rickerman:
Then I guess I would need a capacitor to keep the Arduino powered long enough to write the unwritten data to the SD Card, and finalise the binary file. Any ide how long this would take, and what size of capacitor would be needed?
Who can tell, it would likley depend on what your software is actually doing.
Get the logger (or some test code) working and use a switch to simulate power down, then record how long it actually takes.