Now it's your turn again to deal with the Cessna flying at 50 knots into a 60 knot headwind. What's his groundspeed?
His ground speed is 10 knots. His ground velocity is 10 knots in the direction of the wind. Speed and velocity are two different things. A good definition of velocity is from Wikipedia, which I use for its clarity:
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion (e.g. 60 km/h to the north)
Please note that velocity must have a frame of reference and that's what's leading to all this BS. Define your frame of reference then do all the vector sums from that frame. You can't mix both the 'air' reference and the 'ground' reference. Use one or the other. There is no energy generated when a plane turns constant circles in a constantly moving air stream. The velocity of the reference air stream over the ground doesn't make one whit of difference to the aircraft.
I'm a dumb winemaker and even I understand this.