With all the tuning and tweaking, it quickly became apparent that the best way to calculate the size of the side bearings in particular would be to use a spreadsheet. Which leads me to a brief commercial for my day job.
I used to work for a company named Stellent, which is now owned by Oracle. I helped develop a piece of software called "Outside In HTML Export" which converts files from almost any file format into HTML. You may have unknowingly used it as we license it to a wide range of other software companies for use in their products. For example, I believe that Yahoo! mail uses my software to convert file attachments in e-mail so they can be seen in a web browser.
Anyway, here is my design spreadsheet converted into HTML by my software. To download the spreadsheet, right click on the link and choose "save as" to save the Excel file to your hard disk. Spreadsheets aren't well suited to long descriptions of what the various fields are. So here is a sheet by sheet description of what's going on.
Here are some quick links to the descriptions for the various pages.
| Vars | - Various design variables and constants. |
| CG | - Center of gravity of the scope. |
| Clearance | - Clearance of bottom of scope in rocker box. |
| Bearings | - Side bearing calculations. |
| Cage | - Secondary cage computations. |
| Truss | - Truss tube length computations. |
| f | Primary mirror's f-ratio |
| D | Diameter of primary mirror |
| F | Focal length of the mirror as measured by Swazy |
| Wood density | Used in center of gravity (CG) calculations |
| Aluminum density | Used in CG calculations |
| Bearing radius w/ Formica | This is where I tried out various values the bearing radius. Increasing the radius pushes back the center of gravity. It also makes the scope harder to move. |
| Mirror cell below bearings | My first impulse was to mount the side bearings so their bottom edge would be flush with the bottom of the mirror cell. Later I realized that by moving the bearings up I could push back the CG without increasing the size of the side bearings. This value was based on measurements from my cardboard model of the side bearings. |
| Bearing pad separation deg | Angle between Teflon pads for side bearings. Decreasing this angle makes the scope easier to move. |
| Side bearing arc deg | Bearing pad separation deg + 90 degrees so the scope can swing from the horizon to the zenith. |
| Setting circle clearance | Clearance needed for the mirror cell to clear the digital setting circle encoder in the rocker bottom for the azimuth axis. |
| Formica thickness | Not much, but I tried to account for this when calculating bearing sizes. Given the accuracy of my cuts, I really didn't need to bother. Mostly it reminded me that it was OK to round up the measurement of the Teflon to 1/4" as the Formica always rests on the Teflon. |
| Teflon thickness | The Teflon's thick enough to make the radius of the cut for the rocker box larger than the radius of the side bearings. I also took this into account in calculating the height of the rocker box and baseboard. |
| Veneer thickness | Not sure if I ever used this, but I had it if I needed it. |
| 3/4" wood thickness | Wood is always smaller than the size it is sold as being. I used this in CG calculations. |
| 1/2" wood thickness | Same as above. |
| 1/4" wood thickness | Never got around to measuring this so I just used 1/4" |
| Trunk height without hinges | The best case I had available for how tall a component could be and still fit in the trunk. |
| Trunk height below hinges | How tall I could make something and without having to worry about the hinges. |
| Trunk depth | Worst case value over the widths of the trunk given below. |
| Trunk width between hinges | If I could keep the components narrower than this width, I could use the "Trunk height without hinges" |
| Trunk width outside hinges | If I could avoid the trunk hinges, I could make the secondary cage/rocker box combo as wide as this. |
| Unknowns | |
| Various eyepiece weights | Used for CG calcs. In the end, I just used the weight of a Nagler 31mm as my worst case value. |
| 1/4" wood thickness | A reminder just in case I actually needed this later. |
| Constants | |
| gm/lb | Used for CG calcs. |
Finding the center of gravity (CG) of the telescope was required in order to determine the radius of the curve in the side bearings. To do this, Del showed me an old method airplane guys use to calculate CG.
Because some parts were not finished until late in the process, I put a lot of effort into calculating masses for many objects. Later when the part was ready, I would weigh it if possible. For the top end of the scope it was often easier to calculate distances relative to the bottom of the secondary cage or relative to the focuser. So I kept these values on this sheet in the G and H columns of the spreadsheet.
Here are some extra details on the various items that I considered when calculating CG. Note that the secondary cage values were based on the foam cage we were working on but that didn't work out. As it turns out, the replacement cage I made based on Kriege's plans was almost exactly the same weight as the foam cage. It was also very late in the construction process, so I just left this part of the spreadsheet alone.
| Bearings | I didn't feel like doing a calculus refresher to figure out the area of these (to compute the volume of wood and from there its mass). So I approximated this. By definition, the bearings are very close to the CG anyway, so errors here are not a big deal. |
| Mirror | Swazy provided this value for me. |
| Mirror cell | Only thing the mirror cell was missing when we weighed it were the collimation discs. I estimated where the CG of this was based on the weight of 1" square tubes and the weight of the sides. |
| Collimation discs | Del made some beautiful brass discs to act as the knobs to turn to adjust the primary mirror when doing collimation. |
| Truss connectors (lower) | These are the steel connectors used to attach the truss tubes to the mirror cell. |
| Truss tubes | 5/8" carbon fiber tubes. |
| Secondary cage | This is the foam cage. |
| Truss connectors (upper) | The original aluminum connectors to attach the truss tubes to the foam cage. We didn't have time to make these lighter so they are definitely on the heavy side. |
| Truss inserts (upper) | Aluminum wedges that were going to go into the upper truss connectors for the foam cage. |
| Secondary mirror w/ heater | Someday I will properly wire my secondary mirror dew heater. |
| Secondary holder | The holder for the secondary mirror, without the spider. Another case of my making the best guess I could for the distance due to the odd shape/CG of this part. |
| Spider w/ screws | Easy to measure, so doing this separately from the estimates of the distance for the secondary holder reduced the error in that guess. |
| Spider hard points | Again these were bigger than they should have been. |
| Focuser | Have I mentioned how much I love this focuser? |
| Nagler 31mm | Don't own one (yet). I figure this is likely to be the heaviest eyepiece I would ever get though, so I used it as the worst case eyepiece weight. |
| Paracor | For an f4.5 mirror, I really don't see a lot of coma. But I have the Paracor so use it. |
| Rigel finder | Lighter than a Telrad, but I miss the Telrad's 4 degree circle at times. |
| Outhouse baffle | This oddly named part comes from previous observing sessions with Del. At our favorite site at the time was Bong Recreation area in southeastern Wisconsin. At that location there is an outhouse with a bright light nearby. In an earlier experimental telescope, Del discovered that he needed something to block that light and thus the "outhouse baffle" was born. Basically though it is just a light shield extending above the secondary cage. |
| Secondary heater battery | The secondary heater uses a 9v battery. |
| Digital set circles or slop | I Velcro the computer for the digital setting circles to the cage. This value is probably a bit low. |
| Additional slop | A little extra weight for the future or to fix my mistakes. |
| Totals | Totals of the masses and moments. |
| Center of gravity | Center of gravity as measured from the bottom of the mirror cell in inches. |
| Cage weight | Total weight of all the stuff attached to the secondary cage including eyepieces and every thing. |
I knew that I would eventually want digital setting circles. One thing that worried me though was having enough clearance for the mirror cell to clear the azimuth encoder. So I did these calculations to make sure that there wouldn't be a problem.
| Digital Set Circles | This is the height of the encoder when it is installed. |
| Dip | The depth of the dip cut in the rocker box for the side bearings. |
| Mirror cell below corner | How far the corner of the mirror cell drops below dip. Because of the curve of the bearing and the way that corner of the mirror cell is clipped, this would have been very difficult math to do. So I used a cardboard model of the side bearing/mirror cell combination and measured this value. |
| Mirror below bearing | As mentioned elsewhere, I was able reduce the radius of the side bearings by mounting them above the bottom edge of the mirror cell. I didn't want to mount them too high because I feared that the triangle of bolts holding the bearings in place would turn into a line. Having some of the mirror cell below the bearings also stops the scope from sliding out of the rocker box. |
| Total | Total of all the distances above. |
| Rocker box sides | The total of the heights above must be less than this or crunch! |
| Slop remaining | The height of the rocker box sides - the total of the distances above. |
These are values related to the side bearings.
| Area | Area of the bearing estimated as the area of the largest triangle that can be drawn inside it. |
| Width of bearing | Width of the side bearings. |
| L (bearing) | Length of the bearing that is in the rocker box dip cut. |
| L (rocker box) | Length of the rocker box dip cut. |
| Dip (bearing) | How much of the bearing drops into the dip cut into the rocker box. |
| Dip (rocker box) | Depth of the dip cut into the rocker box sides for the bearings. |
| CG | Side bearing CG calcs. My memory of this is a bit fuzzy hence the poor descriptions. |
| X CG of triangle | Where CG is on the triangle. |
| X relative to radius | Adjusted to the radius of the bearing. |
| Angled X | Side bearing is mounted at an angle. |
| Dist from bot of scope | Moment arm for side bearings. |
The rest of this sheet shows how large a bearing radius I could cut in my 1" thick wood scraps. The math to calculate these values is described in the plans for the side bearings.
The top part of the sheet on the left side shows the calculation for "L" which is used in determining the size of the secondary mirror to use and is self explanatory. The next section shows some distances including the requirements for the cage height. The remainder of the left side is miscellaneous values that again are self explanatory.
The right side of the sheet is devoted to weights for the various eyepiece combinations.
These are the calculations to determine the length of the truss poles. I needed 3D coordinates for this. I pictured the telescope pointed straight up for this with up/down being the Z axis. The first section calculates "Z" which is the variable I used for distance from the top of the mirror cell to the bottom of the secondary cage.
| F | True focal length of the telescope according to Swazy. |
| L | Distance from center of the secondary mirror to eyepiece. |
| Light path inside cage | Distance from the bottom of the secondary cage to the center of the secondary mirror. |
| Cell above mirror | Distance from the top of the mirror to the top of the mirror cell. |
| Eyepiece adj | |
| Hasp block | Height of the wood hasp blocks. |
| Unadjusted Z | This is F minus all the other factors described above. |
The next section is distances on the X or Y axis. I was able to simplify the math a bit by putting the connect points on the mirror cell on a virtual box that is the same width as the widths of the connectors on the secondary cage. I did this by placing the truss tube centers 1/2" from the inside of the mirror cell.
| Std X or Y | The width of the virtual box divided by 2 (from the corner to the center). |
| Cage connection | The truss tubes connect to the secondary cage at wood connector blocks. This is the distance between the centers of the bolts connecting the truss tubes to the block divided by two. |
| Unadjusted X or Y | The first row minus the second. |
The pegs on each end of the truss tubes extend beyond the tubes a bit. The next section shows the amount to subtract from the computed tube length to account for this.
The final section shows the actual calculations. The "back" connectors in this case are the ones that attach to the side bearings. "Left" and "right" are then based on looking at the "front" of the mirror cell. The column heading meanings are as follows:
| X or Y | Additional adjustments to X and Y for the connector block. |
| Z | Additional adjustment to Z for the connector. |
| Total X or Y | Final X and Y distance after all adjustments. |
| Total Z | Final Z distance after all adjustments. |
| Len (raw) | Square root of [(X or Y) squared + Z squared] |
| Len (adj). | The raw length minus the adjustments for the connector pegs. |
| Angle | The angle that the truss tubes are at. I didn't actually use this for anything in the end. |
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Last updated 11/15/23