Headwind and tailwind
A tailwind is a wind that hits an aircraft from behind. This reduces the flight time by increasing the ground speed. Tailwind is an unfavorable characteristic when taking off or landing and is usually countered by landing in the direction of the runway.
For example: If the runway one is approaching is 24; having direction 240 degrees and the wind is blowing from direction 060 degrees then the pilot will land on the opposite side of the runway, namely runway 06 with heading 060, so that he will be in a headwind landing; the same applies in takeoff.
This allows the lowest possible ground speed on takeoff and landing with the highest possible airspeed.
Tailwind component
Pilots calculate the Headwind Component, Tailwind Component and Crosswind Component of any wind, if they do exist. Headwind and Tailwind are cosine functions of the wind while Crosswind Component is a sine function. Headwind and Tailwind do not occur together in normal conditions.
Assume:
A=Angle of the wind from the direction of travel WS=The measured total wind speed CW=Crosswind TW=Headwind
Then
CW=Sin(A)*WS TW=Cos(A)*WS
For example if the wind is at 09015 that means the wind is currently from heading 090 degrees with a speed of 15 Knots and the aircraft is taking-off from runway 24; having heading of 240. We will us the runway side with less than 90 difference from wind direction, in this case Runway 06; heading 060.
Crosswind = Sin(090-060)*15 ≈ 13 Headwind = Cos(090-060)*15 ≈ 7.5
The aircraft is said to have 13 knots of crosswind and 7.5 knots of headwind on runway 06, or 7.5 knots of tailwind on runway 24. Aircrafts usually have maximum tailwind and crosswind components which they cannot exceed. If the wind is at eighty degrees or above it is said to be full-cross. If the wind exceeds 100 degrees it is common practice to takeoff and land from the opposite side of the runway, it has a heading of 060 in the above mentioned example.