NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: accuracy of glass artificial horizon figure
From: Bruce Hamilton
Date: 2008 Aug 21, 15:56 -0700
----- Original Message -----
From: George Huxtable <george@huxtable.u-net.com>
Date: Thursday, August 21, 2008 1:51 pm
Subject: [NavList 6181] Re: accuracy of glass artificial horizon figure
To: NavList@fer3.com
>
> Gary LaPook wrote-
> |
> | Well, the ultimate limit is the 1/8th wavelength of light "Raleigh
> | limit" since anything more perfect is not detectable due to
> the wave
> | character of light. This is the standard for telescope
> mirrors. But,
> | since you will not be trying see the moons of Saturn when
> doing celnav,
> | the artificial horizon doesn't need to be that perfect. Since
> the angle
> | of incidence equals the angle or reflection any error in the
> shape of
> | the mirror is doubled in the reflected ray. So, the answer to your
> | question is that it must be accurate to 1/2 the accuracy limit
> you are
> | trying to achieve. If you only want sight accurate to one
> minute of arc
> | then the mirror must be accurate to 1/2 of a minute. If
> working for one
> | tenth of a minute accuracy then the mirror must be accurate to one
> | twentieth of a minute.
> |
> | gl
> |
> | pls wrote:
> | > Does anyone know how accurate (i.e., level) the surface
> figure of a
> | > sheet of black glass must be to serve as an artificial
> horizon? In
> | > particular I am trying to determine the point beyond which
> additional| > accuracy is irrelevant in terms of the result,
> given the other
> | > variables in a sighting with a hand-held sextant.
> ======================
>
> I wonder whether Gary has that right, or if he is a factor of 2 out?
>
> Yes, if the mirror angle is half a minute out, then the angle
> between the
> incident and reflected light becomes a whole minute out. But
> then, to arrive
> at a measured altitude, you have to divide that resulting angle
> by two. So I
> suggest that, if there were no other sources of error, the
> accuracy in
> measuring altitude will be no better than the accuracy achieved
> in levelling
> the mirror, and there is no such factor-of-two to apply.
>
> Maybe "pls" is concentrating on the wrong question. "Surface
> figure" refers
> to flatness, in a plane, not level-ness. The difficult bit is
> not getting
> the surface figure of the glass right; any decent glass flat
> will be good
> enough. It's getting a sufficiently rigid mounting, that can be
> finely
> adjusted, and tried with sufficiently sensitive levels, so that
> it can be
> got level, and will stay level, throughout a measurement. It
> calls for a
> sensitive spirit-level that's sufficiently light in weight so
> that its
> weight shifting on the glass causes negligible deflection. It
> requires firm
> ground so that no observable shift occurs as the observer moves
> his weight
> around.
>
> If these requirements can be met (and they can be bypassed, in
> the right
> conditions, by using a mercury reflecting surface) then
> altitudes can be
> measured with much greater accuracy than is possible at sea
> using a natural
> horizon. Besides the factor of two reduction in instrument
> errors caused by
> the doubling of the measured angle, and the firm footing on land
> compared
> with a vessel, all the problems inherent in the natural horizon
> disappear,
> particularly the unpredictable refractive component of the dip.
> As long as
> the observed body, preferably a star, isn't too low down (but it
> can't be
> above 60º, of course), then I would expect altitudes to be
> measurable, with
> care, to around 0.3 arc-minutes, or so, as long as the glass
> plate can be
> levelled with corresponding accuracy. And that becomes the
> difficult bit.
>
> George.
>
> contact George Huxtable at george@huxtable.u-net.com
> or at +44 1865 820222 (from UK, 01865 820222)
> or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
>
>
>
>
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Navigation List archive: www.fer3.com/arc
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From: Bruce Hamilton
Date: 2008 Aug 21, 15:56 -0700
|
George: I clipped the information below from an online tool catalogue. How little money would I have to spend to buy two levels accurate enough to calibrate a glass sheet (or mirror) horizon?
Horizontal-Mount Levels | ||||||||
| N | 5/8" Dia. x 3 3/4" Lg. | 0.0015 | 20 sec./2mm | 0.228" | Brass (Black Finish) |
| ||
| N | 5/8" Dia. x 3 3/4" Lg. | 0.005 | 1 min./2mm | 0.228" | Brass (Black Finish) |
| ||
| N | 5/8" Dia. x 4 13/16" Lg. | 0.007 | 2 min./0.1" | 0.196" | Chrome-Plated Brass |
| ||
| P | 13/16" Dia. x 6 3/8" Lg. | 0.0003 | 6 sec./2mm | 0.375" | Brass (Black Finish) |
| ||
| Q | 2 15/16" Lg. x 9/16" Wd. x 9/16" Ht. | 0.033 | 15 min./0.050" | 0.156" | Aluminum |
| ||
| Q | 2 15/16" Lg. x 9/16" Wd. x 9/16" Ht. | 0.033 | 15 min./0.1" | 0.156" | Polycarbonate (Black) |
| ||
| Q | 2 15/16" Lg. x 9/16" Wd. x 9/16" Ht. | 0.122 | 45 min./0.1" | 0.156" | Polycarbonate (Black) |
| ||
| Q | 2 31/32" Lg. x 9/16" Wd. x 37/64" Ht. | 0.122 | 45 min./0.050" | 0.156" | Polycarbonate (Black) |
| ||
| R | 2 5/32" Lg. x 29/64" Wd. x 21/64" Ht. | 0.18 | 51 sec./0.1" | 0.079" | Brass (Black Finish) |
| ||
| R | 2 5/32" Lg. x 29/64" Wd. x 21/64" Ht. | 0.18 | 51 sec./0.1" | 0.079" | Brass (Chrome Finish) |
| ||
| R | 2 1/2" Lg. x 1/2" Wd. x 5/8" Ht. | 0.005 | 1 min./2mm | 0.125" | Brass (Black Finish) |
| ||
| R | 3 23/64" Lg. x 5/8" Wd. x 3/4" Ht. | 0.005 | 1 min./2mm | 0.125" | Brass (Black Finish) |
| ||
----- Original Message -----
From: George Huxtable <george@huxtable.u-net.com>
Date: Thursday, August 21, 2008 1:51 pm
Subject: [NavList 6181] Re: accuracy of glass artificial horizon figure
To: NavList@fer3.com
>
> Gary LaPook wrote-
> |
> | Well, the ultimate limit is the 1/8th wavelength of light "Raleigh
> | limit" since anything more perfect is not detectable due to
> the wave
> | character of light. This is the standard for telescope
> mirrors. But,
> | since you will not be trying see the moons of Saturn when
> doing celnav,
> | the artificial horizon doesn't need to be that perfect. Since
> the angle
> | of incidence equals the angle or reflection any error in the
> shape of
> | the mirror is doubled in the reflected ray. So, the answer to your
> | question is that it must be accurate to 1/2 the accuracy limit
> you are
> | trying to achieve. If you only want sight accurate to one
> minute of arc
> | then the mirror must be accurate to 1/2 of a minute. If
> working for one
> | tenth of a minute accuracy then the mirror must be accurate to one
> | twentieth of a minute.
> |
> | gl
> |
> | pls wrote:
> | > Does anyone know how accurate (i.e., level) the surface
> figure of a
> | > sheet of black glass must be to serve as an artificial
> horizon? In
> | > particular I am trying to determine the point beyond which
> additional| > accuracy is irrelevant in terms of the result,
> given the other
> | > variables in a sighting with a hand-held sextant.
> ======================
>
> I wonder whether Gary has that right, or if he is a factor of 2 out?
>
> Yes, if the mirror angle is half a minute out, then the angle
> between the
> incident and reflected light becomes a whole minute out. But
> then, to arrive
> at a measured altitude, you have to divide that resulting angle
> by two. So I
> suggest that, if there were no other sources of error, the
> accuracy in
> measuring altitude will be no better than the accuracy achieved
> in levelling
> the mirror, and there is no such factor-of-two to apply.
>
> Maybe "pls" is concentrating on the wrong question. "Surface
> figure" refers
> to flatness, in a plane, not level-ness. The difficult bit is
> not getting
> the surface figure of the glass right; any decent glass flat
> will be good
> enough. It's getting a sufficiently rigid mounting, that can be
> finely
> adjusted, and tried with sufficiently sensitive levels, so that
> it can be
> got level, and will stay level, throughout a measurement. It
> calls for a
> sensitive spirit-level that's sufficiently light in weight so
> that its
> weight shifting on the glass causes negligible deflection. It
> requires firm
> ground so that no observable shift occurs as the observer moves
> his weight
> around.
>
> If these requirements can be met (and they can be bypassed, in
> the right
> conditions, by using a mercury reflecting surface) then
> altitudes can be
> measured with much greater accuracy than is possible at sea
> using a natural
> horizon. Besides the factor of two reduction in instrument
> errors caused by
> the doubling of the measured angle, and the firm footing on land
> compared
> with a vessel, all the problems inherent in the natural horizon
> disappear,
> particularly the unpredictable refractive component of the dip.
> As long as
> the observed body, preferably a star, isn't too low down (but it
> can't be
> above 60º, of course), then I would expect altitudes to be
> measurable, with
> care, to around 0.3 arc-minutes, or so, as long as the glass
> plate can be
> levelled with corresponding accuracy. And that becomes the
> difficult bit.
>
> George.
>
> contact George Huxtable at george@huxtable.u-net.com
> or at +44 1865 820222 (from UK, 01865 820222)
> or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
>
>
>
>
--~--~---------~--~----~------------~-------~--~----~
Navigation List archive: www.fer3.com/arc
To post, email NavList@fer3.com
To , email NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---
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