I admit my interest in this thread is somewhat low and I am sure that such a device would soon be another 'dust
collector' around here. With that in mind, let me suggest a third construction alternative that might be useful.
Mechanical devices requiring long scales may be made using very stable 35mm film on a roller arrangement. I know the
sprocket/gear arrangement is a little more expensive than a tube but these may be available 'off the shelf' and need not
be metal. Film bases are very stable so humidity and heat should not be much concern. I've no clue how the master
scale image could
be transferred to the film but it has been done by others. I recall encountering similar arrangements
in various radio equipment many years ago and my impression of the arrangement was favourable. A small red LED
backlight could be easily fitted that would enhance night usage. My background is in electronics and this suggestion is
99% mechanical so forgive me if I innocently overstepped realistic considerations. I might purchase such a device if the
price was not to dear.
I am not associated with Kodak in anyway for what its worth.
Regards,
Frank J.
Rochester, NY
=====================================================================================
From: Brad Morris <
bmorris@tactronics.com>
To: "
NavList@fer3.com" <
NavList@fer3.com>
Date sent: Sat, 25 Jul 2009 22:55:36 -0400
Subject: [NavList 9229] Re: The Bygrave
Send reply to:
NavList@fer3.com> From: Brad Morris <
bmorris@tactronics.com><br>
> Subject: [NavList 9224] Re: The Bygrave<br>
> To: "
NavList@fer3.com"
> <
NavList@fer3.com><br>
> Date sent: Saturday, July 25, 2009, 11:02 AM<br>
> From: Brad Morris <
bmorris@tactronics.com><br>
> Subject: [NavList 9213] Re: The Bygrave<br>
> To: "
NavList@fer3.com"
> <
NavList@fer3.com><br>
> Date sent: Friday, July 24,
2009, 8:53 AM<br>
>
> Hi Hanno
>
> I would suggest that we stick to the scales developed by Bygrave
> himself and carried forward by the
> Germans and the Japanese, when they madetheir respective production
> runs. For the outer scale
> (cosine or secant, depending on your desire), 0 to 89 d 40 minutes
> (and then back to zero). For the
> inner scale (cotangent or tangent, depending on your desire)0 d 20 m
> to 89 d 40 m (and then back
> again).
>
> These scales were proven in practice, by navigators who used them
> for primary navigation. You can
> certainly do worse, but to do better requires a better instrument.
> My German made MHR-1 is a joy
> to manipulate. The feel of the instrument as you RAPIDLY resolve the
> azimuth and altitude is
> fabulous. I could see where a table mounted device with larger and
>
longer scales could give a
> better mathematical result, but then the device looses its
> attractive small size and small weight
> advantage!
>
> And even when reducing an obvious meridian shot, in which the
> Bygrave has limitations, it is always
> nice to see the angles come right to where we expect them to be,
> within reason.
>
> When the NavList Consortium comes with a modern Bygrave, I will
> certainly purchase one. For
> those who can't wait, may I suggest Gary's Flat Bygrave. If you have
> the cash, then get a real one,
> they do turn up on eBay from time to time. Of all the methods for
> celestial reduction, the Bygrave is
> IMHO one of the best.
>
> Best Regards
> Brad
>
>
>
>
> From:
NavList@fer3.com [
NavList@fer3.com] On Behalf
> Of Hanno Ix
> [
hannoix@sbcglobal.net]
> Sent: Saturday, July 25, 2009 2:54 PM
> To:
NavList@fer3.com> Subject: [NavList 9226] Re: The Bygrave
>
>
> Brad:
>
> Makes a lot of sense!
>
> So, then again, what should be the practical navigator's Bygrave
> range be - not the
> mathematician's?
>
> This question is asked because, as you know, for a given length of
> the scale any extension of the
> limits reduces the resolution particularly in the
center.
>
> What would the Commander say?
>
> H
>
>
>
>
> --- On Sat, 7/25/09, Brad Morris <
bmorris@tactronics.com> wrote:
>
> From: Brad Morris <
bmorris@tactronics.com>
> Subject: [NavList 9224] Re: The Bygrave
> To: "
NavList@fer3.com" <
NavList@fer3.com>
> Date: Saturday, July 25, 2009, 11:02 AM
>
> Hi Hanno Ix
>
> It would be helpful if I read all of your questions before shooting
> off a response!
>
> The
limitations of the Bygrave are primarily a computational problem
> related to the trigonometric
> functions. If you look closely at the multiplicity of scales being
> produced by the list, you will note that
> the numbers are bunched and separated as a function of the log
> distance of the trig function. Hence
> around zero degrees, the log(cosine) bearly changes, resulting in an
> in-ability to resolve the angle
> on the scale. The scales on the bygrave are are also truncated due
> to the long length required for
> angles above 89 degrees. Again, you will see the scales produced
> with this truncation. When you
> play with the equations, you will rapidly see the limitations.
>
> The commander will choose his navigational objects wisely. You want
> to get the lines of position to
> cross at steep angles. Depending only on meridian shots and
prime
> meridian shots was a method
> used long ago. Modern methods advocate using LOPs independent of
> these special cases. You
> shouldn't avoid these lines, rather, they are just another line
> without special emphasis.
>
> Consider the rapid fire sun observation recently on the list posed
> by Frank. Observation after
> observation of the sun is taken. Multiple LOPs are created. These
> lines cross at shallow angles, yet
> with enough lines, we can resolve both longitude and latitude to a
> reasonable margin of safety.
> Each of these LOPs can be solved with a Bygrave but the cocked hat
> created by them will require a
> least squares fit (for accuracy). Nothing special about these
> LOPs.
>
> Just be careful when you know you are treading into the problem
> areas!!
>
> Best Regards
> Brad
>
>
>
>
> From:
NavList@fer3.com [
NavList@fer3.com] On Behalf
> Of Brad Morris
> [
bmorris@tactronics.com]
> Sent: Saturday, July 25, 2009 1:41 PM
> To:
NavList@fer3.com> Subject: [NavList 9223] Re: The Bygrave
>
>
> Hi Hanno Ix
>
> modest angular errors at merdian crossings cause minor latitude
> errors. The primary purpose of a
> merdian shot is to get a special line of position which is exactly
> your latitude.
>
> angular errors at 90 degree
hour angles cause errors in longitude.
> This is known as a prime
> meridian shot and gives you a special line of position which is
> exactly your longitude.
>
> Bear in mind that these two special lines can special just for the
> outcome. The Bygrave will give you
> lines of position(when properly plotted) for any angle in between,
> hence these errors are not so
> terrible. For the purist mathematician, the erroneous result is
> troubling, but for practical navigation,
> not so much!
>
> Best Regards
> Brad
>
>
> From:
NavList@fer3.com [
NavList@fer3.com] On Behalf
> Of Hanno Ix
> [
hannoix@sbcglobal.net]
> Sent: Friday, July 24, 2009 6:54 PM
> To:
NavList@fer3.com> Subject: [NavList 9216] Re: The Bygrave
>
>
> Thank you for your response, Brad!
>
> However, if you permit, answers to questions 1 and 2 seem not quite
> complete.
>
> In my Engineering past it has bcome my experience that computational
> issues typically point to ill-
> posed problems. Do computational issues in our application here
> similarly indicate we may be
> using a disadvantageous constellation for the problem we are trying
> to solve? I am thinking of cases
> like shooting "stars", all very close to each other, for position,
> for instance.
>
> Are there alternative solutions known
from the manuals of the
> original Bygrave or the German MHR -
> provided they still exist - for special cases like the ones I
> mentioned? What was the poor
> Commander to do in such instances? I assume he would try to shoot a
> different constellation rather
> than mess with computational issues in the margins, no?
>
> Regards again
>
> H
>
>
>
>
>
> --- On Fri, 7/24/09, Brad Morris <
bmorris@tactronics.com> wrote:
>
> From: Brad Morris <
bmorris@tactronics.com>
> Subject: [NavList 9213] Re: The Bygrave
> To: "
NavList@fer3.com"
<
NavList@fer3.com>
> Date: Friday, July 24, 2009, 8:53 AM
>
> Hi Hanno Ix
>
> See my answers interspaced below
>
> Best Regards
> Brad
>
>
> From:
NavList@fer3.com [mailto:
NavList@fer3.com] On
> Behalf Of
>
hannoix@sbcglobal.net> Sent: Friday, July 24, 2009 11:37 AM
> To:
NavList@fer3.com> Subject: [NavList 9212] Re: The Bygrave
>
>
>
> May I please ask some questions?
>
> 1. I am not a sailor. So, what are the useful ranges of a
> Bygrave? In other terms, what are the
> critical trigonometrical/nautical Regardssituations where the
> knowledge of angles >89deg or
> angles <1deg is important?
>
> Suppose your celestial body is the sun. If reducing for a
> meridian crossing (sun on your line of
> longitude), then the hour angle T is 0 (less than 1 degree). As
> a practical matter, the Bygrave is
> quite compressed under 5 degrees for the LogCosine scale, so
> reductions when the sun is close to
> your meridian
suffer from accuracy issues.
>
> If reducing when the sun is directly east or west of you, when
> the hour angle is 90 degrees
> (sunrise, sunset) similar issues result.
>
>
> 2. Are there practical approximations by polynomials etc. for
> such extreme cases?
>
> Just use the standard azimuth and altitude equations that can be
> directly reduced using a
> calculator.
>
> 3. More generally: Are we aiming at historical replicas of the
> Bygrave, MHR, etc. or are we
> seeking at a modern implemetation of the idea? Or both?
>
>
Depends upon who you talk to. Due to cost, we probably won´t
> be looking at historical replicas.
>
> 4: Similarly: Are we interested in the Bygrave just because it
> is so interesting - which it is! - or
> are we looking for the very simplest means to do accurate sight
> reduction? For the latter, there
> might be attractive alternatives.
>
> HO229 offers accuracies to 0.1 arc-minutes, about 10-20X the
> accuracy of the Bygrave. It is
> heavier, larger and requires tabular lookup instead of slide
> rule manipulation.
>
> Others will have different preferences for tabular reduction or
> for computer aided reduction. The
> beauty of the Bygrave is the small size, small weight and
> rapidity of reduction
>
> Regards</table
>
>
>
>
>
>
>
>
>
>
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