Crosswind and Headwind Component

angle = |wind dir - runway heading| folded to 0-180, crosswind = speed x sin(angle), headwind = speed x cos(angle). A wind '20 kt, 30 deg off' is only 10 kt of crosswind but 17 kt of headwind. Two traps made explicit: the value checked against the aircraft's maximum demonstrated crosswind is the GUST, not the steady wind, and a wind more than 90 deg off the nose becomes a TAILWIND -- it still adds crosswind while erasing the headwind margin, the setup that overruns a runway. Returns both components with a tailwind flag and a demonstrated-crosswind check. A planning aid; the pilot in command and the flight manual govern.

angle = fold(|wind_dir - runway_heading|, 0..180); crosswind = speed x sin(angle); headwind = speed x cos(angle) (negative = tailwind); gust_xwind = (gust > 0 ? gust : speed) x sin(angle).

Runway wind-component resolution (the FAA vector method / POH crosswind chart), first-principles trigonometry, by name; the pilot in command and the aircraft flight manual govern.

The wind-component resolution is first-principles trigonometry; the runway heading, wind, and demonstrated crosswind come from the ATIS/METAR and the aircraft flight manual.

Estimate. AHJ and licensed professional govern.

Field names used by the API: runway_heading_deg, wind_dir_deg, wind_speed_kt, angle_deg, crosswind_kt, headwind_kt

• Gust governs the check the crosswind limit should be checked against the gust, not the steady windPOH crosswind guidance
• Tailwind a wind more than 90 degrees off the runway is a tailwind (negative headwind)vector resolution
• Demonstrated crosswind a capability figure, not a regulatory limitaircraft flight manual