Aviation & Aeronautics
Intermediate

Headwind Component

Wind component along the runway.

Formula

H=Vcos⁡θH = V\cos\theta

Variables

VWind speed
\thetaAngle to runway

Example

Headwind shortens takeoff

How it works

This formula gives the part of the wind that acts directly along the runway direction. It comes from resolving the wind vector into components: the cosine of the angle picks out the portion aligned with the runway, so a wind blowing straight down the runway contributes all of its speed, while a crosswind contributes none to the headwind/tailwind component. In practice, the result is positive for a headwind and negative for a tailwind if the wind direction is measured relative to the runway heading.

When to use it

Use this when checking takeoff or landing performance, since the along-runway wind changes groundspeed and required runway length. It is also useful for flight planning and comparing reported winds to the runway direction at a specific airport.

Worked example, step by step

A runway is oriented 090°. The wind is 20 kt at a 30° angle to the runway direction. H = V cos θ H = 20 cos 30° H = 20 × 0.866 H = 17.32 kt Final answer: the headwind component is about 17.3 knots.

Common mistakes to avoid

  • Using sine instead of cosine for the along-runway component
  • Forgetting that the angle must be measured relative to the runway direction, not compass north
  • Not accounting for tailwind cases, where the component should be treated as negative

Did You Know?

A strong headwind shortens takeoff distance, which is why aircraft take off and land into the wind.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026