Crosswind components, explained

The crosswind component is the wind speed multiplied by the sine of the angle between the wind and the runway. A 20 knot wind 30 degrees off the runway heading puts 10 knots across it and 17 knots down it.

Wind almost never blows straight down a runway. What matters on landing is how much of it is pushing you sideways, because that is the part your rudder and aileron have to hold out, and it is the part that runs out of authority first. Splitting the reported wind into the piece along the runway and the piece across it is one trigonometry step, and there is a mental shortcut that gets you close enough to make the decision from the hold short line.

The formula

Crosswind = wind speed x sin(angle). Headwind = wind speed x cos(angle). The angle is the difference between the wind direction and the runway heading.

Runway 09 points 090 degrees. A wind reported from 120 at 20 knots is 30 degrees off. The crosswind is 20 x sin(30) = 10 knots, and the headwind is 20 x cos(30) = 17 knots. Notice that the two do not add to 20: they are the legs of a right triangle whose hypotenuse is the wind, so they add in quadrature rather than arithmetically.

Two details decide whether your answer is right. The first is that runway numbers are magnetic and rounded to the nearest ten degrees, so runway 09 might really be 088. The second is bigger: a wind read to you by a tower, an ATIS or an AWOS is magnetic, while the wind written in a METAR or a TAF is true. Mixing the two introduces the local magnetic variation as an error, which is about 13 degrees on the US east coast and about 12 degrees the other way on the west coast. At 20 knots, 13 degrees of error is roughly 4 knots of crosswind you did not account for.

The clock rule, for doing it in your head

Treat the angle as minutes on a clock face: 15 degrees is a quarter of the wind, 30 degrees is a half, 45 degrees is three quarters.

For the angles that matter on a runway, the sine of an angle is close to the fraction of an hour that the same number of minutes represents. Thirty degrees is half an hour and sin(30) is exactly 0.5. Fifteen is a quarter and sin(15) is 0.26.

Be honest about where it breaks. The rule tracks the real sine well up to about 45 degrees and then runs away from it: at 45 it says three quarters where the true figure is 0.71, and at 60 it says all of the wind where the truth is 0.87. The error is always an overestimate, which is the safe direction to be wrong in, and that is why the rule survives. But if you are close to your limit, use the real numbers.

Angle off the runway	True fraction across (sine)	True fraction down (cosine)
10°	0.17	0.98
15°	0.25	0.97
20°	0.33	0.94
30°	0.5	0.87
40°	0.65	0.77
45°	0.7	0.7
60°	0.9	0.5
70°	0.94	0.33
90°	1.0	0

Three numbers carry most of the work: 30 degrees is half, 45 is about three quarters, 60 is roughly nine tenths. Past about 75 degrees you may as well call the whole wind a crosswind, because the error is then under a knot in a 20 knot wind. Do not do that at 60 degrees: the shortcut costs you nearly 3 knots there, which is exactly the margin you were trying to check. And at 90 degrees there is no headwind at all, which is the case people forget: a direct crosswind gives you nothing back in reduced ground speed, so the landing roll is as long as a calm day and the sideways problem is at its worst.

Gusts are the number to plan against

Compute the crosswind from the gust, not the steady wind. A 12 knot wind gusting 25 at 40 degrees is a 16 knot crosswind at the moment that matters, not 8.

The steady wind is what you trim for; the gust is what arrives in the flare. Running the arithmetic on the lower number is how a landing that looked comfortable on the ground stops being comfortable at 20 feet. The spread between the two is worth reading on its own: a 12 knot wind gusting 25 is a different airplane on short final than a steady 25, because the difference has to be flown out in the last few seconds rather than held.

A common technique is to add half the gust factor to the approach speed. That buys control authority, and it also lengthens the landing distance, which is the trade to remember on a short runway. The calculator reports the steady and the gust component separately for exactly this reason.

The demonstrated crosswind is not a limit

The maximum demonstrated crosswind in your POH is a certification data point, not an operating limitation, and it says nothing about you.

Under 14 CFR 23.233, as it read for the aircraft most of us fly, a 90 degree crosswind component must be demonstrated safe for taxi, takeoff and landing, and it must be at least 0.2 V_SO, two tenths of the stall speed in the landing configuration. For a light single stalling at 50 knots that floor is only 10 knots; a manufacturer usually demonstrates more and prints that figure in the handbook. What the number tells you is what a test pilot achieved, on a dry runway, in a new airframe, on a day chosen for the purpose.

Check your own handbook before assuming it is not a limit. For most light aircraft the maximum demonstrated crosswind sits in the performance or general section and is advisory: nothing prohibits exceeding it, and nothing promises you can reach it. But some manufacturers do place it in Section 2, Limitations, and where it is written as a limitation it is one, binding under 14 CFR 91.9. Read the section heading, not just the number.

Your real limit is the largest crosswind you have landed in comfortably and recently, and it moves with currency, runway width, surface condition and how tired you are. It belongs in your personal minimums as a number you set on the ground, and the minimums tool checks the live wind against it on every airport page. A wet or contaminated runway pulls the number down hard, because a crosswind you can hold in the air still has to be held once the tires are down and the tires are the part that stops cooperating.

Picking the runway

The favored runway is the one with the largest headwind component, which is usually but not always the one with the smallest crosswind.

At a field with two runways the choice is normally obvious. It gets interesting when the wind sits between them, when one runway is much longer, or when the shorter one points more nearly into wind. A tailwind component is the thing to be strict about: it lengthens the landing roll sharply, most handbooks only publish data to 10 knots, and a modest tailwind on a short wet runway is a worse problem than a larger crosswind on a long dry one.

At a non towered field the runway in use is whatever the traffic is using, and arriving with a plan that disagrees with the pattern is its own hazard. Listen first, and see radio calls at a non towered airport for how to say what you intend to do.

Worked example

You are inbound to runway 32 and the ATIS gives 270 at 18, gusting 26.

• Runway 32 is 320 magnetic; the wind is from 270 magnetic, so the angle is 50 degrees.
• Steady: sin(50) is about 0.77, so 18 x 0.77 is a 14 knot crosswind. The headwind is 18 x cos(50), about 12 knots.
• Gusting: 26 x 0.77 is a 20 knot crosswind when the gust arrives.
• Runway 27 points 270, straight into the wind: the full 18 knots as headwind and nothing across it.

If the field has a runway 27, the decision makes itself. If 32 is all there is, the honest question is not whether the airplane can do 20 knots across, but whether you have done it lately, and what the surface is. That is a personal minimums question, decided before you left.

Sources: 14 CFR 23.233 (directional stability and control); FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C); FAA Airplane Flying Handbook (FAA-H-8083-3C), ch. 8 on crosswind approaches and landings; FAA Advisory Circular AC 91-79B on runway excursions. Educational material; always use your POH or AFM performance data and your own limits for flight decisions.