Wind triangle solver

Every cross-country flight, drone survey, and sailboat race lives inside the same geometry: the wind triangle that links true airspeed, heading, ground speed, track, and the wind vector. Mental E6B rules and paper sine cards disagree by a knot or two; production planners need a single deterministic contract that returns wind correction angle, drift, and headwind or crosswind components without a weather network call. This wind triangle solver accepts any sufficient subset of the five legs—heading, track, airspeed, ground speed, and wind (meteorological from-direction plus speed)—and fills in the missing values with pure vector arithmetic.

What the navigation wind triangle is and which fields define it

The wind triangle is the closed vector relationship ground velocity equals air velocity plus wind velocity. Air velocity is fully fixed by true airspeed and heading—the direction the nose points through the air mass. Ground velocity is fixed by ground speed and track—the path actually followed over the surface.

Wind is the meteorological vector stated as a from-direction and a speed: a wind from two hundred seventy degrees blows toward the east, so its velocity components are opposite the compass reading on a METAR. Because six scalar numbers are tied by two independent equations, four independent scalars determine the remaining two in the generic case.

In product language that means any three of the five conceptual legs work when wind counts as a pair (speed and from-direction), or all four of heading, track, airspeed, and ground speed recover the wind. This capability auto-detects four practical modes: find track and ground speed from heading, airspeed, and wind; find heading and ground speed from desired track, airspeed, and wind; find wind from an observed heading, track, airspeed, and ground speed; and find both speeds from heading, track, and wind when those alone close the system.

Directions are degrees true, clockwise from north, normalized into the zero-to-three-hundred-sixty range. Speeds share one unit you choose—knots, miles per hour, kilometers per hour, or meters per second—because the trigonometry is homogeneous and the service never converts units behind your back.

Who uses the wind triangle, and why

Flight schools and online ground-school products use a wind triangle calculator so students check wind correction angle homework against the same definition later used in dispatch. Charter and corporate flight departments batch-solve tracks for each leg of a release package when the forecast wind grid updates, then push heading and ground-speed targets into the electronic flight bag. Drone and UAS operators convert a required survey track and a METAR-style wind into a heading and ground speed so grid spacing and battery endurance estimates stay honest.

Glider, balloon, and sailboat tooling reuse the same vectors when only the labels change from true airspeed to boat speed through water. Because the implementation is tier-A parse with no outbound network and no model tokens, latency is dominated by the task handshake, which suits form validation on every wind change as well as offline-friendly reprocessing of historical flight logs.