Some Portable Folded-Paper Flat-Dials
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Paper flat-dials with one or two right-angle folds are easily-built and
easily-carried. Some wouldn't be very difficult to use.
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First let me comment on one or two other portable dials:
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The Regiomontanus card altitude-dial is surely the most easily-built
portable dial, and none is easier to use, other than the difficultly-built
Ring-Equinoctial.
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Yes, of course the disadvantage of altitude portable dials is their lower
accuracy around mid-day. I suggest that there's usually no reason why that
would be a problem.
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The Romans must have just had a shared-understanding to not expect
puncuality at mid-day appointments. No problem.
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And, if you're in the wilderness, then why would you need precise mid-day
times? The important times for that application would be when sunset is
near. Of course altitude-dials' accuracy problem is only around mid-day.
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And altitude dials have the great advantage and convenience of telling you
when sunrise and sunset will be. ...especially useful in wilderness
applications.
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But suppose that you want a portable dial for modern urban use, when
appointments and bus-departures often occur around mid-day?
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The Ring-Equinoctial is accurate around mid-day, and is easy to use, but is
difficult to build.
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There are various folded-paper flat-dials that are (at least in principle)
accurate around mid-day, and easy to build. They use a single rectangular
piece of paper, with a right-angle fold at its middle.
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In a book, I ran across such aproposal, with a pre-constructed dial to
Xerox and cut out. It was a right-angle-folded paper Disk-Equatorial.
(Though the surfaces were square, of course the degree-arcs were circuar.)
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I copied it and made the dial. It was easy to build, but a bit awkward to
use. It required a separate little tab, attached to the dial via a slot, to
cast a shadow on a declination-scale, for horizontal-orientation of the
dial.
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Vertical orientation(about the EW axis) was intended to be by aligning the
horizon, at sea, with your latitude on a circular latitude-arc. I instead
used a plumb-line on that arc. But I also tried substituting, for the
horizon, a point that is at the same height above the ground as the dial.
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When that dial is awkward is in winter (negative solar-declination),
because of course it's necessary to read the bottom surface of the
equatorial-section.
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It made me feel quite conspicuous holding it up in that manner. Something
that can be held lower, as if you were using a smartphone or a book, would
be much more comfortable and convenient for me.
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Here are a few such possible designs for a portable right-angle-folded
paper flat-dial:
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1. Rectangularly-Twice-Folded Horizontal & Vertical-Polars Dial:
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The paper is a 3:1 rectangle, with the ends folded up at a right-angle,
box-like, forming 3 squares. That position is held by a piece of thread
connecting the middles of the top-edges of the vertical sections.
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At the middle of the string is a nodus, consisting, for example, of a small
bead, or a short piece of thread tied there.
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So a Horizontal-Dial is drawn on the middle horizontal square, and
Vertical-Polar Dials are drawn on the two vertical squares.
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It tells time sand declination whenever the Sun is above the horizon.
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Horizontal orientation is by the declination-lines. On the back of one of
the squares could be a table of EqT. On the back of another of the squares
could be a table of declination.
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So of course one would horizontally orient the dial so that it reads the
correct declination for the date of use.
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Leveling? Of coures there have been Tablet-Dials with spirit-level or
plumb-line. But the portable tablet-dials that I made didn't have a
spirit-level or a plumb-line, and they were all accurate within 5 minutes
(one of them 3 minues).
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This Twice-Rectangularly-Folded Horizontal and Vertical-Polar Dial would,
with its flat square likely be as easy to level as the Horizontal
Tablet-Dials that I made.
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But it could also have a plumb-line hanging from the connecting-thread; or
have two plumb-lines attached to the vertical squares (anywhere would do).
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2. V-Twin Reclining-Declining-Dial:
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This would have simpler folding--just one fold--but would require drawing
hour & declination lines for Reclining-Declining Dials, which is what would
be on the upper-surfaces of the squares.
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A 2:1 rectangular paper is folded at its middle, into a right-angle V, with
two square sections. The fold is held by a connecting thread between the
middles of the top-edges of the two squares. A nodus (bead or tied short
thread)is at the middle of that connecting thread.
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Reclining-Declining Dials are drawn on the upper surfaces of both squares.
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On the back of one square is the table of EqT. On the back of the other
square is the table of declination.
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Horizontal orientation is by alighning the dial so that the
declination-reading is correct.
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Keeping the crease level likely wouldn't be difficult, but
