Some Portable Folded-Paper Flat-Dials . Paper flat-dials with one or two right-angle folds are easily-built and easily-carried. Some wouldn't be very difficult to use. . First let me comment on one or two other portable dials: . 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. . 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. . The Romans must have just had a shared-understanding to not expect puncuality at mid-day appointments. No problem. . 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. . And altitude dials have the great advantage and convenience of telling you when sunrise and sunset will be. ...especially useful in wilderness applications. . But suppose that you want a portable dial for modern urban use, when appointments and bus-departures often occur around mid-day? . The Ring-Equinoctial is accurate around mid-day, and is easy to use, but is difficult to build. . 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. . 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.) . 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. . 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. . 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. . 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. . Here are a few such possible designs for a portable right-angle-folded paper flat-dial: . 1. Rectangularly-Twice-Folded Horizontal & Vertical-Polars Dial: . 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. . At the middle of the string is a nodus, consisting, for example, of a small bead, or a short piece of thread tied there. . So a Horizontal-Dial is drawn on the middle horizontal square, and Vertical-Polar Dials are drawn on the two vertical squares. . It tells time sand declination whenever the Sun is above the horizon. . 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. . So of course one would horizontally orient the dial so that it reads the correct declination for the date of use. . 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). . 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. . 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). . 2. V-Twin Reclining-Declining-Dial: . 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. . 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. . Reclining-Declining Dials are drawn on the upper surfaces of both squares. . On the back of one square is the table of EqT. On the back of the other square is the table of declination. . Horizontal orientation is by alighning the dial so that the declination-reading is correct. .
Keeping the crease level likely wouldn't be difficult, but the orientation about the crease would be more difficult, and would probably require a plumb-line hanging from the middle (nodus) point of the connecting-thread. Such a plumb-line could achieve correct orientation about both axes (the crease and an EW axis). . ----------------- . Of course, alternatively, either of these dials could use the intersection of the connecting thread with the top-edge of the sunward square as the nodus. . ----------------- . On either of these dials, the declination-lines could be labled for declination, or for ecliptic-longitude (maybe by zodiac-sign, maybe by degree, maybe by numbered ecliptic-months in numbered quarters). Of course then ecliptic-longitude, instead of declination, would be listed in a table on the back of one of the squares. . An advantage of eclicptic-longitude is that it can be fairly-accurately estimated from the date. (...not that that would be necessary if ecliptic-longitude by date is tabulated on the back of one of the squares.) . 48 Su November 24th 2142 UTC . Michael Ossipoff
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