A very easy to use universal sundial/sextant -equivalent type thing to get the angular height of the sun above the horizontal.

Purpose: To determine the elevation i.e. altitude of the sun (full range, i.e. 0 to 90 degrees), when on land and when it's not too windy. Comes with a chart and tables that help you work out your latitude and also the current time, pretty much nearly anywhere/anytime in the world you are. For similar but for stars/Moon at night (or, if you want vertical angles to landscape features) use the StarSquare or StarRings instead.

Caveat: This thing and the associated PDFs are not intended for life-critical or indeed any applications other than educational only! Use for navigation etc. at your own risk!

Accuracy: Perhaps around 0.25 degrees or so: not as accurate as a sextant and an artificial horizon, but unlike that setup it will give you an elevation even when the sun is high in the sky. The half-size version is perhaps around 0.5 degrees.

Usefulness:

From the current angular height (i.e. elevation, altitude) of the sun, and the current date and your latitude, the supplied charts/tables let you easily determine:

• the current solar time: tables/chart supplied: no math or calculator/slide-rule required!
• the bearing to the sun (or add 180 to get the bearing of shadows): no math or calculator/slide-rule required!
• the time to/from solar noon, or to/from sunrise/sunset, or the time-interval since your last elevation observation as long as neither is too-near noon
• the 'wall clock' time: requires knowing your longitude compared to your time-zone's meridian (which equals the +ve offset of the time-zone from UTC times 15 degrees, east is +ve west is -ve; e.g. Jakarta is 7hrs ahead of, i.e. +7hrs from, UTC and so its meridian is 105 degrees east: grab yourself a print of an online timezone map if you're travelling) and any daylight savings rules

The tables/charts can also be used to determine the length of day (sunrise to sunset) for any date, for your latitude, and the approximate bearing of sunrise/sunset.

If you don't know both your latitude and the date, then you can't use the tables to plot your straight-line on the chart(s). But you could possibly use an hour-glass (sand-timer) or other means to take 3+ altitudes (avoiding around noon) at known time-intervals between them, then use trial and error to plot those on the chart so as to give a straight line and to have those altitudes appearing the right time-intervals apart. That line should be good for a day or two at least. Using the line to reverse-lookup the tables to try to establish your latitude and date is possible but the error can be large.

If you don't know the date but you know your latitude, then you can get the approximate date by determining the highest elevation (altitude) seen during the current day, that's the solar noon altitude and from that you can get which two ranges of dates in the 'solar noon altitude on given date' table have that solar noon altitude for your latitude; often if you know the season/month you are in that will suffice to let you determine which of the two date-ranges are correct, otherwise wait for the sun's declination to appreciably differ (e.g. a couple of weeks, count the days) and do it again to get two new date-ranges- one of those will be the right count-of-days different from one of the first date-ranges, that pair is the one to accept. If there's still ambiguity then do it again.

If you don't know your latitude but you know the date, then you can get your latitude by determining the highest elevation (altitude) seen during the current day, that's the solar noon altitude and from that you can get which two latitudes in the 'solar noon altitude on given date' table have that solar noon altitude for the current date; often if you know the hemisphere you are in that will suffice to let you determine which of the two latitudes are correct, otherwise wait for the sun's declination to appreciably differ (e.g. a couple of weeks) and do it again to get two new latitudes- one of those latitudes will be the same as the first time, and that's the one to accept.

If you don't know the date or your latitude, then you can determine the date (approximately) by e.g.:
A) using a star-wheel (not supplied) etc, or
B) consulting a table (not supplied) of full moon / new moon dates for the current year if you know the month, and count days until/since the full moon / new moon. If you don't know the month then perhaps if you observe a few full moon / new moons and count the days between them and trial-and-error against the table to find a match, that would work.
Once you have the approximate date, you can refer to the above to establish your approximate latitude.

If you don't know the date or your latitude, then you can determine your latitude by at least one of:
A) determining the highest altitude ever seen during a year, which if less than 90 degress means you are not in the tropics and are instead further north than 23.4 degrees or further south than -23.4 degrees (if it is 90 degrees then you are in the tropics and see 'B' below instead). That date of highest ever altitude is in summer, and around the 22 December in the southern hemisphere and around 21 June in the northern hemisphere, with a few days error: you can reverse-lookup that highest altitude in the 'solar noon altitude on given date' table against that date to get your latitude, or
B) determine the lowest solar noon altitude seen during the year (if you are within the arctic/antarctic circle i.e. latitude more northerly than 66.5 degrees or more southerly than -66.5 degrees, then some days the sun won't make it over the horizon at all- see 'A' above instead), the date of lowest solar noon altitude is in winter, around the 22 December in the northern hemisphere and around 21 June in the southern hemisphere, even in the tropics, with a few days error: you can reverse-lookup that lowest solar noon altitude in the 'solar noon altitude on given date' table against that date to get your latitude.

If you don't know which hemisphere you are in then face the noon-ish sun, the sun rises to your right in the southern hemisphere, to your left in the northern hemisphere (this is only really applicable outside of the tropics); at night check the constellations to see which are visible and which way they are orientated- e.g. Orion's sword points south, or use a star-wheel.

To refine your estimate of the date or latitude, you could try any or all of:
A) using a compass (ensure you correct for magnetic vs true bearings) to get the true bearing of the sun or shadows (for shadows add 180 degrees to get the bearing of the sun, if the result is higher than 360 then subtract 360) at the same time you take an altitude reading of the sun; which could include at sunrise/sunset (altitude is near zero then). Repeat for different altitudes if you like.
B) using e.g. an hour-glass (sand-timer) to determine the approximate time-interval between the sun rising to a given altitude and then dropping back down to the same altitude, include at sunrise/sunrise and sunset (altitude is near zero then). Repeat for different altitudes if you like.
Then consult the charts/tables as appropriate to use trial-and-error to dial in your estimate: your estimate of the latitude and date is correct if the altitude and bearing pairs, and/or altitude and time-interval pairs, is correct for your estimated date and latitude.

If you don't know how to convert compass (magnetic) bearings into true bearings, at your location:

1. Take the compass bearing of the sun (or, shadows but add 180 degrees) at two times, one in the morning when the sun rises to a given altitude, and one in the afteroon when the sun drops to the exact-same altitude. You can pick an altitude of ~0, i.e. take the compass bearing of the sun at sunrise and sunset.
2. Average those two compass bearings (i.e. add them and divide by two, you can add 360 to one of them first as you like), and compare the result to whichever of 180 or 0 or 360 is the closest to the average.
3. Whatever you have to add (or subtract as the case may be) to the average in order to get 180 (or 0 or 360) is the number you have to generally add (or subtract) to compass bearings to get true bearings. If you need to go the other way, i.e. convert true bearings to compass bearings, just do the reverse: subtract (or add, respectively) the same number.

Instructions:

Hang it via the middle hole off a string (dental floss works well, cut it diagonally to form a point then push/pull it through) from your hand.

Face sideways to the sun, raising your hand holding the ring string, until the ring is face height, and gently rotate the ring using your other hand around the string (while avoiding tilting the ring) until the shadow of the ring falls onto the inner ring and a bright spot appears within the shadow from one of the holes facing the sun.

Read off the marks, counting up from the bottom-most mark, taking note of the hole the sun is shining through, and noting whether your are counting from the bottom towards that hole or from the bottom away from that hole.
(Repeat a few times using the same hole and average for a more-accurate reading)
Look up the table (or apply the simple formula) - PDF attached - to get the altitude of the sun.

Then rotate the ring 180 degrees and get the altitude of the sun again. Average those two altitudes, to get your result (we rotate and average to cancel out any errors due to the ring not hanging perfectly straight).

Avoid windy days if you can't move out of the wind, as the ring blowing around reduces accuracy greatly.

You could probably 3d-print out a float for it and float it on water, if you don't want to hang it, as long as it floats exactly level (i.e. float is symmetrical and the print is centered).

You can scale it freely (as long as X and Y have the same scale-factor), but the holes will also scale. There's a half-size version included too (with full-size holes), you can scale from it or the full-size version. The half-size version has differing markings than the full-size: it has taller multiple-of-5-reading and full-height multiple-of-10-reading lines.

You can write on the hangdial whatever dots or numbers as you like to make taking readings and determining the sun's altitude quicker for you.

Printing:

Resolution- 0.2mm

Supports- No

Brim/Raft- No, you want the ring to be perfectly symmetrical so it hangs truly vertically

Filament- Matte black/dark color works well (can still see the bright spot from the sun on black). Avoid 'silk' filaments and the like as it can be hard to tell where the indents you read from start/end exactly.

Infill- Doesn't matter much (10%-30%)

Z-seam- set to 'front' is likely best, you want z-seams near the holes not on the other side of the ring where you take readings.

Care of the print: don't twist or squash it, don't leave it in the sun for a long time- you want it to stay a circle else it will lose accuracy.

Note: You can use Long Addition/Subtraction to help you do the calculations in the PDFs, if you don't want to use a pen and paper.