This week, build an astrolabe’s tympan—latitude—plate to represent the Azimuth arcs
Tympan Plate: Azimuth Arcs
Among the dense series of overlapping lines and arcs on the face of the front tympan plate lies a spider-web of arcs that represent the azimuth of the night sky.
Azimuth circles form a nest of intersecting arcs between the almucantar circles. An azimuth is formed by splitting the night sky into vertical circles from the zenith—directly above—and the nadir—directly below—the observer.
While the almucantar slices the night sky horizontally, the azimuth splits the night sky vertically, like a net falling all around but connected at the zenith.
The azimuth splits the sky clockwise around the northernmost point from the observer. 0° is North, 90° is East, 180° is South, and 270° is West.
The azimuth extends beyond the horizon at an observer’s feet, and down until it intersects again at the nadir. The midpoint between the zenith and the nadir is in line with the observer’s horizon, so only the top portion of the azimuth will be visible from an observer’s point of view.
Because azimuth circles extend along an entire sphere, it is easy to confuse them with longitude. However, longitude is defined from 0° in Greenwich, England and extends a vertical imaginary circle that runs between the North and the South Pole. Azimuth is defined in respect to an observer, where 0° represents directly north of an observer and extends up and through the zenith and nadir also defined with respect to an observer. Like almucantar circles, 10 different explorers standing together might share the same longitude position, but will all have unique azimuth circles.
To start, determine the latitude for the observer—in this example 65°—remembering to measure from the pole and not the equator. This will create a projection onto the base plate for the horizon.
While azimuth circles extend below an observer’s feet, for clarity on a tympan plate, only azimuth circles that lie within the arc defined for the horizon (0° almucantar circle) are engraved since these are the only section of the arc that will be visible to an observer. As a result, in regions where the horizon is more aligned with the top of the Earth, the larger enclosed area for the horizon circle can be compared to those closer to the equator where the horizon circle is more off center.
Because only azimuth arcs that lie within the horizon circle are included, the plate will need to already include the circles for the tropics and the horizon.
To set up azimuth arcs, from the horizon, measure 90°. This will determine the position of the zenith—directly below—and the nadir—directly above—for the observer.
The azimuth arcs are defined based on the projected positions of the zenith and nadir. Projections are drawn from the south pole up and through the position of the zenith and nadir and continue on until it intersects the center equatorial plane.
The point for the zenith will be formed within the base plate because the zenith is visible to an observer, while the nadir will be projected far outside the base plate as it would not be visible through the horizon to an observer.
Halfway between the two intersections represent the midpoint. The midpoint is where the azimuth circle’s maximum radius will lie.
The projections formed will produce three important lines for the nadir, midpoint, and zenith. However, unlike previous projections for the base plate and almucantar circles, the projection diagrams can now be temporarily removed and the remaining base plate and lines will be rotated until they form a stack of lines with the base plate at the bottom.
Azimuth circles are formed like an imaginary clock from the north, east, south, and west positions all around an observer. In an astrolabe, it is common to include azimuth circles for each 10° around an observer.
From the base plate, form temporary projection lines every 10° to mark where they intersect the middle line representing the midpoint. This will form an angle between the zenith and the midpoint of the arc from which each of the azimuth circles will be formed. A lot of space is needed for this step, since it is common for the maximum and minimum degrees to be very far away from the center (and for clarity have been cropped out of the example below).
The first azimuth circle we will form is at 100°, 10° above the middle projection position at 90°. The azimuth circle is formed by drawing a circle, where the center of the circle lies on the intersection point in the midpoint line, but also touches both the line representing the zenith and the nadir at the top and bottom.
The intersection of the new circle with the zenith and nadir lines will represent the full 360° circle of the azimuth from the zenith above an observer to the nadir below them.
Each new azimuth circle is formed where the projection line intersects the midpoint as the center of the circle that touches the zenith and nadir line. For each circle formed further and further from 90° in the center, the circles will grow in size. For example, next at 110°:
The right half of the azimuth circles are formed from 100° to 170° along the projection lines.
One special case is 90°, a quirk of the geometry, where the center of the azimuth circle will be represented by a long vertical line.
To add, find 90° in the center of the angle marked.
Then draw a line that intersects the midpoint, but extends from the zenith to the nadir in one long vertical line.
As an azimuth circle is formed further from 90°, the circles grow in size, far outgrowing the base plate in the center.
The remaining left half of the azimuth circles are formed from 10° to 80°. The intersection from the zenith to the nadir with the midpoint forming the center in the same method. This will eventually form a mirror image of azimuth circles on either side of 90°.
However, for clarity, only a small part of the azimuth circles are included on the tympan plate. Only the part of the azimuth circle that is contained within the horizon circle is visible, so unlike much of the plate, the azimuth circles will always be represented by a series of arcs. So, for 65°, the azimuth arcs will appear like a nest of interlocking arcs which connect at the zenith.
More of the arc is visible at higher latitudes, closer to the poles, but at lower poles, the horizon circle is more off center, so less of the azimuth would be visible, like at 10°.
Southern Hemisphere:
In the Southern Hemisphere, the construction of the azimuth circles will be built from the north pole projection instead of the south. Everything in the southern hemisphere is a mirror reflection of the northern hemisphere where 0° is North, 90° is West, 180° is South, and 270° is East.
However, without labels, the further construction of the azimuth circles from the nadir and zenith positions are indistinguishable from the northern hemisphere, outside of the position of the horizon arc that contains the azimuth arcs.