# Effect of tailwind on aircraft speed

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 ?

All civilian aircraft are built to be stable in airspeed $V$. They do it by a) being a bit nose-heavy, and b) having an upward-turning tendency proportional to $V^2$, called decalage (controlled by the elevators, usually at the back, sometimes at the front).

In normal flight, the two forces cancel, so the plane travels in a straight line (not necessarily level - it could be climbing or descending, but the line is straight).

If for any reason $V$ decreases (like a sudden tailwind), the upward-turning force decreases, so the nose-heaviness pulls the nose down. That causes the speed $V$ to increase (like going downhill in a car) back toward the stable speed, bringing the nose back up.

A sudden headwind, as you can see, has the opposite effect. $V$ increases, the nose goes up, and $V$ decreases back to the stable speed.

You can see this if you take a flying lesson. In straight-and-level flight, just give the yoke a short shove forward. The plane goes down, then up, and gradually returns to straight-and-level.

So how do you control $V$? There's a "trim wheel". This controls a tab on the elevators. It essentially functions as if it applies a continuous pressure, fore or aft, to the yoke. If the pressure is back, as if you were applying steady back pressure on the yoke, then the steady-state $V$ is decreased. So if the pilot wants to go fast, she applies "nose-down-trim". Since the plane will then be headed in a straight line sloped downward at a higher speed, she applies power, which moves the slope from downward back to level.

This is flying 101: The power does not control speed, it controls climb. The elevators do not control climb, they control speed. All of this is in airspeed - relative to the air, not to the ground.

A sudden increase in tail wind (a gust) will reduce the lift, as experienced when an aircraft hits turbulence. However, a steady tail wind will result in an increase in aircraft speed such that the airspeed achieved is the same as in the absence of the tail wind.

• Can you please expand more on that ? Why should the airplane speed (ground speed) be impacted by the tailwind. For example, if I somehow manage to suspend myself in air, and a steady tailwind blows behind me at 50 kph, will I get carried by the wind @ 50 kph ? I think that I will start to move only when the drag force of the wind behind my back (I am a bluff body) exceeds the skin friction. Am i making it complicated now ? – Masoom Kumar Jul 3 '18 at 7:18
• Simple answer... The airmass you are flying in is itself moving with respect to the ground. I'll post a simple answer.. – RaSullivan Jul 3 '18 at 17:03
• Yes it takes some time for your speed to be altered by the wind speed. – JMLCarter Jul 3 '18 at 22:17

No, speed is measured by pressure through the pitot variable. Tailwinds affect whole standing areas through velocity. In space, a tailwind would indeed affect forward momentum (there is no relative opposition) Picture in your mind, a bubble of air at 1m above Earth sea level. This bubble is moving at 500kph at ground pressure. Within the bubble, a gust of 50kph pushes only small areas of the deflection planes. Dispersion over area by energy loss squared squared and squared again..sucks our the momentum of the gust. ...I could be wrong...?

A tailwind indicates the air mass being flown IN, is itself moving (in your direction of motion ). Assuming identical Vc (velocity, cruise ) is maintained IN a tailwind, ground speed goes up as a result, by the ground speed of that air mass you are flying in. The reverse is true for a headwind.