John,
Unfortunately, I can't direct you to an existing tabulation of the
alignment errors on a vertical dial.
However, I do have a comment regarding your subordinate question about
average errors: in my experience of the world of work, it is always a
good thing to arrive on time or a little early for meetings, being a
minute or two late is accepted, but we are sure to earn a frown when we
are more than about 5 minutes late. So back in the era when I would have
used a sundial to organize my day, I feel sure that knowing the maximum
error would have been as important, if not more so, as knowing the
average error. As well, I do not think that the simple average is
particularly helpful because sometimes the dial will be early and
sometimes late - the result can still be near zero. Instead, I would
have wanted to know the average lateness.
There have been a few times when I've written software to optimize dial
layouts for least error. I usually do it by minimizing the worst case error.
But then again, I'm a crank.
Steve
P.S. As an aside, for a horizontal dial, The Compendium carried a series
of detailed articles from 1995 to 1997, under the title 'Error Analysis
Of The Horizontal Sundial' / T.J. Lauroesch, J.R. Edinger
On 2021-11-08 5:38 a.m., John Foad wrote:
If a vertical dial is relocated and now faces a few degrees east or
west of its designed declination, you might expect it to run a few
minutes slow or fast. Has anyone ever tabulated the greatest error,
and at what times and dates it occurs? And does it make sense to
think about the average error? Clearly the errors depend on the
latitude and the design declination, but for starters they could be
tabulated just for a direct south dial at 52.5 degrees N, and for a
location move of 1, 2 and 5 degrees either way. As the gnomon is no
longer polar-pointing I imagine the maths is a bit hairy.
Best wishes,
John Foad
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