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I recently discovered the Osborne 1 computer, and I noticed it had two floppy disc drives.

What was the purpose of including two drives?

Remember that these systems (not only the Osborne 1) didn't have harddisks. Everything ran from floppies.

So usually you had one floppy where the program was on, together with OS related files. And another floppy for your data, texts and so on.

That was workable with two drives, but still was impractical if you wanted to copy data. Usually there was some way to load a program and then use the first drive for a second data disk while doing the copying, but then you had to re-insert the system disk etc. So a third drive wouldn't have been too bad (but few systems had one).

TL;DR: You could never have enough floppy drives. Working with one floppy drive was a pain sometimes because you often had to switch disks; working with two was enough for most cases; and sometimes more than two would have been nice.

The same was true for other systems like the DEC PDP-8, which used DEC tapes pretty much the same way floppies were used on CP/M systems. And there were tape controllers which allowed for four tape drives. This was there for a reason...

Note CP/M (the Operating system of the Osborne) didn't have subdirectories as we know today (which more or less forced you to dedicate a disk for a specific purpose in order to keep the overview), it also had very limited storage capacity per disk drive (~180k on a SS/SD disk as on the Osborne 1).

That means you typically held the application (for example WordStar, with a typical disk footprint of ~50-60kBytes) on one drive on a write-protected disk (in case it had to load overlays or messages) and the actual text you were working on on a disk in the other drive (the working disk). If you didn't want to be forced to constantly swap disks, you also put the operating system files on your program disk which also took some of the capacity.

You could have worked with only one drive, but that was much more cumbersome and carried the risk of destroying your program disk (because that could not be write-protected, then) or you had to change disks occasionally.

Obviously copying between disks was much simpler with a 2-drive setup, as others have mentioned.

The Osborne 1, like many computers of the time, had no means of data storage other than floppy disks. On powering up, the user would be prompted to insert the operating system disk, so the machine could boot.

Even when running other software, the computer would need to access and run parts of the OS periodically. If you only had one floppy drive, you'd have to continuously eject and insert the OS disk and your data disk when running some commands. It was far more desirable to have two drives available, so the OS disk could be left in one drive for most of the time.

Having two floppy drives also speeds up copying files between different disks, but this is a secondary benefit.

The provision of two floppy drives was also common with other machines, such as the IBM PC and the BBC Micro (though the latter had its OS in a ROM on the motherboard). When hard drives were installed in computers, the OS could be installed there, and there was no longer such a benefit from having a second floppy drive.

Since the computer only has disk drives and no hard-disk, the normal usage was to have the system programs and a word processor or database handler on one diskette and using the other for data or documents.
Those drives were single side, single density as standard, which gave a storage capacity of somewhere around 100 kBytes each.