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Hi everyone,
Can I know the time from the shadow of
a pencilpot on its own inner surface?
Yes, of course, and you can use the same equations
of
the cylindrical sepherd sundial taking the
longitude of the style
equal to the diameter of the pot, that is to
say:
MaximumDepthOfTheShadow(t) = Diameter * tan( Sun's Elevation(t) )
where we know that
cotang( Sun's Elevation ) = cos^2(Lat)
* ( cos(HA) - tan(Decl) * sqrt( sin^2(HA) + tan^2(Lat) ) )
as you can find in any good sundialling
book.
Of course, the formula is good for any other
vertical cylinder.
We could easily modify the equation to fit to a
fixed cylinder like,
for instance, a water well.
Finally, you just have to be careful as well of
having the longitude of the cylinder
bigger than Diam *
tan( 90 - Lat + 23.45 ) because otherwise the shadow would
fall on the base of the cylinder, not on the inner
wall.
The one in my pencil pot works
fantastic around noon and not very bad in the morning and in the
evening.
Anselmo Pérez Serrada
[ 41.63 N 4.73 W]
PS: OK, we might as well take a round tray with a
sharp border so that the shadow would fall on the base most
of
the day. Then it would draw for every day
something like a cardioid, smaller in winter and bigger in summer.
The problem is that all these cardioids are very unevenly distributed so we can't interpolate
very well
and, of course, we can't read the hours close to the sunset or sunrise because they fall on
the little walls of the tray.
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