Before we do so, let me tell you some of the definitions of aircraft's speed. (Mainly for those aircraft's whose speed are less than 300 K), as we have different speed reference to calculate actual ground speed of the aircraft.
2. CAS- Calibrated Air Speed, is Indicated airspeed corrected for any instrument error, if so. If there is no error then IAS=CAS and it is corrected by reading a placard installed in aircraft, installed by aircraft manufacturer.
3. TAS- True Air Speed, is the speed of the aircraft relative to the air mass through which it is flying. It is calculated by flight computer by making an input of IAS and Mean Sea Level Altitude.
4. G.S.- Ground Speed, is the actual speed of the aircraft relative to the ground/ earth surface. It is calculated by flight computer and it varies according to the direction and velocity of wind / wind component.
let’s say if your aircraft's airspeed indicator indicates 90 knots* of Indicated Airspeed【IAS】
(*Knots- Nautical mile per hour, where 1 Nautical Mile is 1.852 Kilometers).
And by assuming that the True Airspeed【TAS】 of aircraft is also 90 knots, Let us say if wind of 20 knots is blowing towards the head of aircraft, i.e. headwind【H.W.】of 20 knots. In this condition the Ground Speed 【G.S.】of aircraft will be 70 Knots, i.e. the actual speed of aircraft on earth.
[90 k TAS - 20 k H.W. = 70 k G.S]
Now if there is a tale wind【T.W.】of 20 k and TAS of aircraft is 90 knots, The wind will push the aircraft from behind and help in gaining speed, the G.S. will be 110 K.
[20 k T.W. + 90 k TAS = 110 k G.S.]
Conclusion from example: 1 & 2
For a given TAS, for H.W. the G.S. decreases because it opposes the aircraft, and for T.W. the G.S. Increases because it pushes the aircraft from behind to gain the speed. When there is 0 K of H.W. or T.W. the TAS=G.S.
Now, what if Tailwind is not blowing directly towards the aircraft's tail or Headwind is not hitting the aircraft's nose directly. Well, need not to worry about cross-wind components.
Another example of such case:
now assume if aircraft is heading on magnetic direction of 360 Degrees (North) and wind is coming towards the aircraft at the speed of 30 knots from the direction of 045 Degrees (North East), aircraft is flying at TAS of 090 knots.
(Note: It is an example of Head-wind component)
Let’s make an input to the E6-B flight computer and calculate the ground speed of the aircraft.
After making an input to the Electronic flight computer we got the result, Ground speed of 72 Knots when TAS is 090 on Headwind component.(Ground-speed reduced on headwind component)
An aircraft with heading of 260 degrees, TAS of 090 Knots, wind coming from 130 degrees at 030 knots. Let’s calculate the Ground Speed.
(Note: It is an example of Tail-wind component)
We obtained Ground Speed of 106 Knots, for a given TAS of 090 Knots on Tailwind component.(Ground-speed increased on Tailwind component)
For a given TAS, with headwind wind component the GS decreases, with tailwind component the GS increases.
With a change in the direction of wind, the speed of aircraft changes.
We can also say that, for the change in aircraft's heading/course by keeping the wind direction constant, the speed of aircraft changes. (Headwind will become Tailwind and vice-verse, if aircraft makes an about turn, by keeping the wind direction same, the Ground Speed of aircraft will change)