Continue tellurion assembly, begin solar and lunar eclipse demo - November 2015
This month we continue the fabrication of the tellurion complication.
These photos show the
central mounting for the tellurion. It can be removed as a single unit and
released with a simple twist.
Buchanan now continues
with the moon armature. The first photo shows one of three holes being
drilled for screws that will secure the hollow post upon which the moon’s
mounting will slide. Notice how close the drill is to the hollow post, next
a few of the completed components with the hollow post shown. The third
photo shows a spring that will bias the rod upon which the moon is secured
within the hollow post. That spring is needed to hold the moon against the
node ring upon which it will ride. Most tellurions are horizontally mounted so
the weight of the moon and its mount use the force of gravity to ride on the
node ring. But since this one will be rotated 900 we must use a
spring to keep it seated on the ring.
The slider is now
mounted within the tube. Notice that a jewel is used here. We use no
metal-to-metal contacting surfaces where there is sliding or rotational
surface contact. Those would need oil, and we are avoiding oil in this
machine. The next photo shows the beginnings of the artwork for the ring set
that will surround the Earth globe.
Notice the plastic indexing plate
behind the drawing to aid in the accuracy of the artwork.
The armature is now beautifully shaped ‘comma’ along with the rest of
the parts for the moon apparatus. Note in the second photo the jewel ‘foot’
that is attached to the spring-loaded rod upon which the moon will be fixed.
That foot will slide along the node ring. The reason we must use a sliding
scheme rather than a wheel is that the moon rotates as it orbits along the
node ring, so a wheel would not stay aligned. A roller within a cup was
considered, but the diminutive size and the susceptibility of the ball
jamming and simply sliding itself on the smooth ring resulting in a
metal-to-metal frictional surface made that
option risky and impractical.
The completed Moon
armature assembly ready for installation into the rest of the tellurion.
Next the unit is installed. Notice the guide fork installed on the tube that
has the sliding rod for the Moon. The circular disc is the node ring which
is angled at 5.140
reflecting the tilt of the Moon’s orbit to the Earth along the
ecliptic. This ring is what will move the Moon up and down on the jewel
slider as it orbits the Earth. That ring also rotates once every 346.6 days
representing when the nodes makes a full circle in relation to the Sun. The
combination of this cycle and the cycle of Earth’s orbit around the Sun in
365.24 days produces the
that closely predicts the repetitive
pattern of just over 18 years of where an eclipse will occur on the Earth.
The first photo shows the top set of nested bearings used in this
assembly. The center photo shows part of the curvilinear multi-level frame,
next a mockup of the node dial.
I received several
photos of the tellurion, in particular Buchanan’s design for the moon’s node
cam disk. In a similar nod to prior makers, that disk has a thin enamel
dial. He has written “Ascending Node and “Descending Node”. The actual point
on the cam where this occurs is marked with a diamond pattern identical to
that found on the main tellurian dial. It is an elegant design and ties in
nicely with the main dial work. He indicated that there will need to be a
counterweight to the earth/ Moon system attached to the rotating armature.
He then suggested that we use a sickle-shaped weight with an enamel cover as
a counter-point to the enamel dial ring for the Moon’s nodes.
the planets, Moon, Sun and Earth are just temporary mockups at this point.
At that point I was
beginning to wonder if the node ring was looking a bit too heavy; making the
entire Earth/ Moon system look cluttered; especially if an enamel covered
sickle counterweight is included at the opposite end of the armature. This
was especially brought to my attention with the photos of the tellurion
mounted upon the clock. I suggested that we try eliminating the enamel dial
ring entirely; replacing it with a thin rim upon which the moon would ride
to give the inclined lunar orbit. The position of the ascending and
descending nodes, and the position of the Moon’s orbit relative to the
ecliptic could be denoted by the astrological symbol for the dragon’s head
which looks very much like the Greek letter Omega. That sign in the inverted
direction depicts the descending node.
An overall front elevation of the dial work. The next photo shows the
detailed turning for each of the two inner planet stalk mounts.
Buchanan now has
substituted a thin rim for the the enamel dial chapter ring. I like this much
better. It eliminates the clutter around the Earth / Moon system. I also
asked that the rim have a rounded edge for the perimeter, like a steering
wheel. We will still be able to include the information on the ascending,
descending nodes within the framework of the eclipse prediction indicators
that are yet to be designed. We will also try to hide the sickle
counterweight behind the main dial. The globe is now painted white to simulate the
eventual Walrus tusk material which will be scrimshawed to reveal
continental and longitude, latitude details. This is in keeping with our
intention to have all of the celestial bodies made of natural materials.
The tellurion assembly is now installed within the context of the rest
of the machine. There are yet many other additions to be made to this
complication before it is complete.
Now begins the work on the solar and lunar
eclipse prediction system.
I will now describe the components involved with the eclipse prediction
system. This is an example of our coming into a good idea as the machine is
being built. We had not thought of having such a capability during the
initial design phases of the tellurian. But as Buchanan thought through the
elements needed to produce an eclipse, he began to formulate a way to
incorporate this important complication within the structure of the
tellurion. This process also occurred with the addition of the dials for the Moon's
synodic and sidereal orbital periods.
There are two sector
‘windows’ that are attached to the base of the mounting for the Earth, and parallel to the ecliptic for the Earth
and these do not move. The ecliptic
is an imaginary line running from the center of the Sun to the center of the
Earth. As the Earth rotates that line traces out a circle around the Earth. The slightly larger window resides between the Earth
and Sun and is used for the solar eclipse reading. The other is 1800
around, is a bit smaller and is used for the lunar eclipse reading. Each
window is 34.340 and 22.960 around the circumference
of the Earth. Since there are 365.242 days in the tropical year, these
translate into 32 and 22 day windows. The two windows represent what is
known as the ‘
’ when the Moon’s nodes are close to the
parallel line between the Sun and Earth, the ecliptic, this is about plus or
minus 180 either side of a node. In the tellurian the Moon rides
upon an inclined circular track that is tilted 5.140 in relation
to the Earth’s orbit around the Sun, the ecliptic. A node is where the Moon’s
inclined orbit crosses the ecliptic. This occurs twice per orbit of the moon
and is known as rising and falling nodes depending on whether the Moon is
rising, northward or falling, moving southward beneath the ecliptic. The
Moon’s orbit also has an 18.6 year precession, where the locations of the
nodes make a complete orbit also known as the
. This is 19.60
per year. There is a set of hands attached to midpoints between the highest
and lowest points on the tilted track indicating the nodes. There is also a
hand located under the Moon’s support armature and it has an orbit of 27.322 days, the
A solar eclipse occurs when the node hand is within the eclipse season
window and the Moon hand is directly between the Earth and Sun. That is the
Moon is very near a node and directly between the Sun and Earth, otherwise
it would be a regular New Moon when not aligned on a node. The eclipse window
covers when an eclipse would be visible somewhere on the Earth all the way
from the northern to the southern latitudes. The windows have a scale in
degrees that will allow one to directly read at what latitude the eclipse
should be visible. The Earth will have surrounding rings showing the degree of latitude.
There will be an indicator telling if the degree reading is north or south
of the equator. The same conditions
apply when the Moon is on the opposite side of the Earth for lunar eclipses.
Given the diminutive size of this whole arrangement of machinery the
accuracy of the predictive qualities of when and where a solar or lunar
eclipse will take place is somewhat limited. But it will make for a
beautiful demonstration! At the end of this segment is a detailed
explanation of the why and how
solar eclipses happen.
The artwork for the
Earth latitude and longitude rings is now complete. One must remember that
these are very small, just over 1.5” or 4 cm in diameter and the surface
upon which the numerals are engraved only 2 mm wide. The first is demarked
in degrees 0 through 180 running clockwise and anticlockwise and is the
equatorial ring. This is the longitudinal ring. The second is divided in
quadrants with 0 through 90 degrees. The letters CAP, for the Tropic of
Capricorn and CAN for the Tropic of Cancer at the 20 degree locations. This
is the latitudinal ring.
These six photos show
the engraving process for the Earth rings. At this small scale a computer
controlled engraver was the only practical solution. After the rings are
engraved they are milled out from the brass blank.
The small scale is
revealed by the first photo; no larger than a wristwatch. Next some of the
finished engravings on the rings.
The initial trial fitting of latitudinal and
longitudinal engraved rings.
Notice the topography of the land masses.
Here we see the drive for earth’s rotation, next the axis. All pivots
for the gears and axis are jeweled.
The earth support mounted to the tellurion, next the Earth
mounted within the rings. The knurl knob allows one to position the inner two rings at
will. This will allow the user to set the inner ring at any location for the
‘zero’ time reading. They also serve to interpolate between the latitude
degrees readings given from the eclipse season window onto the actual
location of the Earth’s surface. Buchanan has decided to fill in the
continental, longitude and latitude lines on the globe. Again this is merely
a rough mockup.
At this juncture we will also be adding another two complications to the
tellurian, two dials to indicate the synodic and sidereal orbit of the Moon..
The synodic dial will have 29.53 days and the sidereal would be 27.32 days.
The dials will move in relation to each other and be located at the base of
The diagram explains the difference between the synodic
and sidereal lunar months. This strongly parallels the relationship between
sidereal and mean solar time. In both instances the sidereal period is
related the movement of a body, in this case the orbit of the Moon as it
relates to the distant fixed stars. In this case the orbit of the Moon as it
relates to the fixed stars takes 27.3 days, whereas it takes 29.5 days for
the Moon to go from one New Moon (or Full Moon) to the next New Moon. This
occurs because of the additional distance the Earth, and therefore the Moon,
has rotated around the Sun.
Next the artwork for the two dials.
The basic components for the eclipse prediction system are now in
place, albeit in a preliminary mockup form. The first photo shows the two
eclipse season window sector dials, these are
from each other with the other just above the
moon drive wheel. The small hand within the eclipse season sector dial is
attached to the Moon node ring at the point of one of the nodes and rotates
counterclockwise a full circle one every 346 days, another
hand is on the opposite side of the ring. It takes 346 days for the nodes to
make a complete circle relative to the Sun. The next photo shows a hand
connected to the armature of the moon which rotates clockwise once every
27.3 days, the sidereal period, the Moon's orbit in relation to the stars.
The combination of these two hand indicators upon the sector dial along
with the latitude rings will allow one to predict where a solar or lunar
eclipse will appear on the surface of the Earth. The tellurion is connected
to the calendar assembly as well as the world time dial, so in the celestial
demonstration mode one will be able to predict down to the hour when an
eclipse will take place. Using these two systems together we have the ability to
predict when and where these events will occur. In both photos we see the
dial mockups for the synodic and sidereal moon orbits.
In this video for the first time we demonstrate the interaction between
the Moon's node ring indicator, the season eclipse window and the position
of the Moon in predicting eclipses. The system is very preliminary and there
are still obvious glitches, but the basics are here. The latitude rings will
later be used to interpolate the position on the face of the Earth an
eclipse will take place as well as the length of its path.
Now begins the fabrication of the components for both the eclipse prediction
function and the synodic, sidereal Moon orbit dial work. In these photos we
see the dial base as well as the tiny pillars that will support that dial
being incorporated into the Moon armature for the synodic, sidereal dials. Even at the scale of one
millimeter, the pillars are finely turned. It is at these scales that the
workmanship and attention to detail separate this clock from most others
that have been built.
The dial base is now installed on the tellurion. Note the hand rendered
drawings in the background, the same design methods used by horologists for
millennia. While modern methods are not eschewed, the vast majority of this
project is done in the traditional ways.
Here the node indicator hand is being fabricated. First the steel blank is
drilled and then positioned upon the node ring for attachment. The size and
tolerances here are extremely small.
The eclipse season windows begin from a thick brass sheet. The next two
photos show the turning of the flat stock into a dish-shape with a tall lip.
That lip around the edge of the dish will become the individual season
windows with the balance of the rim removed. The mockup for the eclipse
season windows support piece is shown above the dish with the node ring
placed within the dish to check for fit in the second photo before the dish is shaped
into the final part.
First a drawing for the eclipse season window support is prepared with the
dish next carefully cut away. While the location of the windows stayed in
the same positions as that on the mockup part, the actual configuration of
the part took a decidedly more decorative turn.
Notice how the raised rim of the dish now
becomes the area where the dial frames are located.
might have taken the route of making the windows separate from the support
frame and simply soldering the two together to avoid the extra complex
machining steps. No such shortcuts are in this project.
Now the eclipse season windows and support piece are checked for fit
within the tellurian. Next holes are drilled and tapped for screws to secure
the eclipse season sector dials.
Below we will see Buchanan's use of computer aided design and manufacture,
CAD-CAM, in the creation of the Earth's rings and dial work for the eclipse prediction
mechanism. Up to this point there has been virtually no employment of the
technology. I have emphasized in the past the hand-made
nature of this project and it remains so. But in some limited applications
the use of this technology allows us to do things that otherwise would be
impossible or nearly so as in the case of the Earth globe. Or as it allows us to
make something with a high quality standard that would be difficult by hand
as in the case of very small scale engravings.
Buchanan uses a computer
simulation to determine the dial layouts for the solar and lunar eclipse
season dials. The first screen shot represents a solar eclipse, the second a
lunar eclipse. Both the Moon and Earth are divided into 24 sections equaling
150 per section. The solar eclipse season is 33 days per year
with the lunar season being 22 days. These are the times where the Moon’s
nodes are close enough in alignment to the Sun’s ecliptic that the Moon will
cause a partial to full solar eclipse or in the case of a lunar eclipse the
Earth’s umbra will cause a partial to full eclipse of the Moon. The node
ring revolves once every 346 days which is the time for the position of the
Moon’s rising or falling node to make a complete orbit all the way back to
that same position in relation to the Sun. Each season’s length translates
into 33 days/346 days x 3600 = 34.340 and 22 days/346
days x 3600 = 22.890 of a full orbit of the earth
around the Sun. These arcs are reflected within the circled areas of the
photos and translate into the size of each dial sector plate. The parallel
lines from 600 North to 600 South are projected onto
the sectors and determine where the dial degree indications will be located.
It is not a linear scale as the lines are closer together near the edges of
each dial than the center.
The two sector dials with corresponding demarcations according to the
designs described above appear in these two screen shots for the computer
controlled engraver. Note how the degree spacing is spread out as they move
from the center to the edges of the dial. This has been mathematically
calculated as the inverse of the line spacing seen on the computer screen
The two node ring dials are now designed as shown in these two screen
shots. These indicate whether the node is ascending or descending and
whether the eclipse will appear north or south of the ecliptic.
The first photo shows one of the eclipse window dials being engraved.
The second shows a completed node ring dial engraving before removal from
the brass blank. Buchanan has silvered the area and filled the engraved lettering with black wax
to make them more legible for the photo.
After the engraving is finished, the parts are milled free of the
surrounding supporting material.
These videos show the computer controlled engraving tool used to
create the script for the node ring sector dials. In the first video the
outline of the dial is being milled out.
This video shows the computer controlled machine and the computer screen in
real time as it creates the tiny
script used on the eclipse window and node ring dials as well as the degree
demarcations on the latitude and longitude Earth rings all used in our
eclipse prediction assembly.
The completed dial work engraving.
Here we see how Buchanan cuts a tiny slot in the head of a small screw
using a precision hand fret saw. The tiny screw is held in the vise by a lathe
collet within a jig that has the two upright pins. Those keep the thin saw
blade straight and perfectly aligned down the center of the screw head. The
head is less than 1 mm in diameter. These screws will secure the dial work.
Here we are back to hand work and elbow grease.
The dial work shown mounted to their respective positions. The first
photo shows one of the season eclipse window dials. Next we see a
node dial plate secured to the node cam ring. Notice the clever way Buchanan
secures the plate, third photo. He uses the rim pointer which is secured to the underside
of the rim in the first photo with two tiny screws and then uses the dark
area of the dial plate pointer on the other side to hide the screw that
secures the plate to the steel back of the rim pointer. This not only
secured the dial plate, but allowed it to rest upon one of the spokes and below
the edge of the perimeter rim; giving the entire presentation a nice reveal
under the rim. This is necessary as the Moon must ride upon this perimeter
without obstruction. There is no other way I could think of doing this
without the evidence of screws, say on the rim’s outside perimeter secured
to the edge of the dial plate. The alternative would be the use of adhesives
which is not allowed in this project, all parts have to be mechanically
secured in a reversible fashion.
The first photo shows all four dials in place, the pair of node ring dials
at the three and nine o'clock positions
and the pair of the eclipse season window dials at the six and twelve. Next the node dial
is rotating counterclockwise
into place over the eclipse season window dial. Nearby is the Moon, which at
this point does not hav
e its indicator hand yet installed moving clockwise. When the Moon
passes over the 'E' tab, an eclipse takes place.
That tab represents just over
the time of a typical eclipse of about 8 hours.
Conditions for an Eclipse:
One can predict eclipses by understanding the conditions
that make them possible. As you begin to think about these conditions, be
sure you are aware of your point of view you must imagine that you can look
up into the sky from your home on Earth and see the sun moving along the
ecliptic and the moon moving along its orbit.
Since there are two nodes in the
Moon’s orbit there will be at least two solar eclipse seasons per year and
with the moon on the opposite side of the Earth, two lunar eclipse seasons.
So why do these eclipses seem so rare? The reason is that in the instance of
a solar eclipse the shadow of the moon on the Earth is extremely thin and
the duration of the eclipse very short. A typical track for a full eclipse
is only 100 to 150 miles wide (161 to 240 km) depending on how close the
Moon is to perigee and about 1000 miles long (1610 km) before the show is over.
Although a solar eclipse occurs about twice yearly, a given place on Earth
only averages one total eclipse of the Sun every 360 to 410 years.
are descriptions and diagrams to illustrate the concepts.
1a and b.
Eclipses can occur only near the nodes of the moon’s orbit. (a) A solar
eclipse occurs when the moon meets the sun near a node. (b) A lunar eclipse
occurs when the sun and moon are near opposite nodes. Partial eclipses are
shown here for clarity
. Next an animation of this.
can only occur when the sun is near one of the nodes of the moon’s orbit. A
solar eclipse happens at new moon if the moon passes in front of the sun.
Most new moons pass too far north or too far south of the sun to cause an
eclipse. Only when the sun is near a node in the moon’s orbit can the moon
cross in front of the sun, as shown in
Figure 1a. A lunar eclipse
doesn’t happen at every full moon because most full moons pass too far north
or too far south of the ecliptic and misses Earth’s shadow. The moon can
enter Earth’s shadow only when the shadow is near a node in the moon’s
orbit, and that means the sun must be near the other node. This is shown in
So there are two conditions for an eclipse: The sun must
be crossing a node, and the moon must be crossing either the same node
(solar eclipse) or the other node (lunar eclipse). That means, of course,
that solar eclipses can occur only when the moon is new, and lunar eclipses
can occur only when the moon is full.
2a and b.
Eclipses can occur only near the nodes of the moon’s orbit. (a) A solar
eclipse occurs when the moon meets the sun near a node. (b) A lunar eclipse
occurs when the sun and moon are near opposite nodes. Partial eclipses are
shown here for clarity
view from Space:
Change your point of view
and imagine that you are looking at the orbits of Earth and the moon from a
point far away in space. You would see the moon’s orbit as a small disk
tipped at an angle to the larger disk of Earth’s orbit. As Earth orbits the
sun, the moon’s orbit remains fixed in direction. The nodes of the moon’s
orbit are the points where it passes through the plane of Earth’s orbit; an
occurs each time the line connecting these nodes, the line of nodes,
points toward the
Figure 2and notice that
the line of nodes does not point at the sun in the example at lower left,
and no eclipses are possible. At lower right, the line of nodes points
toward the sun, and the shadows produce eclipses.
The shadows of Earth and
moon, seen from space, are very long and thin, as shown in the lower part of
Figure 2. It is easy for them to miss their mark at new
moon or full moon and fail to produce an eclipse. Only during an eclipse
season, when the line of nodes points toward the sun, do the long, skinny
shadows produce eclipses.
Saros cycle(sometimes referred to simply as
the Saros). After one Saros cycle of 18 years 11⅓ days, the pattern of
eclipses repeats. In fact, Saros comes from a Greek word that means
The eclipses repeat because, after one Saros cycle, the moon and the
nodes of its orbit return to the same place with respect to the sun. One
saros contains 6585.321 days, which is equal to 223 lunar months. Therefore,
after one Saros cycle the moon is back to the same phase it had when the
cycle began. But one saros is also equal to 19 eclipse years. After one
Saros cycle, the sun has returned to the same place it occupied with respect
to the nodes of the moon’s orbit when the cycle began. If an eclipse occurs
on a given day, then 18 years 11⅓ days later the sun, the moon, and the
nodes of the moon’s orbit return to nearly the same relationship, and the
eclipse occurs all over again.
Although the eclipse repeats almost exactly, it is not visible from the
same place on Earth. The Saros cycle is one-third of a day longer than 18
years 11 days. When the eclipse happens again, Earth will have rotated
one-third of a turn farther east, and the eclipse will occur one-third of
the way westward around Earth Figure 4. That means that after
three Saros cycles—a period of 54 years 1 month—the same eclipse occurs in
the same part of Earth.
graphic shows the path of solar eclipse over the surface of the earth over
the past 100 years.
While Figure 4 shows a few thin tracks
that are produced during a four year saros cycle, over a very long period of
time nearly the entire surface of the earth does experience an eclipse,