headwinds vs. maximum range
eckhard stated "The wind component will have a large effect on the chosen speed, such that in a strong headwind, you may be better off actually increasing speed!"
I once did the exercise of reading off best fuel consumption / speeds from the C172 POH curves and entered the figures against various headwinds into a table, to see how the range was affected by headwinds. (Can't find the spreadsheet....!) The result surprised me, with maximum range consistently being achieved with the still-air-most-economic-speed regardless of headwind, up to a point where the headwind is well over half the TAS - it was counter-intuitive, as one felt that the headwind should require more airspeed.
Obviously the headwind diminishes range does but not so obviously does not seem to change the best speed to use, at least at lower wind speeds. It said to me that in a fuel critical situation, you power right back even with a headwind, unless the wind is very high (but I could not find an analytical method to determine at what relative headwind you must increase power)
Sorry this is a bit garbled but I think you get the drift. (must find that table..) Anybody got a better comment on this?