I have found free software (GRAPE - Graphic Real-Time Analysis Programs for Engineering) that may turn out to be very useful for the ATM...and in this example I'm learning to push the envelope of this software.
Although I do not plan to use a 'typical' rocker box in my next project, many ATM's will continue to do so. That is all well and good if your telescope is not too large, too heavy, or the rocker box bottom is too thin/flimsy. I can't specify size/weight limits here...it depends on your tolerance for flexure in your particular scope. However, I do remember one 36 inch scope I had the privelege of looking through. Considering how it behaved in light breezes...I'd say that it was not stiff enough in several areas, and one of them might have been the bottom of the rocker box.
In the typical amatuer dobsonian, a square rocker box pivots over a ground board. The ground board typically has three feet resting on the ground, and directly over these three feet are teflon pads (or roller bearings in motorized dobs) to support the bottom of the rocker box. The square rocker box bottom rests on these three bearings. See this book, chapter ten, especially figure 10.6 and associated discussion. Note that you can space/arrange the three ground board feet and ground board bearings so that in many cases the rocker box bottom contacts them near the (stiff, reinforced) edge...but not in all cases/orientations. And that's where a problem may crop up with larger and larger dobsonians.
So, let's look at how a rocker box can flex under load. You can consider it a plate that is constrained/stiffened a good deal by the sides of the rocker box. So then, to keep the model simple, we can model a 'square drumhead' with a truss, using points arrayed in a triangular fashion, and all edge nodes 'fixed' in XYZ space.
Here is the initial set up of my model of a rocker box bottom. I have placed loads at three locations...representing the typical locations of loads on the rocker box bottom from the ground board bearings. I have intentionally chosen the worst case, from a flexure standpoint. The loads at nodes 235, 445, and 446 are located as far as possible from the fixed/constrained/rigid edge, which happens when the corner of the rocker box's bottom, the ground board bearing, and the center of the rocker box all lie on the same line. Note that the other two sets of loaded nodes (8, 9, and 30...and...188, 189, and 420) are very close to the extreme edge of the rocker box bottom. They will not deflect the bottom of the rocker box anywhere near as much as the load at nodes 235, 445, and 446. (Note. I have put loads on three nodes that 'surround' the location of the center of the ground board bearing. This helps prevent an overly 'spiky' result with GRAPE.)
Here is the result of analysis by GRAPE. The Z axis scale has been greatly exaggerated to more easily show the resulting deformation and countour. How much flexure will your scope suffer in this manner? It depends on many things. How thick is your rocker box bottom? How wide is it? What material did you use? Did you place the ground board feet as wide as possible, so that (most of the time) they are contacting the rocker box near it's edges? This type of flexure causes two problems. First, it causes your scope to 'droop' different amounts, depending on its orientation in azimuth. Depending on your desired pointing accuracy with motors and digital setting circles, this could be a problem. Second, this flexure means your mount is not stiff. Less stiff scopes will deviate more in a breeze, and will have a lower frequency of oscillation...which means oscillations will tend to die out slower compared to a stiffer mount.
Here is the same analysis, with a slightly different view angle.
Is this GRAPE analysis accurate? I do not yet know. This is a pretty complex problem...kinda hard to crank out by hand for comparison. Maybe I can find some other software against which I can compare results. That will not give me absolute confidence, but at least I'll have a warm feeling that I am not grossly wrong in this analysis.
This particular example has 504 nodes and 1423 elements. It consumes about 26 Meg of memory for the mesh analysis, which takes about 11 minutes on my 800 Mhz Pentium. GRAPE can analyze up to 4096 nodes and 4096 elements.
New analysis from Tony Owens
Tonly uses a commercial FEA (finite element analysis) package, and provides the following analysis for a rocker box setup, using 3/4 inch plywood for the rocker box bottom, for an 18 inch telescope, with the OTA weight at 30 kilograms (approx. 66 pounds). His results are important, especially if you want accurate pointing in a motorized dobsonian telescope. It is wise to pay attention to rocker box flexure.
I have set up a multivariate FE analysis based on a base case consisting of a notional 18" aperture OTA (weighing 30kg) riding on a 3/4 inch Baltic birch ply rocker, supported by three foot pads. The really interesting thing I'm seeing, is not so much the out-of-plane deflections of the underside of the rocker (though that happens, of course) - but rather the effect of azimuthal rotation on the positions of the alt trunnion bearings! I think this is quite an important finding for anyone interested in accurate pointing. The key question is how the coordinate system defining the center of the OTA undergoes angular shift as the scope swings about in azimuth (see the first picture below for the coordinate system). My initial results show a cyclic variation of 17 arcmins in altitude and 2 arcmins in azimuth, as the scope rotates in azimuth on its foot pads - purely due to rocker flex!
This overall view shows the rocker box, supporting a notional OTA, and also defines the telescope coordinate system that Tony mentions above.
This view shows the deflection of the rocker box bottom from the side.
This view shows the deflection of the rocker box bottom from the top.
All feedback is encouraged!
email: t-k-r-a-j-c-i-@-s-a-n-.-o-s-d-.-m-i-l (remove the dashes)
Last update: 17 Feb 2003