# How does an aircraft derive winds aloft on its own?

The G1000 has a feature where it can put up a winds aloft arrow/speed in the PFD. I've been sort of wondering how exactly this is determined. My guess is that the aircraft (or the G1000) knows your airspeed via the pitot/static system and heading via the fluxgate/mag compass. Then, it uses your GPS position to figure out where you should be every X seconds given the airspeed and heading. Any difference must be attributable to winds aloft. Does this make sense?

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Yes, you are correct. You need three pieces of information:

• airspeed
• true compass heading (considering magnetic variation)
• multiple absolute position fixes (eg. from gps)

The aircraft heading has to be measured by a compass within the aircraft (it can't be derived from the gps track), and the gps position can be used to look up the local magnetic variation. The difference between the speed/heading and the ground track (in straight and level flight, anyway) is attributable to winds aloft.

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I look forward to the day when GPS is accurate and cheap enough that we can put one in the nose and one in the tail and derive heading from the difference. – Steve V. Mar 20 '14 at 5:05
@SteveV. Magnetometers are pretty accurate - and they work even when you're not moving (e.g. during the final compass/DG checks before takeoff). You could even put several on an aircraft if you're worried about local influences. – voretaq7 Mar 20 '14 at 5:59
So was this calculation inaccessible pre-GPS days? Or could you do the same calculation using an accurate gyroscope too? – curious_cat Jul 28 '15 at 14:06
@curious_cat: Not gyros but accelerometers (and also gyros to figure out where the accelerometers are pointing). They're called IMU - Inertial Measurement Units. We still use them in submarines because GPS signals can't penetrate more than around 2m of sea water. – slebetman May 23 at 6:41
@slebetman Are compasses useless on subs too? – curious_cat May 23 at 6:48

Close! Here is a simplified example:

• First we use GPS positions to determine the ground vector. This is based on distance traveled and ground track over time. It is a fairly straight-forward calculation based on the time to travel between two coordinates and their relative positions.
• Then we calculate our flight vector. This is based on the aircraft True Airspeed (TAS) and heading.1
• Lastly we use basic geometry/vector math to calculate the difference between the two vectors. This calculated vector is the wind direction and speed.

1 TAS is Calibrated Airspeed corrected for altitude and non-standard temperature - the speed of the aircraft relative to the airmass in which it is flying. It is calculated using the pitot-static inputs along with the Total Air Temperature (TAT) input (if available). To get an idea of the math, take a look at this answer of mine that calculates Mach Number, which is one of the values used to calculate TAS. Also, the TAT isn't really needed for low-speed aircraft that fly below about 100 KIAS.

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Note that it's basically a dynamically updated E6-B calculator. The AHRS isn't doing anything you couldn't do on a circular slide, it's just doing it faster and on the fly. – egid Mar 20 '14 at 5:37