I suspect you will have to consider such criteria as:
1. The amount of data per object
2. The number of objects
3. The number of libraries
Had a similar question some time ago but never solve it accurately as the cartridge could easily hold all the data we wanted to save and an unique cartridge would be used for each save.
I also initialize the cartride each time before a save.
Best of luck
About the only way to find out is to regularly output lists of everything saved, then save more to the cartridge until it fills up. When you know how many objects were saved at the beginning and what their sizes were, you can start matching it up with how much was left over.
And then you should learn the methods used to store data on the medium and work out the relationships.
It used to be that tapefile block sizes would be a major determining factor. Along with that, the sizes of the objects and the number of objects could be used to make some general calculations. The block size was important because a large part of the tape was actually used to hold nothing -- blank areas of tape were between each block and between each object. These were <a href="http://www.freepatentsonline.com/3325796.html">inter-record (or inter-block) gaps</a> and could be significant in size compared to stretches of tape that actually had data recorded. The gaps were part of the logical mechanisms used by the tape drive to know when data was being read, where it started, where it ended.
If thousands of little objects were recorded, there'd be thousands of gaps. If a few large objects were recorded with large block sizes, there'd be very few gaps -- most of the tape would contain data rather than being blank. You could save a lot more bytes if objects were large and they were written in large blocks.
Further, inconsistencies in tape surfaces and simple wear would cause tape errors. Sections of tape would regularly be marked as unusable and skipped. IIRC, many skipped areas were fixed in length with different drives skipping different lengths. Each bad area would reduce remaining capacity.
More recently, helical scans, digital recording, very fine mechanical control of tape movement, etc., have been among advancements that have raised densities and reduced wasted tape area.
Capacities have gone up so far, so fast, that I haven't run across anyone who really seems to know how to estimate "remaining capacity".
So, only idea I have is to save a bunch of stuff, keep track of numbers and sizes, and then see how much more you can save. The pattern of object sizes and blocks at the beginning should eventually be a useful predictor of what stuff might be added at the end.