I'm working on building a custom 8' long desk using the Ikea "Karlby" countertop in walnut. I'm planning to put hairpin legs on each of the four corners, but since the span of the desk is so long, I know I will need some sort of support in the center to prevent the desk from sagging.
The simplest option is just to add 2 legs in the center of the desk, one in the front and one in the rear, which I think should be sufficient to prevent sagging (I don't think the countertop will sag over a 4' span). However, I'd like to avoid having a leg in the front center, as that limits the space available under the desk (I can't roll between workspaces under the desk). My solution would be to only place a leg in the rear of the desk, but I am worried that that will not provide enough support along the front edge (e.g. when I lean on the desk).
The other option I considered was to use angle irons to support the span. I was considering using a set up depicted in the quick sketch below, with an angle iron in both the front and the rear, spanning between the legs. In the front, the angle iron would hang beneath the desk, and in the rear, the angle iron would hug the back edge of the desk. The angle irons would rest directly on the legs (under the desk). However, after a lot of research (and some very amateur calculations), I'm not certain whether 1.5" angle irons would really provide enough rigidity across an 8' span. I'm hesitant to move up to 2" angles, since that will negatively affect the space under the desk (the angle will hang down into the leg space), and I'm still not certain that they will provide enough rigidity.
Any thoughts on this configuration, or the best way to support this desk without impacting usable space?
Edit: To make the scope of this question a little narrower, can anyone help me with calculating the max load and deflection of a steel 1.5" angle iron (1/8" thickness) over an 8' span? That will help validate whether my design will fit normal use.