The wind triangle

The wind triangle

The wind triangle is the geometric basis of dead reckoning (DR). It links three vectors:

1. Aircraft speed vector (TAS / True Heading) — where the aircraft is pointing, how fast relative to the air.
2. Wind vector (wind from / wind speed) — how the airmass is moving.
3. Ground speed vector (GS / True Track) — where the aircraft actually moves over ground.

Geometry: the vector equation TAS vector + wind vector = GS vector

Arrow convention in the wind triangle

In the conventional drawing of the wind triangle, the three vectors are marked with an arrow convention (for clarity):

Convention: "In the wind triangle, the heading vector is marked with one arrow, the ground vector with two and the wind vector is marked by 3 arrows".

Terms and angles

WCA — Wind Correction Angle

The wind correction angle (WCA) is, amongst others, the angle between MC (Course) and MH (Heading). Sign convention:

• WCA is positive when the wind comes from the right — pilot offsets heading to the right to stay on track.
• WCA is negative when the wind comes from the left — pilot offsets heading to the left.

Relation: TH = TT + WCA (positive add for wind from right).

Drift Angle (DA)

The drift angle (DA) is the angle between the aircraft's longitudinal axis (TH) and the actual track over ground (TT):

• DA = TT − TH (sign convention varies).
• DA and WCA are equal in magnitude (DA = −WCA), opposite sign.

Wind Angle (WA) — TC vs wind

The wind angle (WA) is the angle between TC and the direction from which the wind comes:

• Example: TC = 090°, wind from 120° → WA = 120° − 090° = 30° (wind from 30° right-front of track).
• WA is the input angle in wind-correction calculations (CRP-5, E6B).

Relative Wind Angle (RWA) — TH vs wind

The relative wind angle (RWA) is the angle between the direction from which the wind comes and TH:

• Example: TH = 100°, wind from 130° → RWA = 130° − 100° = 30°.
• Difference from WA: WA refers to TC (desired track), RWA to TH (current heading).

Wind convention

Wind in weather reports is always "wind from": e.g. 270/15KT means wind from the west (from 270°) at 15 kt. In the wind triangle the wind vector is drawn in the "where to" direction (eastward in this example).

GS vs TAS — wind effect

The difference between GS and the corresponding TAS is the effect of the wind:

• Headwind: GS < TAS.
• Tailwind: GS > TAS.
• Pure crosswind: GS ≈ TAS, but heading must be corrected.

Component decomposition

Wind splits into two components relative to the desired track:

• Headwind/tailwind component (parallel): HW/TW = wind × cos(angle between wind direction and track)
• Crosswind component (perpendicular): XW = wind × sin(angle between wind direction and track)

Worked example

• TT = 090° (east)
• TAS = 100 kt
• Wind = 150°/20 kt
• WA = 150° − 90° = 60° (wind from right-rear)

HW/TW: 20 × cos(60°) = 20 × 0.5 = 10 kt — wind from rear → +10 kt tailwind.

XW: 20 × sin(60°) = 20 × 0.866 = 17.3 kt from right.

WCA: sin(WCA) = XW / TAS = 17.3 / 100 = 0.173 → WCA ≈ +10° (positive, wind from right).

Wind from right → aircraft drifts left → offset heading right: TH = TT + WCA = 090° + 10° = 100°.

GS: 100 × cos(10°) + 10 ≈ 98.5 + 10 ≈ 108 kt.

→ GS-TAS difference = 108 − 100 = 8 kt → wind effect increases ground speed.

Can TC = TH = TT?

It is possible for TC, TH and TT to be equal — with no wind or pure headwind/tailwind:

• No wind: heading = track = course.
• Pure headwind or tailwind: heading = track, no drift.
• With crosswind: TH ≠ TT (heading offset by WCA).

Calculation tools

• Flight computer E6B / CRP-1 / CRP-5 (whiz wheel): mechanical, still common in exams.
• Electronic E6B (Sporty's, ASA): faster, simpler.
• EFB apps (SkyDemon, ForeFlight, Garmin Pilot): fully automatic.
• Slide-rule formula: sin(WCA) = (wind × sin(wind angle)) / TAS

Simplified PPL rules of thumb (mental)

• Wind 0°/180° to track (pure HW/TW): component = wind itself.
• Wind 30° to track: HW/TW ≈ 87 % of wind, XW ≈ 50 % (cos 30° = 0.87; sin 30° = 0.5).
• Wind 45° to track: HW/TW ≈ XW ≈ 71 % of wind.
• Wind 60° to track: HW/TW ≈ 50 %, XW ≈ 87 %.
• Wind 90° (pure crosswind): XW = wind, HW/TW = 0.

Operational use

1. Before flight: derive cruise-altitude wind from TAF/GAFOR/WINTEM → precompute WCA and GS per leg in the PLOG.
2. In flight: by GPS or track measurement get real GS and TT → back-calculate wind, correct as needed.
3. For landing: compute crosswind component before final — check POH limit.