Below is an illustration of the wind speed effect on a flight leg,
comparing a BLIPMAP Track Average "optimal flight" calculation for a
headwind of 20 kt to one with no head/tail wind (for a LS-3 polar). The
former requires a larger airspeed between thermals and a larger amount
of time spent thermalling to make progress. And of course the ground
speed is lower, but note that it is _higher_ than one would get by
simply subtracting the headwind from the "no headwind" groundspeed -
this is what is gained by using a higher airspeed when a headwind
exists. For this example the "add half the headwind" rule of thumb
would give an airspeed higher than optimal. (I suspect the column
formatting will be lost in this posting, so the numbers in order are the
leg distance (km), tailwind (kt), climb rate(m/s), leg time (min),
average groundspeed (kt), between-thermal airspeed (kt), and
percent time spent thermalling.)

---- Optimal-Flight-Avg ----
-- Tail Clmb Gnd Air Thm
-- Dist Wind Rate Time Spd Spd Pct
-- km kt m/s min kt kt %
-- 45 -20 1.4 43 34 85 60
-- *** WITH NO HEADWIND ***
-- 45 0 1.4 32 45 80 44