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> *From: *Brian Walton
> *Date: *2024 May 31, 19:08 -0700
>
> I also worry about the achievable accuracy with a 10" sliderule, as with
> tha accuracy of Robin Stuart's hand-drawn graphical method. I say this,
> because Bygrave needed spiral scale lengths of 30 odd feet (30') to get
> within one minute/mile.

When I think a message might need a reply I have a practice of saving a
copy to the Drafts folder in my email program, as a reminder. But often
I'm careless about checking my reminders, hence this late reply.

Regarding Bygrave formula accuracy with a 10 inch slide rule, in a test
with 10 simulated observations the root of the mean squared altitude
error was 1.5 minutes.

The problems were generated at random by a program which distributed
stars uniformly on the celestial sphere, and observer positions
uniformly on the Earth (both hemispheres). I excluded altitudes greater
than 80 or within 5° of zero, and latitudes greater than 70. However, I
did not exclude negative altitudes, since the Bygrave formulas can be
used for great circle distance and direction on the Earth. I admit
that's not consistent with exclusion of some altitudes. If I were doing
this again I would allow all altitudes.

I did the calculations some time ago, so I don't remember which slide
rule I used. It was probably a K&E Log Log Duplex Decitrig, a good
science and engineering rule but not fancy. I worked carefully but not
with extreme care (strong reading glasses but no magnifier).

Computer generated inputs were latitude, declination, and LHA. I
calculated W, X, azimuth angle, and altitude.

   51.7575 lat
   -5.1860 dec
   27.9717 LHA
    5.86   W (not so easy to read on some rules)
   32.382  X
147.86   Z (212.14 az) (error = .113°)
   28.25   Hc (error = -.009°)

   -1.1816 lat
   47.0243 dec
213.7008 LHA
127.78   W
141.038  X (alt neg)
152.25   Z (27.75 az) (error = -.032)
-35.60   Hc (error = -.002)

   22.1846 lat
   43.1575 dec
333.0564 LHA
   46.44   W
114.255  X
   40.50   Z (error = .033)
   59.37   Hc (error = .005)

-47.9567 lat
-58.8701 dec
296.4248 LHA
   74.96   W
117.003  X
   49.00   Z (error = -.012)
   52.16   Hc (error = -.038)

-11.1965 lat
   30.3719 dec
304.7456 LHA
   45.80   W
   33.004  X
129.82   Z (error = -.058)
   22.58   Hc (error = -.035)

   40.7939 lat
   -3.3744 dec
259.7277 LHA
161.70   W
   67.506  X (alt neg)
   85.82   Z (error = -.005)
-10.00   Hc (error = .025)

-50.1163 lat
-51.0710 dec
   97.9351 LHA
   96.37   W
136.254  X
   47.78   Z (error = .039)
   32.74   Hc (error = -.033)

   65.9394 lat
-17.9946 dec
    9.2966 LHA
   18.20   W
    5.861  X
171.11   Z (error = -.024)
    5.79   Hc (error = .021)
That one required cosines of small angles.

-28.7610 lat
-35.6695 dec
233.0997 LHA
129.86   W
   11.099  X (alt neg)
   41.02   Z (error = -.099)
   -8.42   Hc (error = .035)

   -9.1664 lat
-54.4142 dec
   10.8386 LHA
   54.86   W
135.694  X
    8.76   Z (error = -.001°)
   43.94   Hc (error = -.016°)

--
Paul Hirose
sofajpl.com

   

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