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I am trying to calculate the bit density of a disc shaped magnetic tape.

Okay so I know the following

The diameter is 3.38 inches

The film is 0.003 inches thick (when viewed on its side)

The bit density is 0.62 Gb/mm2

I made the following attempt which I know to be incorrect

The disc has 35.8909 square inches in total

There are 23155.37304 mm2 in 35.8909 square inches

The bit density is 0.62 Gb/mm2 

23155.37304 x 0.62 =  14356.3312848 Gb

This yields 14.3563312848 (14.36Tb) which sounds wayyyyy too low

I am guessing the issue is that I am calculating in 2-Dimensions and not accounting for thickness? How can I more accurately calculate the bit density considering we are working in 3D?

Ninja2k
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  • The length of a spool of tape (or roll of toilet paper) can be found here. If you know the tape width (= spool height) you can calculate the total area and hence total bytes. – Jens Nov 18 '17 at 20:35
  • @Jens it isn't a spool, it is just a circle like a CD but it is made of tape instead of plastic. – Ninja2k Nov 18 '17 at 21:57
  • OK, but then I don't understand how the 3D comes into it. Are there bits inside the disc as well as on the surface? – Jens Nov 18 '17 at 22:25
  • @Jens Imagine a cake, the first layer has cream, the second chocolate and the third jam, each layer has magnetic information on it, now if our cake is very thick and each layer is very thin we can store a lot of information, if I use the above formula am I accounting for each layer or would I have to use a more 3D formula such as the volume of a sphere? – Ninja2k Nov 19 '17 at 00:07

1 Answers1

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My understanding now is that you have a cylinder divided into layers and the surface of each layer has a fixed bit density of $a$. Assuming each layer has the same thickness $t$ and that the thickness of the disc is $T$, you will then have $N=\frac{T}{t}$ layers. If the radius of the cylinder is $r$, the total number of bits is $$B = N \cdot \pi \cdot r^2 \cdot a$$ From the info you gave, it is unclear to me what the thickness of the disc is (I assume the thickness of the "film" is the thickness of each layer).

Jens
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