It’s a funny thing pprune. I was just having coffee with TMT when this very subject cropped up and the rationale behind rules of thumb.
Plain maths of sin, cos, tan suggests that if the flight path is at angle “k” to the horizon and true airspeed is “V” then RoD is Vsin k or as Jimmy Gilmour used to say “Vee Sink” is “Vee Sink”..
Of course if RoD is measured in feet per minute then so must airspeed.
I attach an example taken from Course Notes. Should you wish to check it out as I did then with an Excel spreadsheet it is useful to know that the time for descent can be calculated in simple stages. If H2 and H1 are two “heights” and F2 and F1 two “RoDs” then time = [{H2-H1)/(F2-F1)] x LN(F2/F1) where “LN” is the natural log function on your calculator. Easy to do in steps of 1000ft during smokoe.
The coursework example was an A330 and I just recreated a spreadsheet on the laptop out of curiosity obtaining a ground distance of 145nm from 39000ft. So 145/39 is 3.7 (indeed, why not use 4?) and another good and useful rule of thumb is tested and passes muster.
Amazin what you do while the missis is shopping.
PS image URL didn't seem to work!
PPS oh yes it did!!