Im going to go with what ever the width of the side panel holder door is so i can slide that sise disc lieing flat with a couple chocker cables and some 16 in pieces of cold roll stock so maybe 18 to 20 inch disc and dont forget your round point shovel (very handy for many other things to have on your trucks)
The problem with a disc, is connecting to the center WITHOUT a rigid lever arm, means that it will need to be buried completely with a channel down to the disc center.
Even then that is no guarantee. since it can pivot where you attach to it, it may push up the soil above the pivot(path of least resistance) and as soon as it tilts past vertical it will slide up out of the hole.
There is a fairly easy way to attach a lever(t rod thru center with a chain from top of T to top edge of disc to hold it at a dig-in angle).
I dont see a disc wanting to dig in by itself in anything but sand though. Thats where the ground grabber or danforth anchor design has an edge. Basically self digging, and only go as deep as they need to. The ground grabber can be made flat, a danforth anchor is already flat. You can also easilly daisy chain them...