My co-workers found a bunch of our old backup tapes and I have been trying to find out the length of the tape that fits on these spools. We found out that sticking a magnet on the ceiling, and then the unpacked tape spool to the magnet, that the whole spool would unravel itself into a big pile of tape (fun practical joke).
Out of curioisity, I have been trying to find the length of the tape on the spool, but have not had much luck searching about. I’ve taken some rough measurements and am hoping someone could do the calculations for me because my first result was something in the neighborhood of 4,900 km. I’m fairly certain that my math skills have diminished since graduating a decade ago.
Entire spool diameter = 9cm
Inner spool that the tape is wrapped around = 4.2cm
Rough estimate of tape thickness(based of a cassette tape) = 10 micrometers (.001cm)
Area* of tape on spool = pi * (4.5^2 - 2.1^2) = 49.76 cm^2
Area* of 1 cm length of tape = 0.01 cm^2
Length of tape on spool = 49.7 cm^3 / 0.01 = 4,976 cm.
*Width doesn’t matter because there is just one layer wound on the spool widthwise (if it were a wire, you’d have to include the width of the spool and wire)
FWIW, if you start with centimeters, the final answer should also be in centimeters unless you converted units (you may have done the calculation right, just read it as kilometers; you can also do this by calculating the number of layers, which is 240 (4.5 - 2.1 / 0.01) and multiplying that by the inner and outer circumferences, which give 3,167 and 6,786 cm; add these and divide by two and you get 4,976 cm.
If the thickness of the wrapped tape from inner to outer edge is 2.4cm (4.5 - 2.1) then there should be 2,400 layers since the tape thickness is 0.001cm, correct?
I haven’t actually tried extending the unraveled tape, but it sure does seem a lot longer than 49 meters.
It’s likely to be 3600 feet (1097 meters). The 10.5" tape reels gradually became larger as technology made it possible to make the tape thinner and still be able to retain data. I remember 1200’ and 2400’ tapes in the early Eighties and I think they topped out at 3600" before the technology was obsoleted by tape cartridges.