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The Sun's amplitude is readily calculated by sin amplitude = sec Latitude
x sin Declination; the nautical almanac being necessary only to ascertain
the declination. Simplistically speaking, the gentleman's calculation is
correct if his latitude and declination are, as longitude is unnecessary:
however, there is no indication as to just what exactly is being used as
the horizon on land, or what the Sun's altitude was with respect to that
horizon at time of observation. If observed with Sun's center on the
visible horizon as at sea, a correction for refraction + parallax + dip
(if applicable) would technically be necessary; it was, however,
customary for seagoing navigators to observe the Sun when a diameter
above the horizon and to ignore this correction - certainly not "precise"
but good enough in ascertaining compass error at sea. One may also refer
to Tables 27 + 28 in Bowditch and achieve the same result by
interpolation.

Henry

On Mon, 2 May 2005 00:25:14 +0100 George Huxtable
 writes:
> Kieran Kelly asked-
>
> >As part of the research for an upcoming expedition, I am trying to
> ascertain
> >how accurate were nineteenth century calculations of compass error
> when
> >derived on land-based exploring expeditions. These calculations
> combined
> >declination and compass error and in this case were expressed as
> variation.
> >They were vital for turning explorers field books (based on magnetic
> >bearings) into maps (orientated to true north)
> >
> >My main worry is the errors in the Nautical Almanac for the period,
> which
> >have come to light on this site. An example calculation is shown
> below. I
> >wonder if one of the list members could run the calculation though
> modern
> >software and check for accuracy. The explorer is taking a bearing
> to the sun
> >at sunrise using a magnetic compass. Longitude is approx 132� 20'
> East
> >although this was not recorded in the field book calculation:
> >
> >Example 1
> >Date:                July 3rd 1856
> >
> >Latitude:            15� 18'  South
> >
> >Azimuth:           N64�  0' E Magnetic
> >(Sun Centre at sunrise)
> >
> >Altitude:            0� 0'
> >
> >Sun Declination: 23� 0' north
> >
> >Amplitude Sun: 23� 50'
> >-------------------------------------------------------
> >Calculation:
> >Amplitude Sun:  E 23� 50' North
> >                           90� 00'
> >                        N 66� 10' East True
> >Az                    N 64� 00' East Magnetic
> >Var                        2� 10' East Variation
> >
> >This is an exact copy of the explorer�s field book entry.
> Declination and
> >amplitude came, presumably, from the Nautical Almanac.
> >
> >Example 2
> >This example was not worked in the field book but would appreciate
> an
> >answer.
> >
> >Date:                March 1st, 1856
> >
> >Latitude:            19� 28' 05" South
> >
> >Azimuth:           N98�  0' E Magnetic
> >(Sun Centre at sunrise)
> >
> >Altitude:            0� 0'
> >
> >Long was approx 127� 40'  east although not recorded in the field
> book.
> >
> >Any solutions would be greatly appreciated.
> >
> >The dates are for local time in northern Australia, not the date at
> >Greenwich
>
> ====================
>
> Response from George.
>
> Tell us about the terrain, Kieran. That seems to be the most likely
> source
> of error, if the explorer is taking the direction of Sunrise as the
> azimuth
> at which he sees the Sun when it's bisected by his local
> land-horizon. How
> horizontal is that land-horizon? If he wanted real accuracy, he
> would have
> done better to take a magnetic bearing of the risen Sun, when a few
> degrees
> up, using a sextant and artificial horizon to determine true Sun
> altitude.
> But it's rather too late, now, to ask him to go back and do it
> again...
>
> As for the calculation of amplitude (see Raper table 59), a factor
> that's
> been neglected in the calculation is the correction for refraction
> (in
> Raper, table 59A) which amounts, in the circumstances stated, to
> about 0.3
> degrees. If that was allowed for, then in example 1 the expected
> azimuth of
> Sunrise  would be greater by that amount, to be about 66deg 30' true,
> rather than 66 deg 10' true. That would increase the calculated
> variation
> from 2deg 10' E to 2deg 30' East, if I have all my factors the right
> way
> round.
>
> How accurately could the compass be read, though? From the two
> examples
> given, it seems likely that compass readings were being taken to no
> better
> than the nearest degree. Put that together with the errors due to a
> non-flat horizon, and there we have the main sources of error.
>
> What makes Kieran suspect errors in the Nautical almanac? What are
> the "the
> errors in the Nautical Almanac for the period, which have come to
> light on
> this site" that worry him? The Sun declination is about right, and
> changing
> little from day to day. That's the only almanac prediction that's
> relevant.
>
> George.
>
> ================================================================
> contact George Huxtable by email at george@huxtable.u-net.com, by
> phone at
> 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1
> Sandy
> Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
> ================================================================
>

   

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