Groundspeed, Wind Triangle & Wind Correction Angle
The airplane’s air-velocity vector plus the wind vector gives its motion over the ground. For a desired course, solve that relationship to find the heading and groundspeed.
The three vectors
True airspeed and heading describe the airplane through the air. Wind direction and speed describe the moving air mass. Their vector sum gives the airplane's ground track and groundspeed.
Wind correction angle
If the wind pushes from the right, the airplane normally needs a correction toward the right to hold the desired course. PilotDesk solves the vector relationship and reports the corrected heading, groundspeed and wind correction angle.
Strong-wind cases
Some combinations have no steady solution, such as a crosswind component greater than the entered true airspeed. PilotDesk rejects those cases rather than returning a misleading number.
Course 090°, wind from 020°
Plan to fly course 090° true at 120 kt TAS in wind from 020° true at 20 kt. The wind is 70° left of the course, so its crosswind component is 20 × sin(70°) = 18.8 kt from the left, and its headwind component is 20 × cos(70°) = 6.8 kt. To cancel the rightward drift, steer left: the exact wind correction angle is about 9.0° left. The resulting true heading is about 081° and groundspeed about 112 kt. Check the signs: a wind from the left calls for a left correction; a headwind component makes groundspeed lower than TAS.
These are rounded planning values. The calculator resolves the vectors rather than adding the rounded components, so small differences are normal.
Course, heading, and track are different
Course is the intended path over the ground; heading is where the nose points; track is the path actually made over the ground. A wind correction makes heading differ from course so the resulting track can match the course. If the actual wind differs from the forecast, the airplane drifts and actual track changes.
Common wind-triangle mistakes
Aviation winds are reported as the direction they come from, not the direction they blow toward. Keep true course with true wind unless you deliberately convert both to magnetic. Do not subtract the full wind speed from TAS as if every wind were directly on the nose. When crosswind approaches TAS, no steady heading can hold the course; a simple small-angle rule is no longer appropriate.
Use the answer in the flight plan
Groundspeed affects leg time, and leg time affects fuel. A forecast change can therefore alter heading, ETA, and fuel together. Recalculate for the planned altitude and current forecast, then compare the result with the route planner's navlog. That navlog uses the entered enroute wind; endpoint METAR wind is airport context, not a substitute for winds aloft.
From true heading to magnetic heading
Keep course and wind on the same north reference while solving the triangle. Then apply local charted variation to the resulting heading. In the example above, 081° true with an assumed 8° east variation becomes 073° magnetic: subtract east variation when converting true to magnetic, add west. Reverse that operation to convert back. Compass deviation is a separate aircraft-specific correction; variation alone does not give compass heading.
Use current variation for the route location, not this illustrative 8° value. A METAR wind uses true north; do not mix it directly with a magnetic runway heading. Use the true/magnetic converter when the sources differ.
Carry groundspeed into time and fuel
For a 56 NM leg at the example's approximately 112 kt groundspeed, time = 56 ÷ 112 × 60 = 30 minutes. At an assumed cruise flow of 10 US gal/hour, that leg consumes approximately 5 US gal before climb, taxi, contingencies or required reserves. Using 120 kt TAS instead would predict 28 minutes and understate the leg time. Replace the illustrative fuel flow with the aircraft's approved planning data.
References
The vector method follows the FAA Pilot's Handbook of Aeronautical Knowledge, chapter on navigation. See the FAA PHAK and PilotDesk Sources & Methods.