Last weekend, I carried out an experiment to determine the exact position of the saddle for my newly built tenor ukulele.
The strings are D'Addario tenor, J71. I have no instruction manual or anything like that.
I use the side of my workbench as the "ukulele", on the left is one tuner hardware, then the nut (fixed), then 8.5 inch to the right is the "fret#12".
At 17" (my tenor uke scale length), I put a little empty can upside down (the "top") and a triangular section wood (as the floating bridge), at the right most side, one end of the string is attached there.
Then I string up one string at a time, tune it to pitch, then play the note at fret#12 (the only fret) and move the "floating bridge/saddle" until I got good intonation. I also make sure that the action at "fret#12" is 0.090 inch as that would be on the real instrument.
Then I wrote down the distance between fret#12 to the saddle, substract 8.5" from it and write down the number (compensation) on the envelope of this string. Here are what I got.
A and high G: ~ 1.5mm (I only measure one of them, not both as they are almost identical)
E: ~1mm
C: ~3mm
What this says is the center of the saddle has to be 1mm more than the scale length (from fret zero)
[CORRECTION: the edge of the saddle has to be ~ 0.5mm more than the scale length ]
My saddle is 3mm thick, so its center will be 2mm more than the scale length.
I will have room fine tune the saddle to meet the strings G / C and A compensation.
2mm is the exact number given to me by another member in this forum. I just double check with the strings I will use.