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    Re: Longhand Sight Reduction
    From: Hanno Ix
    Date: 2014 Nov 13, 10:58 -0800

     you might just look up Greg's latest RIC. Here is the story:

    Greg Rudzinski  and I have an ongoing discussion about long hand sight reduction formulas. Our goal was to simplify them down to the bones like eliminate logs, compress tables to a few pages, minimize sign rules, eliminate special cases etc.
    Also, Greg insisted the work has to be such that it can be done on a single index card, teasingly called "Rudzinsky Index Card " or RIC. There a several ones now.

    When you look them up you can see we progressed haltingly. One thing, though, was established : 4 digit arithmetic is sufficient in CelNav. Real progress came when Greg dug up the very simple Doniol formula. In Doniol both, the cos and the haversine appear but only a single multiplication is necessary. Recently, I transcribed Doniol into a haversine-only version reducing the number of tables needed to one and taking full advantage of haversine's virtues. A description, a comparison and an example you may find in my posting from Nov 5. Greg compressed the whole thing finally into his latest RIC making it practical for regular CelNav work.

    For the ease of its application  I designed later a new  2 - pg  haversine table. And this was the concept: basing a trig. table on 2' - steps would compress it nicely and would not require written interpolation. Greg suggested modifications that made that new haversine table actually readable! See 129181.

    Greg and I have some disagreement of the use of Hc v. Zenith Distance-only. I opted for the latter dubbing it s2s. For the multiplication I prefer the Vedic method while Greg sticks with the classic one. I think Greg would now like to pack our progress into a simple but accurate CelNav package containing also a dip table, a refraction table, my azimuth diagram, a "perpetual" almanac etc.

    I know you are interested in such packages. So your input is very much invited.


    On Thu, Nov 13, 2014 at 2:31 AM, Gary LaPook <NoReply_LaPook@fer3.com> wrote:
    I've only paid very little attention to the discussion of the Donial method but now it has grabbed by attention. Since it is now well developed can one of you put together, in one post, a description and a step by step instruction?


    From: Francis Upchurch <NoReply_Upchurch@fer3.com>
    To: garylapook---.net
    Sent: Wednesday, November 12, 2014 11:41 PM

    Subject: [NavList] Re: Longhand Sight Reduction

    Thanks Hanno,
    Yes please, I think your 2’ tables are better than mine. Please do the format changes as suggested by Greg. I can then have Hv, sin and cosine in the crash box.
    I agree with your comments. Even slide rules may fail and your Hv longhand method is the best ultimate back up.
    Re. Slide rule accuracy, I’ve always assumed that all other factors being equal, accuracy would largely depend on length of scales. E.g. the Original Fuller has 500 inch, the Bygrave 288 inch, Otis King 66 inch, my homemade mini Fuller about same as the Bygrave (haven’t measured it, but I get same accuracy as full size with magnifiers).
    I do not know what the scale length of the 8 inch circular would be? Greg says not accurate enough for doing cos formula?
    I’ve only done a few LOPs using the Otis King /cos formula and have got surprisingly good results, albeit probably lucky guessing the 4th decimal place. ( no need to guess with the Fullers). Maybe part of the accuracy of the Otis King is due to the precision engineering which is far better than the  Bygrave or Fuller.
    Any thoughts?
    Anyways, great work and thanks for the Hv Doniol. I look forward to seeing the re-formatted Hv, sin, cos tables when you have time.
    Best wishes

    From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of Hanno Ix
    Sent: 13 November 2014 03:21
    To: francisupchurch---.com
    Subject: [NavList] Re: Longhand Sight Reduction
    thank you for your comparisons.
    I think longhand sight reductions will probably never pass the Chichester test but would love to be proved wrong. As I see it, the real advantage of a minimized longhand sight reduction method is that it does not depend on a mechanical device that can, and probably will, fail. Even a ripped and wrinkled haversine table however will do the job and do so in short order.
    It seems you like the 2 arcmin format. You realize of course the same trick works for all trig functions. In the attachment there is such a table for sin() and cos(). It is actually older than the haversine table and was certainly not optimized for size of fonts. If you like I will implement the changes to the typography as suggested by Greg for the haversine table. But before I embark on this let me know if you - and Greg, you, too! - if there are other suggestions you might have.
    On Wed, Nov 12, 2014 at 1:36 PM, Francis Upchurch <NoReply_Upchurch@fer3.com> wrote:
    One more question (oh, apologies for the typos, for “break” read brake!. Going senile). Please give information on 8 inch circular slide rule. I know nothing of these but plan to build a “Poor” 12inch one day. (see my previous postings on this. An LOP slide rule pre-dating the Bygrave).The Otis King is very compact and surprisingly accurate for the relatively short length of the scales.( I get 3-4 decimal spaces routinely with the O.K ,but 5-7 with the Fullers which have much longer scales.) I suspect some of that is down to the shear quality of construction. The best I have seen in any cylindrical slide rule.(my Otis King is a superb piece of engineering.)
    Anyways, keep up the excellent work.
    Best wishes
    From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of Greg Rudzinski
    Sent: 12 November 2014 16:21
    To: francisupchurch---.com
    Subject: [NavList] Re: Longhand Sight Reduction
    I am in total agreement with you on avoiding interpolation where possible. Two thumbs up on the 2' table :)  A few additional benefits of the haversine Doniol table. There are no special rules for L+d > 90° or LHA Meridian Angle > 90° and the majority of observations (especially the Sun) can be reduced from the same side of the haversine table vs. page turning of other methods. After a week of trials it has become clear that this is the best short table sight reduction method that uses the DR position as the assumed position. I have a shelf of sight reduction tables that will now be collecting lots of dust ;-)
    Greg Rudzinski
    P.S. The 8" circular slide rule does almost as good a job on the multiplication step as the Ottis King.
    From: Francis Upchurch
    Date: 2014 Nov 11, 23:35 -0800
    Many thanks Greg,
    My original confusion resulted from missing Hanno's posting of Nov 5th re the Hv only formula. Now I've found it. Congratulations to Hanno for this and his 2'Hv table which I find eaiser to use than your 10' table.(I keep making mistakes with interpolation).
    I have test driven your e.g. using the Doniol, and compared it to Bygrave, and other slide rules (using cos formula, not Doniol).
    Please see attachments if interested.
    I'll certainly put your/Hanno's Doniol (Hv) into my minimalist crash bag, but also the Otis King+sin table.
    If space is not a problem, I still prefer the Bygrave, with my prototype minifuller 2cos  a close second.
    Keep up the good work both.
    Best wishes
    Francis Upchurch

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