Friday, May 18, 2007

Carbon Fiber Composite

I've been looking at aluminum square tubing for Big Bertha's rebuild--but I'm running into some interesting issues. I would prefer to use two square tubes on opposite sides of the optical components, primarily because it makes it easier to mount it in a Dobsonian mounting as a short term strategy.

There's also a cost issue. One 4" square tube (which is as light as I can go if I only use one tube) gives a deflection of .00053", which I consider sufficient for my purposes. But that one 4" tube is substantially more expensive than two 3" tubes would be--and the two 3" tubes gives a deflection of .00068", assuming that the stiffness is additive.

I'm told by a PhD in Mechanical Engineering that using two tubes on opposite sides of the optical components, as long as everything is firmly attached at both ends, will give a stiffness that is quite a bit more than the sum of each tube, because you are effectively creating an I-beam. But how much stiffer than the sum of two tubes is that? I'm not sure.

Anyway, I'm looking at carbon fiber composite. I see figures for its modulus of elasticity quoted of 33 million pounds per square inch, or about 220 gigapascals--more than three times stiffer than aluminum or steel. At the same time, it is far lighter than aluminum. Unfortunately, while there are a lot of vendors of carbon fiber composite tubes, all that I am finding seem to be aimed at the bicycle enthusiast, so no square tubes, and finding one that is 72" is also difficult. (Perhaps I should check with whoever makes racing bicycles for the Jolly Green Giant.) Any suggestions on where I might find 2" square tubing made of this miraculous material?

UPDATE: It turns out that the formula for computing the stiffness of an I-beam is described here. You compute the moment of inertia based on the cross-section of the flanges (the top and bottom horizontal strokes of the "I"), a factor that includes the height of the vertical member (and that gets squared), and a third factor that multiples the width of the bottom flange by the height of the vertical member--and then raises it to the third power. If I regard the two aluminum hexagons that will sit between the tubes as effectively a very tall, very wide vertical member, then the combination will be very stiff indeed. Unlike a conventional I-beam, the two hexagonal members are many times wider and taller than the flanges (although not full length). Best of all, because they are effectively round, unlike an I-beam, which is much stiffer vertically than horizontally (because of that cubed factor on the height of the vertical member), there should not be an enormous difference in stiffness of the telescope depending on whether the tubes are vertical or horizontal.

I haven't tried to calculate the deflection of the combination, but I suspect that having these hexagonal structures between will enhance stiffness quite impressively. It also argues for going a little stiffer on the hexagons, so that I can go a bit thinner on the tubes.

No comments:

Post a Comment