I am slowly slogging my way through this zombie thread. Awesome work, Predator! I love reading this stuff!
I am on page 15, poised to read the first technical essay and looking forward to it. But on the previous page was a discussion about the number of Excelcior ships. I understand it is probably bad form to bring up an old dead arguement but I can't help but adding a thought.
Using Geoffrey Mandel's Star Charts as a reference, I counted the total square sectors on the maps that were claimed to be Federation: about 53, 23 in alpha quad and 30 in Beta. I then estimated the depth of each sector by assuming it and its neighbors horizontally were representative of them vertically and got an average of 2.4 sectors tall. Rounding down to 50 and 2, respectively, that's about 100 sectors of Federation space. (A very rough estimate.) Assuming you want to have enough ships to patrol that volume of space such that any point may be accessed by just one ship by one days travel at warp 9, you would need about 8600 ships to patrol that volume. Reducing your speed to warp 8 requires 27,000.
And that's just to patrol the volume. Not to mention the places you're exploring or that a day away seems irresponsible in some sectors.
As someone else said, the scope of the Federation at TNG era is hard to fathom.
How I calculated: total volume devided by volume travelable.
total volume is the number of sectors times the cubic volume in light days of a sector: 100*(20*365)^3 cubic light days.
volume travelable is volume of a sphere with radius of one day at the given warp speed: ~(4/3)*(wf^(10/3))^3) cubic light days