What is the Rationale behind System Deltas (besides confusing the pilot)?
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Frederf and Keith Rosenkranz both have good explanations of it. There is no issue loading your flight plan into the mission computer on the jet, no loss of precision. However in flight, due to a variety of processes, the INS will lose positional accuracy. When the jet starts, the pilot loads its position with high accuracy, and it measures all subsequent accelerations (linear and rotational) to determine its current position (which is its starting position modified by all accelerations). Over time small errors in position accumulate (INS drift). A couple miles in a hundred is not unusual for older systems. Civilian gyros get drift that is noticeable in just 10 to 15 minutes of flight (somewhat less on more expensive jets). But the flight plan is not less accurate, just the position relative to the flight plan. So the pilot can slew the flight plan around (nav deltas) or essentially slew the plane around relative to the flight plan (same thing really). If you see in the hUD that a stpt meant to be over a tower is a half mile to its north, you can guess the whole plan is off by the same amount. So if you slew the stpt back south a half mile, so the stpt diamond is on the tower, that should have updated the accuracy of the INS or if you like, slewed all points on the flight plan back to where they should be.
The kink in your think comes from thinking of it as slewing the flight plan over the ground, when the flight plan only exists inside the mission computer. Really its just changing the positional accuracy of the INS.