Wndsn Quadrant Telemeter Tutorials
Making the most out of our graphical telemetry computers.
Like with many complex instruments, there are multiple ways to solve certain problems and to measure the required inputs. Combining the various functions leads to a multitude of advanced uses. See also the printed manual.
Finding Latitude with a Compass
One way to find local latitude is to take a compass bearing of sunrise or sunset. This works best at higher latitudes around the solstices, where sunrise and sunset occur a fair bit north or south along the horizon.
In fact, above a certain latitude, for every degree of latitude, the sunrise moves more than one degree along the horizon. This makes it a little easier to measure and calculate on the (Sine) Quadrant.
arccos(sin(23.44°)/sin(38°)) = 50°
Where does that happen? A Sine Quadrant can help calculate it. The formula for the direction of sunrise is:
sin(direction) = sin(declination) / cos(latitude)
The resulting value tells us where the sun rises, in degrees along the horizon from East. See the tutorial for more on the direction of sunrise.
On the Sine Quadrant
Note that up to about 32°, the sine of any angle α is about α/60.
We want the direction of sunrise to increase by more than one degree for each degree of latitude. Look at the sine scale and note that up to about 32°, the sine of any angle α is about α/60. (Second picture. If you hadn’t noticed that earlier, make some tea and enjoy a moment of contemplation.) The sine of 38° is (α-1)/60 or 37/60, which comes out to 0.616. This is where angles start growing faster than their sine values.
Going back to our formula, we see that we are calculating the sine of the direction. We want this value to be at least 37/60, and that the direction of sunrise is at least 38°. Where does this happen on the solstice, when solar declination is 23.44°? The answer is arccos(sin(23.44°)/sin(38°)) or 50° latitude (first picture).
Using our direction of sunrise formula, we confirm that at 52° latitude, the direction of sunrise is 40.25°, just a little over one degree more than at 51° latitude.
This applies to the solstices. How about a month before or after the solstices, when solar declination is at least 20°? To answer this, just use 20° instead of 23.44° in the method described above.
Tip: when taking a compass bearing of sunrise or sunset, it may be helpful to wait until the sun is just high enough over the horizon that another sun would fit underneath. This compensates for atmospheric refraction and helps the observation match the math.
I don’t have a sharp photo of a sunrise, so here’s a moonrise.
(Tutorial written by Cute Puppy.)
See also: