Headwind and tailwind

A tailwind is a wind that blows in the direction of travel of an object, while a headwind blows against the direction of travel. A tailwind increases the object's speed and reduces the time required to reach its destination, while a headwind has the opposite effect. Tailwinds and headwinds are commonly measured in relation to the speed of vehicles — commonly air and watercraft — as well as in running events — particularly sprints.

In aeronautics, a headwind is favorable in takeoffs and landings because an airfoil moving into a headwind is capable of generating greater lift than the same airfoil moving through tranquil air or a tailwind at equal ground speed. As a result, aviators and air traffic controllers commonly choose to take off or land in the direction of a runway that will provide a headwind. In sailing, a headwind may make forward movement difficult, and necessitate tacking into the wind.

Aeronautics calculations

Headwind component

Pilots calculate the Headwind Component, Tailwind Component and Crosswind Component of any wind, if they do exist. The direction of wind is calculated using wind sock. 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. Determining the ground speed of an aircraft requires the calculation of the head or tailwind.

Assume:

$A=\text{Angle of the wind from the direction of travel}$

$WS=\text{The measured total wind speed}$

$CW=\text{Crosswind}$

$HW=\text{Headwind}$

Then

$CW=\sin(A) \cdot WS$

$HW=\cos(A) \cdot WS$

For example: if the wind is at 24015 that means the wind is currently from heading 240 degrees with a speed of 15 Knots and the aircraft is taking-off from runway 18, giving it a heading of 180 degrees. Then $A=60^\circ$, and

$\text{Crosswind} = \sin[60^\circ] \cdot 15 \mathsf{knots} \approx 13 \mathsf{knots}$

$\text{Headwind} = \cos[60^\circ] \cdot 15 \mathsf{knots} \approx 7.5 \mathsf{knots}$

The aircraft is said to have 13 knots of crosswind and 7.5 knots of headwind. Aircraft usually have maximum headwind 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 90 degrees it is common practice to takeoff and land from the opposite side of the runway, it has a heading of 360 in the above mentioned example.

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:

$A=\text{Angle of the wind from the direction of travel}$

$WS=\text{The measured total wind speed}$

$CW=\text{Crosswind}$

$TW=\text{Tailwind}$

Then

$CW=\sin(A) \cdot WS$

$TW=\cos(A) \cdot WS$

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 use the runway side with less than 90 difference from wind direction, in this case Runway 06; heading 060. Here, $A=30^\circ$.

$\text{Crosswind} = \sin[30^\circ] \cdot 15 \mathsf{knots} \approx 7.5 \mathsf{knots}$

$\text{Tailwind} = \cos[30^\circ] \cdot 15 \mathsf{knots} \approx 13 \mathsf{knots}$

The aircraft is said to have 7,5 knots of crosswind and 13 knots of headwind on runway 06, or 13 knots of tailwind on runway 24. Aircraft 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 end of the runway, it has a heading of 060 in the above mentioned example.

See also

• Crosswind
• Air navigation
• Thrust
• Wind assistance
• Wind sock