A B737-300 Flight Crew reported both autopilots would mis-trim the aircraft; so they continued with the autopilot disengaged. They realized later they were no longer legal for RVSM operations.
Synopsis
A B737-300 Flight Crew reported both autopilots would mis-trim the aircraft; so they continued with the autopilot disengaged. They realized later they were no longer legal for RVSM operations.
Narrative
I was the Pilot Monitoring while the First Officer was flying the departure. After climbing above about 17;000' MSL; the 'Stab out of Trim' light illuminated. We followed the checklist while continuing the climb. The stab trim worked properly with the autopilot disengaged. Following the recommendation of the checklist; we re-engaged the autopilot in the climb; again after several minutes of use; the 'Stab out of Trim' light illuminated. We then retrimmed the aircraft and switched the control of the aircraft to me. I then engaged the 'A' autopilot to see if that would make a difference. After a few minutes; it did the same thing. At that point; we were leveling off at FL360. After completing the level off and stabilizing the airspeed/retrimming; we re-engaged the 'A' autopilot. After a few minutes; the autopilot began to trim the stab into an out of trim position. At that time; I gave the flight controls back to the First Officer; notified Dispatch; and continued. There should be mention on the 'Stab out of Trim' Checklist about flying in RVSM airspace without an autopilot.
Second reporter narrative
After referencing the MEL; we realized we should have notified ATC about the inoperable autopilot; and requested an altitude below FL 290 (below RVSM airspace).
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Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.