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Re: The development of bubble sextants
From: George Huxtable
Date: 2009 Aug 14, 19:55 +0100
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 --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---