Notice it just went basically forward, climbing as it got lighter due to fuel being burned off
Ground Track of Payne Stewart Accident Flgiht
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Accident Aircraft N47BA
Payne Stewart Plane Crash Information
http://www.airsafe.com/stewart.htm -- Revised: 5 April 2012
There have been significant changes to autopilot technology since Payne Stewart's LearJet 35 was built (1976??). That makes it hard to use that incident to predict how a more modern aircraft would react in a similar situation. I think of it as just an example of one *possible* reaction.