The wind triangle: heading, groundspeed and component winds

The wind triangle relates three vectors: where the aircraft is pointed and how fast it moves through the air, what the wind is doing to it, and where it actually goes over the ground. Nearly every navigation question is one of those three quantities with the other two supplied.

The vocabulary, precisely

• True course is the intended path over the ground, measured from true north.
• True heading is the direction the aircraft is pointed, measured from true north.
• The wind correction angle is the difference between the two. It is applied into the wind.
• True airspeed is the speed of the aircraft through the air mass.
• Groundspeed is the speed of the aircraft over the ground.

Applying variation and deviation

Variation is the angular difference between true north and magnetic north at a location. Deviation is the error in the individual aircraft's compass caused by the aircraft itself. They are applied in a fixed order, working from true to compass.

1. Start with true course.
2. Apply the wind correction angle to obtain true heading.
3. Apply variation to obtain magnetic heading. East is least, so subtract easterly variation; west is best, so add westerly variation.
4. Apply deviation to obtain compass heading.

Resolving component winds

For a takeoff or landing calculation you need the wind split into the component along the runway and the component across it. Take the angle between the wind direction and the runway heading, then resolve.

The headwind component is the wind speed multiplied by the cosine of that angle. The crosswind component is the wind speed multiplied by the sine of that angle. At 90 degrees the wind is entirely crosswind. At 0 degrees it is entirely headwind. At 30 degrees the crosswind is half the wind speed, and at 45 degrees each component is about 70 percent of it.