Power applied is force x velocity for either a bike or an aircraft. But consider that on a bike, force is applied to a fixed road via the pedals to the rear tire. Regardless of the wind conditions, it takes the same cadence to achieve a given Vg, and the speed is always measured relative to the road. Winds only change the force required (aero drag) part of the equation, not the velocity. This is good news, because it means that with a head wind, we "only" have to pedal harder (to match aero drag force), not both harder and fasterFday said:Since there are no resistances on the road, how can the bike rider know the difference between riding the bike 50 m/s against a 1 m/s head wind and riding 51 m/s into a zero head wind without a speedometer telling him how fast he is going over the ground? It is the same issue the plane has. The plane only knows how hard it is working and what the airspeed is. It cannot know its ground speed without looking or somehow measuring it.
OTOH, in aviation, propulsion force is applied to the air mass itself, so velocity of the air mass passing the aircraft (Vg + Vw) is the only thing that counts for determining power (at a steady altitude). As you said, the aircraft doesn't know what it's doing relative to the ground, and as a result the pilot must use nav aids or ground cues to determine groundspeed and progress. To make up for a headwind and hold a given ground speed, the aircraft has to actually fly faster, not just maintain speed like we do on the bike.