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Pilots should strive to fly precisely, but we sometimes reach task saturation.

When ATC gives a heading, receives the correct readback, but observes a 10- to 15-degree difference between the actual and intended tracks, does the specialist incorporate this difference into future vectors? Do approach and traffic separation vectors generally have a healthy margins of error?

How does apparent compass deviation or directional gyro precession factor into vectors that ATC issues?

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    $\begingroup$ It's the pilots responsibility to verify and correct the gyro drift, but if a controller sees you on the wrong heading they will issue it again or give you a correction. I believe it's the pilots responsibility to factor that in our correct the gyro drift for future vectors. $\endgroup$ – Ron Beyer Feb 20 '16 at 15:50
  • $\begingroup$ Wind drift is another factor affecting the track seen on radar scopes, and not one that is due to pilot error. Apart from comparison to other aircraft tracks at a comparable altitude, location, and speed, a controller may not be able to tell the difference between wind drift and pilot error. $\endgroup$ – J Walters Feb 20 '16 at 16:23
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This question is a partial duplicate of this one and this one.

When ATC gives a heading, receives the correct readback, but observes a 10- to 15-degree difference between the actual and intended tracks, does the specialist incorporate this difference into future vectors?

Sometimes. The controller issues headings but observes ground track. If the wind is causing drift, the controller will compensate for it when she provides vectors. Sometimes, if an aircraft is suitably equipped, a controller will ask for a wind report in order to better judge the winds at altitude.

Do approach and traffic separation vectors generally have a healthy margins of error?

Yep. See here.

How does apparent compass deviation or directional gyro precession factor into vectors that ATC issues?

It's up to the pilot, not the controller, to correct for compass deviation (since only the pilot can see the compass correction card inside the aircraft) and gyro precession (since only the pilot can turn the little knob to reset the gyro).

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