This picture illustrates the meanings of some of the
variables related to the side bearings. The dark region represents
the actual side bearing. The lighter gray area is the piece of a
semicircle one would remove to make it into a side bearing. There are
many times when it was important to think of the side bearing related
to how things would have worked if I were using a full semicircle. The
following variables and equations were also used to calculate bearing
size:
x = Thickness of Formica L = Length of dip in rocker box r = radius of bearings D = Dip in rocker box θ = Angle covered by side bearing. s = Angle of separation between Teflon pads L = (sin(s/2)) * (r + x) * 2 D = (1 - cos(s/2)) * (r + x)θ = s + 90 degrees (to go from zenith to horizon)
Here are some general notes from Kriege I kept in mind during the design process:
Note the symmetry of the last two items on this list. I was able to move the Teflon pads closer together to balance out the loss of friction caused by making my bearing radius larger than suggested.
I made my bearings out of wood left over after I cut my ground board out of the half sheets of 1/4" and 3/4" Baltic Birch I glued together to make it an inch thick. The resulting pieces were 11" wide so I wanted to figure out the largest radius I would have available to me for various spacings of the Teflon pads - and corresponding values of θ.
Max θ/2 = ArcCos(1 - 11"/r)
From this I generated the following table of maximum radius values based on various values of θ.
| θ | Maximum "r" |
|---|---|
| 160 degrees | 13.31" |
| 155 degrees | 14.03" |
| 150 degrees | 14.84" |
| 145 degrees | 15.73" |
One of the nice things about the design of this scope was that I could correct balance issues by tuning the size of the side bearings. Remember that the point that the scope is balanced on is at the center point of the circles the bearings are cut from. If the center of gravity of the scope is not at that center point, then the scope will be top or bottom heavy and tend to tip over.
Because the bearings had to attach to the mirror cell, the bottom edge of the bearings was going to be near the bottom of the mirror cell. This means that as I made the diameter of the side bearings larger, the center point of the bearings and hence the center of gravity (CG) is pushed up towards the secondary cage and the scope becomes more bottom heavy. This in turn meant that before I could cut the side bearings, I needed to finish work on the mirror cell and secondary cage so I knew how much each end would weigh. See the design spreadsheet for more information on how I calculated the center of gravity and from it the bearing sizes.
I was able to make the bearings slightly smaller (and lighter) by mounting them 3/4" above the bottom of the mirror cell. This pushed up the CG, making the bearings in effect 3/4" larger in radius for the purposes of CG calculations. I wasn't able to push the bearings up any further though or the mirror cell wouldn't clear the bottom of the rocker box as the scope rocked up or down. More specifically, it wouldn't clear the top of the azimuth encoder for the digital setting circles.
The scope was made as light as is reasonably possible. Special attention was paid to making the top end light of course. The bearings are also slightly bigger than they should be to make the scope slightly tail heavy. This means that extra weight may be added to the front of the scope in the future if necessary. By design, the balance allows the use of a Paracor and 31mm Nagler at the same time.
In the field, small bags of lead shot are used to tune the balance. There's sufficient friction in the bearings that tipping doesn't become a problem as long as I am within a pound or so of the proper weight on the cage end. There is also enough friction to prevent the scope from tipping upwards on its own as I am changing eyepieces.
In the future if a new toy causes the scope to become top heavy, two fixes are available. The first would be to use springs to pull the scope back into balance. The other, rather brute force method, is to lug around 5 pounds of weight to put on the back end of the scope to balance out each pound of weight stuck on the front.
The original plans for the rocker bearings included a brace between the bearings to keep them from racking when the scope is turned. Del told me one wouldn't be needed though and final assembly most definitely proved him right. There is zero wobble.
It is a mathematical coincidence that my side bearings are mounted at a 45 degree angle. In the final design, the bearing pads are 65 degrees apart. That meant that my side bearings covered 90+65=155 degrees - or 25 degrees less than 180 degrees. Everything else more or less follows from there. My original, incorrect math had them at a different angle. Fortunately the error was so large that it was evident in the shop before we started cutting. Of course cutting had to halt while I worked out the right angle. Here's how I did it.
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Last updated 1/12/06