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    Re: The development of bubble sextants
    From: Gary LaPook
    Date: 2009 Aug 15, 02:07 +0200

    There is something wrong with the basis of Hanno's idea.
    
    Gravity is just an acceleration like any other acceleration. (Having
    jumped out of airplanes skydiving hundreds of times I can tell you it is
    a REAL ACCELERATION!) Since is is just like other accelerations it is a
    tenant of physics that you can't separate its effect from other
    accelerations. Hanno's system is already in used in all of our inner
    ears where we have semi-circular canals filled with fluid that we use to
    sense gravity and are used to maintain our balance. They work pretty
    well when you are standing on a non- moving earth but they don't work at
    all well when subjected to the accelerations in flight. I have been a
    flight instructor for 37 years. We demonstrate to all student pilots
    that they can't use their natural balance sense to determine which way
    is "up" while in flight. We demonstrate this by having the student close
    his eyes and then we maneuver the aircraft and ask the student to tell
    us what the airplane is doing. We then tell them to open their eyes and
    they are then surprised that they were completely wrong in their
    estimate based on their semi-circular canal senses. This basic training
    is to impress the student why he must avoid flying into a cloud where he
    will lose visual reference with the ground and will not be able to tell
    where "up" is and will lose control the plane and crash. We do much more
    of this type of training with those working on obtaining an instrument
    rating to allow them to fly inside clouds without any visual reference
    to the natural horizon. It takes a long time and a lot of hours of
    training before the student can control the plane solely by reference to
    the gyroscopic flight instruments and to ignore the powerful but
    erroneous input from the inner ear. Sometimes even pretty well trained
    pilots screw this up and get '"spatial disorientation" or "vertigo" and
    end up with spectacular crashes. This is what happened to John Kennedy
    Jr. who had almost finished his instrument training course. Flying over
    the ocean at night with no visual reference to the natural horizon he
    gave in to his spatial disorientation and ended up in the ocean with his
    wife and sister-in-law,
    
    The accelerations in flight combine with gravity and the vector sum
    determines the vertical shown by the bubble in the level vial. The same
    thing happens on a boat but the accelerations are greater and the
    deflection of the vertical is even more pronounced.
    
    Here is another way to look at it. Break the vial and instead of having
    a bubble on the center have the level determined by the level of the
    liquid at the ends of the tube. You can connect short sections of clear
    tubing to the ends of a garden hose, fill the hose with water and the
    fluid level in each of the clear pieces of tube will be level. with each
    other You can lay the hose across you yard, snarl it up, lead it over
    your roof (unless your roof is more than 32 feet high in which case you
    will pull a vacuum at the to of the loop) and there will be no change in
    the level shown by the liquid in the tubes. You could even twirl the
    hose around in the center and the water level won't change. As my father
    told me many years ago, "water seeks its own level." However if you
    accelerate the whole rig longitudinally the water will run out of the
    end of the tube and this will happen even if the hose was looped above
    the ends of the tubes. Think of carrying a shallow bowl of water across
    the room, if you don't move smoothly the water will slosh over the edge.
    
    So I think Hanno needs to give this some more thought.
    
    gl
    
    George Huxtable wrote:
    > 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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