    got no further, which is unsurprising.

    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" <hannoix@sbcglobal.net>
    To: <navlist@fer3.com>
    Sent: Tuesday, August 18, 2009 4:57 AM
    Subject: [NavList 9559] Re: The development of bubble sextants


    Gentlemen:

    Please refer to:

    US Patent 1,912,358
    V. Bush: Apparatus for establishing an artificial datum
    Filed April 8, 1928

    The inventor means an artificial horizon. Please refer to the attachments
    for the drawings.

    He has implemented a mechanical lowpass filter. We have discussed LP's
    before. Better yet: This filter simultaneously works in 2 coordinates, roll
    and pitch.

    He also points out that the natural oscillating frequency of the mirror
    should be as "low as possible" but he doesn't give any data. Since the roll
    frequency of ships is rather low to begin with (judging from you-tube:
    about. 0.1 Hz = 1 period per 10 sec for an oil-tanker ) the filter has to
    have a cut-off frequency of about 0.01Hz which amounts to 1 period per 100
    sec. The filter also needs to be sufficiently damped. The reason is
    simply avoiding resonant oscillations of the filter/mirror in response to
    the ship's movements. To build an LP of this kind is the challenge!

    The inventor has made every effort to decouple the housing of the mirror
    from the body of the sextant. So to speak, he created something like a
    bubble level floating within bubble level.

    With a lowpass of this kind, influences from pitch/roll would be reduced by
    a factor of 100, possibly more. So, a 10 degree roll would create 0.1 degree
    (6 arc-min) deflection of the mirror. Smaller ship will have higher
    roll/pitch frequencies than oil-tankers, maybe 0.5 Hz. Accordingly, on
    smaller ships 1 arc-min oscillation of the mirror might be possible. Is that
    error sufficiently low given the circumstances? It is certainly much less
    than I saw once in a bubble sextant.

    Perhaps most importantly, this patent points out how
    to separate accelerations of the sextant which are instantaneous from
    gravitation which is constant in time.

    When I made my proposal with the tubular ring the other day I had similar
    ideas in mind, however I had not fully understood the interaction between
    bubble and spirit.

    Regards














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