Crosswind Component on a Runway

The wind has a part that blows along the runway and a part that blows across it. This page gives the crosswind part: the wind speed times the sine of the angle between the wind direction and the runway heading. At 0 degrees the sine is zero and there is no crosswind; at 90 degrees the whole wind is crosswind. Take both directions as the direction the wind blows from and the runway points to, and use the smaller of the two ways round, 0 to 180 degrees. The crosswind is the same from the left or the right, so this page gives its size only.

It is the number a pilot checks against the aircraft's maximum demonstrated crosswind. The FAA's Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C, chapter 11) says the aircraft is tested at 90 degrees to a wind of up to 0.2 times the stalling speed with power off, gear and flaps down. The gust, not the steady wind, is what is usually checked against a limit, so enter the gust speed when it matters. An airport report gives the wind direction and speed but not the runway heading, which has to come from the airport's runway list.

The handbook's Sample Problem 10 is the page's example. Runway 17 is a heading of 170 degrees, the wind is from 140 degrees at 25 knots, and the angle is 170 minus 140, or 30 degrees. The handbook's chart gives a crosswind component of 13 knots. The page gives $25\sin 30^{\circ} = 12.5$ knots, and the chart, read to the whole knot, shows 12.5 as 13, so the two agree to within half a knot. A swapped sine and cosine would give 21.65 knots, which that comparison would catch.

The relation is trigonometry, not an empirical fit, so its accuracy is that of the wind and heading you give it. It also runs backwards. A 13 knot crosswind at 30 degrees means a wind of $13/0.5 = 26$ knots. A 12.5 knot crosswind in a 25 knot wind gives 30 degrees, but only the acute angle: a sine cannot tell the acute angle from its obtuse partner, and the page says so. The other half of the split is the headwind or tailwind along the runway.