Estimate the density of disks and tapes

Important notice: This is an individual homework. You should not help classmates, nor seek help from anyone other than the instructor or TA's. (Exception - it's OK to ask a classmate what the questions mean if it isn't clear. Still, it would be good to check with me anyway.) In particular, do not even suggest web sites or other sources for finding information to other students. Each student should perform his or her own search for information on the technologies, and figure out how to perform the estimates.

There is no single correct answer to the question. In fact, I'm interested in seeing the range of answers that the class members come up with.

Imagine that you want to set up a business that will provide long-term storage of huge data archives, and need to decide whether to use magnetic disk or tape technology. One issue -- the one we will focus on here -- is how much space will the disks drives or tape reels or cartridges take up, projecting forward to (possible) future improvements.

Aside: Actually, this is one of the less important considerations, compared to questions about cost, convenience, and especially reliability. But let's pretend you plan to store the data in special shielded bank vaults that cost thousands of dollars per cubic foot per year, so space is an important issue.

We assume that the customers will probably never need access their data, and you'll copy it to a newer disk or tape every decade, so all we care about is the amount of space taken up by the magnetic media. Thus, for tapes, you are concerned only with the volume that a reel or cartridge of tape occupies, not the size of the tape drive. For disks, I suspect the most compact technology is to use ordinary hard drives (including the motor and electronics as well as the platters) rather than removable disk packs.

Your assignment is:

1. Find (either on the web or in published material) the information you will need to estimate the three-dimensional volume required by disks for three dates, one being within the last year or two, another about 5 or 10 years ago, and the third 10 to 20 years ago. It's important that your information corresponds to technologies that are up-to-date but available commercially at the respective times. For instance, don't use press releases about laboratory prototypes - they are often years ahead of when the corresponding commercial products are actually available. For each "factoid" you use, you should indicate the source (web page, book, educated guess, or whatever) of the information in enough detail that I can check your figures. But I don't want to see reams of information that you don't use in the calculations below.
2. For each of the dates, calculate the "data density" (i.e. data capacity to three-dimensional volume ratio) in megabytes per cubic inch that can be stored on a hard drive. Be sure to always indicate the units of your numbers (e.g. MB/drive, inches/foot, etc) in your intermediate calculations as well as the final answer.
3. Plot the points on a logarithmic scale to see if the exponential rate of improvement has been roughly uniform.
4. Making the totally bogus assumption that the exponential rate of improvement given by your two most recent dates will continue exactly the same for the next 50 years, estimate the data densities of disks for the year 2050.
5. Repeat the above four questions for tapes. NOTE: This will only count one point (as opposed to the answers for disk, which count four points), so it's OK to decide it's not worth your time. But you'll probably learn something about tape technologies if you do it.

Please make your answers as clear as possible, but also keep them short and to the point. I'll have a lot of papers to go through, and don't want to spend time trying to figure out what various scribblings on your paper mean. The example below (of something we did in class) might serve as an example of brevity and clarity.

1. Factoids
   
   • ScreenSize: 1,000,000 pixels/image (estimating a 1000x1000 screen)
   • RefreshRate: 30 images/second (text, page 12 says "30 to 75 times per second")
   • Data requirement: 3 Bytes/pixel (standard for "24 bit color")
2. Calculation
   Bandwidth to screen: about 10^6 pixels/image x 30 images/sec x 3 Bytes/pixel
   = 90x10^6 Bytes/sec
   = 90 MByte/sec