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.
How to use the Analemma symbol on the Latitude Quadrant
Instrument used: Wndsn Latitude Quadrant
On more recent Wndsn Latitude Quadrants, you will find an analemma symbol in the lower left of the calendar scale. This symbol does not serve a decorative purpose, instead, it is designed to help memorizing its shape and overlay on the calendar scale to determine the rough equation of time for a given day.
The analemma symbol on a Latitude Quadrant.
The Equation of Time
The equation of time is the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth.
The equation of time (EOT) is the difference between mean time and true solar time.
EOT = GHA (apparent Sun) - GHA (mean Sun)
where GHA is the Greenwich hour angle. Alternatively, one could calculate using the right ascension (RA) of the Sun:
RA of the fictitious mean Sun - RA of the apparent (actual) Sun
The Analemma
The analemma is a diagram showing the position of the Sun in the sky as seen from a fixed location on Earth at the same mean solar time, as that position varies over the course of a year. Here shown sideways to illustrate the overlay direction.
| EOT [mm:ss] |
Max | +03:41 | -14:15 | Min | ||||
| MAY-15 | FEB-11 | |||||||
| MAR-21 | ||||||||
| ±0 | JUN-14 | ±0 | APR-15 | ±0 | DEC-25 | |||
| SEP-01 | ||||||||
| JUN-21 | SEP-23 | DEC-21 | ||||||
| Min | JUL-25 | NOV-04 | Max | |||||
| -06:30 | +16:25 | |||||||
| ε | 23.44° | 0° | -23.44° | |||||
During the year, the equation of time varies as shown in the graph above. Apparent time, like the time we measure using the Quadrant, can be ahead (fast) by as much as +16:25 (around NOV-04), or behind (slow) by as much as -14:15 (around FEB-11). The equation of time crosses the x-axis (at ±0) around APR-15, JUN-14, SEP-01, and DEC-25. (If you squint, you may be able to make out the shape of the analemma in the table.)
Now, if we overlay (and bend) the analemma diagram along the calendar scale of the Latitude Quadrant, we can visually determine whether we are in slow or fast (apparent) time, and by how much compared to mean time.
This way, using the tiny symbol of the analemma on the Quadrant, we can infer where we are in the EOT and thus determine the mean local Sun (time) from the apparent Sun (time) we take with the horary lines of our Latitude Quadrant.
See also:
- Example date and EOT on Tycho