Find wind from heading, track and GS

How can actual flight reveal the wind?

Subtract the air vector from the observed ground vector.

Subtract the air vector from the ground vector

Heading and TAS define air velocity; track and GS define ground velocity. Convert both directions to a common north reference first. Since ground velocity equals air velocity plus wind velocity, wind is ground minus air. Convert the resulting wind-to vector into a wind-from direction by taking its reciprocal.

For heading 090°, TAS 150 kt, track 080° and GS 140 kt, the air vector is (150, 0) kt. Ground velocity is (137.87, 24.31) kt. Their difference is (−12.13, 24.31) kt, with magnitude about 27.17 kt, pointing toward 333.49°. The inferred wind is therefore from 153.49° at 27.17 kt.

Check the geometry before accepting the number

Track 080° lies left of heading 090°, so the wind must provide a northward component. GS below TAS is consistent here with a westward wind component opposing part of the eastward air velocity. This visual check is independent of the calculator’s atan2 argument order and can catch a reciprocal or sign mistake.

When the difference vector has essentially zero magnitude, wind direction is undefined. Report calm rather than a precise arbitrary bearing. Small inferred winds are particularly sensitive to errors in heading, TAS, track and GS; the observations can be less accurate than the apparent precision of the computed result.

Solve a cardinal example without trigonometry

Heading 000°, TAS 100 kt, observed track 000° and GS 120 kt imply a 20 kt northward wind vector: wind from 180°. If observed GS were 80 kt instead, the vector would be 20 kt southward, giving wind from 000°. These simple cases test subtraction sense. Then change the heading slightly in the laboratory and observe how both wind components change. A drift angle alone cannot specify wind magnitude; complete velocity observations are needed.

How do you verify an inferred wind?

Feed it back into a different track requirement.

Reconstruct the observation

An inferred wind should reproduce the original ground motion when added back to the air vector. For the 090°/150 kt air vector and wind from 153.49° at 27.17 kt, the reconstructed result should be track 080° and GS 140 kt within rounding. A reciprocal track suggests an incorrect wind-from conversion or reversed vector subtraction.

The inverse problem needs sufficient information. Track minus heading gives a drift angle but not the whole wind vector. Without reliable TAS and GS, many combinations of wind speed and direction fit the same angular difference. A position observation without an accurate time interval cannot by itself establish GS.

Transfer only when the air mass estimate is relevant

An observed wind can be more useful than a forecast for the immediate next leg when location, time and altitude remain comparable. It should not be treated as a timeless property of the region. A climb, frontal crossing or long delay can invalidate the estimate. Retain the source and time of the observation in the reasoning.

At TAS 150 kt and desired track 000°, the example wind from 153.5° has a tailwind component but also a westward component. A small right crab cancels that westward motion. This combination shows why a wind can improve GS while still requiring a heading correction.

Distinguish a wind change from a measurement fault

Suppose two fixes imply a 40 kt wind shift but the second fix is a visually ambiguous feature timed a minute late. Repeating the subtraction does not resolve that uncertainty. Compare a subsequent independent position and the aircraft’s data status before replacing a credible forecast. If observations disagree, report the uncertainty rather than inventing a highly precise wind. A useful revised estimate predicts the next track and GS so that it can be checked, rather than merely explaining the previous mismatch.

Can you explain and apply the mechanism?

Four original questions. Work from the stated facts, then compare your reasoning with the explanation.