This is a follow on to Monday’s post. If you haven’t read it, you might want to give it a glance.

I’m going to show you how to construct a simple instrument to measure sun angles. It works especially well at the solstice, but a few days late won’t hurt if you are only out to amuse yourself and maybe learn something. I first used this when I was considering where to place windows in a building to get north light without afternoon glare. You could use it to pick out the optimum placement for solar panels, or decide how deep to make a south-facing porch.

FYI to my followers in Brazil, New Zealand, and Australia. I am going to write as if everybody lived in the north latitudes; I’m sure you are used to modifying that kind of writing to meet your own needs. Sorry, but it’s just too clumsy to qualify every statement.

All you need to measure sun angles is a board with a vertical dowel or wire set into it near the center. You could use a carpenter’s square for that. You will need a spirit level to level the board, and it wouldn’t hurt to then use the level to see if the dowel is still vertical (what carpenters call plumb). You will mark the shadows as they fall directly on the board.

This is what I used the second year. The first year i drove a rusty used pipe into the ground and drove stakes into the shadows. Same principle, but far too clumsy.

Next, you need your local sun time. Subtract daylight savings time, but that isn’t enough. Noon, by the sun, is when the sun is directly south of you. Clearly that is an hour earlier on the east side of your time zone than it it on the west side, so you need your longitude and some simple arithmetic.

There are twenty four time zones, each 15 degrees wide. The first time zone is at zero longitude in Greenwich, England but, again, it’s not that simple. Time zones center on their base longitude. The first zone lies from seven and a half degrees east longitude to seven and a half degrees west longitude, and the other zones follow suit. Then all is adjusted to match up with political boundaries, but we can ignore that.

Let’s choose Oklahoma City as a neutral site, so I can give  a shout out to their wonderful Fleming Fellowship, celebrating its sixtieth anniversary this month. OKC is at 97.5 west longitude. If you ignore political gerrymandering, OKC’s time zone centers on 90 degrees longitude, so OKC is on the western boundary of the theoretical time zone; the political time zone ends on the western border of the state. The sun is south of OKC when your watch says 1:30 PM, if your watch is accurate and you have it set for daylight savings time.

To find solar noon for the longitude where you live, add or subtract 3 minutes for every degree you are west or east of the theoretical center of you time zone.

I like to set my board up the day before and rotate it so that the (solar) noon shadow lies parallel to this sides of the board. That isn’t necessary, but it makes for a neater project. Then I’m ready to record the shadow that falls at sunrise.

Sunrise is problematical. You can look it up for your area, but it’s not that simple. (Have I said that before?) If you live on a mountaintop, sunrise will come earlier. If you live in a valley – or, in my case, on the west side of the Sierras – it will come later. How much can’t be calculated. It depends on how far west of that hill you are, and how high that hill is, and whether today’s sunrise happens to fall behind your neighbor’s house, or behind that big oak tree. It will come when it will come. Have a straight edge handy and draw a line from the dowel down the center of its shadow, then write down the time. Continue through the day. I try to make a mark every hour on the (solar) hour.

Early and late shadows will probably run off the board, but for the rest you can calculate the sun’s vertical angle because you will know the height of the dowel and the length of the shadow. Personally, I take the measurements, redraw the triangle on another piece of paper, and measure with a protractor; but then, I grew up before calculators.

You do realize that this is the year’s extreme for north tending sunrise and sunset and for high sun angles, and that every other day until December will be slightly different.

Even if you never design windows for north light without afternoon glare, or plan the placement of solar panels, or decide how deep to make a new porch, taking the sun’s angles throughout the day will give you a better feel for your personal environment, and a new appreciation for the complexities of astronomical observations.

Extreme astronomy geeks will repeat the process at the equinox and winter solstice, but good luck if you try. I’ve never been able to pull off any shadow measurements in December because of clouds.