Crosswind Landing - Crab Angle Simulation
A Boeing 747 flies its final approach while the wind blows straight across the runway. The nose is held at an angle into the wind — the crab — and the simulation draws the three velocity vectors as they add, so the reason the aircraft still travels straight down the centreline is visible rather than asserted.
How to use this simulation
- Set the approach airspeed and the crosswind strength, and choose which side the wind comes from
- Watch the crab angle, ground speed and the sideways airspeed v·sin θ update together
- Pause, restart the approach, or run it at 1x, 2x or 4x
- Switch between a follow view, dead astern, the tower, straight down, the cockpit and free orbit
What to look for
- The nose points well off the centreline, yet the green ground-track vector lies exactly along it
- The red crosswind vector always lands the tip-to-tail sum back on the centreline — that is v·sin θ = w drawn out
- The ground speed is always lower than the airspeed, by exactly the factor cos θ
- From the cockpit the runway sits off to one side of the nose the whole way down the approach
- At touchdown the nose swings straight, the green vector swings off the centreline, and beyond about 56 km/h of crosswind the tyres lose and the aircraft drifts off the runway
The physics behind it
The aircraft moves through the air along its nose at speed v, while the whole body of air moves sideways at w. The velocity over the ground is the vector sum of the two. To keep the ground track on the centreline the sideways part of the airspeed must cancel the crosswind exactly: v·sin θ = w, so the crab angle is θ = arcsin(w/v). What is left along the runway is v·cos θ, so the ground speed is √(v² − w²) — always a little less than the airspeed. Because the three vectors form a right-angled triangle, a stronger crosswind or a slower approach both mean a larger crab angle. At touchdown the pilot straightens the nose so the wheels roll along the runway instead of sideways; the sideways airspeed vanishes with the crab, the crosswind is no longer balanced, and only the tyres are left to resist it.