OK, I'll bite, but disclaimer, my ticket is MUCH more limited than yours, but I'm ready to muster up and take my punishment for being incorrect in the attempt (hoping there is credits for being close at least)
I guess, at the end of a watch, if you knew how many RPM's the shaft was turning during the watch period, how long the watch was (say 4 hrs), what the pitch of the prop was (inches per rotation), what the slip was (a fraction of those inches you loose), you could do some simple math and figure out how far you went.
Please correct the following equation:
Distance = (4 hours) * (60 Min/hour) * (rotations/minute) * (inches of pitch) * (1- (fractional slip))
This would give distance travelled in inches. To translate inches to nm:
Distance in nm = (6076 ft/nm) / ((Distance in inches)/12 feet)
Not sure how you get negative slip?