NavList:

From: Brad Morris <bmorris@tactronics.com>
Subject: [NavList 9229] Re: The Bygrave
To: "NavList@fer3.com" <NavList@fer3.com>
Date: Saturday, July 25, 2009, 7:55 PM

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 made their 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

 

 

 

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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   "Confidentiality and Privilege Notice The information transmitted by this electronic mail (and any attachments) is being sent by or on behalf of Tactronics; it is intended for the exclusive use of the addressee named above and may constitute information that is privileged or confidential or otherwise legally exempt from disclosure. If you are not the addressee or an employee or agent responsible for delivering this message to same, you are not authorized to retain, read, copy or disseminate this electronic mail (or any attachments) or any part thereof. 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