Wind triangle calculator
An aircraft flies through a moving block of air. To travel along the line you drew on the chart, you have to point somewhere slightly different. This works out where.
Calculator
This is an educational and planning aid. Use current official weather, your aircraft flight manual, and the rules that apply to your flight before you act on any figure here. See the aviation disclaimer.
What the result means
The true heading is where to point the nose. The wind correction angle is the difference between that and your intended course, and it is always into wind.
Groundspeed is what governs how long the leg takes and how much fuel it needs. It can be well below true airspeed into a headwind and well above it with a tailwind.
The crosswind and along track components shown alongside are the same wind resolved against your course, which is useful for a quick mental check of the answer.
When this is useful
- Planning each leg of a cross country, before working out leg times and fuel.
- In flight, when the actual wind turns out to be different from the forecast and the whole leg needs reworking.
- Checking whether a planned track is even flyable in a strong wind, since a crosswind stronger than your true airspeed makes the course impossible to hold.
How it is calculated
The wind is resolved into a component across the course and a component along it. The angle whose sine equals the crosswind component divided by true airspeed is the wind correction angle, and adding it to the course gives the heading.
Groundspeed is then the true airspeed multiplied by the cosine of the correction angle, minus the along track wind component. This is the exact vector solution, the same one a mechanical flight computer approximates.
wind correction angle = asin(wind speed x sin(wind angle) / TAS), groundspeed = TAS x cos(WCA) - wind speed x cos(wind angle)
Worked example
- True course
- 000 degrees
- True airspeed
- 100 kt
- Wind
- From 090 at 20 kt
Turn about 12 degrees right, on to a true heading of 012, to make good a course of 000. Groundspeed is 98 kt.
Check: A direct crosswind at 90 degrees to the course should barely change groundspeed, and it does not: 98 kt against a true airspeed of 100 kt. The correction angle has a sine of 20 divided by 100, which is 0.2, and the angle whose sine is 0.2 is 11.5 degrees.
Limitations
- Everything here is in degrees true. If you are working from a compass or a runway designator, convert the heading afterwards using magnetic variation.
- It assumes one steady wind for the whole leg. Real wind changes with height and along the route, which is why the reverse calculation exists to check it in flight.
- If the crosswind component exceeds your true airspeed, no heading holds the course and the calculator says so rather than returning a misleading figure.
Common mistakes
- Entering the direction the wind is blowing towards. Aviation always reports the direction the wind is coming from.
- Mixing indicated airspeed with true airspeed. The wind triangle only works with true airspeed, so convert first if you are cruising at altitude.
- Applying the correction the wrong way. The heading always moves into the wind, so if the wind is from the right the heading goes right of course.
Sources
- Pilot's Handbook of Aeronautical Knowledge, navigation chapter , US Federal Aviation Administration
- Aviation Formulary , Ed Williams