## Monday, April 9, 2012

### Calculating Moment of Inertia Widget

One of the most annoying aspects of doing deflection calculations for C-channels is that the moment of inertia is a pretty complicated formula, and even worse, the moment of inertia is different depending on whether the C-channel is pointing upward or sideways.  I was therefore pleased to find this calculator that computes the moment of inertia in both directions.

Now that I am temporarily free of teaching classes and not busily writing law review articles, I have time to return to the Big Bertha 3.0 rebuild.  My initial calculations of using aluminum tubes to construct a half-Serrurier truss (sometimes called a simple truss) indicates that I am not going to save more than three our four pounds off the current design--and that's not enough gain to justify the effort.

I have thought of trimming the 4" x 2" aluminum channel on which the telescope is mounted.  One possibility was to trim the walls from 2" high to 0.5" high--which would knock off many pounds, but at the cost of substantial stiffness.  The other possibility was to put lightening holes in the 4" wide part, reducing the weight with little reduction in stiffness--but again, the weight loss wasn't worth the work.

I am still playing with the calculations, but it is now looking like the solution may be to go half-Serrurier truss using 0.5" OD graphite composite tubes (which gives me better stiffness than the aluminum, and much less weight), and replacing the 11 pound aluminum C-channel which runs the whole length of the telescope with a 24" long graphite composite C-channel like this to support the mirror end of the telescope to the dovetail that goes into the mount saddle.   This is comparable stiffness to the aluminum, with a fraction of the weight (both because of less material, and just over half the density of aluminum).

Currently, there is 26" from the mirror end of the aluminum C-channel to the top of the dovetail plate, but removing the aluminum C-channel will knock 7-8 pounds off the weight of the telescope, most of it above the dovetail plate.  I am quite sure that the balance point will still let me do this.  In addition, I may move the graphite C-channel up a couple of inches, both to make sure that the mounting point for the truss tubes doesn't interfere with it, and to improve the balance point.