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Continue balance springs testing, fabricate tellurion Earth globe  - September 2016


Here are two screen shots of the first spring adjustment tests. The first rate of gaining 18.8sec/day was with the springs stretched as far as possible. The second step was with the springs relaxed by 1mm on both vernier scales which gave us a losing rate of 18.8sec/day. The scale was set at a random position, so Buchanan adjusted the graph to position the two rates as seen in the first screen shot photo. So to get a theoretically correct rate he should halve the adjustment he had just made. This required a tensioning of the springs by 1/2mm. He then made the adjustment and the new rate is as seen in the next screen shot photo. So one mm release of the springs gives us 37.6sec day change. So one division on the vernier will give us a change of 3.6 sec/day or 26.3 sec/week, and 1mm adjustment will give us a 4.38 minute/week change This is with springs that give us a 1.32 instead of a 2 second tick  This is a reasonable adjustment for rating the clock when it is running  Next we will see what it does to the isochronism. Unfortunately the construction of the clock is such, that, we have in reality, about 4mm total adjustment.  He doesn't think that it will make that much difference to the isochronism, as he agrees with what Mr. Drumheller wrote below, that most of the error comes from the escapement.

Mr. Drumheller wrote: If we ignore the amplitude change in your plots, you’ve just shown that simultaneously stretching all of the springs by 1 mm increases their average stiffness by 0.04%. This seems to be a neat way to fine adjust the rate of the clock. Now you should note that as the balances swing two of springs are stretched an additional amount while the other two contract. Thus the stiffness of two of the springs undergoes an additional increase while the other two decrease. I suspect the net change due to the swing will add to zero. That suggests the spring nonlinearity you’ve just measured will not affect the isochronism.

It will be interesting to see just how temperature stable this alloy is. The Harrison balance is interesting in that its beat time is only sensitive to the change in stiffness of the spring. It is not sensitive to the thermal expansion of the balances because both the balance inertia and the restoring torque change proportionally so as to offset one another and not affect the rate. Your test data may yield the most accurate measurement of the temperature stability of this alloy that has even been made.

Buchanan replies: You say: The Harrison balance is interesting in that its beat time is only sensitive to the change in stiffness of the spring. It is not sensitive to the thermal expansion of the balances because both the balance inertia and the restoring torque change proportionally so as to offset one another and not affect the rate.”  Is this because the point,  where the spring is attached,  moves away from the center of the balance, so the spring has more ‘leverage’ to overcome the extra inertia due the weights also moving away from the center of the balance. Would this make the ratio between the distance from the center of the balance to the spring attachment point and the distance from the center of the balance to the center of mass  critical. If this could be made adjustable then could one ‘tune’ the balance to compensate for any residual temperature error?

Mr. Drumheller replies: Yeah! Frankly, I’ve noticed that you seem to have a knack for this kind of stuff! There’s a few additional tricks I’ve had to add to this idea, but I’m building it as we speak to see if it compensates my replica.

Now Buchanan has received the Elinvar-type wire. It is actually Ni-Span-C alloy 902. a nickel-iron-chromium-titanium alloy made precipitation (42%, 47%, 5.25%, 2.5% plus several other trace elements), hardenable by additions of aluminum and titanium. The titanium content also helps provide a controllable thermoelastic coefficient, which is the alloy's outstanding characteristic. The alloy can be processed to have a constant modulus of elasticity at temperatures from -50F to 150F (-45 to 65C). That makes it ideal in the use of precision springs and is similar to the alloy Elinvar used in watch balance hair springs, and is exactly what is needed for this application giving the pendulums isochronism.

The conversation below refers to the data sheet that came with the wire.

Buchanan writes: The heat treatment looks interesting. I have attached a data sheet on Ni-Span-C if you read it you will be as much of a Ni-Span-C expert as I am! I aim to carry out tests on extension/force, as I did on the original springs, but at different temperatures, on both carbon steel springs and Ni-Span-C springs. Mr, Drumheller, would you know what force change per degree I would expect. I understand principals, but my maths is poor as when at school I had bad attitude as well as a bad teacher in a critical year. Buchanan is funny!

 Mr. Drumheller relies: The temperature error of my replica is about dt = 7.3 s per day per deg F. There are t = 86400 s per day. Thus the ratio dt/t = 7.3/86400 = .0000844 = 84e-6 /deg F.

The thermo elastic coefficient in the PDF article is defined to be dE / E, which is the change in the Elastic Modulus divided by the Elastic Modulus itself. In our clocks we need to know the change in the Shear Modulus dG divided by the Shear Modulus G itself. In Figure 2 they mix the data for both these parameters together. The bending tests measure dE/E and the torsion tests measure dG/G. I’m not sure they understand this issue.

For our clocks I have derived the very interesting result that dG/G = 2 x dt/t. Thus based on the value of the temperature error that I have measured the thermo elastic coefficient for the wire I used in the replica is dG/G = 168 e-6.  Notice that this value is similar to the larger values that they have seen in many of the iron-nickel alloys shown in Figure 1. Figure 2 indicates that you should see values of dG/G that are about 10 to 100 times smaller. That corresponds to temperature errors in your clock of 0.73 s per day per deg F  to 73 milliseconds per day per deg F. The lower values that they report are obtained from a torsional pendulum test. If the wire in that test was subjected to a twisting oscillation of 1 Hz, that would be very similar to the twisting action in your clock springs because indeed the wire in a helical spring is twisted and not bent.


Figure 1 and Figure 2.


The Ni-Span wire as received and Buchanan begins trialling springs. Buchanan writes: I have been trialling springs. The paper shows the tension readings for each diameter or material. I have installed the last test spring. The 1mm Ni-Span-C is rather too stiff so I have to have a 1.85 inch diameter spring to get a 4.08 second beat. These interfere with the centre adjusters so I removed them and fitted a wire link between the springs. The springs have become rather heavy now, I will send a video of the clock running and you will see the sag when the springs are relaxed. The timer is running and as soon as the clock is stabilised I will up the temperature and see what happens.  


The last photo shows a fairly steady rate over a temperature swing of nearly ten degrees. It looks like the invar springs are going to go a long way towards correcting for temperature error. I asked about the error introduced by the physical changes to the pendulum balances, which is as temperature increases will tend to become longer. With the Ni-Span springs in place and assuming the stiffness of the springs do not change, the small additional restorative forces (torque) of the springs due to the fact that the distance from where they are connected to the top of the pendulum to where they are anchored to the vernier on the clock frame is slightly further apart as the pendulums expand, will compensate for the thermal expansion of the pendulums. Imagine the joy Harrison would have had if he could have eliminated the complicated, multiple grid iron compensation system on H1 with the simple substitution of a nifty set of Ni-Span springs!

Buchanan now turns to the fabrication of the Earth globe in the tellurion.


We explored a number of designs for the Earth globe. This besides the Sun is the largest planetary body represented in any the celestial displays, (we still have an orrery to complete). So it will command special attention. I wanted it to be immediately recognizable as the Earth so a natural stone analogy would not work. There are globes commercially made from stone mosaic but these need to be much larger than our 1.3” (3 cm) diameter to get the detail necessary. We will, however, be using semiprecious stone spheres for the remaining planetary bodies as well as the Sun in both the tellurion and future orrery. The current Earth, Sun and other planets as seen up to this point are still mockups. These two photos show the Earth globe modeled on the computer, the South American Andes mountain range is clearly visible.


I wanted the Earth globe to have a special look. I have always admired the quality of walrus and ivory scrimshaw artwork. Scrimshaw allows the artist to create a very detailed design on the bone surface and when dyed with black tea or ink creates a beautiful effect. Since ivory importation has been banned in many countries as well as this machine’s ultimate destination, we had to use an alternate material. Walrus was the first choice, but it was too difficult to find a piece of walrus tusk large enough to obtain the piece we needed. One must remember that these are natural materials and often have cracks and other imperfections around the perimeter reaching inward. One needs a large cross section of material to get a perfect area at the heart of the tusk to obtain a flawless piece. This is especially true with Mammoth ivory since it is very old and so is prone to greater cracking. Any imperfections would be picked up in the dying process after the scrimshaw had been completed. The first photo shows the Mammoth ivory piece we used. One can see how large it needed to be to get the perfect rough blank. Mammoth also has a nice patina with natural growth markings, just the look I wanted. There is enough material left over for us to use elsewhere for winding handles. Another feature that Mammoth afforded was the ability to create land features on the globe. From the beginning we decided against political boundaries. First these are simply too complicated for a globe of this size and second these will change throughout the life of the machine. But we could outline the land masses as well as adding longitude and latitude lines. This material also allows one to carve the piece in relief to illustrate the various continental mountain ranges; another departure from the standard smooth Earth globe found on other tellurians, especially at this scale. Mammoth also yields easily to the cutting tool and is not brittle, so an accurate model could be produced.


The ivory blank is mounted into the mill and begins to take shape. Here again is one of the few but absolutely necessary areas where a computer designed and manufactured process is employed. If we had gone with a smooth globe a normal machining process could have been used. But to get the continental land mass reliefs coupled with perfect spherical areas for the oceans would have been very difficult to achieve otherwise. Buchanan had practiced on several plastic test pieces prior to the final material. The tool will travel nearly 300 meters to complete the job. One other advantage to this material is the fact that it is soft enough that cutting fluid is not needed to cool the tool thus avoiding the contamination that would happen if one used stone where the fluid would infiltrate into the rough-cut surfaces. Still the machining took two days.


The video below shows the early steps in the machining process.  After the machining process is complete, the machine tool marks had to be smoothed out by hand. The entire globe took an additional two days to be finished off and polished by hand.

Buchanan writes: I will just take a quick course on scrimshaw and the globe should be finished by lunch time. The machining went well. I am now removing all machine ridges with gravers. Then I will outline the continents and then ink the outlines. Then onto the lathe with the ball turning attachment and protractors I will add the latitude and longitude lines. Have you thought about the spacing of the degree lines? I thought of 24 longitude lines, each representing an hour. Then for latitude something equally spaced with darker lines for the equator, topics and arctic circle. Also darker for Greenwich meridian. Also thought of two solid gold pins (Major Expense) for Chicago and Moss vale where it was made. These would be 12 thou in diameter. Real small, just a speck.



The globe surface with its final polish and the beginnings of the continental outlines inked in. The process is slow, first the outline in pencil, then engrave, then the ink then repeat for another one-half inch of coast line.


These two photos show the scrimshaw process for cutting the latitude and longitude lines. Notice the two protractor scales attached to the tooling used to rotate the globe and move the cutter. This gives an accurate positioning of both the globe and cutter in the X-Y axis for perfectly accurate lines.



The finished globe is ready for installation into the tellurion. We decided to go with the standard twenty-four for latitude lines, but Buchanan, wisely, chose not to put all of the longitude lines, it would have been too distracting from the geography depicted on the globe’s surface.  


In the first photo Buchanan drills out the brass mount used up to this point to hold the globe during the prior machining processes. Next is the initial fitting of the globe within the globe longitude ring. Notice how Mt. Everest barely clears the ring! This photo really shows off the exaggerated topography of the globe. Here is where the use of computer aided design and machining produced a superior result, one that would have been very difficult to reproduce accurately by hand and sets this globe apart from others.


Buchanan now inserts a gold speck at the location of Chicago, USA and Moss Vale, Australia. If one looks closely at the North American continent there is something missing and very important to the city of Chicago, the Great Lakes. Chicago sits astride Lake Michigan the fifth largest body of fresh water in the world.


The first photo shows a new, heavier counterbalance that was needed because the Mammoth ivory is considerably heavier than the aluminum mockup globe. To reduce this heavier look a lead insert within the sickle structure was needed. In the second photo the final profile of the sickle is much reduced. Note how neat and tidy the lead insert is.

Look, the great lakes have appeared and Chicago now has its beautiful lakefront! Also note the pair of sun and moon horizon arc-markers as well as the detail engraving on the longitude, latitude and ecliptic rings. Below reside the synodic and sidereal month dials, and in the background the eclipse dials. As you look over the remaining photos note the incredible detail, complexity and the numerous (nine) complications that are incorporated into these three inches (7 cm) of volume. These mechanical, design and artistic skills are repeated hundreds of times within the six cubic feet ( 0.16 cubic meter) volume of the entire machine. 

The gold pin for Moss Vale can be seen just below the lower horizontal ring.


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