I have been spending some time in analyzing the impact of tailwind on the ground speed of the aircraft. My analysis is based around the following equation : VAW = VAG - VWG ; where VAW is the velocity of aircraft with respect to wind, VAG is the velocity of the aircraft with respect to the ground, and VWG is the velocity of the wind with respect to the ground frame of reference. I am using the simplified lift equation to quantify the aerodynamic lift on the aircraft wings : .5 * k * V2AW
Assuming the aircraft takes off with no wind at a speed of 200 kmph (VAW). Hence, VAG = VAW. In other words indicated airspeed is same as ground speed. Now if we assume that the aircraft is cruising at a speed of 500 kph, and it encounters tailwinds at 50 kph. By the above equation, the ground speed of the aircraft (VAG) should be 550 kph
This is where my intuition starts working against me. I am somehow not able to correlate it with the situation of a boat moving in a steam of river, where the stream velocity impacts the velocity of the boat directly - some kind of tight coupling between boat and water surface. In the case of airplane, it is difficult for my brain to imagine a similar "tight coupling"
My understanding says that a tailwind will cause a reduction in VAW, which will decrease lift. The pilot thus adds extra thrust to increase the VAW, and this increases the ground speed VAG of the aircraft
Can anyone help me to clarify the real reason behind the increase in the ground speed of the aircraft ?