Hazelnuts,
Sorry, but no it doesn't. All that graph shows is that, as the thrust-to-weight ratio increases, the vertical speed increases (as we would expect), and that there is only one airspeed for each T to W that will provide maximum climb performance ie top of each curve. The curve clearly shows that if you change the airspeed then the ROC will reduce.
The 20m/s headwind speed bar merely shows the groundspeed, not the new airspeed as you claim, in that wind; all the groundspeeds are simply 20m/s less than the airspeed. What is does show is that in a headwind, you will get a higher gradient when at the best IAS for the ROC, but only because same ROC is being achieved at a slower groundspeed, not a lower IAS.
So I maintain that a headwind has no effect on the Vx speed. It affects the resulting gradient but not the speed itself.
Originally Posted by Golf-Sierra
Imagine an aircraft that has a Vx of 60kts. The aircraft is flying in a 50kt headwind. So the aircraft has a ground speed of 10kts, and one could imagine that it is climbing farily steeply (relative to the ground). If the pilot were to now slow down to an airspeed of 50 kts, thus reducing the groundspeed to 0, provided the aircraft can climb at 50 knots - it will now have a climb angle of 90 degrees.
Correct. See Bubbers post above. Tigers used to do it. A vertical circuit. Takeoff, Up, fly "backwards", down, touch and go, up...
Reducing your speed from Vx of 60KIAS to 50 would problably reduce your climb performance somewhat (as per Hazelnut's graph), but
any climb would in effect be vertical.