Suerrier Truss Again

Suerrier Truss Again

I can't find a formula that exactly does the job, but I can use a worst case scenario to solve my problem, I think.

Unlike the current design for Big Bertha 2.0, where the load is about 1/4 of the way up the channel that is the primary support, here the deflection on the tubes that position the upper optical cage is just its weight on the end of the round tubes. For a single round tube, the worst loading will be gravity pulling the upper optical cage when the telescope is horizontal. (This is a position that it isn't in very often.)

There are a total of six tubes in a typical Suerrier truss, but I'll do the math here for a single tube holding the force. The reason is that this is by far the worst case--so whatever I come up with for an answer will be more than adequate.

The deflection for a beam supported at one end with a force at the other end is computed by the formula:

D=FL^3/3EI

where D = deflection
F = force
L = length
E = Young's modulus for the beam
I = moment of inertia for the beam

The moment of inertia (or second moment of area) for a tube is calculated by the formula:

I = pi/4 * (RO ^4 - RI^ 4)

where RO = outside radius of the tube and RI = inside radius of the tube

For the 1" OD, .050" wall aluminum tubes that Moonlite Telescope Accessories sells, I = 1.12 x 10-7.

For aluminum, E is approximately 70 gigapascals. For my application, I need 62 inch long tubes, so that I can use the existing bolt holes for the square tubes that I am currently using. (If I went a bit shorter, it would reduce deflection very slightly, but put a bunch of unsightly holes in the lower cage.)

I'm assuming that the entire ten pound load of the upper cage (including possibly having a camera in the eyepiece focuser) is carried on one tube. Converting everything to metric, this gives us a length of 1.57 meters, a force of 4.55 kg, and a worst case deflection with the telescope horizontal of .00075 meters, or about .03" inches. In practice, with six tubes carrying the load, and the upper cage providing additional stiffness, I suspect that I will get down into the thousandths of an inch of deflection.

Here's where it gets a little more tricky. While each tube by itself only weighs 0.41 kg (because they are hollow), six of them gets the weight up to 2.46 kg, or a bit under five and a half pounds. My goal was to knock at least ten pounds off the weight of the scope, by removing the square tubes, the turnbuckles, the guy wires, and most of the aluminum channel that provides both the mounting base for the telescope, and the bottom stiffness member. That aluminum channel right now weighs 10.22 pounds; cutting most of it away, so that it only connects the lower cage to the saddle for the mount, knocks off 6.25 pounds. Losing the turnbuckles and guy wires probably gets me another pound. Losing the two square aluminum tubes gets me another 0.44 pounds--so perhaps this would gain me about two pounds--hardly worth the effort.

A couple of possibilities:

1. Skeletonize the aluminum channel to reduce weight, since even it flexes slightly, that doesn't matter much--the upper and lower cages will be rigid relative to each other, and that's what matters.

2. Find some way to reduce the number of tubes, since it looks like one is barely sufficiently.

3. Use carbon fiber composite tubes. These are about three times as stiff, and even at the same size, about 1/2 the weight. There are commercial sources for carbon fiber composite tubes of these dimensions, and instead of five pounds, we're talking 2.5 pounds. Or look for some way to use even smaller carbon fiber composite tubes instead to get the same stiffness as aluminum, and get the weight down to perhaps 1.5 pounds. (And the price of carbon fiber composite tubes is such that going smaller both saves money, and increases the number of suppliers.) Unfortunately, as you shrink the diameter of the tubes, the stiffness declines rapidly, so you can't really go below 0.75" outside diameter--and that takes away much of the weight savings.

The temptation is to look at ways to replace that aluminum channel completely--and this might be a place where using carbon fiber composite could be most cost effective--if I could find an off the shelf carbon fiber composite channel of the right dimensions.

UPDATE: Here's a supplier of carbon fiber composite tubes that are small enough that they would probably give me the right stiffness, and would only weigh .24 pounds for all six. My concern is that the deflection for one tube would .1". If the load was evenly distributed, that would be .016" deflection--just barely acceptable. And they have carbon fiber channel--at a typical hefty price.

UPDATE 2: Yet another possibility is to remove the aluminum channel completely, and replace it with a a cradle that supports the lower cage where it needs to be supported--but is otherwise flat. The reasons for the channel were:

1. Stiffness.

2. To prevent the lower cage from rocking back and forth.

If the Suerrier truss provides all the stiffness, I can start with a flat piece of aluminum, and add some supports where the lower cage will be. (If I had a big vertical mill, I would start with a 1/2" thick piece of aluminum, and mill away everything else!)

I also notice that DragonPlate is quoting 138 gigapascals for the Young's modulus for their carbon fiber. I've had to adjust my calculations accordingly.

UPDATE 3: I took a nap this evening--hence, I'm full of energy late into the evening. If I dispense with the aluminum channel completely, I could use a 4" wide, 1/4" thick, 24" long piece of aluminum to tie the lower cage to the mounting plate. This would give me a half pound where I currently have more than ten pounds, and a maximum deflection of about .02"--in a place where that's a completely acceptable deflection, since it is outside the optical axis of the scope.

In combination with the other proposed changes above, using aluminum tubes, I could get it down by about six pounds. If I can find 1", .050" wall carbon fiber tubes at least 62" long, I can get the weight down by eleven pounds--so the whole telescope assembly would probably weigh about 45-47 pounds--light enough that the current mount should be sufficient. Of course, the price of the 1" carbon fiber tubes is horrifying. Finding them long enough is also a problem, but these splices let you epoxy shorter pieces together, and keeping the stiffness of the individual pieces.