Calculating the crosswind component

Splitting the wind into components

The wind rarely blows exactly along the runway. So you split it into two parts: the crosswind component across the runway and the headwind component along the runway. Both follow from the wind speed and the wind angle. The wind angle is the angle between the wind direction and the runway direction. The wind direction is the direction the wind blows from. The runway number is the magnetic direction of the runway in tens of degrees, rounded: runway 27 therefore points to about 270°. To find the wind angle:

1. Read the wind direction, for example from the METAR.
2. Work out the runway direction: runway number times ten.
3. Take the difference between the two directions. If it is more than 180°, subtract it from 360°.

Examples: with runway 36 and wind from 020°, the difference is 340°, so the wind angle is 360° minus 340° = 20°. With runway 18 and wind from 250°, it is 70°.

The formulas

With the wind angle, two formulas apply (EASA):

• Crosswind = wind speed × sine of the wind angle
• Headwind = wind speed × cosine of the wind angle

Depending on the wind direction, the second formula gives the headwind or the tailwind component. If the wind angle is more than 90°, the wind comes from behind and it gives the tailwind component. The most useful values, rounded:

Wind angle	Sine (crosswind)	Cosine (headwind)
15°	0.26	0.97
30°	0.50	0.87
45°	0.71	0.71
60°	0.87	0.50
90°	1.00	0.00

The clock rule for your head

In its CPL and ATPL learning objectives (navigation), EASA describes a method for mental arithmetic, the clock code rule: every 15° of wind angle is a quarter of an hour on the clock face, so a quarter of the wind speed. The wind angle is taken to the nearest 10°. At 15° the crosswind is 25% of the wind speed, at 30° 50%, at 45° 75% and at 60° 100%.

Wind angle	Crosswind as a share of the wind speed
15°	25%
30°	50%
45°	75%
60°	100%

So at 60° you use the whole wind speed, and at 90° all of the wind is crosswind anyway. Compared with the sine, the rule is higher at 45° and 60° (0.75 instead of 0.71 and 1.00 instead of 0.87), so it errs on the safe side. At 15° it is slightly below the sine: 0.25 against 0.26.

Comparing with the limit

Compare the crosswind with the maximum demonstrated crosswind component of your aeroplane. According to the FAA handbook PHAK, it is published in the flight manual. In the CPL and ATPL learning objectives (flight performance), EASA also requires you to explain why an aeroplane has a maximum crosswind limit and to determine the crosswind component from runway direction, wind speed and wind direction.