Re: New compact backup CELNAV system RENAMED Accuracyof Bygrave Slide Rule
From: Gary LaPook
Date: 2009 Apr 11, 09:52 +0200

Since you have a MHR-1 maybe you can help me. Bygrave states a rule for 
the special case when declination is too close to zero so that it cannot 
be found on the cotangent scale that you interchange declination with 
latitude and compute altitude that way. But I have never found a rule 
from Brygave on how you calculate the azimuth in this case. I have been 
using an approximation that works within one degree to simply skip the 
first step and set "y" (Bygrave's terminolgy) "W" (my terminology) equal 
to declination. Do you have instructions for the MHR-1 that gives the 
procedure to calculate azimuth in this case?


Brad Morris wrote:
> Hi Gary
> While I fully agree that the Flat Bygrave has an accuracy perfectly 
adequate for normal celnav, I have some small issues with your statement that 
it is about the same accuracy as using sight reduction tables.
> Since the Flat Bygrave is modeled after the Bygrave Slide rule, I will 
substitute that instrument for the Flat Bygrave.  I am much more familiar 
with the cylindrical Bygrave in practice.  We must first accept that the 
Bygrave Slide Rule (cylindrical) provides resolution to 1 arc-minute.
> The inputs to the Bygrave Slide Rule (cylindrical) are rounded to whole 
arc-minutes, again, due to the resolution provided by the instrument.  In 
use, I merely round up or down.  There are, however, 4 terms involved.  Each 
must be rounded.  On my MHR-1 they are "Deklination", "Studenwinkel", 
"Briete" and "b" OR
> declination, hour angle, latitiude and co-latitude.
> Upon each of the three steps of the manipulation, one makes a judgement 
as to what line the pointer is closest to, again, due to the resolution of 
the instrument.  We determine first x, then Az using x, and finally h using 
Az.  The resolution of the instrument plays into each step.  I am sure that 
the Flat Bygrave requires these same approximations and judgements.
> While the Flat-Bygrave may not suffer from the resolution defect simply 
because you can draw the lines at any resolution you desire, I suspect that, 
as a practical matter, you have maintained the 1 arc-minute resolution of the 
logarithmic scales.  Please understand this is not a critique of your device, 
merely a practical limitation of printing the scales.  You could expand the 
overall size, just as linear slide rules do to increase resolution and 
accuracy, but the expansion has practical limits as well.
> The accuracy of the resultant calculation is a function of the resolution 
of the values input and cascaded down through the manipulation.  I typically 
get within 1 arc minute results on my Bygrave Slide Rule (cylindrical), but 
there are practical cases where this is simply unobtainable.
> Now let us switch to the accuracy afforded by sight reduction tables.
> First is the choice of WHICH table.  Perhaps it is due to your familiarly 
as an aviator, that the choice of  HO 249 "Sight Reduction Tables for Air 
Navigation" is made.  Perhaps that is what you learned with? Others on the 
list would prefer HO 214 or as the US Navy recommended via Dutton, HO 229.   
Of course, there are the older methods, as you state, such as the Weems Line 
of Position, Ageton or Dresionstok.  You may wish to step back in time once 
more to the "Sumner Line of Position Books" but then you have that nasty RA 
to GHA conversion to contend with.  Or, just for fun, go back to the tables 
of Bowditch, Norie and Moore.  It is possible to use them.  WHICH table then? 
 I say which ever you are comfortable with.  But there are ramifications to 
the choice you make.
> The choice offered in comparison to the Flat Bygrave was HO 249.  It is 
true that HO 249 affords reduced resolution and accuracy and thus compares 
"equally" with the Bygrave.  However, HO 249 suffers in resolution and 
accuracy when compared to sight reduction table HO 214 and certainly to HO 
> The vast majority of cases of solution using HO 229 afford us a final 
answer with an accuracy of less than  0.1 arcminutes, when compared to the 
classical cosine calculation using a calculator.  Again, there are some 
special cases which suffer from reduced accuracy,  Fundamentally, the US Navy 
developed HO 229 last and it represents the "state of the art" when it comes 
to printed Sight Reduction Tables.  It was the culmination of the efforts of 
75 years of printed sight reduction table methods.  I find it no more 
troublesome than any of the other tables, in use.
> If we are to compare the best I can normally achieve with the Bygrave 
Slide Rule (cylindrical) to the best I can normally achieve with HO 229, 
there is about an order of magnitude difference in resolution and in 
accuracy.  That is, I get about 1 arc minute using my MHR-1 Bygrave and about 
0.1 arc minutes when using HO 229.
> What value of accuracy and resolution do you state for the Flat Bygrave?  
If it is finer and better than 1 arc-minute, please provide cogent arguments 
as to why.  I may wish to upgrade!!!
> ----------------------------
> In every calculation, there is a trade off.  The MHR-1 Bygrave is fast, 
easy and compact.  HO 229 is slow and bulky but frankly still pretty easy.  
In other words, I use the Bygrave when I want to get quick and dirty answer 
and HO 229 when I want a final, as good as I can get, answer.
> Note that NONE of this discussion is a downgrading of the Flat Bygrave.  
I retain my admiration of it.
> Further note that none of this discussion considers the in-accuracies in 
the sextant or in its use.  Those errors persist independent of the reduction 
method, be it Bygrave, Table or calculator.
> Best Regards
> Brad
> ________________________________________
> From: [] On Behalf Of Gary LaPook []
> Sent: Friday, April 10, 2009 5:22 PM
> To:
> Subject: [NavList 7908] Re: New compact backup CELNAV system
> I've been traveling for a while and haven't been able to get back to
> this (Amsterdam, Athens, Rhodes, Crete, Istanbul, Cairo, Rome and now in
> Naples.)
> Ken, maybe we see the word "backup" slightly differently. My suggested
> method was meant for those who already know celnav, it was not meant to
> be "Celestial Navigation For Dummies" a self teaching book. I meant it
> for a navigator who was considering whether it was worth the bother
> anymore to carry the sextant, requisite tables (H.O. 249, H.O. 229,
> etc.) and to remember to get a new Nautical Almanac every year (may be
> difficult where you are) or just give up celnav and buy an additional
> GPS to use as a backup. The flat Bygrave allows a navigator to decide,
> that without having to allow shelf space for books he will probably
> never use and not having to remember to get any almanac except once in
> every ten years (that can be downloaded for free from the Government web
> site,)  he will just go ahead and keep that old sextant and these couple
> of pages and forgo spending money on that additional GPS unit.
> Especially since an additional GPS doesn't offer complete redundancy
> since the whole system could be made unavailable by some military action
> or by our government shutting it down at the most inopportune moment in
> order to deal with an enemy attack or terrorist plot. Celnav, on the
> contrary, does supply complete redundancy and is self contained needing
> nothing from the outside except a hole in the clouds.
> Or the flat Bygrave could be used as the primary sight reduction method
> for a sailor who practices celnav regularly but appreciates the
> reduction in storage space and hassles of obtaining Nautical Almanacs
> each year. The accuracy of this method is perfectly adequate for normal
> celnav and is about the same as that obtained with H.O 249 a popular
> method used by small boat navigators. Call it a "compact" sight
> reduction method instead of a "backup."
> For anybody looking for a compact method and who doesn't like the flat
> Bygrave I would recommend getting a copy of  Weems Line of Position Book
> or Dresionstok (each are easier than Ageton) to replace their H.O 229,
> H.O. 214 or H.O 249 and then to also use the long term almanac from H.O
> 249 that I included with the flat Bygrave.
> As you will see my other post today, I have nothing against crossing a
> morning sun line with an afternoon sun line to provide a running fix,
> use any method you like to accomplish this.
> gl
> Ken Gebhart wrote:Gary,
>> The interest in your Bygrave project has been great and well
>> deserved.  But when talking about "backup" systems, I think about one
>> who is ill versed in CN, and just wants to make a safe landfall
>> without his failed GPS.  In this situation, I feel that using simple
>> noon sight procedures supplemented by sunrise/sunset longitudes, and
>> polaris Lats would be fine.  All that would be needed would be the
>> Nautical Almanac (for the Sunrise/ Sunset things) and would have the
>> included SR Tables for intermediate sights.  One might not prefer
>> these NA SR tables, but they DO work, and in a backup situation, why
>> be choosey?
>> Ken
>> On Mar 17, 2009, at 6:26 PM, glapook{at}PACBELL.NET wrote:
>>> I am real happy that I kicked off this topic and am impressed by the
>>> level of interest shown in using this simple to produce modification
>>> of the Bygrave for a backup celnav system. I am also impressed by the
>>> improved scales created by the other members on this list. A while ago
>>> I contacted Ken Gephart at Celestaire to get his opinion on whether he
>>> thought there would be any interest in a commercially produced version
>>> but he didn't think there would be. He thought that a simpler system
>>> would be better considering the lack of celestial training of your
>>> everyday sailor. I started this discussion stating that it was meant
>>> for those knowledgeable in CELNAV, the virtue of this system being its
>>> compact size and its low cost. He said that if they already had the
>>> Nautical Almanac they had the reduction tables already published in
>>> the N.A. (I, for one, really dislike those tables, your mileage may
>>> vary.) Work out an example with the N.A tables and compare the work
>>> with the came computation with the Bygrave and I think you will agree
>>> the Bygrave is easier to use. Those same non celnav sailors wouldn't
>>> be expected to buy an N.A. every year either so another advantage of
>>> this system is the long term almanac.
>>> So Ken, any more thoughts about this considering the great interest
>>> shown on this list?
>>> gl
>>> On Mar 17, 1:09 pm, <> wrote:
>>>> I am another long time lurker, who got all excited about Gary
>>>> LaPook's flat Bygrave scales, and also got cracking on my own
>>>> version of scales. Unfortunately it took me a while to complete
>>>> due to distractions like family and job. So Dave beat me to it by
>>>> a month or so.
>>>> In any case I decided to publish my version of scales as well. Not
>>>> because they are better than Dave's, but because they are written
>>>> in Postscript, and can be easily customized by each individual
>>>> user. It's easy to change width of scales to the size of your
>>>> sheet or cylinder, number of lines, font size, frequency and
>>>> thickness of tickmarks etc.
>>>> The files and can be edited with text editor like
>>>> notepad, and then converted to PDF using free Ghostview tool. To
>>>> do that you also need to install Ghostscript. Here are links to
>>>> download page.
>>>> You could even easily define other scales using this template e.g.
>>>> sec()/csc() for Ageton method like Andrew suggested in one of the
>>>> previous posts. Though this would require to write up the function
>>>> in Postscript stack based form using just (sin, cos, and atan) as
>>>> these are only available trigonometric functions in postscript. I
>>>> would be glad to help, if somebody decides to do that.
>>>> Note that common procedures for drawing the scale are in
>>>> file and it must be in the current directory when opening .ps
>>>> files with ghostview.
>>>> And I must also repeat Gary's warning, when printing PDF files
>>>> make sure to set Page Scaling to None. I wasted few transparent
>>>> sheets before figuring that out.
>>>> Martin
>>>> 1KViewDownload
>>>> 2KViewDownload
>>>> 2KViewDownload
>>>>  cos.pdf
>>>> 23KViewDownload
>>>>  cot.pdf
>>>> 85KViewDownload
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