Hi folks,
The equatorial sundial at Vandusen Gardens in Vancouver BC is a lovely
piece but I think it is set up wrong - I suspect the dial's axis is not
aligned to the meridian. This suspicion is based on the measurements
described below, but also because when I viewed the dial today I
concluded it is not aligned north-south (but then again, my idea of n-s
was based on my potentially unreliable cell phone compass).
I want to figure out the angle that the dial is twisted by so I have
some kind of spherical geometry problem to solve. Unfortunately, I've
never been able to get my head around spherical trig. I've tried to
learn about it a few times, but it's still a dark art for me.
The dial is an equatorial, latitude 49.2N, 123.2W. As far as I can tell,
the slope angle of the axis of the equatorial is correct for the
latitude. As well, the dial base is flush to the plinth, which appears
to be a properly flat (horizontal) surface. Today at 12:27 pm Pacific
Daylight Time, the dial showed 12:45 pm (note, although the dial shows
local solar hours, the hour labels are advanced by one hour - like a
Daylight Saving shift).
My thinking: The site is 3.2 degrees west of the timezone meridian,
which is 12.8 minutes of time, so 12:27 PDT is like 12:14.2 local mean
time, or 11:14.2 if we take out the Daylight hour. The Equation of Time
is 8.3 minutes today (dial is fast), so the actual reading of 12:45 is
like 12:36.7 local mean time, or 11:36.7 if we take out the Daylight
hour. Hence it seems to me that the dial was off by 22.5 minutes of
time, which is the difference between 11:36.7 and 11:14.2.
The thing I want to know: assuming all the error is due to rotation
about a vertical axis, what is the angle that the dial is twisted by?
Please could some kind soul help me out by explaining the steps involved
in the calculation - my problem is in knowing which equations to use,
and why.
Steve
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