How many SMS messages fit on a floppy?

March 3, 2008 11:19 AM

Mathfilter: How many text messages (SMS) will fit on a floppy disk, or a CD-ROM? Once that number is derived, how much will it cost to send or receive that many messages if a consumer pays per message (American carriers or Intl carriers would be great)?

Probably best to assume assume that each message uses the maximum amount of characters permitted (although if you know the minimums allowed, then let's do the math on that as well.) Please show your work.

posted by kenneth to technology (6 comments total)

wtf? Do the math yourself!
Here, I will dave you 30 seconds of googling.

SMS are 160 characters (bytes) max per message (min=0 bytes)
1.44Mb Floppy disks have 1,474,560 bytes
CDROMs have between 681,984,000 bytes (74m) and 737,280,000 bytes (80m)

so, a lot of messages will fit on a floppy. A hell of a lot of messages will fit on a CD. Both will cost a ridiculous amount to send via SMS when charged per message, no matter what the per message cost is...

(Flagged as homework)
posted by nielm at 11:39 AM on March 3, 2008

A CD has 333,000 sectors of 2352 bytes each. I'm not sure, but I'm guessing that an individual file must take up at least one sector, even though a text message (at 140 chars?) would be less. So, 333,000 SMS messages.

At $0.10 each, that'd be $33,000 to send.

If you put all the messages into a zip file, you could get a lot more on--you wouldn't need to worry about the sector-size floor, and you'd get compression. Assuming 140 bytes for each message, plus another 20 bytes (?) overhead, and 2:1 compression, that'd be 1.5 GB worth of messages at 160 bytes each, or 9,375,000 messages. At $0.10 each, that's $937,500. You might want to sign up for an all-you-can-text plan.
posted by adamrice at 11:41 AM on March 3, 2008

Assuming Latin encoding, I'll make the following estimate:

160 bytes of message + 40 bytes of header (estimate; can't find a real number) = 200 bytes per message.

A megabyte is 2²⁰ bytes.

So, 2²⁰ / 200 = 5242.8.

You can now multiply this by the capacity of a floppy disk: 1.44 * 5242.8 = 7549.7

A CD: 750 * 5242.8 = 3932160.0.

Also, this is like fourth-grade math...
posted by Netzapper at 11:44 AM on March 3, 2008

It sounds like any definitive answer is going to be based upon a bunch of assumptions regarding how the messages are going to be stored on the floppy/CD/whatever.

If each is stored as a a separate ASCII textfile then you need to consider file system (iso9660, fat, ntfs) limitations and storage quirks. If you were to store it in a single huge (delimited) file, then those limitations are not as relevant.

In either case, compression would make a huge difference (since that text should crunch down nicely).

Because these are such small files to begin with, changing these assumptions can greatly vary the results. (This is a roundabout way of asking what level of precision are you looking for, and why?)
posted by QuantumMeruit at 12:40 PM on March 3, 2008

Fun fact: text messages use 7 bit encoding by default, not 8 bit. That same description on Wikipedia implies that messages don't have a header (which doesn't make sense, since it needs routing info of some sort), but some digging reveals this detail about headers used in the server -> server (ie, AT&T forwarding to Sprint) communications. That link says 60 "octets" (bytes).

So each message is 160 * 7 bits + 60 * 8 bits = 1600 bits = 200 bytes.

Since that happens to work out to what Netzapper estimated, the rest of his calculations are correct.
posted by cschneid at 1:52 PM on March 3, 2008

It should be pointed out that the overhead of moving messages through the cellular network is significant, when you look at the bandwidth limits of the control channel that SMS rides, and the necessity of locating each phone in the HLR/VLR before it can be addressed, and all that.

It doesn't come anywhere near justifying $0.10/message. Not even a hundredth of that. But if you're thinking that SMS should be as cheap per meg as other data service, you're suffering a severe misunderstanding of how SMS works.

It'd be akin to saying that, because you can ship a 20-lb package for ten bucks, you should be able to mail 20 lbs of individual postcards for the same price.

If you for some reason need to move lots of data over a cellular connection, don't do it with SMS. Look into different packet data options. Even the circuit-switched data which occupies a voice channel as long as you're "dialed up", is more efficient than SMS because the routing of each piece of data is handled by an ISP's routers, rather than cellular switches. (Setting up a CSD connection involves several transactions on the control channel in addition to the voice channel it takes, so for occasional short messages, SMS is indeed more efficient.)
posted by Myself at 3:42 PM on March 3, 2008 [1 favorite has favorites]