Pilot DAR, I was sort of with you until the end of the second paragraph when you said "If you are flying for best fuel economy, you do not care about getting somewhere quickly, so groundspeed is not a factor."
This is completely wrong. Take the case where the headwind is the same as the airspeed, you will burn all of the fuel in the tank and still be where you started from. Zero MPG. However If you open the throttle a tad more, fuel consumption (ltrs per hour) will go up a bit, groundspeed will have a value greater than zero and voila! MPG will have a value, albeit a low value, but progress is made for the fuel consumed.
In my Rans I get through about 11 ltrs an hour at 55 mph, 15 ltrs an hour at 70 mph and 20 ltrs an hour at 85 mph. So in still air at 55 mph a ltr of fuel takes me 5 miles. At 70 mph a litre of fuel takes me only 4.6 miles and at 85 miles an hour a ltr of fuel takes me just 4.25 miles. 55 mph is clearly the best economy speed.
Now see what happens when there is a headwind of, say, 30 mph. At an airspeed of 55 mph the groundspeed is now down to (55-30) = 25 mph. A ltr of fuel now takes me just (25/11) = 2.27 miles. If I push the throttle open a bit and raise the airspeed to 70 mph the groundspeed rises to 40 mph. A ltr of fuel takes me (40/15) = 2.67 miles at 70 mph. If I open the throttle a bit more and raise the airspeed to 85 mph the groundspeed rises to 55 mph and the ltr of fuel now takes me (55/20) = 2.75 miles. So when there is a good headwind you need to fly faster than the most economical still air airspeed for best economy. Now 85 mph is the best airspeed for fuel economy.
For a 10 mph headwind the figures for 55, 70, 85 mph are 4.1 miles per ltr, 4.0 and 3.7 so 55 mph is the best airspeed still.
For 20 mph headwind the figures are 3.2, 3.33 and 3.25 so 70 mph is the best economy airspeed.
Andrew.
These are real figures from a real aircraft.