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    Re: New compact backup CELNAV system RENAMED Accuracy of Bygrave Slide Rule
    From: Gary LaPook
    Date: 2009 Apr 15, 00:28 +0200

     I agree, use the tables that will provide the most accurate answer that 
    you have available. The difference in the time and effort required in 
    the various inspection tables is insignificant except when using Volume 
    One of H.O 249 which allows working a round of sights much quicker than 
    with the other tables. But how important is speed in doing this 
    computation on a sail boat anyway, it's not like doing CN in a plane? 
    But my complete set of H.O. 229 takes up about two feet of shelf space 
    and H.O 249 only about four inches. I wouldn't take H.O 229 on a sail 
    boat, maybe H.O. 249 or maybe Weems LOP Book and /or the flat Bygrave. 
    We all strive for the most accuracy possible and I usually use a digital 
    calculator, I can compute Hc and Az  in less than one minute and do it 
    in my sleep on one using the classic sine-cosine formulas or the Bygrave 
    formulas. But, at the end of the day, even doing the computations to ten 
    decimal places, CN is still limited by other sources of error so it 
    should only be used for enroute navigation.
    My uncle told me a story once. It seems a wealthy man needed to hire a 
    new coachman. He had three applicants for the post so he called them all 
    in to be interviewed. He asks the first one "how close can you drive a 
    coach and four near to the edge of a cliff?"
    "I'm a good driver and I can drive within five feet of the edge of a 
    cliff" he answers.
    The second one, not to be outdone, says "I'm an even better and more 
    skilled driver and I can drive within two feet of the edge of a cliff."
    The third guy said simply "I won't drive anywhere near to the edge of a 
    Who do you think got the job?
    So even using ten decimal place accuracy  wouldn't get me much closer to 
    a reef than using the Bygrave.
    Speaking of using the Sumner method, which required working out two time 
    sights, many years ago I programed my TI-59 programable calculator to do 
    just that. For a calculator it is trivial. I just put in my D.R. and it 
    calculated the latitude of the LOP where it crossed the whole degree of 
    longitude graticle to the east and west of the D.R.
    Made it very easy to plot. Just lay the straight edge on these two 
    graduated lines and draw the LOP. For LOPs running mainly north and 
    south it did the same but output longitudes to plot on the latitude 
    graticle. No intercepts and no laying out an azimuth.
    Brad Morris wrote:
    > Hi Gary
    > You wrote:
    > But let me ask you this, would you enter a narrow unlit channel at
    > night based on a celnav fix worked out on H.O.229 that you wouldn't
    > enter if you had worked out the same celnav fix using H.O. 249 or your
    > MHR-1?  My point is that the flat Bygrave provides the level of
    > accuracy needed for practical celnav.
    > My response:
    > The Flat Bygrave would clearly provide the level of accuracy for normal
    > celestial navigation.
    > For any method, however, you wouldn't be using celestial navigation for a
    > narrow unlit channel, rather coastal piloting would be the choice at that point.
    > If it is unlit, you would certainly be taking a chance of wrecking.
    > Your comments earlier as to what level of precision is needed at each stage
    > of the journey is quite apropos. Celestial navigation not meant for narrow channels,
    > in the dark.
    > There is a bit of a conundrum here.  The amount of work needed to extract a
    > value from a set of tables varies little, except if you are using Sumner
    > Line of Position or earlier.  There will be some quibbling about the arrangement
    > of the tables being "inconvenient" in HO229 or that there is no interpolation
    > required of HO249, but at the end of the day, you have spent just a few minutes
    > in the tables themselves.  Why not get the maximum resolution that you can?
    > You wrote:
    > Since you have a MHR-1 I would like it if you could make a trial flat Bygrave
    > and test it against your German model and let me know how they compare.
    > My response:
    > Being a typical engineer, I took your question literally and not
    > in the manner intended.  As such, maybe we can clarify a little bit
    > as to what you are after. I wrote that there was some pixilation error, but it was
    > insignificant.  That was the engineering answer.  Are you asking for a
    > manipulation comparison?  Solve a few problems using the Cylindrical and the Flat
    > and see how they stack up in handling?  Or are we after the numerical results?
    > There may be some cosine error in manipulation.  That is, if the first scale
    > is at an angle to the second scale, the numerical result will vary by the cosine
    > of that angle.  While no one will expect a serious result when the scales are skewed
    > at 45 degrees, it does plainly demonstrate the cosine error.  Place scale B on scale A
    > at a 45 degree angle and see how the logarithmic addition (natural number multiplication)
    > gives an erroneous result.  But inject a more realistic angle, one that happens through
    > imprecise alignment.  The logarithmic addition does not span the correct distance and therefore
    > contributes to a numerical answer in the result.  Since the scales are manipulated three
    > times, this error can cascade through all of the manipulations.  This misalignment
    > CANNOT occur on a cylindrical Bygrave, since the cylinders are concentric and mechanical
    > aligned to each other.  How serious is the problem?  I suggest that it depends on the span
    > of the calculation on the rule itself.  As the span gets larger, the offset and error in result
    > do as well.  For short span calculations, the cosine error may be small enough to be
    > ignored.
    > Please clarify what you would like me to check.  I won't mind it a bit!
    > Best Regards
    > Brad
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    > >
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