Michael,
On 2018-10-24 8:25 p.m., Michael Ossipoff wrote:
A Shephard’s Dial wouldn’t help as a sun-compass. It just gives time
if you know the date, or date if you know the time.
By writing "a Shepard's Dial marked out as a solar compass" I meant that
one for which the lines drawn on the cylinder are the azimuth
corresponding to altitude instead of the usual option of the hour
corresponding to altitude. So, yes, a sun compass.
Sure, an Altitude-Dial is at its least accurate near noon, but this AW
method, and the TA that it’s based on, are different. The error is 0
at noon, if you’re using the right EoT and longitude. The altitude
(ideally along with the declination) adjusts h, to get the azimuth
from south.
.
The error is max sometime during mid-afternoon because, because it’s 0
at noon, and because, when the sun is low near sunset,h is multiplied
by a only a factor, closer to 1, because cos dec * sec Alt is closer
to 1 then.
.
AW’s error comes from the fact that it substitutes h and Azimuth for
their sines. When the factor by which sin h is multiplied is closer to
1, the error from that substitution is smaller.
.
So AW has its greatest error around mid-afternoon, between noon when
it’s 0, and near sunset when it’s error is low due to that
multiplicative factor being closer to 1.
OK, I see what you're saying now. I was coming at it just by imagining
how hard it must be to get an accurate altitude measurement - perhaps a
few degrees out. My thinking was that around noon the azimuth changes a
lot from a small change in altitude so any measurement error would be
multiplied considerably, whereas later or earlier in the day the same
small change in altitude would correspond to a smaller change of azimuth.
Cheers,
Steve
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