from Ed Williams Aviation Formulary
TAS and windspeed from three (GPS) groundspeeds.
Determine your groundspeed on three headings that differ by 120
degrees (eg 40, 160 and 280 degrees), call these v1, v2 and v3
Let vms = (v1^2 + v2^2 + v3^2)/3
a1= v1^2/vms -1
a2= v2^2/vms -1
a3= v3^2/vms -1
mu= (a1^2 + a2^2 + a3^2)/6
Let bp and bm be the roots of the quadratic b^2 -b + mu =0 ie:
bp= 1/2 +sqrt(1/4-mu)
bm= mu/bp
The TAS and windspeed are then given by sqrt(vms*bp) and sqrt(vms*bm)
-- provided that the TAS exceeds the windspeed. If this is not the
case, the roots are exchanged.
This is a handy way to check your TAS (and the calibration of your
airspeed indicator) using your GPS groundspeed, even though the wind
is unknown.
obviously this is something that you'd preprogram into a PDA or calculator beforehand.