It is a small application to compute information such as length, time, tape pack, and tape thickness using known elements such as hub sizes, tape speeds, thicknesses, and lengths.
I was curious as to how I would mathematically model the non-linear phenomenon of tape reels in order to visually simulate graphically, the angular velocity of reels as they were running on a tape deck.
Once I knew the thickness of the tape pack, I would have the correct radius for the angular velocity of the reel for at least one revolution. Because every revolution of the reel will change the pack radius as the tape spools, the angular velocity will be constantly changing.
Later I found other uses for this math. For instance, when I'm making recordings off the radio, I liked to maximize the space I used on the tape but I was never sure how much time I had left as I was never monitoring how long the recording sessions had been going.
So I applied the math to determine how much tape I had left based on the pack size, tape thickness, and hub size. Since most reels had standard sized hubs, and I would use a good ruler to measure the tape pack within fractions of 1/64th of an inch, I was able to get a great estimate of the time I had left within about ~1 min +/- a few seconds on average. I could have gotten more accuracy using a caliper but even then, sometimes the variance was due to the slight differences in the hub sizes which would affect the end result. Also, this assumes there was no leader tape spliced on the ends.
I never did determine the thickness of leader tapes, but anyone with a good caliper could easily measure them or take a known length of leader, measure its pack size, and manually adjust the thickness until the numbers lined up. I used this technique to determine some of the tape thickness were I couldn't find the manufacturer specifications.
Another use I found was determining the exact lengths of tape I could get away with spooling on reels from pancakes. Also, I could use it to plan the best reel to fit the recording I had. Say, for instance, I had a 23 minute program recorded at 7 ½ ips. on Scotch 207 (a 1.51 mil tape), and I wanted to find the best reel for it. What I found out was that the tape length was 863 ft., and that it would fit quite nicely on either a 5 in., small hub reel or a 7 in., large hub real.