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Short answer: a pure vertical updraft has no direct effect on ground speed if the helicopter's airspeed and heading stay constant — but in practice there are indirect effects worth knowing.

The vector logic

Ground speed is airspeed plus wind, added as vectors. Only the horizontal component of wind changes horizontal ground speed. An updraft is (by definition) a vertical air movement, so mathematically it shouldn't touch the horizontal ground speed vector at all — it should only create a climb tendency, which the pilot cancels by reducing lift, not by changing airspeed.

Why it's messier in a real helicopter

The bigger real-world factor

True atmospheric updrafts are rarely purely vertical. Thermals drift with the ambient wind, ridge lift has a horizontal inflow component, and gust fronts mix vertical and horizontal shear together. So while the "pure updraft" case leaves ground speed untouched, the updrafts a helicopter actually flies through usually come bundled with a horizontal wind component that does change ground speed — it's just not the updraft itself doing it.