The simplest way to measure the angle of elevation to the horizon is with your D-shaped protractor.
Notice the tiny hole in the center.
Put a piece of thread through the hole and and tie a weight on it so that it will hang somewhat below the sweeping arc of the D.
Notice that when the flat edge of the D is held perfectly horizontal, the thread cuts the arc at 90°.
Sight along the flat edge of the D and align it with the point on the horizon that you wish to measure the angle of.
You need a second person here. Have them read the number of degrees away from 90 that the thread cuts the arc.
A note on accuracy. Obviously this is a very crude way to measure this angle of elevation to the horizon. There are many tools that can do this more accurately. I use a Suunto Clinometer.
The Sun doesn't rise straight up.
If the horizon is elevated the Sun will rise further to the South of where our calculations have shown us.
The animation at the top of this page shows a level horizon. If the horizon had been elevated the Sun would have set further South.
But how can we measure this?
Let's try this problem:
At what azimuth does the Equinox Sun rise at the 40th latitude given an angle of elevation to the horizon of 10°?
When the horizon is elevated, the Equinox Sun rises at a different place on the horizon - South of due East.
First let's make this at a latitude of 40°. This line comes into the United States just above Los Angeles and Denver, goes through Indianapolis, Indiana and Philadelphia, Pennsylvania. The 40th latitude enters Europe between Madrid and Toledo in Spain and heads Eastward through Southern Italy, the ancient city of Troy, the Caspian Sea, Beijing in China and out into the Pacific through Northern Japan.
Let's look for where the Equinox Sun rises at the 40th latitude with an elevation to the horizon of 10°. You would begin by drawing the 40° latitude.
There follows a quick review of the orthographic process for deriving the path of the Sun on the Equinoxes and the two Solstices.
The rising azimuth of the Equinox Sun, when there is an angle of elevation to the horizon of 10°, can be determined by raising the level horizon we have been working with up until now by 10°.
Measure 10° on the Meridian (red arc) up from the horizon to the North and same on the South, then connect the two points.
We are looking for the point where the Equinox Sun Crosses the elevated horizon E2. With your pair of compasses put your point where the horizon Crosses the zenith C1, and measure out to point E2. Go down to the lower circle and mark that out from C' at E2'
In rare cases - like a shot taken on top of a high mountain – there's a negative angle of elevation to the horizon. In this case extend the red arc of the meridian below the level of the horizon N-C-S, and continue as above. You might have to extend the actual paths of the Sun below the horizon.
This elevated equinoctal line Crosses the circular horizon at E3. Given a level horizon, on the Equinox the Sun will rise due East anywhere on Earth. Notice that the azimuth of the Sun with an elevated horizon is shunted towards the South. Likewise, with an elevated horizon, the Equinox setting Sun will also be shunted towards the South.
Notice that due East is 90°, but with the 10° elevation to the horizon the Sun rises at an azimuth 8.5° further South.
You can now find the quarter and Cross-quarter solar alignments for any place on Earth (within the Arctic and Antarctic Circles). In Section 4, we include information about how to determine major and minor standstills of the Moon.
Before long, it is our intent to have a page where you can enter your latitude, azimuth and angle of elevation to the horizon, and you will be able to find out what day of the year the Sun would rise in that particular direction. You will also be able to see the orthographic projection from which the specific day(s) were derived. This projection can be saved for later use.
This will be a useful tool not only if you want to check out an alignment at a sacred site, but also if you want to build a new sacred site locked into the astronomy of that place.